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diff --git a/.gitattributes b/.gitattributes new file mode 100644 index 0000000..d7b82bc --- /dev/null +++ b/.gitattributes @@ -0,0 +1,4 @@ +*.txt text eol=lf +*.htm text eol=lf +*.html text eol=lf +*.md text eol=lf diff --git a/LICENSE.txt b/LICENSE.txt new file mode 100644 index 0000000..6312041 --- /dev/null +++ b/LICENSE.txt @@ -0,0 +1,11 @@ +This eBook, including all associated images, markup, improvements, +metadata, and any other content or labor, has been confirmed to be +in the PUBLIC DOMAIN IN THE UNITED STATES. + +Procedures for determining public domain status are described in +the "Copyright How-To" at https://www.gutenberg.org. + +No investigation has been made concerning possible copyrights in +jurisdictions other than the United States. Anyone seeking to utilize +this eBook outside of the United States should confirm copyright +status under the laws that apply to them. diff --git a/README.md b/README.md new file mode 100644 index 0000000..6cfbcb3 --- /dev/null +++ b/README.md @@ -0,0 +1,2 @@ +Project Gutenberg (https://www.gutenberg.org) public repository for +eBook #51555 (https://www.gutenberg.org/ebooks/51555) diff --git a/old/51555-0.txt b/old/51555-0.txt deleted file mode 100644 index bf0ccfa..0000000 --- a/old/51555-0.txt +++ /dev/null @@ -1,20321 +0,0 @@ -The Project Gutenberg EBook of On the Philosophy of Discovery, Chapters -Historical and Critical, by William Whewell - -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/license - - -Title: On the Philosophy of Discovery, Chapters Historical and Critical - -Author: William Whewell - -Release Date: March 25, 2016 [EBook #51555] - -Language: English - -Character set encoding: UTF-8 - -*** START OF THIS PROJECT GUTENBERG EBOOK PHILOSOPHY OF DISCOVERY *** - - - - -Produced by Sonya Schermann, Les Galloway and the Online -Distributed Proofreading Team at http://www.pgdp.net (This -file was produced from images generously made available -by The Internet Archive) - - - - - - - - - - ON THE - - PHILOSOPHY - - OF - - DISCOVERY. - - - - - Cambridge: - - PRINTED BY C. J. CLAY, M.A. - - AT THE UNIVERSITY PRESS. - - - - - ON THE - - PHILOSOPHY OF DISCOVERY, - - CHAPTERS HISTORICAL AND CRITICAL; - - BY - - WILLIAM WHEWELL, D.D. - - MASTER OF TRINITY COLLEGE, CAMBRIDGE, AND - CORRESPONDING MEMBER OF THE INSTITUTE OF FRANCE. - - INCLUDING THE COMPLETION OF THE THIRD EDITION - OF THE PHILOSOPHY OF THE INDUCTIVE SCIENCES. - - [Illustration: Hand passing torch to hand] - - ΛΑΜΠΑΔΙΑ ΕΧΟΝΤΕΣ ΔΙΑΔΩΣΟΥΣΙΝ ΑΛΛΗΛΟΙΣ - - LONDON: - - JOHN W. PARKER AND SON, WEST STRAND. - - 1860. - - - - -The following are the latest editions of the series of works which has -been published connected with the present subject: - - _History of the Inductive Sciences_, 3 Vols. 1857. - _History of Scientific Ideas_, 2 Vols. 1858. - _Novum Organon Renovatum_, 1 Vol. 1858. - _On the Philosophy of Discovery_, 1 Vol. 1860. - -To the _History of the Inductive Sciences_ are appended two Indexes (in -Vol. 1.), an Index of Proper Names, and an Index of Technical Terms. -These Indexes, and the Tables of Contents of the other works, will -enable the reader to refer to any person or event included in this -series. - - - - -PREFACE - - -The two works which I entitled _The History of the Inductive Sciences_, -and _The Philosophy of the Inductive Sciences_, were intended to -present to the reader a view of the steps by which those portions of -human knowledge which are held to be most certain and stable have -been acquired, and of the philosophical principles which are involved -in those steps. Each of these steps was a scientific _Discovery_, in -which a _new_ conception was applied in order to bind together observed -facts. And though the conjunction of the observed facts was in each -case an example of logical _Induction_, it was not the inductive -process merely, but the _novelty_ of the result in each case which gave -its peculiar character to the History; and the Philosophy at which -I aimed was not the Philosophy of Induction, but the _Philosophy of -Discovery_. In the present edition I have described this as my object -in my Title. - -A great part of the present volume consists of chapters which composed -the twelfth Book of the Philosophy in former editions, which Book was -then described as a 'Review of Opinions on the nature of Knowledge -and the Method of seeking it.' I have added to this part several new -chapters, on Plato, Aristotle, the Arabian Philosophers, Francis Bacon, -Mr. Mill, Mr. Mansel, the late Sir William Hamilton, and the German -philosophers Kant, Fichte, Schelling and Hegel. I might, if time had -allowed, have added a new chapter on Roger Bacon, founded on his _Opus -Minus_ and other works, recently published for the first time under the -direction of the Master of the Rolls; a valuable contribution to the -history of philosophy. But the review of this work would not materially -alter the estimate of Roger Bacon which I had derived from the _Opus -Majus_. - -But besides these historical and critical surveys of the philosophy of -others, I have ventured to introduce some new views of my own; namely, -views which bear upon the philosophy of religion. I have done so under -the conviction that no philosophy of the universe can satisfy the minds -of thoughtful men which does not deal with such questions as inevitably -force themselves on our notice, respecting the Author and the Object -of the universe; and also under the conviction that every philosophy -of the universe which has any consistency must suggest answers, at -least conjectural, to such questions. No _Cosmos_ is complete from -which the question of Deity is excluded; and all Cosmology has a side -turned towards Theology. Though I am aware therefore how easy it is, on -this subject, to give offence and to incur obloquy, I have not thought -it right to abstain from following out my philosophical principles -to their results in this department of speculation. The results do -not differ materially from those at which many pious and thoughtful -speculators have arrived in previous ages of the world; though they -have here, as seems to me, something of novelty in their connection -with the philosophy of science. But this point I willingly leave to the -calm decision of competent judges. - -I have added in an Appendix various Essays, previously published at -different times, which may serve perhaps to illustrate some points of -the history and philosophy of science. - - TRINITY LODGE, - - _February 8, 1856_. - - - - - ON - - THE PHILOSOPHY OF DISCOVERY. - - - - -CONTENTS. - - The chapters marked thus * appear now for the first time. - - The chapters marked thus † have appeared in other works. - - - CHAP. I. INTRODUCTION. - - CHAP. II. PLATO. - - CHAP. III. * ADDITIONAL REMARKS ON PLATO. - 1. The Doctrine of Ideas. - 2. The Doctrine of the One and Many. - 3. The notion of the nature and aim of Science. - 4. The Survey of existing Sciences. - 5. The Constitution of the human Mind. - - CHAP. IV. ARISTOTLE. - - CHAP. V. * ADDITIONAL REMARKS ON ARISTOTLE. - 1. Induction. - 2. Invention. - 3. The One in the Many. - 4. The "Five Words." - 5. Aristotle's contribution to the Physical Sciences. - 6. Aristotle's Astronomy. - 7. Aristotle on Classification. - 8. F. Bacon on Aristotle. - 9. Discovery of Causes. - 10. Plato and Aristotle. - 11. Aristotle against Plato's _Ideas_. - - CHAP. VI. THE LATER GREEKS. - - CHAP. VII. THE ROMANS. - - CHAP. VIII. * ARABIAN PHILOSOPHERS. - - CHAP. IX. THE SCHOOLMEN OF THE MIDDLE AGES. - - CHAP. X. THE INNOVATORS OF THE MIDDLE AGES. - Raymond Lully. - - CHAP. XI. THE INNOVATORS OF THE MIDDLE AGES--_continued_. - Roger Bacon. - - CHAP. XII. THE REVIVAL OF PLATONISM. - 1. Causes of Delay in the Advance of Knowledge. - 2. Causes of Progress. - 3. Hermolaus Barbarus, &c. - 4. Nicolaus Cusanus. - 5. Manilius Ficinus. - 6. Francis Patricius. - 7. Picus, Agrippa, &c. - 8. Paracelsus, Fludd, &c. - - CHAP. XIII. THE THEORETICAL REFORMERS OF SCIENCE. - 1. Bernardinus Telesius. - 2. Thomas Campanella. - 3. Andrew Cæsalpinus. - 4. Giordano Bruno. - 5. Peter Ramus. - 6. The Reformers in General. - 7. Melancthon. - - CHAP. XIV. THE PRACTICAL REFORMERS OF SCIENCE. - 1. Character of the Practical Reformers. - 2. Leonardo da Vinci. - 3. Copernicus. - 4. Fabricius. - 5. Maurolycus. - 6. Benedetti. - 7. Gilbert. - 8. Galileo. - 9. Kepler. - 10. Tycho. - - CHAP. XV. FRANCIS BACON. - 1. (I.) General Remarks. - 2. Common estimate of him. - 3. We consider only Physical Science. - 4. He is placed at the head of the change: - 5. (II.) _He proclaims a New Era_; - 6. (III.) _By a Change of Method_; - 7. Including successive Steps; - 8. Gradually ascending. - 9. (IV.) _He contrasts the Old and the New Method._ - 10. (V.) _Has he neglected Ideas?_ - 11. No. - 12. Examples of Ideas treated by him. - 13. He has failed in applying his Method; - 14. (VI.) _To the Cause of Heat._ - 15. He seeks Causes before Laws. - 16. (VII.) _His Technical Form worthless._ - 17. He is confused by words. - 18. His "Instances." - 19. Contain some good Suggestions. - 20. (VIII.) _His "Idols."_ - 21. (IX.) _His view of Utility._ - 22. (X.) _His Hopefulness._ - 23. (XI.) _His Piety._ - - CHAP. XVI. * ADDITIONAL REMARKS ON FRANCIS BACON. - 1. Mr. Ellis's views. - 2. Mr. Spedding's views. - - CHAP. XVII. FROM BACON TO NEWTON. - 1. Harvey. - 2. Descartes. - 3. Gassendi. - 4. Actual Progress in Science. - 5. Otto Guericke, &c. - 6. Hooke. - 7. Royal Society. - 8. Bacon's _New Atalantis_. - 9. Cowley. - 10. Barrow. - - CHAP. XVIII. NEWTON. - 1. Animating effect of his Discoveries. - 2. They confirm Bacon's views. - 3. Newton shuns Hypotheses. - 4. His views of Inductive Philosophy. - 5. His "Rules of Philosophizing." - 6. _The First Rule._ - 7. What is a "True Cause"? - 8. _Such_ as are real? - 9. Or _those_ which are proved? - 10. Use of the Rule. - 11. Rule otherwise expressed. - 12. _The Second Rule._ - 13. What are Events "of the same kind"? - 14. _The Third Rule_: - 15. Not safe. - 16. _The Fourth Rule._ - 17. Occult Qualities. - 18. Ridiculed. - 19. Distinction of Laws and Causes. - - CHAP. XIX. LOCKE AND HIS FRENCH FOLLOWERS. - 1. Cause of Locke's popularity. - 2. Sensational School. - 3. His inconsistencies. - 4. Condillac, &c. - 5. Importance of Language. - 6. Ground of this. - 7. The Encyclopedists. - 8. Helvetius. - 9. Value of Arts. - 10. Tendency to Reaction. - - CHAP. XX. THE REACTION AGAINST THE SENSATIONAL SCHOOL. - 1. "Nisi intellectus ipse." - 2. Price's "Review." - 3. Stewart defends Price. - 4. Archbishop Whately. - 5. Laromiguière. - 6. M. Cousin. - 7. M. Ampère. - 8. His Classification of Sciences. - 9. Kant's Reform of Philosophy. - 10. Its Effect in Germany. - - CHAP. XXI. FURTHER ADVANCE OF THE SENSATIONAL SCHOOL. - M. Auguste Comte. - 1. M. Comte on three States of Science. - 2. M. Comte rejects the Search of Causes. - 3. Causes in Physics. - 4. Causes in other Sciences. - 5. M. Comte's Practical Philosophy. - 6. M. Comte on Hypotheses. - 7. M. Comte's Classification of Sciences. - - CHAP. XXII. † MR. MILL'S LOGIC. - (I.) What is Induction? §§ 1-14. - (II.) Induction or Description, §§ 15-23. - (III.) In Discovery a new Conception is introduced, §§ 24-37. - (IV.) Mr. Mill's Four Methods of Inquiry, §§ 38-40. - (V.) His Examples, §§ 41-48. - (VI.) Mr. Mill against Hypotheses, §§ 49, 50. - (VII.) Against prediction of Facts, §§ 51-53. - (VIII.) Newton's Vera Causa, §§ 54, 55. - (IX.) Successive Generalizations, §§ 56-62. - (X.) Mr. Mill's Hope from Deductions, §§ 63-67. - (XI.) Fundamental opposition of our Doctrines, §§ 68-71. - (XII.) Absurdities in Mr. Mill's Logic, §§ 72-74. - - CHAP. XXIII. * POLITICAL ECONOMY AS AN INDUCTIVE SCIENCE. - 1. Moral Sciences. - 2. Political Economy. - 3. Wages, Profits, and Rents. - 4. Premature Generalizations. - 5. Correction of these by Induction--Rent. - 6. " Wages. - 7. " Population. - - CHAP. XXIV. † MODERN GERMAN PHILOSOPHY. - (I.) Science is the Idealization of Facts, §§ 1-8. - (II.) Successive German Philosophies. - Kant, Fichte, Schelling, Hegel, §§ 9-16. - - CHAP. XXV. † THE FUNDAMENTAL ANTITHESIS AS IT EXISTS IN THE MORAL WORLD. - Moral Progress is the Realization of Ideas. - - CHAP. XXVI. * OF THE "PHILOSOPHY OF THE INFINITE." - God is Eternal. - - CHAP. XXVII. * SIR WILLIAM HAMILTON ON INERTIA AND WEIGHT. - 1. Primary and Secondary Qualities. - 2. Meaning of the Distinction. - 3. Sir W. Hamilton adds "Secundo-Primary." - 4. Inertia. - 5. Sir W. Hamilton's arguments and reply. - 6. Gravity. - Sir W. Hamilton's arguments and reply. - - CHAP. XXVIII. † INFLUENCE OF GERMAN SYSTEMS OF PHILOSOPHY IN BRITAIN. - 1. Stewart on Kant. - 2. Mr. G. H. Lewes on Kant. - 4-6. Mr. Mansel on Kant. - His objection to our Fundamental Ideas, and Reply. - 7-10. New Axioms are possible. - 11-13. Mr. Mansel's Kantianism. - 14-16. Axioms are not from experience. - - CHAP. XXIX. * NECESSARY TRUTH IS PROGRESSIVE. - Objections considered. - - CHAP. XXX. * THE THEOLOGICAL BEARING OF THE PHILOSOPHY OF DISCOVERY. - 1-4. How can necessary truths be actual? - 5, 6. Small extent of necessary truth. - 7. How did things come to be as they are? - 8. View of the Theist. - 9-12. Is this Platonism? - 13. Idea of Time. - 14, 15. Ideas of Force and Matter. - 16. Creation of Matter. - 17. Platonic Ideas. - 18-21. Idea of Kind. - 22. Idea of Substance. - 23. Idea of Final Cause. - 24, 25. Human immeasurably inferior to Divine. - 26. Science advances towards the Divine Ideas. - 27. Recapitulation. - - CHAP. XXXI. * MAN'S KNOWLEDGE OF GOD. - 1, 2. Opinions. - 3. From Nature we learn something of God. - 4-6. Though but little. - 7, 8. From ourselves we learn something concerning God. - 9-11. Objections answered. - 12. Creation. - 13. End of the World. - 14. Moral and Theological views enter. - - CHAP. XXXII. * ANALOGIES OF PHYSICAL AND RELIGIOUS PHILOSOPHY. - 1, 2. Idealization of Facts and Realization of Ideas; - 3, 4. Both imperfect. - 5, 6. Divine Ideas perfect. - 7-9. Realization of Divine Love. - 10-13. Realization of Divine Justice. - 14. Analogy of Physical and Moral Philosophy. - 15, 16. Supernatural Beginning, Middle, and End indicated. - 17. Suggestion of a Future State. - 18-20. Confirmation from the Intellect of Man. - 21. From the Moral Nature of Man. - - - APPENDIX. - - PAGE - - APPEND. A. OF THE PLATONIC THEORY OF IDEAS 403 - B. ON PLATO'S SURVEY OF THE SCIENCES 417 - BB. ON PLATO'S NOTION OF DIALECTIC 429 - C. OF THE INTELLECTUAL POWERS ACCORDING - TO PLATO 440 - D. CRITICISM OF ARISTOTLE'S ACCOUNT OF - INDUCTION 449 - E. ON THE FUNDAMENTAL ANTITHESIS OF - PHILOSOPHY 462 - F. REMARKS ON A REVIEW OF THE PHILOSOPHY - OF THE INDUCTIVE SCIENCES 482 - G. ON THE TRANSFORMATION OF HYPOTHESES - IN THE HISTORY OF SCIENCE 492 - H. ON HEGEL'S CRITICISM OF NEWTON'S - PRINCIPIA 504 - Appendix to the Memoir on Hegel's Criticism - of Newton's Principia 513 - K. DEMONSTRATION THAT ALL MATTER IS - HEAVY 522 - - - - - ON THE - PHILOSOPHY - OF - DISCOVERY. - - - Wär' nicht das Auge sonnenhaft - Wie könnten wir das Licht erblicken? - Lebt' nicht in uns des Gottes eigne Kraft - Wie könnte uns das Göttliche entzücken? - GOETHE. - - Were nothing sunlike in the Eye - How could we Light itself descry? - Were nothing godlike in the Mind - How could we God in Nature find? - - -CHAPTER I. - -INTRODUCTION. - - -By the examination of the elements of human thought in which I have -been engaged, and by a consideration of the history of the most clear -and certain parts of our knowledge, I have been led to doctrines -respecting the progress of that exact and systematic knowledge which -we call Science; and these doctrines I have endeavoured to lay before -the reader in the History of the Sciences and of Scientific Ideas. The -questions on which I have thus ventured to pronounce have had a strong -interest for man from the earliest period of his intellectual progress, -and have been the subjects of lively discussion and bold speculation in -every age. I conceive that in the doctrines to which these researches -have conducted us, we have a far better hope that we possess a body of -permanent truths than the earlier essays on the same subjects could -furnish. For we have not taken our examples of knowledge at hazard, -as earlier speculators did, and were almost compelled to do; but have -drawn our materials from the vast store of unquestioned truths which -modern science offers to us: and we have formed our judgment concerning -the nature and progress of knowledge by considering what such science -is, and how it has reached its present condition. But though we have -thus pursued our speculations concerning knowledge with advantages -which earlier writers did not possess, it is still both interesting -and instructive for us to regard the opinions upon this subject which -have been delivered by the philosophers of past times. It is especially -interesting to see some of the truths which we have endeavoured to -expound, gradually dawning in men's minds, and assuming the clear -and permanent form in which we can now contemplate them. I shall -therefore, in the ensuing chapters, pass in review many of the opinions -of the writers of various ages concerning the mode by which man best -acquires the truest knowledge; and I shall endeavour, as we proceed, -to appreciate the real value of such judgments, and their place in the -progress of sound philosophy. - -In this estimate of the opinions of others, I shall be guided by -those general doctrines which I have, as I trust, established in the -histories already published. And without attempting here to give any -summary of these doctrines, I may remark that there are two main -principles by which speculations on such subjects in all ages are -connected and related to each other; namely, the opposition of _Ideas_ -and _Sensations_, and the distinction of _practical_ and _speculative_ -knowledge. The opposition of Ideas and Sensations is exhibited to us -in the antithesis of Theory and Fact, which are necessarily considered -as distinct and of opposite natures, and yet necessarily identical, -and constituting Science by their identity. In like manner, although -practical knowledge is in substance identical with speculative, (for -all knowledge is speculation,) there is a distinction between the two -in their history, and in the subjects by which they are exemplified, -which distinction is quite essential in judging of the philosophical -views of the ancients. The alternatives of identity and diversity, -in these two antitheses,--the successive separation, opposition, and -reunion of principles which thus arise,--have produced, (as they may -easily be imagined capable of doing,) a long and varied series of -systems concerning the nature of knowledge; among which we shall have -to guide our course by the aid of the views already presented. - -I am far from undertaking, or wishing, to review the whole series of -opinions which thus come under our notice; and I do not even attempt to -examine all the principal authors who have written on such subjects. I -merely wish to select some of the most considerable forms which, such -opinions have assumed, and to point out in some measure the progress -of truth from age to age. In doing this, I can only endeavour to seize -some of the most prominent features of each time and of each step, and -I must pass rapidly from classical antiquity to those which we have -called the dark ages, and from them to modern times. At each of these -periods the modifications of opinion, and the speculations with which -they were connected, formed a vast and tangled maze, the byways of -which our plan does not allow us to enter. We shall esteem ourselves -but too fortunate, if we can discover the single track by which ancient -led to modern philosophy. - -I must also repeat that my survey of philosophical writers is here -confined to this one point,--their opinions on the nature of knowledge -and the method of science. I with some effort avoid entering upon other -parts of the philosophy of those authors of whom I speak; I knowingly -pass by those portions of their speculations which are in many cases -the most interesting and celebrated;--their opinions concerning the -human soul, the Divine Governor of the world, the foundations or -leading doctrines of politics, religion, and general philosophy. I -am desirous that my reader should bear this in mind, since he must -otherwise be offended with the scanty and partial view which I give in -this place of the philosophers whom I enumerate. - - - - -CHAPTER II. - -PLATO. - - -There would be small advantage in beginning our examination earlier -than the period of the Socratic School at Athens; for although the -spirit of inquiry on such subjects had awakened in Greece at an earlier -period, and although the peculiar aptitude of the Grecian mind for -such researches had shown itself repeatedly in subtle distinctions -and acute reasonings, all the positive results of these early efforts -were contained in a more definite form in the reasonings of the -Platonic age. Before that time, the Greeks did not possess plain and -familiar examples of exact knowledge, such as the truths of Arithmetic, -Geometry, Astronomy and Optics became in the school of Plato; nor -were the antitheses of which we spoke above, so distinctly and fully -unfolded as we find them in Plato's works. - -The question which hinges upon one of these antitheses, occupies -a prominent place in several of the Platonic dialogues; namely, -whether our knowledge be obtained by means of Sensation or of Ideas. -One of the doctrines which Plato most earnestly inculcated upon his -countrymen was, that we do not _know_ concerning sensible objects, but -concerning ideas. The first attempts of the Greeks at metaphysical -analysis had given rise to a school which maintained that material -objects are the only realities. In opposition to this, arose another -school, which taught that material objects have no permanent reality, -but are ever waxing and waning, constantly changing their substance. -"And hence," as Aristotle says[1], "arose the doctrine of ideas which -the Platonists held. For they assented to the opinion of Heraclitus, -that all sensible objects are in a constant state of flux. So that if -there is to be any knowledge and science, it must be concerning some -permanent natures, different from the sensible natures of objects; -for there can be no permanent science respecting that which is -perpetually changing. It happened that Socrates turned his speculations -to the moral virtues, and was the first philosopher who endeavoured -to give universal definitions of such matters. He wished to reason -systematically, and therefore he tried to establish definitions, for -definitions are the basis of systematic reasoning. There are two things -which may justly be looked upon as steps in philosophy due to Socrates; -inductive reasonings, and universal definitions;--both of them steps -which belong to the foundations of science. Socrates, however, did not -make universals, or definitions separable from the objects; but his -followers separated them, and these essences they termed _Ideas_." And -the same account is given by other writers[2]. "Some existences are -sensible, some intelligible: and according to Plato, if we wish to -understand the principles of things, we must first separate the _ideas_ -from the _things_, such as the ideas of Similarity, Unity, Number, -Magnitude, Position, Motion: second, that we must assume an absolute -Fair, Good, Just, and the like: third, that we must consider the ideas -of relation, as Knowledge, Power: recollecting that the Things which -we perceive have this or that appellation applied to them because -they partake of this or that Idea; those things being _just_ which -participate in the idea of The Just, those being _beautiful_, which -contain the idea of The Beautiful." And many of the arguments by which -this doctrine was maintained are to be found in the Platonic dialogues. -Thus the opinion that true knowledge consists in sensation, which had -been asserted by Protagoras and others, is refuted in the _Theætetus_: -and, we may add, so victoriously refuted, that the arguments there -put forth have ever since exercised a strong influence upon the -speculative world. It may be remarked that in the minds of Plato and -of those who have since pursued the same paths of speculation, the -interest of such discussions as those we are now referring to, was by -no means limited to their bearing upon mere theory; but was closely -connected with those great questions of morals which have always a -practical import. Those who asserted that the only foundation of -knowledge was sensation, asserted also that the only foundation of -virtue was the desire of pleasure. And in Plato, the metaphysical -part of the disquisitions concerning knowledge in general, though -independent in its principles, always seems to be subordinate in its -purpose to the questions concerning the knowledge of our duty. - -Since Plato thus looked upon the Ideas which were involved in each -department of knowledge as forming its only essential part, it was -natural that he should look upon the study of Ideas as the true mode -of pursuing knowledge. This he himself describes in the _Philebus_[3]. -"The best way of arriving at truth is not very difficult to point out, -but most hard to pursue. All the arts which have ever been discovered, -were revealed in this manner. It is a gift of the gods to man, which, -as I conceive, they sent down by some Prometheus, as by Prometheus -they gave us the light of fire; and the ancients, more clear-sighted -than we, and less removed from the gods, handed down this traditionary -doctrine: that whatever is said to be, comes of One and of Many, and -comprehends in itself the Finite and the Infinite in coalition -(being One Kind, and consisting of Infinite Individuals). And this -being the state of things, we must, in each case, endeavour to seize -the One Idea (the idea of the Kind) as the chief point; for we shall -find that it is there. And when we have seized this one thing, we may -then consider how it comprehends in itself two, or three, or any other -number; and, again, examine each of these ramifications separately; -till at last we perceive, not only that One is at the same time One -and Many, but also _how many_. And when we have thus filled up the -interval between the Infinite and the One, we may consider that we -have done with each one. The gods then, as I have said, taught us by -tradition thus to contemplate, and to learn, and to teach one another. -But the philosophers of the present day seize upon the One, at hazard, -too soon or too late, and then immediately snatch at the Infinite; but -the intermediate steps escape them, in which resides the distinction -between a truly logical and a mere disputatious discussion." - -It would seem that what the author here describes as the most perfect -form of exposition, is that which refers each object to its place in -a classification containing a complete series of subordinations, and -which gives a definition of each class. We have repeatedly remarked -that, in sciences of classification, each new definition which gives a -tenable and distinct separation of classes is an important advance in -our knowledge; but that such definitions are rather the last than the -first step in each advance. In the progress of real knowledge, these -definitions are always the results of a laborious study of individual -cases, and are never arrived at by a pure effort of thought, which is -what Plato appears to have imagined as the true mode of philosophizing. -And still less do the advances of other sciences consist in seizing -at once upon the highest generality, and filling in afterwards all -the intermediate steps between that and the special instances. On the -contrary, as we have seen, the ascents from particular to general are -all successive; and each step of this ascent requires time, and labour, -and a patient examination of actual facts and objects. - -It would, of course, be absurd to blame Plato for having inadequate -views of the nature of progressive knowledge, at the time when -knowledge could hardly be said to have begun its progress. But we -already find in his speculations, as appears in the passages just -quoted from his writings, several points brought into view which will -require our continued attention as we proceed. In overlooking the -necessity of a gradual and successive advance from the less general to -the more general truths, Plato shared in a dimness of vision[4] which -prevailed among philosophers to the time of Francis Bacon. In thinking -too slightly of the study of actual nature, he manifested a bias from -which the human intellect freed itself in the vigorous struggles which -terminated the dark ages. In pointing out that all knowledge implies -a unity of what we observe as manifold, which unity is given by the -mind, Plato taught a lesson which has of late been too obscurely -acknowledged, the recoil by which men repaired their long neglect of -facts having carried them for a while so far as to think that facts -were the whole of our knowledge. And in analysing this principle of -Unity, by which we thus connect sensible things, into various Ideas, -such as Number, Magnitude, Position, Motion, he made a highly important -step, which it has been the business of philosophers in succeeding -times to complete and to follow out. - -But the efficacy of Plato's speculations in their bearing upon physical -science, and upon theory in general, was much weakened by the confusion -of practical with theoretical knowledge, which arose from the ethical -propensities of the Socratic school. In the Platonic Dialogues, Art and -Science are constantly spoken of indiscriminately. The skill possessed -by the Painter, the Architect, the Shoemaker, is considered as a just -example of human science, no less than the knowledge which the geometer -or the astronomer possesses of the theoretical truths with which he -is conversant. Not only so; but traditionary and mythological tales, -mystical imaginations and fantastical etymologies, are mixed up, as -no less choice ingredients, with the most acute logical analyses, and -the most exact conduct of metaphysical controversies. There is no -distinction made between the knowledge possessed by the theoretical -psychologist and the physician, the philosophical teacher of morals -and the legislator or the administrator of law. This, indeed, is the -less to be wondered at, since even in our own time the same confusion -is very commonly made by persons not otherwise ignorant or uncultured. - -On the other hand, we may remark finally, that Plato's admiration of -Ideas was not a barren imagination, even so far as regarded physical -science. For, as we have seen[5], he had a very important share in -the introduction of the theory of epicycles, having been the first to -propose to astronomers in a distinct form, the problem of which that -theory was the solution; namely, "to explain the celestial phenomena -by the combination of equable circular motions." This demand of an -ideal hypothesis which should exactly express the phenomena (as well -as they could then be observed), and from which, by the interposition -of suitable steps, all special cases might be deduced, falls in well -with those views respecting the proper mode of seeking knowledge -which we have quoted from the _Philebus_. And the Idea which could -thus represent and replace all the particular Facts, being not only -sought but found, we may readily suppose that the philosopher was, by -this event, strongly confirmed in his persuasion that such an Idea -was indeed what the inquirer ought to seek. In this conviction all -his genuine followers up to modern times have participated; and thus, -though they have avoided the error of those who hold that facts alone -are valuable as the elements of our knowledge, they have frequently run -into the opposite error of too much despising and neglecting facts, and -of thinking that the business of the inquirer after truth was only a -profound and constant contemplation of the conceptions of his own mind. -But of this hereafter. - -FOOTNOTES: - -[Footnote 1: _Metaph._ xii. 4.] - -[Footnote 2: Diog. Laert. _Vit. Plat._] - -[Footnote 3: T. ii. p. 16, c, d. ed. Bekker, t. v. p. 437.] - -[Footnote 4: See the remarks on this phrase in the next chapter.] - -[Footnote 5: _Hist. Ind. Sc._ b. iii. c. ii.] - - - - -CHAPTER III. - -ADDITIONAL REMARKS ON PLATO. - - -The leading points in Plato's writings which bear upon the philosophy -of discovery are these: - - 1. The Doctrine of Ideas. - 2. The Doctrine of the One and the Many. - 3. The notion of the nature and aim of Science. - 4. The survey of existing Sciences. - -1. The Doctrine of Ideas is an attempt to solve a problem which in all -ages forces itself upon the notice of thoughtful men; namely, How can -certain and permanent knowledge be possible for man, since all his -knowledge must be derived from transient and fluctuating sensations? -And the answer given by this doctrine is, that certain and permanent -knowledge is _not_ derived from _Sensations_, but from _Ideas_. There -are in the mind certain elements of knowledge which are not derived -from sensation, and are only imperfectly exemplified in sensible -objects; and when we reason concerning sensible things so as to obtain -real knowledge, we do so by considering such things as partaking of -the qualities of the Ideas concerning which there can be truth. The -sciences of Geometry and Arithmetic show that there _are_ truths which -man can know; and the Doctrine of Ideas explains how this is possible. - -So far the Doctrine of Ideas answers its primary purpose, and is a -reply (by no means the least intelligible and satisfactory reply) to -a question still agitated among philosophers: What is the ground of -geometrical (and other necessary) truth? - -But Plato seems, in many of his writings, to extend this doctrine much -further; and to assume, not only Ideas of Space and its properties, -from which geometrical truths are derived; but of Relations, as the -Relations of Like and Unlike, Greater and Less; and of mere material -objects, as Tables and Chairs. Now to assume Ideas of such things as -these solves no difficulty and is supported by no argument. In this -respect the Ideal theory is of no value in Science. - -It is curious that we have a very acute refutation of the Ideal theory -in this sense, not only in Aristotle, the open opponent of Plato on -this subject, but in the Platonic writings themselves: namely, in the -Dialogue entitled _Parmenides_; which, on this and on other accounts, I -consider to be the work not of Plato, but of an opponent of Plato[6]. - - -2. I have spoken, in the preceding chapter, of Plato's doctrine that -truth is to be obtained by discerning the One in the Many. This -expression is used, it would seem, in a somewhat large and fluctuating -way, to mean several things; as for instance, finding the one _kind_ in -many _individuals_ (for instance, the one idea of dog in many dogs); -or the one _law_ in many _phenomena_ (for instance, the eccentrics and -epicycles in many planets). In any interpretation, it is too loose and -indefinite a rule to be of much value in the formation of sciences, -though it has been recently again propounded as important in modern -times. - - -3. I have said, in the preceding chapter, that Plato, though he saw -that scientific truths of great generality might be obtained and -were to be arrived at by philosophers, overlooked the necessity of a -_gradual_ and _successive_ advance from the less general to the more -general; and I have described this as a 'dimness of vision.' I must now -acknowledge that this is not a very appropriate phrase; for not only -no acuteness of vision could have enabled Plato to see that gradual -generalization in science of which, as yet, no example had appeared; -but it was very fortunate for the progress of truth, at that time, that -Plato had imagined to himself the object of science to be general -and sublime truths which prove themselves to be true by the light of -their own generality and symmetry. It is worth while to illustrate this -notice of Plato by some references to his writings. - -In the Sixth Book of the _Republic_, Plato treats of the then existing -sciences as the instruments of a philosophical education. Among the -most conspicuous of these is astronomy. He there ridicules the notion -that astronomy is a sublime science because it makes men look _upward_. -He asserts that the really sublime science is that which makes men look -at the _realities_, which are suggested by the appearances seen in the -heavens: namely, the spheres which revolve and carry the luminaries -in their revolutions. Now it was no doubt the determined search for -such "realities" as these which gave birth to the Greek _Astronomy_, -that first and critical step in the progress of science. Plato, by his -exhortations, if not by his suggestions, contributed effectually, as -I conceive, to this step in science. In the same manner he requires -a science of _Harmonics_ which shall be free from the defects and -inaccuracies which occur in actual instruments. This belief that the -universe was full of mathematical relations, and that these were the -true objects of scientific research, gave a vigour, largeness of mind, -and confidence to the Greek speculators which no more cautious view of -the problem of scientific discovery could have supplied. It was well -that this advanced guard in the army of discoverers was filled with -indomitable courage, boundless hopes, and creative minds. - -But we must not forget that this disposition to what Bacon calls -_anticipation_ was full of danger as well as of hope. It led Plato -into error, as it led Kepler afterwards, and many others in all ages -of scientific activity. It led Plato into error, for instance, when it -led him to assert (in the _Timæus_) that the four elements, Earth, Air, -Fire and Water, have, for the forms of their particles respectively, -the Cube, the Icosahedron, the Pyramid, and the Octahedron; and again, -when it led him to despise the practical controversies of the musicians -of his time; which controversies were, in fact, the proof of the -truth of the mathematical theory of Harmonics. And in like manner it -led Kepler into error when it led him to believe that he had found the -reason of the number, size and motion of the planetary orbits in the -application of the five regular solids to the frame of the universe[7]. - -How far the caution in forming hypotheses which Bacon's writings urge -upon us is more severe than suits the present prospects of science, -we may hereafter consider; but it is plainly very conceivable that -a boldness in the invention and application of hypotheses which was -propitious to science in its infancy, may be one of the greatest -dangers of its more mature period: and further, that the happy effect -of such a temper depended entirely upon the candour, skill and labour -with which the hypotheses were compared with the observed phenomena. - - -4. Plato has given a survey of the sciences of his time as Francis -Bacon has of _his_. Indeed Plato has given two such surveys: one, -in the _Republic_, in reviewing, as I have said, the elements of a -philosophical education; the other in the _Timæus_, as the portions -of a theological view of the universe--such as has been called a -_Theodicæa_, a justification of God. In the former passage of Plato, -the sciences enumerated are Arithmetic, Plane Geometry, Solid Geometry, -Astronomy and Harmonics[8]. In the _Timæus_ we have a further notice -of many other subjects, in a way which is intended, I conceive, to -include such knowledge as Plato had then arrived at on the various -parts of the universe. The subjects there referred to are, as I have -elsewhere stated[9], these: light and heat, water, ice, gold, gems, -rust and other natural objects:--odours, taste, hearing, lights, -colour, and the powers of sense in general:--the parts and organs of -the body, as the bones, the marrow, the brain, flesh, muscles, tendons, -ligaments and nerves; the skin, the hair, the nails; the veins and -arteries; respiration; generation; and in short, every obvious point -of physiology. But the opinions thus delivered in the _Timæus_ on the -latter subject have little to do with the progress of real knowledge. -The doctrines, on the other hand, which depend upon geometrical and -arithmetical relations are portions or preludes of the sciences which -the fulness of time brought forth. - - -5. I may, as further bearing upon the Platonic notion of science, -notice Plato's view of the constitution of the human mind. According -to him the Ideas which are the constituents of science form an -Intelligible World, while the visible and tangible things which we -perceive by our senses form the Visible World. In the visible world we -have shadows and reflections of actual objects, and by these shadows -and reflections we may judge of the objects, even when we cannot do -so directly; as when men in a dark cavern judge of external objects -by the shadows which they cast into the cavern. In like manner in the -Intelligible World there are conceptions which are the usual objects of -human thought, and about which we reason; but these are only shadows -and reflections of the Ideas which are the real sources of truth. -And the Reasoning Faculty, the Discursive Reason, the _Logos_, which -thus deals with conceptions, is subordinate to the Intuitive Faculty, -the Intuitive Reason, the _Nous_, which apprehends Ideas[10]. This -recognition of a Faculty in man which contemplates the foundations--the -_Fundamental Ideas_--of science, and by apprehending such Ideas, makes -science possible, is consentaneous to the philosophy which I have -all along presented, as the view taught us by a careful study of the -history and nature of science. That new Fundamental Ideas are unfolded, -and the Intuitive Faculty developed and enlarged by the progress of -science and by an intimate acquaintance with its reasonings, Plato -appears to have discerned in some measure, though dimly. And this is -the less wonderful, inasmuch as this gradual and successive extension -of the field of Intuitive Truth, in proportion as we become familiar -with a larger amount of derived truth, is even now accepted by few, -though proved by the reasonings of the greatest scientific discoverers -in every age. - -The leading defect in Plato's view of the nature of real science is his -not seeing fully the extent to which experience and observation are the -basis of all our knowledge of the universe. He considers the luminaries -which appear in the heavens to be not the true objects of astronomy, -but only some imperfect adumbration of them;--mere diagrams which may -assist us in the study of a higher truth, as beautiful diagrams might -illustrate the truths of geometry, but would not prove them. This -notion of an astronomy which is an astronomy of Theories and not of -Facts, is not tenable, for Theories _are_ Facts. Theories and Facts -are equally _real_; true Theories are Facts, and Facts are familiar -Theories. But when Plato says that astronomy is a series of problems -suggested by visible things, he uses expressions quite conformable -to the true philosophy of science; and the like is true of all other -sciences. - -FOOTNOTES: - -[Footnote 6: This matter is further discussed in the Appendix, Essay A.] - -[Footnote 7: These matters are further discussed in the Appendix, Essay -B.] - -[Footnote 8: See Appendix, Essay B.] - -[Footnote 9: _Hist. Ind. Sc._ b. ii. Additions to 3rd Ed.] - -[Footnote 10: See these views further discussed in the Appendix, Essay -C.] - - - - -CHAPTER IV. - -ARISTOTLE. - - -The views of Aristotle with regard to the foundations of human -knowledge are very different from those of his tutor Plato, and are -even by himself put in opposition to them. He dissents altogether -from the Platonic doctrine that Ideas are the true materials of our -knowledge; and after giving, respecting the origin of this doctrine, -the account which we quoted in the last chapter, he goes on to reason -against it. "Thus," he says[11], "they devised Ideas of all things -which are spoken of as universals: much as if any one having to count a -number of objects, should think that he could not do it while they were -few, and should expect to count them by making them more numerous. For -the kinds of things are almost more numerous than the special sensible -objects, by seeking the causes of which they were led to their Ideas." -He then goes on to urge several other reasons against the assumption of -Ideas and the use of them in philosophical researches. - -Aristotle himself establishes his doctrines by trains of reasoning. But -reasoning must proceed from certain First Principles; and the question -then arises, Whence are these First Principles obtained? To this he -replies, that they are the result of _Experience_, and he even employs -the same technical expression by which we at this day describe the -process of collecting these principles from observed facts;--that they -are obtained by _Induction_. I have already quoted passages in which -this statement is made[12]. "The way of reasoning," he says[13], "is -the same in philosophy, and in any art or science: we must collect -the _facts_ (τὰ ὑπὰρχοντα), and the things to which the facts happen, -and must have as large a supply of these as possible, and then we must -examine them according to the terms of our syllogisms." ... "There are -peculiar principles in each science; and in each case these principles -must be obtained from _experience_. Thus astronomical observation -supplies the principles of astronomical science. For the phenomena -being rightly taken, the demonstrations of astronomy were discovered; -and the same is the case with any other Art or Science. So that if -the facts in each case be taken, it is our business to construct the -demonstrations. For if _in our natural history_ (κατὰ τὰν ἱστορί αν) -we have omitted none of the facts and properties which belong to the -subject, we shall learn what we can demonstrate and what we cannot." -And again[14], "It is manifest that if any sensation be wanting, there -must be some knowledge wanting, which we are thus prevented from -having. For we acquire knowledge either _by Induction_ (ἐπαγωγῆ) or -by Demonstration: and Demonstration is from universals, but Induction -from particulars. It is impossible to have universal theoretical -propositions except by Induction: and we cannot make inductions without -having sensation; for sensation has to do with particulars." - -It is easy to show that Aristotle uses the term _Induction_, as we use -it, to express the process of collecting a general proposition from -particular cases in which it is exemplified. Thus in a passage which -we have already quoted[15], he says, "Induction, and Syllogism from -Induction, is when we attribute one extreme term to the middle by means -of the other." The import of this technical phraseology will further -appear by the example which he gives: "We find that several animals -which are deficient in bile are long-lived, as man, the horse, the -mule; hence we infer that _all_ animals which are deficient in bile are -long-lived." - -We may observe, however, that both Aristotle's notion of induction, -and many other parts of his philosophy, are obscure and imperfect, in -consequence of his refusing to contemplate ideas as something distinct -from sensation. It thus happens that he always assumes the ideas -which enter into his proposition as _given_; and considers it as the -philosopher's business to determine whether such propositions are true -or not: whereas the most important feature in induction is, as we have -said, the _introduction_ of a new idea, and not its employment when -once introduced. That the mind in this manner gives unity to that which -is manifold,--that we are thus led to speculative principles which have -an evidence higher than any others,--and that a peculiar sagacity in -some men seizes upon the conceptions by which the facts may be bound -into true propositions,--are doctrines which form no essential part -of the philosophy of the Stagirite, although such views are sometimes -recognized, more or less clearly, in his expressions. Thus he says[16], -"There can be no knowledge when the sensation does not continue in -the mind. For this purpose, it is necessary both to perceive, and to -have some _unity_ in the mind (αἰσθανομένοις εχειν ἔν τι[17] ἐν τῇ -ψυχῇ); and many such perceptions having taken place, some difference -is then perceived: and from the remembrance of these arises Reason. -Thus from Sensation comes Memory, and from Memory of the same thing -often repeated comes Experience: for many acts of Memory make up one -Experience. And from Experience, or from any Universal Notion which -takes a permanent place in the mind,--from the _unity in the manifold_, -the same some one thing being found in many facts,--springs the first -principle of Art and of Science; of Art, if it be employed about -production; of Science, if about existence." - -I will add to this, Aristotle's notice of _Sagacity_; since, although -little or no further reference is made to this quality in his -philosophy, the passage fixes our attention upon an important step in -the formation of knowledge. "Sagacity" (ἀγχίνοια), he says[18], "is a -hitting by guess (εὐστοχία τις) upon the middle term (the conception -common to two cases) in an inappreciable time. As for example, if any -one seeing that the bright side of the moon is always towards the sun, -suddenly perceives why this is; namely, because the moon shines by the -light of the sun:--or if he sees a person talking with a rich man, he -guesses that he is borrowing money;--or conjectures that two persons -are friends, because they are enemies of the same person."--To consider -only the first of these examples;--the conception here introduced, -that of a body shining by the light which another casts upon it, is -not contained in the observed facts, but introduced by the mind. It -is, in short, that conception which, in the act of induction, the mind -superadds to the phenomena as they are presented by the senses: and to -invent such appropriate conceptions, such "eustochies," is, indeed, the -precise office of inductive sagacity. - -At the end of this work (the _Later Analytics_) Aristotle ascribes -our knowledge of principles to Intellect (νοῦς), or, as it appears -necessary to translate the word, _Intuition_[19]. "Since, of our -intellectual habits by which we aim at truth, some are always true, but -some admit of being false, as Opinion and Reasoning, but Science and -Intuition are always true; and since there is nothing which is more -certain than Science except Intuition; and since Principles are better -known to us than the Deductions from them; and since all Science is -connected by reasoning, we cannot have Science respecting Principles. -Considering this then, and that the beginning of Demonstration cannot -be Demonstration, nor the beginning of Science, Science; and since, as -we have said, there is no other kind of truth, Intuition must be the -beginning of Science." - -What is here said, is, no doubt, in accordance with the doctrines which -we have endeavoured to establish respecting the nature of Science, -if by this _Intuition_ we understand that contemplation of certain -Fundamental Ideas, which is the basis of all rigorous knowledge. But -notwithstanding this apparent approximation, Aristotle was far from -having an habitual and practical possession of the principles which he -thus touches upon. He did not, in reality, construct his philosophy by -giving Unity to that which was manifold, or by seeking in Intuition -principles which might be the basis of Demonstration; nor did he -collect, in each subject, fundamental propositions by an induction -of particulars. He rather endeavoured to divide than to unite; he -employed himself, not in combining facts, but in analysing notions; -and the criterion to which he referred his analysis was, not the facts -of our experience, but our habits of language. Thus his opinions -rested, not upon sound inductions, gathered in each case from the -phenomena by means of appropriate Ideas; but upon the loose and vague -generalizations which are implied in the common use of speech. - -Yet Aristotle was so far consistent with his own doctrine of the -derivation of knowledge from experience, that he made in almost -every province of human knowledge, a vast collection of such special -facts as the experience of his time supplied. These collections are -almost unrivalled, even to the present day, especially in Natural -History; in other departments, when to the facts we must add the right -Inductive Idea, in order to obtain truth, we find little of value -in the Aristotelic works. But in those parts which refer to Natural -History, we find not only an immense and varied collection of facts and -observations, but a sagacity and acuteness in classification which it -is impossible not to admire. This indeed appears to have been the most -eminent faculty in Aristotle's mind. - -The influence of Aristotle in succeeding ages will come under our -notice shortly. - - -FOOTNOTES: - -[Footnote 11: _Metaph._ xii. 4.] - -[Footnote 12: _Hist. Ind. Sc._ b. i. c. iii. sect. 2.] - -[Footnote 13: _Analyt. Prior._ i. 30.] - -[Footnote 14: _Analyt. Post._ i. 18.] - -[Footnote 15: _Analyt. Prior._ ii. 23, περὶ τῆς ἐπαγωγῆς.] - -[Footnote 16: _Analyt. Post._ ii. 19.] - -[Footnote 17: But the best reading seems to be not ἔν τι but ἔτι: -and the clause must be rendered "both to perceive and to retain the -perception in the mind." This correction does not disturb the general -sense of the passage, that the first principles of science are obtained -by finding the One in the Many.] - -[Footnote 18: _Analyt. Post._ i. 34.] - -[Footnote 19: _Ibid._ ii. 19.] - - - - -CHAPTER V. - -ADDITIONAL REMARKS ON ARISTOTLE. - - -1. One of the most conspicuous points in Aristotle's doctrines as -bearing upon the philosophy of Science is his account of that mode of -attaining truth which is called _Induction_; for we are accustomed -to consider Induction as the process by which our Sciences have been -formed; and we call them collectively the _Inductive Sciences_. -Aristotle often speaks of Induction, as for instance, when he says that -Socrates introduced the frequent use of it. But the cardinal passage -on this subject is in his _Analytics_, in which he compares Syllogism -and Induction as two modes of drawing conclusions[20]. He there says -that all belief arises either from Syllogism or from Induction: and -adds that Induction is, when by means of one extreme term we infer -the other extreme to be true of the middle term. The example which -he gives is this: knowing that particular animals are long-lived, as -elephant, horse, mule; and finding that these animals agree in having -no gall-bladder; we infer, by _Induction_, that _all_ animals which -have no gall-bladder are long-lived. This may be done, he says, if the -middle and the second extreme are convertible: as the following formal -statement may show. - - Elephant, horse, mule, &c. are long-lived. - Elephant, horse, mule, &c. are all gall-less. - -If we might convert this proposition, and say - -All gall-less animals are as elephant, horse, mule, &c.: - -we might infer _syllogistically_ that - -All gall-less animals are long-lived. - -And though we cannot infer this syllogistically, we infer it by -Induction, when we have a sufficient amount of instances[21]. - -I have already elsewhere given this account of Induction, as a process -employed in the formation of our knowledge[22]. What I have now to -remark concerning Aristotle is, that it does not appear to have -occurred to him, that in establishing such a proposition as that which -he gives as his instance, the main difficulty is the _discovery_ of -a _middle term_ which will allow us to frame such a proposition as -we need. The zoologist who wanted to know what kind of animals are -long-lived, might guess long before he guessed that the absence of the -gall-bladder supplied the requisite middle term; (if the proposition -were true; which it is not.) And in like manner in other cases, it -is difficult to find a middle term, which enables us to collect a -proposition by Induction. And herein consists the imperfection of his -view of the subject; which considers the main point to be the proof -of the proposition when the conceptions are _given_, whereas the main -point really is, the _discovery_ of conceptions which will make a true -proposition possible. - - -2. Since the main characteristic of the steps which have occurred in -the formation of the physical sciences, is not merely that they are -propositions collected by Induction, but by the introduction of a _new_ -conception; it has been suggested that it is not a characteristic -designation of these Sciences to call them _Inductive Sciences_. Almost -every discovery involves in it the introduction of a new conception, -as the element of a new proposition; and the novelty of the conception -is more characteristic of the stages of discovery than the inductive -application of it. Hence as bearing upon the Philosophy of Discovery, -the statements of Aristotle concerning Induction, though acute and -valuable, are not so valuable as they might seem. Even Francis Bacon, -it has been asserted, erred in the same way (and of course with less -excuse) in asserting Induction, of a certain kind, to be the great -instrument for the promotion of knowledge, and in overlooking the -necessity of the _Invention_ which gives Induction its value. - - -3. The invention or discovery of a conception by which many facts -of observation are conjoined so as to make them the materials of a -proposition, is called in Plato, as we have seen, _finding the One in -the Many_. - -In the passage quoted from the _Later Analytics_, Aristotle uses the -same expression, and speaks very justly respecting the formation of -knowledge. Indeed the _Titles_ of the chapters of this and many parts -of Aristotle's works would lead us to expect just such a Philosophy -of Discovery as is the object of our study at present. Thus we have, -_Anal. Post._ B. II. chap. 13: "How we are to hunt (θηρεύειν) the -predications of a Definition." Chap. 14: "Precepts for the invention -of Problems and of a Middle Term:" and the like. But when we come to -read these chapters, they contain little that is of value, and resolve -themselves mostly into permutations of Aristotle's logical phraseology. - - -4. The part of the Aristotelian philosophy which has most permanently -retained its place in modern Sciences is a part of which a use has been -made quite different from that which was originally contemplated. The -"Five words" which are explained in the Introduction to Aristotle's -_Categories_: namely, the words _Genus_, _Species_, _Difference_, -_Property_, _Accident_, were introduced mainly that they might be used -in the propositions of which Syllogisms consist, and might thus be the -elements of reasoning. But it has so happened that these words are -rarely used in Sciences of Reasoning, but are abundantly and commonly -used in the Sciences of Classification, as I have explained in -speaking of the Classificatory Sciences[23]. - - -5. Of Aristotle's actual contributions to the Physical Sciences I have -spoken in the History of those Sciences[24]. I have[25] stated that -he conceived the globular form of the earth so clearly and gave so -forcibly the arguments for that doctrine, that we may look upon him as -the most effective teacher of it. Also in the Appendix to that History, -published in the third edition, I have given Aristotle's account of the -Rainbow, as a further example of his industrious accumulation of facts, -and of his liability to error in his facts. - - -6. We do not find Aristotle so much impressed as we might have expected -by that great monument of Grecian ingenuity, the theory of epicycles -and excentrics which his predecessor Plato urged so strongly upon the -attention of his contemporaries. Aristotle proves, as I have said, -the globular form of the earth by good and sufficient arguments. He -also proves by arguments which seem to him quite conclusive[26], that -the earth is in the center of the universe, and immoveable. As to the -motions of the rest of the planets, he says little. The questions -of their order, and their distances, and the like, belong, he says, -to Astrology[27]. He remarks only that the revolution of the heaven -itself, the outermost revolution, is simple and the quickest of all: -that the revolutions of the others are slower, each moving in a -direction opposite to the heaven in its own circle: and that it is -reasonable that those which are nearest to the first revolution should -take the longest time in describing their own circle, and those that -are furthest off, the least time, and the intermediate ones in the -order of their distances, "as also the mathematicians show." - -In the _Metaphysics_[28] he enumerates the circular movements which -had been introduced by the astronomers Eudoxus and Calippus for the -explanation of the phenomena presented by the sun, moon and planets. -These, he says, amount to fifty-five; and this, he says, must be the -number of essences and principles which exist in the universe. - - -7. In the Sciences of Classification, and especially in the -classification of animals, higher claims have been made for Aristotle, -which I have discussed in the History[29]. I have there attempted to -show that Aristotle's classification, inasmuch as it enumerates all -the parts of animals, may be said to contain the _materials_ of every -subsequent classification: but that it cannot be said to anticipate -any modern system, because the different grades of classification are -not made _subordinate_ to one another as a _system_ of classification -requires. I have the satisfaction of finding Mr. Owen agreeing with me -in these views[30]. - - -8. Francis Bacon's criticism on Aristotle which I have quoted in the -Appendix to the History[31], is severe, and I think evidently the -result of prejudice. He disparages Aristotle in comparison with the -other philosophers of Greece. 'Their systems,' he says, 'had some -savour of experience, and nature, and bodily things; while the Physics -of Aristotle, in general, sound only of Logical Terms. - -'Nor let anyone be moved by this: that in his books _Of Animals_, -and in his _Problems_, and in others of his tracts, there is often a -quoting of experiments. For he had made up his mind beforehand; and did -not consult experience in order to make right propositions and axioms, -but when he had settled his system to his will, he twisted experience -round and made her bend to his system.' - -I do not think that this can be said with any truth. I know no -instances in which Aristotle has twisted experience round, and made -her bend to his system. In his _Problems_, he is so far from giving -dogmatical solutions of the questions proposed, that in most cases, he -propounds two or three solutions as mere suggestions and conjectures. -And both in his History of Animals, as I have said, and in others of -his works, the want of system gives them an incoherent and tumultuary -character, which even a false system would have advantageously removed; -for, as I have said elsewhere, it is easier to translate a false system -into a true one, than to introduce system into a mass of confusion. - - -9. It is curious that a fundamental error into which Aristotle fell in -his view of the conditions which determine the formation of Science -is very nearly the same as one of Francis Bacon's leading mistakes. -Aristotle says, that Science consists in knowing the _causes_ of -things, as Bacon aims at acquiring a knowledge of the _forms_ or -_essences_ of things and their qualities. But the history of all the -sciences teaches us that sciences do not begin with such knowledge, and -that in few cases only do they ever attain to it. Sciences begin by a -knowledge of the _laws_ of _phenomena_, and proceed by the discovery -of the scientific ideas by which the phenomena are colligated, as I -have shown in other works[32]. The discovery of causes is not beyond -the human powers, as some have taught. Those who thus speak disregard -the lessons taught by the history of Physical Astronomy, of Geology, of -Physical Optics, Thermotics and other sciences. But the discovery of -causes, and of the essential forms of qualities, is a triumph reserved -for the later stages of each Science, when the knowledge of the laws of -phenomena has already made great progress. It was not to be expected -that Aristotle would discern this truth, when, as yet, there was no -Science extant in which it had been exemplified. Yet in Astronomy, the -theory of epicycles and excentrics had immense value, and even has -still, as representing the laws of phenomena; while the attempt to find -in it, as Aristotle wished to do, the ultimate causes of the motions -of the universe, could only mislead. The Aristotelian maxim, which -sounds so plausible, and has been so generally accepted, that "to know -truly is to know the causes of things," is a bad guide in scientific -research. Instead of it we might substitute this: that "though we may -aspire to know at last _why_ things are, we must be content for a long -time with knowing _how_ they are." - - -10. Hence if we are asked whether Plato or Aristotle had the truer -views of the nature and property of Science, we must give the -preference to Plato; for though his notion of a real Intelligible -World, of which the Visible world was a fleeting and changeable shadow, -was extravagant, yet it led him to seek to determine the forms of the -Intelligible Things, which are really the laws of visible phenomena; -while Aristotle was led to pass lightly over such laws, because they -did not at once reveal the causes which produced the phenomena. - - -11. Aristotle, throughout his works, takes numerous occasions to -argue against Plato's doctrine of Ideas. Yet these Ideas, so far as -they were the Intelligible Forms of Visible Things, were really fit -objects of philosophical research; and the search after them had a -powerful influence in promoting the progress of Science. And we may -see in the effect of this search the answer to many of Aristotle's -strongest arguments. For instance, Aristotle says that Plato, by way of -explaining things, adds to them as many Ideas, and that this is just -as if a man having to reckon a large number, were to begin by adding -to it another large number. It is plain that to this we may reply, -that the adopting the Ideas of Cycles, along with the motions of the -Planets, does really explain the motions; and that the Cycles are not -simply added to the phenomena, but include and supersede the phenomena: -a finite number of Cycles include and represent an infinite number of -separate phenomena. - -To Aristotle's argument that Ideas cannot be the Causes or Principles -of Things, we should reply, that though they cannot be this, they may -nevertheless be, and must be, the Conditions and Principles of our -Knowledge, which is what we want them to be. - -I have given an account of the main features of Aristotle's philosophy, -so far as it concerns the Physical Sciences, in the History of the -Inductive Sciences, Book I. - - -FOOTNOTES: - -[Footnote 20: _Analyt. Prior._ ii. 25.] - -[Footnote 21: See on this subject Appendix, Essay D.] - -[Footnote 22: See the chapter on Certain Characteristics of Scientific -Induction in the _Phil. Ind. Sc._ or in the _Nov. Org. Renov._] - -[Footnote 23: _Phil. Ind. Sc._ b. viii. c. i. art. 11, or _Hist. Sc. -Id._ b. viii.] - -[Footnote 24: B. i. c. xi. sect. 2.] - -[Footnote 25: B. iii. c. i. sect. 9.] - -[Footnote 26: _De Cælo_, ii. 13.] - -[Footnote 27: _Ibid._ ii. 10.] - -[Footnote 28: xii. 8.] - -[Footnote 29: B. xvi. c. vi.] - -[Footnote 30: _On the Classification of Mammalia, &c.: a Lecture -delivered at Cambridge_, May 10, 1859, p. 3.] - -[Footnote 31: B. i. c. xi.] - -[Footnote 32: _History of Scientific Ideas_, and _Novum Organum -Renovatum_.] - - - - -CHAPTER VI. - -THE LATER GREEKS. - - -Thus while Plato was disposed to seek the essence of our knowledge -in Ideas alone, Aristotle, slighting this source of truth, looked to -Experience as the beginning of Science; and he attempted to obtain, by -division and deduction, all that Experience did not immediately supply. -And thus, with these two great names, began that struggle of opposite -opinions which has ever since that time agitated the speculative -world, as men have urged the claims of Ideas or of Experience to our -respect, and as alternately each of these elements of knowledge has -been elevated above its due place, while the other has been unduly -depressed. We shall see the successive turns of this balanced struggle -in the remaining portions of this review. - -But we may observe that practically the influence of Plato predominated -rather than that of Aristotle, in the remaining part of the history -of ancient philosophy. It was, indeed, an habitual subject of dispute -among men of letters, whether the sources of true knowledge are -to be found in the Senses or in the Mind; the Epicureans taking -one side of this alternative, and the Academics another, while the -Stoics in a certain manner included both elements in their view. But -none of these sects showed their persuasion that the materials of -knowledge were to be found in the domain of Sense, by seeking them -there. No one appears to have thought of following the example of -Aristotle, and gathering together a store of observed facts. We may -except, perhaps, assertions belonging to some provinces of Natural -History, which were collected by various writers: but in these, the -mixed character of the statements, the want of discrimination in -the estimate of evidence, the credulity and love of the marvellous -which the authors for the most part displayed, showed that instead -of improving upon the example of Aristotle, they were wandering -further and further from the path of real knowledge. And while they -thus collected, with so little judgment, such statements as offered -themselves, it hardly appears to have occurred to any one to enlarge -the stores of observation by the aid of experiment; and to learn -what the laws of nature were, by trying what were their results in -particular cases. They used no instruments for obtaining an insight -into the constitution of the universe, except logical distinctions -and discussions; and proceeded as if the phenomena familiar to their -predecessors must contain all that was needed as a basis for natural -philosophy. By thus contenting themselves with the facts which the -earlier philosophers had contemplated, they were led also to confine -themselves to the ideas which those philosophers had put forth. For -all the most remarkable alternatives of hypothesis, so far as they -could be constructed with a slight and common knowledge of phenomena, -had been promulgated by the acute and profound thinkers who gave the -first impulse to philosophy: and it was not given to man to add much -to the original inventions of _their_ minds till he had undergone -anew a long discipline of observation, and of thought employed upon -observation. Thus the later authors of the Greek Schools became little -better than commentators on the earlier; and the commonplaces with -which the different schools carried on their debates,--the constantly -recurring argument, with its known attendant answer,--the distinctions -drawn finer and finer and leading to nothing,--render the speculations -of those times a _scholastic_ philosophy, in the same sense in which -we employ the term when we speak of the labours of the middle ages. It -will be understood that I now refer to that which is here my subject, -the opinions concerning our knowledge of nature, and the methods in -use for the purpose of obtaining such knowledge. Whether the moral -speculations of the ancient world were of the same stationary kind, -going their round in a limited circle, like their metaphysics and -physics, must be considered on some other occasion. [33] Mr. Grote, -in his very interesting discussion of Socrates's teaching, notices -also[34] the teaching of Hippocrates, which he conceives to have in -one respect the same tendency as the philosophy of Socrates; namely, -to turn away from the vague aggregate of doctrines and guesses which -constituted the Physical Philosophy of that time, and to pursue instead -a special and more practical course of inquiry: Hippocrates selecting -Medicine and Socrates selecting Ethics. By this limitation of their -subject, they avoided some of the errors of their predecessors. For, -as Mr. Grote has also remarked, "the earlier speculators, Anaxagoras, -Empedocles, Democritus, the Pythagoreans, all had still present to -their minds the vast and undivided problems which have been transmitted -down from the old poets; bending their minds to the invention of some -system which would explain them all at once, or assist the imagination -in conceiving both how the Kosmos first began and how it continued to -move on." There could be no better remedy for this ambitious error of -the human mind than to have a definite subject of study, such as the -diseases and the health of the human body. Accordingly, we see that the -study of medicine did draw its cultivators away from this ancient but -unprofitable field. Hippocrates[35] condemns those who, as Empedocles, -set themselves to make out what man was from the beginning, how he -began first to exist, and in what manner he was constructed. This is, -he says, no part of medicine. In like manner he blames and refutes -those who make some simple element, Hot, or Cold, or Moist, or Dry, the -cause of diseases, and give medical precepts professing to be founded -on this hypothesis. - -These passages are marked by the prudence which practical study -suggests to a calm and clear-sighted man. They can hardly be said to -have opened the way to a Science of Medicine; for in the sense in which -we here use the word _Science_, namely, a collection of general truths -inferred from facts by successive discoverers, we have even yet no -Science of Medicine. The question with regard to the number and nature -of the Elements of which bodies are composed began to be agitated, as -we have seen, at a very early period of Greek philosophy, and continued -long to be regarded as a chief point of physiological doctrine. In -Galen's work we have a treatise entitled, _On the Elements according -to Hippocrates_; and the writer explains[36] that though Hippocrates -has not written any work with the title _On the Elements_, yet that -he has in his _Treatise on the Nature of Man_ shown his opinion on -that subject. That the doctrine of the Four Elements, Hot, Cold, -Moist, Dry, subsisted long in the schools, we have evidence in Galen. -He tells us[37] that when he was a student of nineteen years old a -teacher urged this lore upon him, and regarded him as very contentious -and perverse, because he offered objections to it. His account of the -Dialogue between him and the teacher is curious. But in Hippocrates the -doctrine of these four elements is replaced, in a great measure, by the -doctrine of the Four Humours of which the human body is constituted; -namely, Blood, Phlegm, Yellow Bile and Black Bile. Galen dwells with -emphasis upon Hippocrates's proof that there must be more than one such -element[38]. - -"What," he asks, "is the method of finding the Elements of bodies? -There can, in my opinion, be no other than that which was introduced by -Hippocrates; namely, we must inquire whether there be only one element, -everywhere the same in kind, or whether there are more than one, -various and unlike each other. And if the Element be not one only, but -several, various and dissimilar, we must inquire in the second place, -how many elements there are, and what, and of what kind they are, and -how related in their association. - -"Now that the First Element is not one only of which both our bodies -and those of all other creatures were produced, Hippocrates shows -from these considerations. And it is better first to put down his own -expressions and then to expound them. 'I assert that if man consisted -of one element only he could not fall sick; for there would be nothing -which could derange his health, if he were all of one Element.'" - -The doctrine of One Element did not prevail much after the time of -Hippocrates: the doctrine of Four Elements continued, as I have said, -long to hold possession of the Schools, but does not appear as an -important part of the doctrine of Hippocrates. The doctrine of the Four -Humours (Blood, Phlegm, Yellow Bile and Black Bile) is more peculiarly -his, and long retained its place as a principle of physiological -Science. - -But we are here not so much concerned with his discoveries in medicine -as with his views respecting the method of acquiring sound knowledge, -and in this respect, as has been said, he recommends by his practice -a prudent limitation of the field of inquiry, a rejection of wide, -ambitious, general assertions, and a practical study of his proper -field. - -In ascribing these merits to Hippocrates's medical speculations as -to the ethical speculations of his contemporary Socrates, we assign -considerable philosophical value to Hippocrates, no less than to -Socrates. These merits were at that time the great virtues of physical -as well as of ethical philosophy. But, as Mr. Grote well observes, the -community of character which then subsisted between the physical and -ethical speculations prevailing at that time, ceased to obtain in later -times. Indeed, it ceased to exist just at that time, in consequence of -the establishment of scientific astronomy by the exertions of Plato -and his contemporaries. From that time the Common Sense (as we call it) -of a man like Socrates, though it might be a good guide in ethics, was -not a good guide in physics. I have shown elsewhere[39] how the Common -Sense of Socrates was worthless in matters of astronomy. From that time -one of the great intellectual lessons was, that in order to understand -the external world, we must indeed observe carefully, but we must also -guess boldly. Discovery here required an inventive mind like Plato's -to deal with and arrange new and varied facts. But in ethics all the -facts were old and familiar, and the generalizations of language by -which they were grouped as Virtues and Vices, and the like, were common -and well-known words. Here was no room for invention; and thus in the -ethical speculations of Socrates or of any other moral teacher, we are -not to look for any contributions to the Philosophy of Discovery. - -Nor do I find anything on this subject among later Greek writers, -beyond the commendation of such intellectual virtues as Hippocrates and -Galen, and other medical writers, schooled by the practice of their -art, enjoined and praised. But before we quit the ancients I will point -out some peculiarities which may be noticed in the Roman disciples of -the Greek philosophy. - - -FOOTNOTES: - -[Footnote 33: The remainder of this chapter is new in the present -edition.] - -[Footnote 34: _Hist. of Greece_, Part ii. chap. 68.] - -[Footnote 35: _De Antiqua Medicina_, c. 20.] - -[Footnote 36: Lib. i. c. 9.] - -[Footnote 37: _De Elem._ i. 6.] - -[Footnote 38: In former editions I have not done justice to this -passage.] - -[Footnote 39: _Hist. Ind. Sc._ Addition to Introduction in Third -Edition.] - - - - -CHAPTER VII. - -THE ROMANS. - - -The Romans had no philosophy but that which they borrowed from the -Greeks; and what they thus received, they hardly made entirely their -own. The vast and profound question of which we have been speaking, -the relation between Existence and our Knowledge of what exists, they -never appear to have fathomed, even so far as to discern how wide and -deep it is. In the development of the ideas by which nature is to be -understood, they went no further than their Greek masters had gone, -nor indeed was more to be looked for. And in the practical habit of -accumulating observed facts as materials for knowledge, they were much -less discriminating and more credulous than their Greek predecessors. -The descent from Aristotle to Pliny, in the judiciousness of the -authors and the value of their collections of facts, is immense. - -Since the Romans were thus servile followers of their Greek teachers, -and little acquainted with any example of new truths collected from -the world around them, it was not to be expected that they could have -any just conception of that long and magnificent ascent from one set -of truths to others of higher order and wider compass, which the -history of science began to exhibit when the human mind recovered -its progressive habits. Yet some dim presentiment of the splendid -career thus destined for the intellect of man appears from time to -time to have arisen in their minds. Perhaps the circumstance which -most powerfully contributed to suggest this vision, was the vast -intellectual progress which they were themselves conscious of having -made, through the introduction of the Greek philosophy; and to this -may be added, perhaps, some other features of national character. Their -temper was too stubborn to acquiesce in the absolute authority of the -Greek philosophy, although their minds were not inventive enough to -establish a rival by its side. And the wonderful progress of their -political power had given them a hope in the progress of man which -the Greeks never possessed. The Roman, as he believed the fortune of -his State to be destined for eternity, believed also in the immortal -destiny and endless advance of that Intellectual Republic of which he -had been admitted a denizen. - -It is easy to find examples of such feelings as I have endeavoured -to describe. The enthusiasm with which Lucretius and Virgil speak of -physical knowledge, manifestly arises in a great measure from the -delight which they had felt in becoming acquainted with the Greek -theories. - - Me vero primum dulces ante omnia Musæ - Quarum sacra fero ingenti perculsus amore - Accipiant, cœlique vias et sidera monstrent, - Defectus Solis varios, Lunæque labores!... - Felix qui potuit rerum cognoscere causas! - - Ye sacred Muses, with whose beauty fir'd, - My soul is ravisht and my brain inspir'd: - Whose Priest I am, whose holy fillets wear, - Would you your Poet's first petition hear, - Give me the ways of wand'ring stars to know, - The depth of Heaven above and Earth below; - Teach me the various labours of the Moon, - And whence proceed th' eclipses of the Sun; - Why flowing Tides prevail upon the main, - And in what dark abyss they shrink again; - What shakes the solid Earth; what cause delays - The Summer Nights; and shortens Winter Days.... - Happy the man who, studying Nature's Laws, - Through known effects can trace the secret cause! - -Ovid[40] expresses a similar feeling. - - Felices animos quibus hæc cognoscere primis - Inque domos superas scandere cura fuit!... - Admovere oculis distantia sidera nostris - Ætheraque ingenio supposuere suo. - Sic petitur cœlum: non ut ferat Ossam Olympus - Summaque Peliacus sidera tanget apex. - - Thrice happy souls! to whom 'twas given to rise - To truths like these, and scale the spangled skies! - Far distant stars to clearest view they brought, - And girdled ether with their chain of thought. - So heaven is reached:--not as of old they tried - By mountains piled on mountains in their pride. - - -And from the whole tenour of these and similar passages, it is evident -that the intellectual pleasure which arises from our first introduction -to a beautiful physical theory had a main share in producing this -enthusiasm at the contemplation of the victories of science; although -undoubtedly the moral philosophy, which was never separated from the -natural philosophy, and the triumph over superstitious fears, which -a knowledge of nature was supposed to furnish, added warmth to the -feeling of exultation. - -We may trace a similar impression in the ardent expressions which -Pliny[41] makes use of in speaking of the early astronomers, and which -we have quoted in the _History_. "Great men! elevated above the common -standard of human nature, by discovering the laws which celestial -occurrences obey, and by freeing the wretched mind of man from the -fears which eclipses inspired." - -This exulting contemplation of what science had done, naturally led the -mind to an anticipation of further achievements still to be performed. -Expressions of this feeling occur in Seneca, and are of the most -remarkable kind, as the following example will show[42]: - -"Why do we wonder that comets, so rare a phenomenon, have not yet had -their laws assigned?--that we should know so little of their beginning -and their end, when their recurrence is at wide intervals? It is not -yet fifteen hundred years since Greece, - - Stellis numeros et nomina fecit, - -'reckoned the stars, and gave them names.' There are still many nations -which are acquainted with the heavens by sight only; which do not yet -know why the moon disappears, why she is eclipsed. It is but lately -that among us philosophy has reduced these matters to a certainty. The -day shall come when the course of time and the labour of a maturer age -shall bring to light what is yet concealed. One generation, even if it -devoted itself to the skies, is not enough for researches so extensive. -How then can it be so, when we divide this scanty allowance of years -into no equal shares between our studies and our vices? These things -then must be explained by a long succession of inquiries. We have but -just begun to know how arise the morning and evening appearances, -the stations, the progressions, and the retrogradations of the fixed -stars which put themselves in our way;--which appearing perpetually -in another and another place compel us to be curious. Some one will -hereafter demonstrate in what region the comets wander; why they move -so far asunder from the rest; of what size and nature they are. Let -us be content with what we have discovered: let posterity contribute -its share to truth." Again he adds[43] in the same strain: "Let us -not wonder that what lies so deep is brought out so slowly. How many -animals have become known for the first time in this age! And the -members of future generations shall know many of which we are ignorant. -Many things are reserved for ages to come, when our memory shall -have passed away. The world would be a small thing indeed, if it did -not contain matter of inquiry _for_ all the world. Eleusis reserves -something for the second visit of the worshipper. _So too Nature -does not at once disclose all_ HER _mysteries_. We think ourselves -initiated; we are but in the vestibule. The arcana are not thrown open -without distinction and without reserve. This age will see some things; -that which comes after us, others." - -While we admire the happy coincidence of these conjectures with the -soundest views which the history of science teaches us, we must not -forget that they are merely conjectures, suggested by very vague -impressions, and associated with very scanty conceptions of the laws -of nature. Seneca's _Natural Questions_, from which the above extract -is taken, contains a series of dissertations on various subjects of -Natural Philosophy; as Meteors, Rainbows, Lightnings, Springs, Rivers, -Snow, Hail, Rain, Wind, Earthquakes and Comets. In the whole of these -dissertations, the statements are loose, and the explanations of little -or no value. Perhaps it may be worth our while to notice a case in -which he refers to an observation of his own, although his conclusion -from it be erroneous. He is arguing[44] against the opinion that -Springs arise from the water which falls in rain. "In the first place," -he says, "I, a very diligent digger in my vineyard, affirm that no rain -is so heavy as to moisten the earth to the depth of more than ten feet. -All the moisture is consumed in this outer crust, and descends not to -the lower part." We have here something of the nature of an experiment; -and indeed, as we may readily conceive, the instinct which impels man -to seek truth by experiment can never be altogether extinguished. -Seneca's experiment was deprived of its value by the indistinctness of -his ideas, which led him to rest in the crude conception of the water -being "consumed" in the superficial crust of the earth. - -It is unnecessary to pursue further the reasonings of the Romans on -such subjects, and we now proceed to the ages which succeeded the fall -of their empire. - - -FOOTNOTES: - -[Footnote 40: Lib. i. _Fast._] - -[Footnote 41: _Hist. Nat._ i. 75.] - -[Footnote 42: _Quæst. Nat._ vii. 25.] - -[Footnote 43: _Quæst. Nat._ vii. 30, 31.] - -[Footnote 44: _Ibid._ iii. 7.] - - - - -CHAPTER VIII. - -ARABIAN PHILOSOPHERS. - - -I have noticed certain additions to Physical Science made by the -Arabians; namely, in Astronomy[45]. The discovery of the motion of -the Sun's Apogee by Albategnius, and the discovery of the Moon's -_Variation_ by Aboul-Wefa; and in Optics[46] the assertion of Alhazen -that the angle of refraction is not proportional to the angle of -incidence, as Ptolemy had supposed: and certain steps in the philosophy -of vision. We must also suppose, as the Arabic word _alkali_ reminds -us, that the Arabians contributed to lay the foundations of chemistry. -The question which we have here to ask is, whether the Arabians made -any steps beyond their predecessors in the philosophy of discovery. -And to this question, I conceive the answer must be this: that among -them as among the Greeks, those who practically observed nature, and -especially those who made discoveries in Science, must have had a -practical acquaintance with some of the maxims which are exemplified -in the formation of Science. To discover that the Apogee of the Sun -was 17 degrees distant from the point where Ptolemy had placed it, -Albategnius made careful observations, and referred them to the theory -of the eccentric, so as to verify or correct that theory. And when, in -the eleventh century, Arzachel found the Apogee to be less advanced -than Albategnius had found it, he proceeded again to correct the -theory by introducing a new movement of the equinoctial points, which -was called the _Trepidation_. It appeared afterwards, however, that, -in doing this, he had had too much confidence in the observations of -his predecessors, and that no such movement as the Trepidation really -existed. In like manner to correct Ptolemy's law of refraction, Alhazen -had recourse to experiment: but he did not put his experiments in the -form of a Table, as Ptolemy had done. If he had done this, he might -possibly have discovered the law of sines, which Snell afterwards -discovered. - -But though the Arabian philosophers thus, in some cases, observed -facts, and referred those facts to general mathematical laws, it does -not appear that they were led to put in any new or striking general -form such maxims as this: That the progress of Science consists in the -exact observation of facts and in colligating them by ideas. Those of -them who were dissatisfied with the existing philosophy as barren and -useless (for instance Algazel[47]), were led to point at the faults -and contradictions of that philosophy, but did not attempt, so far -as I know, to substitute for it anything better. If they rejected -Aristotle's _Organon_, they did not attempt to construct a new Organon -for themselves. - -Indeed they do not appear even to have had sufficient confidence in the -real truth of the astronomical theories which they had adopted from the -Greeks, always to correct and extend those where their observations -showed that they required correction and extension. Sometimes they did -this, but not generally enough. When Arzachel found by observation -the Apogee of the Sun to be situated too far back, he ventured to -correct Ptolemy's statement of its motion. But when Aboul-Wefa had -really discovered the _Variation_ of the Moon's motion, he did not -express it by means of an epicycle. If he had done so, he would have -made it unnecessary for Tycho Brahe at a later period to make the same -discovery. - -The moral of this incident is the same moral which we have perpetually -to note as taught us at every step by the history of Science:--namely, -the necessity of constant, careful and exact observation of Facts; and -the advantage of devising a Theory, (even if it have to be afterwards -rejected,) by which the Facts shall be bound together into a coherent -whole. - -FOOTNOTES: - -[Footnote 45: _Hist. Ind. Sc._ b. iii. c. iv. sect. 8.] - -[Footnote 46: _Ibid._ b. ix. c. ii.] - -[Footnote 47: See _Hist. Ind. Sc._ b. iv. c. i.] - - - - -CHAPTER IX. - -THE SCHOOLMEN OF THE MIDDLE AGES. - - -In the _History of the Sciences_ I have devoted a Book to the state -of Science in the middle ages, and have endeavoured to analyse the -intellectual defects of that period. Among the characteristic features -of the human mind during those times, I have noticed Indistinctness of -Ideas, a Commentatorial Spirit, Mysticism, and Dogmatism. The account -there given of this portion of the history of man belongs, in reality, -rather to the History of Ideas than to the History of Progressive -Science. For, as we have there remarked, theoretical Science was, -during the period of which we speak, almost entirely stationary; and -the investigation of the causes of such a state of things may be -considered as a part of that review in which we are now engaged, of the -vicissitudes of man's acquaintance with the methods of discovery. But -when we offered to the world a history of science, to leave so large a -chasm unexplained, would have made the series of events seem defective -and broken; and the survey of the Middle Ages was therefore inserted. -I would beg to refer to that portion of the former work the reader who -wishes for information in addition to what is here given. - -The Indistinctness of Ideas and the Commentatorial Disposition of those -ages have already been here brought under our notice. Viewed with -reference to the opposition between Experience and Ideas, on which -point, as we have said, the succession of opinions in a great measure -turns, it is clear that the commentatorial method belongs to the ideal -side of the question: for the commentator seeks for such knowledge -as he values, by analysing and illustrating what his author has said; -and, content with this material of speculation, does not desire to -add to it new stores of experience and observation. And with regard -to the two other features in the character which we gave to those -ages, we may observe that Dogmatism demands for philosophical theories -the submission of mind, due to those revealed religious doctrines -which are to guide our conduct and direct our hopes: while Mysticism -elevates ideas into realities, and offers them to us as the objects -of our religious regard. Thus the Mysticism of the middle ages and -their Dogmatism alike arose from not discriminating the offices of -theoretical and practical philosophy. Mysticism claimed for ideas the -dignity and reality of principles of moral action and religious hope: -Dogmatism imposed theoretical opinions respecting speculative points -with the imperative tone of rules of conduct and faith. - -If, however, the opposite claims of theory and practice interfered -with the progress of science by the confusion they thus occasioned, -they did so far more by drawing men away altogether from mere physical -speculations. The Christian religion, with its precepts, its hopes, and -its promises, became the leading subject of men's thoughts; and the -great active truths thus revealed, and the duties thus enjoined, made -all inquiries of mere curiosity appear frivolous and unworthy of man. -The Fathers of the Church sometimes philosophized ill; but far more -commonly they were too intent upon the great lessons which they had to -teach, respecting man's situation in the eyes of his Heavenly Master, -to philosophize at all respecting things remote from the business of -life and of no importance in man's spiritual concerns. - -Yet man has his intellectual as well as his spiritual wants. He has -faculties which demand systems and reasons, as well as precepts and -promises. The Christian doctor, who knew so much more than the heathen -philosopher respecting the Creator and Governor of the universe, was -not long content to know or to teach less, respecting the universe -itself. While it was still maintained that Theology was the only -really important study, Theology was so extended and so fashioned as to -include all other knowledge: and after no long time, the Fathers of the -Church themselves became the authors of systems of universal knowledge. - -But when this happened, the commentatorial spirit was still in its -full vigour. The learned Christians could not, any more than the -later Greeks or the Romans, devise, by the mere force of their own -invention, new systems, full, comprehensive, and connected, like those -of the heroic age of philosophy. The same mental tendencies which led -men to look for speculative coherence and completeness in the view of -the universe, led them also to admire and dwell upon the splendid and -acute speculations of the Greeks. They were content to find, in those -immortal works, the answers to the questions which their curiosity -prompted; and to seek what further satisfaction they might require, -in analysing and unfolding the doctrines promulgated by those great -masters of knowledge. Thus the Christian doctors became, as to general -philosophy, commentators upon the ancient Greek teachers. - -Among these, they selected Aristotle as their peculiar object of -admiration and study. The vast store, both of opinions and facts, which -his works contain, his acute distinctions, his cogent reasons in some -portions of his speculations, his symmetrical systems in almost all, -naturally commended him to the minds of subtle and curious men. We -may add that Plato, who taught men to contemplate Ideas separate from -Things, was not so well fitted for general acceptance as Aristotle, who -rejected this separation. For although the due apprehension of this -opposition of Ideas and Sensations is a necessary step in the progress -of true philosophy, it requires a clearer view and a more balanced mind -than the common herd of students possess; and Aristotle, who evaded the -necessary perplexities in which this antithesis involves us, appeared, -to the temper of those times, the easier and the plainer guide of the -two. - -The Doctors of the middle ages having thus adopted Aristotle as -their master in philosophy, we shall not be surprised to find them -declaring, after him, that experience is the source of our knowledge -of the visible world. But though, like the Greeks, they thus talked of -experiment, like the Greeks, they showed little disposition to discover -the laws of nature by observation of facts. This barren and formal -recognition of experience or sensation as one source of knowledge, -not being illustrated by a practical study of nature, and by real -theoretical truths obtained by such a study, remained ever vague, -wavering, and empty. Such a mere acknowledgment cannot, in any times, -ancient or modern, be considered as indicating a just apprehension of -the true basis and nature of science. - -In imperfectly perceiving how, and how far, experience is the source of -our knowledge of the external world, the teachers of the middle ages -were in the dark; but so, on this subject, have been almost all the -writers of all ages, with the exception of those who in recent times -have had their minds enlightened by contemplating philosophically the -modern progress of science. The opinions of the doctors of the middle -ages on such subjects generally had those of Aristotle for their basis; -but the subject was often still further analysed and systematized, with -an acute and methodical skill hardly inferior to that of Aristotle -himself. - -The Stagirite, in the beginning of his _Physics_, had made the -following remarks. "In all bodies of doctrine which involve principles, -causes, or elements, Science and Knowledge arise from the knowledge -of these; (for we then consider ourselves to _know_ respecting any -subject, when we know its first cause, its first principles, its -ultimate elements.) It is evident, therefore, that in seeking a -knowledge of nature, we must first know what are its principles. But -the course of our knowledge is, from the things which are better known -and more manifest to us, to the things which are more certain and -evident in nature. For those things which are most evident in truth, -are not most evident to us. [And consequently we must advance from -things obscure in nature, but manifest to us, towards the things which -are really in nature more clear and certain.] The things which are -first obvious and apparent to us are complex; and from these we obtain, -by analysis, principles and elements. We must proceed from universals -to particulars. For the whole is better known to our senses than the -parts, and for the same reason, the universal better known than the -particular. And thus words signify things in a large and indiscriminate -way, which is afterwards analysed by definition; as we see that the -children at first call all men _father_, and all women _mother_, but -afterwards learn to distinguish." - -There are various assertions contained in this extract which came to -be considered as standard maxims, and which occur constantly in the -writers of the middle ages. Such are, for instance, the maxim, "Verè -scire est per causas scire;" the remark, that compounds are known -to us before their parts, and the illustration from the expressions -used by children. Of the mode in which this subject was treated by -the schoolmen, we may judge by looking at passages of Thomas Aquinas -which treat of the subject of the human understanding. In the _Summa -Theologiæ_, the eighty-fifth Question is _On the manner and order of -understanding_, which subject he considers in eight Articles; and -these must, even now, be looked upon as exhibiting many of the most -important and interesting points of the subject. They are, _First_, -Whether our understanding understands by abstracting ideas (_species_) -from appearances; _Second_, Whether intelligible species abstracted -from appearances are related to our understanding as that _which_ we -understand, or that _by which_ we understand; _Third_, Whether our -understanding does naturally understand universals first; _Fourth_, -Whether our understanding can understand many things at once; _Fifth_, -Whether our understanding understands by compounding and dividing; -_Sixth_, Whether the understanding can err; _Seventh_, Whether one -person can understand the same thing better than another; _Eighth_, -Whether our understanding understands the indivisible sooner than -the divisible. And in the discussion of the last point, for example, -reference is made to the passage of Aristotle which we have already -quoted. "It may seem," he says, "that we understand the indivisible -before the divisible; for _the Philosopher_ says that we understand -and know by knowing principles and elements; but indivisibles are the -principles and elements of divisible things. But to this we may reply, -that in our receiving of science, principles and elements are not -always first; for sometimes from the sensible effects we go on to the -knowledge of intelligible principles and causes." We see that both the -objection and the answer are drawn from Aristotle. - -We find the same close imitation of Aristotle in Albertus Magnus, who, -like Aquinas, flourished in the thirteenth century. Albertus, indeed, -wrote treatises corresponding to almost all those of the Stagirite, and -was called the _Ape of Aristotle_. In the beginning of his _Physics_, -he says, "Knowledge does not always begin from that which is first -according to the nature of things, but from that of which the knowledge -is easiest. For the human intellect, on account of its relation to the -senses (_propter reflexionem quam habet ad sensum_), collects science -from the senses; and thus it is easier for our knowledge to begin from -that which we can apprehend by sense, imagination, and intellect, than -from that which we apprehend by intellect alone." We see that he has -somewhat systematized what he has borrowed. - -This disposition to dwell upon and systematize the leading doctrines -of metaphysics assumed a more definite and permanent shape in the -opposition of the Realists and Nominalists. The opposition involved -in this controversy is, in fact, that fundamental antithesis of Sense -and Ideas about which philosophy has always been engaged; and of -which we have marked the manifestation in Plato and Aristotle. The -question, What is the object of our thoughts when we reason concerning -the external world? must occur to all speculative minds: and the -difficulties of the answer are manifest. We must reply, either that our -own Ideas, or that Sensible Things, are the elements of our knowledge -of nature. And then the scruples again occur,--how we have any -_general_ knowledge if our thoughts are fixed on particular objects; -and, on the other hand,--how we can attain to any _true_ knowledge of -nature by contemplating ideas which are not identical with objects in -nature. The two opposite opinions maintained on this subject were, on -the one side,--that our general propositions refer to objects which -are _real_, though divested of the peculiarities of individuals; and, -on the other side,--that in such propositions, individuals are not -represented by any reality, but bound together by a _name_. These two -views were held by the Realists and Nominalists respectively: and thus -the Realist manifested the adherence to Ideas, and the Nominalist the -adherence to the impressions of Sense, which have always existed as -opposite yet correlative tendencies in man. - -The Realists were the prevailing sect in the Scholastic times: for -example, both Thomas Aquinas and Duns Scotus, the _Angelical_ and the -_Subtle_ Doctor, held this opinion, although opposed to each other -in many of their leading doctrines on other subjects. And as the -Nominalist, fixing his attention upon sensible objects, is obliged to -consider what is the _principle of generalization_, in order that the -possibility of any general proposition may be conceivable; so on the -other hand, the Realist, beginning with the contemplation of universal -ideas, is compelled to ask what is the _principle of individuation_, in -order that he may comprehend the application of general propositions -in each particular instance. This inquiry concerning the principle of -individuation was accordingly a problem which occupied all the leading -minds among the Schoolmen[48]. It will be apparent from what has -been said, that it is only one of the many forms of the fundamental -antithesis of the Ideas and the Senses, which we have constantly before -us in this review. - -The recognition of the derivation of our knowledge, in part at least, -from Experience, though always loose and incomplete, appears often -to be independent of the Peripatetic traditions. Thus Richard of St. -Victor, a writer of contemplative theology in the twelfth century, -says[49], that "there are three sources of knowledge, experience, -reason, faith. Some things we prove by experiment, others we collect -by reasoning, the certainty of others we hold by believing. And -with regard to temporal matters, we obtain our knowledge by actual -experience; the other guides belong to divine knowledge." Richard -also propounds a division of human knowledge which is clearly not -derived directly from the ancients, and which shows that considerable -attention must have been paid to such speculations. He begins by laying -down clearly and broadly the distinction, which, as we have seen, is -of primary importance, between _practice_ and _theory_. _Practice_, -he says, includes seven mechanical arts; those of the clothier, the -armourer, the navigator, the hunter, the physician, and the player. -_Theory_ is threefold, divine, natural, doctrinal; and is thus divided -into Theology, Physics, and Mathematics. _Mathematics_, he adds, -treats of the invisible _forms_ of visible things. We have seen that -by many profound thinkers this word _forms_ has been selected as best -fitted to describe those relations of things which are the subject of -mathematics. Again, Physics discovers causes from their effects and -effects from their causes. It would not be easy at the present day to -give a better account of the object of physical science. But Richard -of St. Victor makes this account still more remarkably judicious, by -the examples to which he alludes; which are earthquakes, the tides, -the virtues of plants, the instincts of animals, the classification of -minerals, plants and reptiles. - - Unde tremor terris, quâ vi maria alta tumescant, - Herbarum vires, animos irasque ferarum, - Omne genus fruticum, lapidum quoque, reptiliumque. - -He further adds[50], "Physical science ascends from effects to -causes, and descends again from causes to effects." This declaration -Francis Bacon himself might have adopted. It is true, that Richard -would probably have been little able to produce any clear and -definite instances of knowledge, in which this ascent and descent -were exemplified; but still the statement, even considered as a -mere conjectural thought, contains a portion of that sagacity and -comprehensive power which we admire so much in Bacon. - -Richard of St. Victor, who lived in the twelfth century, thus exhibits -more vigour and independence of speculative power than Thomas Aquinas, -Albertus Magnus, and Duns Scotus, in the thirteenth. In the interval, -about the end of the twelfth century, the writings of Aristotle had -become generally known in the West; and had been elevated into the -standard of philosophical doctrine, by the divines mentioned above, who -felt a reverent sympathy with the systematizing and subtle spirit of -the Stagirite as soon as it was made manifest to them. These doctors, -following the example of their great forerunner, reduced every part -of human knowledge to a systematic form; the systems which they thus -framed were presented to men's minds as the only true philosophy, and -dissent from them was no longer considered to be blameless. It was an -offence against religion as well as reason to reject the truth, and -the truth could be but one. In this manner arose that claim which the -Doctors of the Church put forth to control men's opinions upon all -subjects, and which we have spoken of in the _History of Science_ as -the Dogmatism of the Middle Ages. There is no difficulty in giving -examples of this characteristic. We may take for instance a Statute of -the University of Paris, occasioned by a Bull of Pope John XXI., in -which it is enacted, "that no Master or Bachelor of any faculty, shall -presume to read lectures upon any author in a private room, on account -of the many perils which may arise therefrom; but shall read in public -places, where all may resort, and may faithfully report what is there -taught; excepting only books of Grammar and Logic, in which there can -be no presumption." And certain errors of Brescian are condemned in a -Rescript[51] of the papal Legate Odo, with the following expressions: -"Whereas, as we have been informed, certain Logical professors -treating of Theology in their disputations, and Theologians treating -of Logic, contrary to the command of the law are not afraid to mix and -confound the lots of the Lord's heritage; we exhort and admonish your -University, all and singular, that they be content with the landmarks -of the Sciences and Faculties which our Fathers have fixed; and that -having due fear of the curse pronounced in the law against him who -removeth his neighbour's landmark, you hold such sober wisdom according -to the Apostles, that ye may by no means incur the blame of innovation -or presumption." - -The account which, in the _History of Science_, I gave of Dogmatism as -a characteristic of the middle ages, has been indignantly rejected by -a very pleasing modern writer, who has, with great feeling and great -diligence, brought into view the merits and beauties of those times, -termed by him _Ages of Faith_. He urges[52] that religious authority -was never claimed for physical science: and he quotes from Thomas -Aquinas, a passage in which the author protests against the practice -of confounding opinions of philosophy with doctrines of faith. We -might quote in return the Rescript[53] of Stephen, bishop of Paris, -in which he declares that there can be but one truth, and rejects -the distinction of things being true according to philosophy and not -according to the Catholic faith; and it might be added, that among the -errors condemned in this document are some of Thomas Aquinas himself. -We might further observe, that if no physical doctrines were condemned -in the times of which we now speak, this was because, on such subjects, -no new opinions were promulgated, and not because opinion was free. -As soon as new opinions, even on physical subjects, attracted general -notice, they were prohibited by authority, as we see in the case of -Galileo[54]. - -But this disinclination to recognize philosophy as independent of -religion, and this disposition to find in new theories, even in -physical ones, something contrary to religion or scripture, are, it -would seem, very natural tendencies of theologians; and it would be -unjust to assert that these propensities were confined to the periods -when the authority of papal Rome was highest; or that the spirit which -has in a great degree controlled and removed such habits was introduced -by the Reformation of religion in the sixteenth century. We must trace -to other causes, the clear and general recognition of Philosophy, -as distinct from Theology, and independent of her authority. In -the earlier ages of the Church, indeed, this separation had been -acknowledged. St. Augustin says, "A Christian should beware how he -speaks on questions of natural philosophy, as if they were doctrines of -Holy Scripture; for an infidel who should hear him deliver absurdities -could not avoid laughing. Thus the Christian would be confused, and the -infidel but little edified; for the infidel would conclude that our -authors really entertained these extravagant opinions, and therefore -they would despise them, to their own eternal ruin. Therefore the -opinions of philosophers should never be proposed as dogmas of faith, -or rejected as contrary to faith, when it is not certain that they are -so." These words are quoted with approbation by Thomas Aquinas, and -it is said[55], are cited in the same manner in every encyclopedical -work of the middle ages. This warning of genuine wisdom was afterwards -rejected, as we have seen; and it is only in modern times that its -value has again been fully recognized. And this improvement we must -ascribe, mainly, to the progress of physical science. For a great body -of undeniable truths on physical subjects being accumulated, such as -had no reference to nor connexion with the truths of religion, and -yet such as possessed a strong interest for most men's minds, it was -impossible longer to deny that there were wide provinces of knowledge -which were not included in the dominions of Theology, and over which -she had no authority. In the fifteenth and sixteenth centuries, the -fundamental doctrines of mechanics, hydrostatics, optics, magnetics, -chemistry, were established and promulgated; and along with them, -a vast train of consequences, attractive to the mind by the ideal -relations which they exhibited, and striking to the senses by the power -which they gave man over nature. Here was a region in which philosophy -felt herself entitled and impelled to assert her independence. From -this region, there is a gradation of subjects in which philosophy -advances more and more towards the peculiar domain of religion; -and at some intermediate points there have been, and probably will -always be, conflicts respecting the boundary line of the two fields -of speculation. For the limit is vague and obscure, and appears to -fluctuate and shift with the progress of time and knowledge. - -Our business at present is not with the whole extent and limits -of philosophy, but with the progress of physical science more -particularly, and the methods by which it may be attained: and we are -endeavouring to trace historically the views which have prevailed -respecting such methods, at various periods of man's intellectual -progress. Among the most conspicuous of the revolutions which opinions -on this subject have undergone, is the transition from an implicit -trust in the internal powers of man's mind to a professed dependence -upon external observation; and from an unbounded reverence for the -wisdom of the past, to a fervid expectation of change and improvement. -The origin and progress of this disposition of mind;--the introduction -of a state of things in which men not only obtained a body of -indestructible truths from experience, and increased it from generation -to generation, but professedly, and we may say, ostentatiously, -declared such to be the source of their knowledge, and such their -hopes of its destined career;--the rise, in short, of Experimental -Philosophy, not only as a habit, but as a Philosophy of Experience, is -what we must now endeavour to exhibit. - - -FOOTNOTES: - -[Footnote 48: See the opinion of Aquinas, in Degerando, _Hist. Com. des -Syst._ iv. 499; of Duns Scotus, _ibid._ iv. 523.] - -[Footnote 49: _Liber Excerptionum_, Lib. i. c. i.] - -[Footnote 50: _Tr. Ex._ Lib. i. c. vii.] - -[Footnote 51: Tenneman, viii. 461.] - -[Footnote 52: _Mores Catholici, or Ages of Faith_, viii. p. 247.] - -[Footnote 53: Tenneman, viii. 460.] - -[Footnote 54: If there were any doubt on this subject, we might -refer to the writers who afterwards questioned the supremacy of -Aristotle, and who with one voice assert that an infallible authority -had been claimed for him. Thus Laurentius Valla: "Quo minus ferendi -sunt recentes Peripatetici, qui nullius sectæ hominibus interdicunt -libertate ab Aristotele dissentiendi, quasi sophos hic, non -philosophus." _Pref. in Dial._ (Tenneman, ix. 29.) So Ludovicus Vives: -"Sunt ex philosophis et ex theologis qui non solum quo Aristoteles -pervenit extremum esse aiunt naturæ, sed quâ pervenit eam rectissimam -esse omnium et certissimam in natura viam." (Tenneman, ix. 43.) We -might urge too, the evasions practised by philosophical Reformers, -through fear of the dogmatism to which they had to submit; for example, -the protestation of Telesius at the end of the Proem to his work, _De -Rerum Natura_: "Nec tamen, si quid eorum quæ nobis posita sunt, sacris -literis, Catholicæve ecclesiæ decretis non cohæreat, tenendum id, quin -penitus rejiciendum asseveramus contendimusque. Neque enim _humana_ -modo _ratio_ quævis, sed _ipse_ etiam _sensus_ illis _posthabendus_, et -si illis non congruat, abnegandus omnino et ipse etiam est sensus."] - -[Footnote 55: _Ages of Faith_, viii. 247: to the author of which I am -obliged for this quotation.] - - - - -CHAPTER X. - -THE INNOVATORS OF THE MIDDLE AGES. - - -_Raymond Lully._ - -1. _General Remarks._--In the rise of Experimental Philosophy, -understanding the term in the way just now stated, two features have -already been alluded to: the disposition to cast off the prevalent -reverence for the opinions and methods of preceding teachers with an -eager expectation of some vast advantage to be derived from a change; -and the belief that this improvement must be sought by drawing our -knowledge from external observation rather than from mere intellectual -efforts;--_the Insurrection against Authority_, and _the Appeal to -Experience_. These two movements were closely connected; but they may -easily be distinguished, and in fact, persons were very prominent in -the former part of the task, who had no comprehension of the latter -principle, from which alone the change derives its value. There were -many Malcontents who had not the temper, talent or knowledge, which -fitted them to be Reformers. - -The authority which was questioned, in the struggle of which we speak, -was that of the Scholastic System, the combination of Philosophy with -Theology; of which Aristotle, presented in the form and manner which -the Doctors of the Church had imposed upon him, is to be considered -the representative. When there was demanded of men a submission of -the mind, such as this system claimed, the natural love of freedom in -man's bosom, and the speculative tendencies of his intellect, rose in -rebellion, from time to time, against the ruling oppression. We find -in all periods of the scholastic ages examples of this disposition -of man to resist overstrained authority; the tendency being mostly, -however, combined with a want of solid thought, and showing itself -in extravagant pretensions and fantastical systems put forwards by -the insurgents. We have pointed out one such opponent[56] of the -established systems, even among the Arabian schoolmen, a more servile -race than ever the Europeans were. We may here notice more especially -an extraordinary character who appeared in the thirteenth century, and -who may be considered as belonging to the Prelude of the Reform in -Philosophy, although he had no share in the Reform itself. - -2. _Raymond Lully._--Raymond Lully is perhaps traditionally best known -as an Alchemist, of which art he appears to have been a cultivator. But -this was only one of the many impulses of a spirit ardently thirsty -of knowledge and novelty. He had[57], in his youth, been a man of -pleasure, but was driven by a sudden shock of feeling to resolve on a -complete change of life. He plunged into solitude, endeavoured to still -the remorse of his conscience by prayer and penance, and soon had his -soul possessed by visions which he conceived were vouchsafed to him. -In the feeling of religious enthusiasm thus excited, he resolved to -devote his life to the diffusion of Christian truth among Heathens and -Mahomedans. For this purpose, at the age of thirty he betook himself -to the study of Grammar, and of the Arabic language. He breathed -earnest supplications for an illumination from above; and these were -answered by his receiving from heaven, as his admirers declare, his -_Ars Magna_ by which he was able without labour or effort to learn -and apply all knowledge. The real state of the case is, that he put -himself in opposition to the established systems, and propounded a New -Art, from which he promised the most wonderful results; but that his -Art really is merely a mode of combining ideal conceptions without any -reference to real sources of knowledge, or any possibility of real -advantage. In a Treatise addressed, in A.D. 1310, to King Philip of -France, entitled _Liber Lamentationis Duodecim Principiorum Philosophiæ -contra Averroistas_, Lully introduced Philosophy, accompanied by her -twelve Principles, (Matter, Form, Generation, &c.) uttering loud -complaints against the prevailing system of doctrine; and represents -her as presenting to the king a petition that she may be upheld and -restored by her favourite, the Author. His _Tabula Generalis ad omnes -Scientias applicabilis_ was begun the 15th September, 1292, in the -Harbour of Tunis, and finished in 1293, at Naples. In order to frame an -Art of thus tabulating all existing sciences, and indeed all possible -knowledge, he divides into various classes the conceptions with which -he has to deal. The first class contains nine _Absolute Conceptions_: -Goodness, Greatness, Duration, Power, Wisdom, Will, Virtue, Truth, -Majesty. The second class has nine _Relative Conceptions_: Difference, -Identity, Contrariety, Beginning, Middle, End, Majority, Equality, -Minority. The third class contains nine _Questions_: Whether? What? -Whence? Why? How great? How circumstanced? When? Where? and How? -The fourth class contains the nine _Most General Subjects_: God, -Angel, Heaven, Man, _Imaginativum_, _Sensitivum_, _Vegetativum_, -_Elementativum_, _Instrumentativum_. Then come nine _Prædicaments_, -nine _Moral Qualities_, and so on. These conceptions are arranged in -the compartments of certain concentric moveable circles, and give -various combinations by means of triangles and other figures, and thus -propositions are constructed. - -It must be clear at once, that real knowledge, which is the union of -facts and ideas, can never result from this machinery for shifting -about, joining and disjoining, empty conceptions. This, and all similar -schemes, go upon the supposition that the logical combinations of -notions do of themselves compose knowledge; and that really existing -things may be arrived at by a successive system of derivation from -our most general ideas. It is imagined that by distributing the -nomenclature of abstract ideas according to the place which they can -hold in our propositions, and by combining them according to certain -conditions, we may obtain formulæ including all possible truths, and -thus fabricate a science in which all sciences are contained. We thus -obtain the means of talking and writing upon all subjects, without the -trouble of thinking: the revolutions of the emblematical figures are -substituted for the operations of the mind. Both exertion of thought, -and knowledge of facts, become superfluous. And this reflection, adds -an intelligent author[58], explains the enormous number of books which -Lully is said to have written; for he might have written those even -during his sleep, by the aid of a moving power which should keep his -machine in motion. Having once devised this invention for manufacturing -science, Lully varied it in a thousand ways, and followed it into -a variety of developments. Besides Synoptical Tables, he employs -Genealogical Trees, each of which he dignifies with the name of the -Tree of Science. The only requisite for the application of his System -was a certain agreement in the numbers of the classes into which -different subjects were distributed; and as this symmetry does not -really exist in the operations of our thoughts, some violence was done -to the natural distinction and subordination of conceptions, in order -to fit them for the use of the system. - -Thus Lully, while he professed to teach an Art which was to shed new -light upon every part of science, was in fact employed in a pedantic -and trifling repetition of known truths or truisms; and while he -complained of the errors of existing methods, he proposed in their -place one which was far more empty, barren, and worthless, than the -customary processes of human thought. Yet his method is spoken of[59] -with some praise by Leibnitz, who indeed rather delighted in the -region of ideas and words, than in the world of realities. But Francis -Bacon speaks far otherwise and more justly on this subject[60]. "It is -not to be omitted that some men, swollen with emptiness rather than -knowledge, have laboured to produce a certain Method, not deserving -the name of a legitimate Method, since it is rather a method of -imposture: which yet is doubtless highly grateful to certain would-be -philosophers. This method scatters about certain little drops of -science in such a manner that a smatterer may make a perverse and -ostentatious use of them with a certain show of learning. Such was -the art of Lully, which consisted of nothing but a mass and heap of -the words of each science; with the intention that he who can readily -produce the words of any science shall be supposed to know the science -itself. Such collections are like a rag shop, where you find a patch of -everything, but nothing which is of any value." - - -FOOTNOTES: - -[Footnote 56: Algazel. See _Hist. Ind. Sc._ b. iv. c. i.] - -[Footnote 57: Tenneman, viii. 830.] - -[Footnote 58: Degerando, iv. 535.] - -[Footnote 59: Leibnitz's expressions are, (_Op._ t. vi. p. 16): "Quand -j'étais jeune, je prenois quelque a l'_Art_ de Lulle, mais je crus y -entrevoir bien des défectuosités, dont j'ai dit quelque chose dans un -petit Essai d'écolier intitulé _De Arte Combinatoria_, publié en 1666, -et qui a été réimprimé après malgré moi. Mais comme je ne méprise -rien facilement, excepté les arts divinatoires que ne sont que des -tromperies toutes pures, j'ai trouvé quelque chose d'estimable encore -dans l'_Art_ de Lulle."] - -[Footnote 60: _Works_, vii. 296.] - - - - -CHAPTER XI. - -THE INNOVATORS OF THE MIDDLE AGES--CONTINUED. - - -_Roger Bacon._ - -We now come to a philosopher of a very different character, who was -impelled to declare his dissent from the reigning philosophy by the -abundance of his knowledge, and by his clear apprehension of the mode -in which real knowledge had been acquired and must be increased. - -Roger Bacon was born in 1214, near Ilchester, in Somersetshire, of -an old family. In his youth he was a student at Oxford, and made -extraordinary progress in all branches of learning. He then went to -the University of Paris, as was at that time the custom of learned -Englishmen, and there received the degree of Doctor of Theology. At -the persuasion of Robert Grostête, bishop of Lincoln, he entered the -brotherhood of Franciscans in Oxford, and gave himself up to study -with extraordinary fervour. He was termed by his brother monks _Doctor -Mirabilis_. We know from his own works, as well as from the traditions -concerning him, that he possessed an intimate acquaintance with all the -science of his time which could be acquired from books; and that he had -made many remarkable advances by means of his own experimental labours. -He was acquainted with Arabic, as well as with the other languages -common in his time. In the title of his works, we find the whole -range of science and philosophy, Mathematics and Mechanics, Optics, -Astronomy, Geography, Chronology, Chemistry, Magic, Music, Medicine, -Grammar, Logic, Metaphysics, Ethics, and Theology; and judging from -those which are published, these works are full of sound and exact -knowledge. He is, with good reason, supposed to have discovered, or to -have had some knowledge of, several of the most remarkable inventions -which were made generally known soon afterwards; as gunpowder, lenses, -burning specula, telescopes, clocks, the correction of the calendar, -and the explanation of the rainbow. - -Thus possessing, in the acquirements and habits of his own mind, -abundant examples of the nature of knowledge and of the process of -invention, Roger Bacon felt also a deep interest in the growth and -progress of science, a spirit of inquiry respecting the causes which -produced or prevented its advance, and a fervent hope and trust in its -future destinies; and these feelings impelled him to speculate worthily -and wisely respecting a Reform of the Method of Philosophizing. The -manuscripts of his works have existed for nearly six hundred years in -many of the libraries of Europe, and especially in those of England; -and for a long period the very imperfect portions of them which were -generally known, left the character and attainments of the author -shrouded in a kind of mysterious obscurity. About a century ago, -however, his _Opus Majus_ was published[61] by Dr. S. Jebb, principally -from a manuscript in the Library of Trinity College, Dublin; and this -contained most or all of the separate works which were previously -known to the public, along with others still more peculiar and -characteristic. We are thus able to judge of Roger Bacon's knowledge -and of his views, and they are in every way well worthy our attention. - -The _Opus Majus_ is addressed to Pope Clement the Fourth, whom Bacon -had known when he was legate in England as Cardinal-bishop of Sabina, -and who admired the talents of the monk, and pitied him for the -persecutions to which he was exposed. On his elevation to the papal -chair, this account of Bacon's labours and views was sent, at the -earnest request of the pontiff. Besides the _Opus Majus_, he wrote -two others, the _Opus Minus_ and _Opus Tertium_; which were also sent -to the pope, as the author says[62], "on account of the danger of -roads, and the possible loss of the work." These works still exist -unpublished, in the Cottonian and other libraries. The _Opus Majus_ is -a work equally wonderful with regard to its general scheme, and to the -special treatises with which the outlines of the plan are filled up. -The professed object of the work is to urge the necessity of a reform -in the mode of philosophizing, to set forth the reasons why knowledge -had not made a greater progress, to draw back attention to the sources -of knowledge which had been unwisely neglected, to discover other -sources which were yet almost untouched, and to animate men in the -undertaking, by a prospect of the vast advantages which it offered. -In the development of this plan, all the leading portions of science -are expounded in the most complete shape which they had at that time -assumed; and improvements of a very wide and striking kind are proposed -in some of the principal of these departments. Even if the work had had -no leading purpose, it would have been highly valuable as a treasure of -the most solid knowledge and soundest speculations of the time; even -if it had contained no such details, it would have been a work most -remarkable for its general views and scope. It may be considered as, -at the same time, the _Encyclopedia_ and the _Novum Organon_ of the -thirteenth century. - -Since this work is thus so important in the history of Inductive -Philosophy I shall give, in a note, a view[63] of its divisions and -contents. But I must now endeavour to point out more especially the way -in which the various principles, which the reform of scientific method -involved, are here brought into view. - -One of the first points to be noticed for this purpose, is the -resistance to authority; and at the stage of philosophical history -with which we here have to do, this means resistance to the authority -of Aristotle, as adopted and interpreted by the Doctors of the -Schools. Bacon's work[64] is divided into Six Parts; and of these -Parts, the First is, Of the four universal Causes of all Human -Ignorance. The causes thus enumerated[65] are:--the force of unworthy -authority;--traditionary habit;--the imperfection of the undisciplined -senses;--and the disposition to conceal our ignorance and to make an -ostentatious show of our knowledge. These influences involve every man, -occupy every condition. They prevent our obtaining the most useful and -large and fair doctrines of wisdom, the secret of all sciences and -arts. He then proceeds to argue, from the testimony of philosophers -themselves, that the authority of antiquity, and especially of -Aristotle, is not infallible. "We find[66] their books full of doubts, -obscurities, and perplexities. They scarce agree with each other in -one empty question or one worthless sophism, or one operation of -science, as one man agrees with another in the practical operations -of medicine, surgery, and the like arts of Secular men. Indeed," he -adds, "not only the philosophers, but the saints have fallen into -errors which they have afterwards retracted," and this he instances -in Augustin, Jerome, and others. He gives an admirable sketch[67] of -the progress of philosophy from the Ionic School to Aristotle; of whom -he speaks with great applause. "Yet," he adds[68], "those who came -after him corrected him in some things, and added many things to his -works, and shall go on adding to the end of the world." Aristotle, he -adds, is now called peculiarly[69] the Philosopher, "yet there was a -time when his philosophy was silent and unregarded, either on account -of the rarity of copies of his works, or their difficulty, or from -envy; till after the time of Mahomet, when Avicenna and Averroes, and -others, recalled this philosophy into the full light of exposition. And -although the Logic and some other works were translated by Boethius -from the Greek, yet the philosophy of Aristotle first received a quick -increase among the Latins at the time of Michael Scot; who, in the year -of our Lord 1230, appeared, bringing with him portions of the books of -Aristotle on Natural Philosophy and Mathematics. And yet a small part -only of the works of this author is translated, and a still smaller -part is in the hands of common students." He adds further[70] (in the -Third Part of the _Opus Majus_, which is a Dissertation on language), -that the translations which are current of these writings, are very -bad and imperfect. With these views, he is moved to express himself -somewhat impatiently[71] respecting these works: "If I had," he says, -"power over the works of Aristotle, I would have them all burnt; for -it is only a loss of time to study in them, and a cause of error, and -a multiplication of ignorance beyond expression." "The common herd of -students," he says, "with their heads, have no principle by which they -can be excited to any worthy employment; and hence they mope and make -asses of themselves over their bad translations, and lose their time, -and trouble, and money." - -The remedies which he recommends for these evils, are, in the first -place, the study of that only perfect wisdom which is to be found in -the sacred Scripture[72], in the next place, the study of mathematics -and the use of experiment[73]. By the aid of these methods, Bacon -anticipates the most splendid progress for human knowledge. He takes up -the strain of hope and confidence which we have noticed as so peculiar -in the Roman writers; and quotes some of the passages of Seneca which -we adduced in illustration of this:--that the attempts in science were -at first rude and imperfect, and were afterwards improved;--that the -day will come, when what is still unknown shall be brought to light by -the progress of time and the labours of a longer period;--that one age -does not suffice for inquiries so wide and various;--that the people -of future times shall know many things unknown to us;--and that the -time shall arrive when posterity will wonder that we overlooked what -was so obvious. Bacon himself adds anticipations more peculiarly in -the spirit of his own time. "We have seen," he says, at the end of the -work, "how Aristotle, by the ways which wisdom teaches, could give to -Alexander the empire of the world. And this the Church ought to take -into consideration against the infidels and rebels, that there may be a -sparing of Christian blood, and especially on account of the troubles -that shall come to pass in the days of Antichrist; which by the grace -of God, it would be easy to obviate, if prelates and princes would -encourage study, and join in searching out the secrets of nature and -art." - -It may not be improper to observe here that this belief in the -appointed progress of knowledge, is not combined with any overweening -belief in the unbounded and independent power of the human intellect. -On the contrary, one of the lessons which Bacon draws from the state -and prospects of knowledge, is the duty of faith and humility. "To -him," he says[74], "who denies the truth of the faith because he is -unable to understand it, I will propose in reply the course of nature, -and as we have seen it in examples." And after giving some instances, -he adds, "These, and the like, ought to move men and to excite them -to the reception of divine truths. For if, in the vilest objects of -creation, truths are found, before which the inward pride of man must -bow, and believe though it cannot understand, how much more should -man humble his mind before the glorious truths of God!" He had before -said[75]: "Man is incapable of perfect wisdom in this life; it is -hard for him to ascend towards perfection, easy to glide downwards -to falsehoods and vanities: let him then not boast of his wisdom, or -extol his knowledge. What he knows is little and worthless, in respect -of that which he believes without knowing; and still less, in respect -of that which he is ignorant of. He is mad who thinks highly of his -wisdom; he most mad, who exhibits it as something to be wondered at." -He adds, as another reason for humility, that he has proved by trial, -he could teach in one year, to a poor boy, the marrow of all that -the most diligent person could acquire in forty years' laborious and -expensive study. - -To proceed somewhat more in detail with regard to Roger Bacon's views -of a Reform in Scientific Inquiry, we may observe that by making -Mathematics and Experiment the two great points of his recommendation, -he directed his improvement to the two essential parts of all -knowledge, Ideas and Facts, and thus took the course which the most -enlightened philosophy would have suggested. He did not urge the -prosecution of experiment, to the comparative neglect of the existing -mathematical sciences and conception; a fault which there is some -ground for ascribing to his great namesake and successor Francis -Bacon: still less did he content himself with a mere protest against -the authority of the schools, and a vague demand for change, which -was almost all that was done by those who put themselves forward as -reformers in the intermediate time. Roger Bacon holds his way steadily -between the two poles of human knowledge; which, as we have seen, it -is far from easy to do. "There are two modes of knowing," says he[76]; -"by argument, and by experiment. Argument concludes a question; but -it does not make us feel certain, or acquiesce in the contemplation -of truth, except the truth be also found to be so by experience." -It is not easy to express more decidedly the clearly seen union of -exact conceptions with certain facts, which, as we have explained, -constitutes real knowledge. - -One large division of the _Opus Majus_ is "On the Usefulness of -Mathematics," which is shown by a copious enumeration of existing -branches of knowledge, as Chronology, Geography, the Calendar and -(in a separate Part) Optics. There is a chapter[77], in which it is -proved by reason, that all science requires mathematics. And the -arguments which are used to establish this doctrine, show a most just -appreciation of the office of mathematics in science. They are such as -follows:--That other sciences use examples taken from mathematics as -the most evident:--That mathematical knowledge is, as it were, innate -in us, on which point he refers to the well-known dialogue of Plato, -as quoted by Cicero:--That this science, being the easiest, offers the -best introduction to the more difficult:--That in mathematics, things -as known to us are identical with things as known to nature:--That -we can here entirely avoid doubt and error, and obtain certainty and -truth:--That mathematics is prior to other sciences in nature, because -it takes cognizance of quantity, which is apprehended by intuition, -(_intuitu intellectus_). "Moreover," he adds[78], "there have been -found famous men, as Robert, bishop of Lincoln, and Brother Adam -Marshman (de Marisco), and many others, who by the power of mathematics -have been able to explain the causes of things; as may be seen in the -writings of these men, for instance, concerning the Rainbow and Comets, -and the generation of heat, and climates, and the celestial bodies." - -But undoubtedly the most remarkable portion of the _Opus Majus_ is the -Sixth and last Part, which is entitled "De Scientia experimentali." -It is indeed an extraordinary circumstance to find a writer of the -thirteenth century, not only recognizing experiment as one source -of knowledge, but urging its claims as something far more important -than men had yet been aware of, exemplifying its value by striking -and just examples, and speaking of its authority with a dignity of -diction which sounds like a foremurmur of the Baconian sentences -uttered nearly four hundred years later. Yet this is the character of -what we here find[79]. "Experimental science, the sole mistress of -speculative sciences, has three great Prerogatives among other parts -of knowledge: First she tests by experiment the noblest conclusions of -all other sciences: Next she discovers respecting the notions which -other sciences deal with, magnificent truths to which these sciences of -themselves can by no means attain: her Third dignity is, that she by -her own power and without respect of other sciences, investigates the -secret of nature." - -The examples which Bacon gives of these "Prerogatives" are very -curious, exhibiting, among some error and credulity, sound and clear -views. His leading example of the First Prerogative, is the Rainbow, -of which the cause, as given by Aristotle, is tested by reference to -experiment with a skill which is, even to us now, truly admirable. -The examples of the Second Prerogative are three:--_first_, the art -of making an artificial sphere which shall move with the heavens by -natural influences, which Bacon trusts may be done, though astronomy -herself cannot do it--"et tunc," he says, "thesaurum unius regis -valeret hoc instrumentum;"--_secondly_, the art of prolonging life, -which experiment may teach, though medicine has no means of securing -it except by regimen[80];--_thirdly_, the art of making gold finer -than fine gold, which goes beyond the power of alchemy. The Third -Prerogative of experimental science, arts independent of the received -sciences, is exemplified in many curious examples, many of them -whimsical traditions. Thus it is said that the character of a people -may be altered by altering the air[81]. Alexander, it seems, applied -to Aristotle to know whether he should exterminate certain nations -which he had discovered, as being irreclaimably barbarous; to which -the philosopher replied, "If you can alter their air, permit them to -live, if not, put them to death." In this part, we find the suggestion -that the fire-works made by children, of saltpetre, might lead to the -invention of a formidable military weapon. - -It could not be expected that Roger Bacon, at a time when experimental -science hardly existed, could give any _precepts_ for the discovery -of truth by experiment. But nothing can be a better _example_ of the -method of such investigation, than his inquiry concerning the cause of -the Rainbow. Neither Aristotle, nor Avicenna, nor Seneca, he says, have -given us any clear knowledge of this matter, but experimental science -can do so. Let the experimenter (_experimentator_) consider the cases -in which he finds the same colours, as the hexagonal crystals from -Ireland and India; by looking into these he will see colours like those -of the rainbow. Many think that this arises from some special virtue of -these stones and their hexagonal figure; let therefore the experimenter -go on, and he will find the same in other transparent stones, in dark -ones as well as in light-coloured. He will find the same effect also -in other forms than the hexagon, if they be furrowed in the surface, -as the Irish crystals are. Let him consider too, that he sees the same -colours in the drops which are dashed from oars in the sunshine;--and -in the spray thrown by a millwheel;--and in the dew-drops which lie on -the grass in a meadow on a summer-morning;--and if a man takes water -in his mouth and projects it on one side into a sunbeam;--and if in an -oil-lamp hanging in the air, the rays fall in certain positions upon -the surface of the oil;--and in many other ways, are colours produced. -We have here a collection of instances, which are almost all examples -of the same kind as the phenomenon under consideration; and by the help -of a principle collected by induction from these facts, the colours of -the rainbow were afterwards really explained. - -With regard to the form and other circumstances of the bow he is still -more precise. He bids us measure the height of the bow and of the sun, -to show that the center of the bow is exactly opposite to the sun. -He explains the circular form of the bow,--its being independent of -the form of the cloud, its moving when we move, its flying when we -follow,--by its consisting of the reflections from a vast number of -minute drops. He does not, indeed, trace the course of the rays through -the drop, or account for the precise magnitude which the bow assumes; -but he approaches to the verge of this part of the explanation; and -must be considered as having given a most happy example of experimental -inquiry into nature, at a time when such examples were exceedingly -scanty. In this respect, he was more fortunate than Francis Bacon, as -we shall hereafter see. - -We know but little of the biography of Roger Bacon, but we have every -reason to believe that his influence upon his age was not great. -He was suspected of magic, and is said to have been put into close -confinement in consequence of this charge. In his work he speaks -of Astrology as a science well worth cultivating. "But," says he, -"Theologians and Decretists, not being learned in such matters and -seeing that evil as well as good may be done, neglect and abhor such -things, and reckon them among Magic Arts." We have already seen, that -at the very time when Bacon was thus raising his voice against the -habit of blindly following authority, and seeking for all science -in Aristotle, Thomas Aquinas was employed in fashioning Aristotle's -tenets into that fixed form in which they became the great impediment -to the progress of knowledge. It would seem, indeed, that something -of a struggle between the progressive and stationary powers of the -human mind was going on at this time. Bacon himself says[82], "Never -was there so great an appearance of wisdom, nor so much exercise of -study in so many Faculties, in so many regions, as for this last forty -years. Doctors are dispersed everywhere, in every castle, in every -burgh, and especially by the students of two Orders, (he means the -Franciscans and Dominicans, who were almost the only religious orders -that distinguished themselves by an application to study[83],) which -has not happened except for about forty years. And yet there was never -so much ignorance, so much error." And in the part of his work which -refers to Mathematics, he says of that study[84], that it is the door -and the key of the sciences; and that the neglect of it for thirty or -forty years has entirely ruined the studies of the Latins. According to -these statements, some change, disastrous to the fortunes of science, -must have taken place about 1230, soon after the foundation of the -Dominican and Franciscan Orders[85]. Nor can we doubt that the adoption -of the Aristotelian philosophy by these two Orders, in the form in -which the Angelical Doctor had systematized it, was one of the events -which most tended to defer, for three centuries, the reform which Roger -Bacon urged as a matter of crying necessity in his own time. - - -FOOTNOTES: - -[Footnote 61: _Fratris Rogeri Bacon, Ordinis Minorum_, Opus Majus, _ad -Clementem Quartum, Pontificem Romanum, ex MS. Codice Dubliniensi cum -aliis quibusdam collato, nunc primum edidit_ S. Jebb, M.D. Londini, -1733.] - -[Footnote 62: _Opus Majus_, Præf.] - -[Footnote 63: Contents of Roger Bacon's _Opus Majus_. - -Part I. On the four causes of human ignorance:--Authority, Custom, -Popular Opinion, and the Pride of supposed Knowledge. - -Part II. On the source of perfect wisdom in the Sacred Scripture. - -Part III. On the Usefulness of Grammar. - -Part IV. On the Usefulness of Mathematics. - -(1) The necessity of Mathematics in Human Things (published separately -as the _Specula Mathematica_). - -(2) The necessity of Mathematics in Divine Things.--1°. This study -has occupied holy men: 2°. Geography: 3°. Chronology: 4°. Cycles; -the Golden Number, &c.: 5°. Natural Phenomena, as the Rainbow: 6°. -Arithmetic: 7°. Music. - -(3) The necessity of Mathematics in Ecclesiastical Things.--1°. The -Certification of Faith: 2°. The Correction of the Calendar. - -(4) The necessity of Mathematics in the State.--1°. Of Climates: 2°. -Hydrography: 3°. Geography: 4°. Astrology. - -Part V. On Perspective (published separately as _Perspectiva_). - -(1) The organs of vision. - -(2) Vision in straight lines. - -(3) Vision reflected and refracted. - -(4) De multiplicatione specierum (on the propagation of the impressions -of light, heat, &c.) - -Part VI. On Experimental Science.] - -[Footnote 64: _Op. Maj._ p. 1.] - -[Footnote 65: _Ibid._ p. 2.] - -[Footnote 66: _Ibid._ p. 10.] - -[Footnote 67: I will give a specimen. _Opus Majus_, c. viii. p. 35: -"These two kinds of philosophers, the Ionic and Italic, ramified -through many sects and various successors, till they came to the -doctrine of Aristotle, who corrected and changed the propositions -of all his predecessors, and attempted to perfect philosophy. In -the [Italic] succession, Pythagoras, Archytas Tarentinus and Timæus -are most prominently mentioned. But the principal philosophers, as -Socrates, Plato, and Aristotle, did not descend from this line, but -were Ionics and true Greeks, of whom the first was Thales Milesius.... -Socrates, according to Augustine in his 8th book, is related to have -been a disciple of Archelaus. This Socrates is called the father of the -great philosophers, since he was the master of Plato and Aristotle, -from whom all the sects of philosophers descended.... Plato, first -learning what Socrates and Greece could teach, made a laborious voyage -to Egypt, to Archytas of Tarentum and Timæus, as says Jerome to -Paulinus. And this Plato is, according to holy men, preferred to all -philosophers, because he has written many excellent things concerning -God, and morality, and a future life, which agree with the divine -wisdom of God. And Aristotle was born before the death of Socrates, -since he was his hearer for three years, as we read in the life of -Aristotle.... This Aristotle, being made the master of Alexander the -Great, sent two thousand men into all regions of the earth, to search -out the nature of things, as Pliny relates in the 8th book of his -_Naturalia_, and composed a thousand books, as we read in his life."] - -[Footnote 68: _Ibid._ p. 36.] - -[Footnote 69: _Autonomaticè._] - -[Footnote 70: _Op. Maj._ p. 46.] - -[Footnote 71: See _Pref._ to Jebb's edition. The passages, there -quoted, however, are not extracts from the _Opus Majus_, but -(apparently) from the _Opus Minus_ (_MS. Cott._ Tib. c. 5.) "Si haberem -potestatem supra libros Aristotelis, ego facerem omnes cremari; quia -non est nisi temporis amissio studere in illis, et causa erroris, et -multiplicatio ignorantiæ ultra id quod valeat explicari.... Vulgus -studentum cum capitibus suis non habet unde excitetur ad aliquid -dignum, et ideo languet et _asininat_ circa male translata, et tempus -et studium amittit in omnibus et expensas."] - -[Footnote 72: Part ii.] - -[Footnote 73: Parts iv. v. and vi.] - -[Footnote 74: _Op. Maj._ p. 476.] - -[Footnote 75: _Op. Maj._ p. 15.] - -[Footnote 76: _Ibid._ p. 445, see also p. 448. "Scientiæ aliæ sciunt -sua principia invenire per experimenta, sed conclusiones per argumenta -facta ex principiis inventis. Si vero debeant habere experientiam -conclusionum suarum particularem et completam, tunc oportet quod -habeant per adjutorium istius scientiæ nobilis (experimentalis)."] - -[Footnote 77: _Op. Maj._ p. 60.] - -[Footnote 78: _Ibid._ p. 64.] - -[Footnote 79: "Veritates magnificas in terminis aliarum scientiarum in -quas per nullam viam possunt illæ scientiæ, hæc sola scientiarum domina -speculativarum, potest dare." _Op. Maj._ p. 465.] - -[Footnote 80: One of the ingredients of a preparation here mentioned, -is the flesh of a dragon, which it appears is used as food by the -Ethiopians. The mode of preparing this food cannot fail to amuse the -reader. "Where there are good flying dragons, by the art which they -possess, they draw them out of their dens, and have bridles and saddles -in readiness, and they ride upon them, and make them bound about in the -air in a violent manner, that the hardness and toughness of the flesh -may be reduced, as boars are hunted and bulls are baited before they -are killed for eating." _Op. Maj._ p. 470.] - -[Footnote 81: _Op. Maj._ p. 473.] - -[Footnote 82: Quoted by Jebb, _Pref._ to _Op. Maj._] - -[Footnote 83: Mosheim, _Hist._ iii. 161.] - -[Footnote 84: _Op. Maj._ p. 57.] - -[Footnote 85: Mosheim, iii. 161.] - - - - -CHAPTER XII. - -THE REVIVAL OF PLATONISM. - - -1. _Causes of Delay in the Advance of Knowledge._--In the insight -possessed by learned men into the method by which truth was to be -discovered, the fourteenth and fifteenth centuries went backwards, -rather than forwards, from the point which had been reached in the -thirteenth. Roger Bacon had urged them to have recourse to experiment; -but they returned with additional and exclusive zeal to the more -favourite employment of reasoning upon their own conceptions. He had -called upon them to look at the world without; but their eyes forthwith -turned back upon the world within. In the constant oscillation of the -human mind between Ideas and Facts, after having for a moment touched -the latter, it seemed to swing back more impetuously to the former. -Not only was the philosophy of Aristotle firmly established for a -considerable period, but when men began to question its authority, they -attempted to set up in its place a philosophy still more purely ideal, -that of Plato. It was not till the actual progress of experimental -knowledge for some centuries had given it a vast accumulation of force, -that it was able to break its way fully into the circle of speculative -science. The new Platonist schoolmen had to run their course, the -practical discoverers had to prove their merit by their works, the -Italian innovators had to utter their aspirations for a change, before -the second Bacon could truly declare that the time for a fundamental -reform was at length arrived. - -It cannot but seem strange, to any one who attempts to trace the -general outline of the intellectual progress of man, and who considers -him as under the guidance of a Providential sway, that he should -thus be permitted to wander so long in a wilderness of intellectual -darkness; and even to turn back, by a perverse caprice as it might -seem, when on the very border of the brighter and better land which was -his destined inheritance. We do not attempt to solve this difficulty: -but such a course of things naturally suggests the thought, that a -progress in physical science is not the main object of man's career, -in the eyes of the Power who directs the fortunes of our race. We -can easily conceive that it may have been necessary to man's general -welfare that he should continue to turn his eyes inwards upon his own -heart and faculties, till Law and Duty, Religion and Government, Faith -and Hope, had been fully incorporated with all the past acquisitions of -human intellect; rather than that he should have rushed on into a train -of discoveries tending to chain him to the objects and operations of -the material world. The systematic Law[86] and philosophical Theology -which acquired their ascendancy in men's minds at the time of which -we speak, kept them engaged in a region of speculations which perhaps -prepared the way for a profounder and wider civilization, for a more -elevated and spiritual character, than might have been possible without -such a preparation. The great Italian poet of the fourteenth century -speaks with strong admiration of the founders of the system which -prevailed in his time. Thomas, Albert, Gratian, Peter Lombard, occupy -distinguished places in the Paradise. The first, who is the poet's -instructor, says,-- - - Io fui degli agni della santa greggia - Che Domenico mena per cammino - U' ben s'impingua se non si vaneggia. - Questo che m'è a destra piu vicino - Frate e maestro fummi; ed esso Alberto - E di Cologna, ed io Tomas d'Aquino.... - Quell' altro fiammeggiar esce del riso - De Grazian, che l'uno et l'altro foro - Ajutò si che piace in Paradiso. - - I, then, was of the lambs that Dominic - Leads, for his saintly flock, along the way - Where well they thrive not swoln with vanity. - He nearest on my right-hand brother was - And master to me; Albert of Cologne - Is this; and of Aquinum Thomas, I.... - That next resplendence issues from the smile - Of Gratian, who to either forum lent - Such help as favour wins in Paradise. - -It appears probable that neither poetry, nor painting, nor the other -arts which require for their perfection a lofty and spiritualized -imagination, would have appeared in the noble and beautiful forms which -they assumed in the fourteenth and fifteenth century, if men of genius -had, at the beginning of that period, made it their main business -to discover the laws of nature, and to reduce them to a rigorous -scientific form. Yet who can doubt that the absence of these touching -and impressive works would have left one of the best and purest parts -of man's nature without its due nutriment and development? It may -perhaps be a necessary condition in the progress of man, that the Arts -which aim at beauty should reach their excellence before the Sciences -which seek speculative truth; and if this be so, we inherit, from the -middle ages, treasures which may well reconcile us to the delay which -took place in their cultivation of experimental science. - -However this may be, it is our business at present to trace the -circumstances of this very lingering advance. We have already noticed -the contest of the Nominalists and Realists, which was one form, -though, with regard to scientific methods, an unprofitable one, of -the antithesis of Ideas and Things. Though, therefore, this struggle -continued, we need not dwell upon it. The Nominalists denied the real -existence of Ideas, which doctrine was to a great extent implied -in the prevailing systems; but the controversy in which they thus -engaged, did not lead them to seek for knowledge in a new field and -by new methods. The arguments which Occam the Nominalist opposes to -those of Duns Scotus the Realist, are marked with the stamp of the -same system, and consist only in permutations and combinations of the -same elementary conceptions. It was not till the impulse of external -circumstances was added to the discontent, which the more stirring -intellects felt towards the barren dogmatism of their age, that the -activity of the human mind was again called into full play, and a new -career of progression entered upon, till then undreamt of, except by a -few prophetic spirits. - - -2. _Causes of Progress._--These circumstances were principally the -revival of Greek and Roman literature, the invention of Printing, the -Protestant Reformation, and a great number of curious discoveries and -inventions in the arts, which were soon succeeded by important steps -in speculative physical science. Connected with the first of these -events, was the rise of a party of learned men who expressed their -dissatisfaction with the Aristotelian philosophy, as it was then -taught, and manifested a strong preference for the views of Plato. It -is by no means suitable to our plan to give a detailed account of this -new Platonic school; but we may notice a few of the writers who belong -to it, so far at least as to indicate its influence upon the Methods of -pursuing science. - -In the fourteenth century[87], the frequent intercourse of the most -cultivated persons of the Eastern and Western Empire, the increased -study of the Greek language in Italy, the intellectual activity of the -Italian States, the discovery of manuscripts of the classical authors, -were circumstances which excited or nourished a new and zealous study -of the works of Greek and Roman genius. The genuine writings of the -ancients, when presented in their native life and beauty, instead of -being seen only in those lifeless fragments and dull transformations -which the scholastic system had exhibited, excited an intense -enthusiasm. Europe, at that period, might be represented by Plato's -beautiful allegory, of a man who, after being long kept in a dark -cavern, in which his knowledge of the external world is gathered from -the images which stream through the chinks of his prison, is at last -led forth into the full blaze of day. It was inevitable that such a -change should animate men's efforts and enlarge their faculties. Greek -literature became more and more known, especially by the influence of -learned men who came from Constantinople into Italy: these teachers, -though they honoured Aristotle, reverenced Plato no less, and had never -been accustomed to follow with servile submission of thought either -these or any other leaders. The effect of such influences soon reveals -itself in the works of that period. Dante has woven into his _Divina -Commedia_ some of the ideas of Platonism. Petrarch, who had formed his -mind by the study of Cicero, and had thus been inspired with a profound -admiration for the literature of Greece, learnt Greek from Barlaam, a -monk who came as ambassador from the Emperor of the East to the Pope, -in 1339. With this instructor, the poet read the works of Plato; struck -by their beauty, he contributed, by his writings and his conversation, -to awake in others an admiration and love for that philosopher, which -soon became strongly and extensively prevalent among the learned in -Italy. - - -3. _Hermolaus Barbarus, &c._--Along with the feeling there prevailed -also, among those who had learnt to relish the genuine beauties of -the Greek and Latin writers, a strong disgust for the barbarisms in -which the scholastic philosophy was clothed. Hermolaus Barbarus[88], -who was born in 1454, at Venice, and had formed his taste by the -study of classical literature, translated, among other learned works, -Themistius's paraphrastic expositions of the Physics of Aristotle; -with the view of trying whether the Aristotelian Natural Philosophy -could not be presented in good Latin, which the scholastic teachers -denied. In his Preface he expresses great indignation against those -philosophers who have written and disputed on philosophical subjects -in barbarous Latin, and in an uncultured style, so that all refined -minds are repelled from these studies by weariness and disgust. They -have, he says, by this barbarism, endeavoured to secure to themselves, -in their own province, a supremacy without rivals or opponents. Hence -they maintain that mathematics, philosophy, jurisprudence, cannot -be expounded in correct Latin;--that between these sciences and the -genuine Latin language there is a great gulf, as between things that -cannot be brought together: and on this ground they blame those who -combine the study of philology and eloquence with that of science. -This opinion, adds Hermolaus, perverts and ruins our studies; and is -highly prejudicial and unworthy in respect to the state. Hermolaus -awoke in others, as for instance, in John Picus of Mirandula, the same -dislike to the reigning school philosophy. As an opponent of the same -kind, we may add Marius Nizolius of Bersallo, a scholar who carried -his admiration of Cicero to an exaggerated extent, and who was led, -by a controversy with the defenders of the scholastic philosophy, -to publish (1553) a work _On the True Principles and True Method of -Philosophizing_. In the title of this work, he professes to give "the -true principles of almost all arts and sciences, refuting and rejecting -almost all the false principles of the Logicians and Metaphysicians." -But although, in the work, he attacks the scholastic philosophy, he -does little or nothing to justify the large pretensions of his title; -and he excited, it is said, little notice. It is therefore curious that -Leibnitz should have thought it worth his while to re-edit this work, -which he did in 1670, adding remarks of his own. - - -4. _Nicolaus Cusanus._--Without dwelling upon this opposition to the -scholastic system on the ground of taste, I shall notice somewhat -further those writers who put forwards Platonic views, as fitted to -complete or to replace the doctrines of Aristotle. Among these, I may -place Nicolaus Cusanus, (so called from Cus, a village on the Moselle, -where he was born in 1401;) who was afterwards raised to the dignity -of cardinal. We might, indeed, at first be tempted to include Cusanus -among those persons who were led to reject the old philosophy by being -themselves agents in the progressive movement of physical science. -For he published, before Copernicus, and independently of him, the -doctrine that the earth is in motion[89]. But it should be recollected -that in order to see the possibility of this doctrine, and its claims -to acceptance, no new reference to observation was requisite. The -Heliocentric System was merely a new mode of representing to the mind -facts, with which all astronomers had long been familiar. The system -might very easily have been embraced and inculcated by Plato himself; -as indeed it is said to have been actually taught by Pythagoras. The -mere adoption of the Heliocentric view, therefore, without attempting -to realize the system in detail, as Copernicus did, cannot entitle a -writer of the fifteenth century to be looked upon as one of the authors -of the discoveries of that period; and we must consider Cusanus as a -speculative anti-Aristotelian, rather than as a practical reformer. - -The title of Cusanus's book, _De Doctâ Ignorantiâ_, shows how far -he was from agreeing with those who conceived that, in the works -of Aristotle, they had a full and complete system of all human -knowledge. At the outset of this book[90], he says, after pointing -out some difficulties in the received philosophy, "If, therefore, -the case be so, (as even the very profound Aristotle, in his _First -Philosophy_, affirms,) that in things most manifest by nature, there -is a difficulty, no less than for an owl to look at the sun; since -the appetite of knowledge is not implanted in us in vain, we ought -to desire to know that we are ignorant. If we can fully attain to -this, we shall arrive at _Instructed Ignorance_." How far he was from -placing the source of knowledge in experience, as opposed to ideas, -we may see in the following passage[91] from another work of his, -_On Conjectures_. "Conjectures must proceed from our mind, as the -real world proceeds from the infinite Divine Reason. For since the -human mind, the lofty likeness of God, participates, as it may, in -the fruitfulness of the creative nature, it doth from itself, as the -image of the Omnipotent Form, bring forth reasonable thoughts which -have a similitude to real existences. Thus the Human Mind exists as a -conjectural form of the world, as the Divine Mind is its real form." We -have here the Platonic or ideal side of knowledge put prominently and -exclusively forwards. - - -5. _Marsilius Ficinus, &c._--A person who had much more influence -on the diffusion of Platonism was Marsilius Ficinus, a physician -of Florence. In that city there prevailed, at the time of which we -speak, the greatest enthusiasm for Plato. George Gemistius Pletho, -when in attendance upon the Council of Florence, had imparted to -many persons the doctrines of the Greek philosopher; and, among -others, had infused a lively interest on this subject into the elder -Cosmo, the head of the family of the Medici. Cosmo formed the plan -of founding a Platonic academy. Ficinus[92], well instructed in the -works of Plato, Plotinus, Proclus, and other Platonists, was selected -to further this object, and was employed in translating the works of -these authors into Latin. It is not to our present purpose to consider -the doctrines of this school, except so far as they bear upon the -nature and methods of knowledge; and therefore I must pass by, as I -have in other instances done, the greater part of their speculations, -which related to the nature of God, the immortality of the soul, the -principles of Goodness and Beauty, and other points of the same order. -The object of these and other Platonists of this school, however, was -not to expel the authority of Aristotle by that of Plato. Many of -them had come to the conviction that the highest ends of philosophy -were to be reached only by bringing into accordance the doctrines -of Plato and of Aristotle. Of this opinion was John Picus, Count of -Mirandula and Concordia; and under this persuasion he employed the -whole of his life in labouring upon a work, _De Concordiâ Platonis et -Aristotelis_, which was not completed at the time of his death, in -1494; and has never been published. But about a century later, another -writer of the same school, Francis Patricius[93], pointing out the -discrepancies between the two Greek teachers, urged the propriety of -deposing Aristotle from the supremacy he had so long enjoyed. "Now all -these doctrines, and others not a few," he says[94], "since they are -Platonic doctrines, philosophically most true, and consonant with the -Catholic faith, whilst the Aristotelian tenets are contrary to the -faith, and philosophically false, who will not, both as a Christian and -a Philosopher, prefer Plato to Aristotle? And why should not hereafter, -in all the colleges and monasteries of Europe, the reading and study -of Plato be introduced? Why should not the philosophy of Aristotle be -forthwith exiled from such places? Why must men continue to drink the -mortal poison of impiety from that source?" with much more in the same -strain. - -The Platonic school, of which we have spoken, had, however, reached -its highest point of prosperity before this time, and was already -declining. About 1500, the Platonists appeared to triumph over the -Peripatetics[95]; but the death of their great patron, Cardinal -Bessarion, about this time, and we may add, the hollowness of their -system in many points, and its want of fitness for the wants and -expectations of the age, turned men's thoughts partly back to the -established Aristotelian doctrines, and partly forwards to schemes of -bolder and fresher promise. - - -6. _Francis Patricius._--Patricius, of whom we have just spoken, was -one of those who had arrived at the conviction that the formation of -a new philosophy, and not merely the restoration of an old one, was -needed. In 1593, appeared his _Nova de Universis Philosophia_; and -the mode in which it begins[96] can hardly fail to remind us of the -expressions which Francis Bacon soon afterwards used in the opening of -a work of the same nature. "Francis Patricius, being about to found -anew the true philosophy of the universe, dared to begin by announcing -the following indisputable principles." Here, however, the resemblance -between Patricius and true inductive philosophers ends. His principles -are barren _à priori_ axioms; and his system has one main element, -_Light_, (_Lux_, or _Lumen_,) to which all operations of nature are -referred. In general cultivation, and practical knowledge of nature, -he was distinguished among his contemporaries. In various passages of -his works he relates[97] observations which he had made in the course -of his travels, in Cyprus, Corfu, Spain, the mountains of the Modenese, -and Dalmatia, which was his own country; his observations relate to -light, the saltness of the sea, its flux and reflux, and other points -of astronomy, meteorology, and natural history. He speaks of the sex of -plants[98]; rejects judicial astrology; and notices the astronomical -systems of Copernicus, Tycho, Fracastoro, and Torre. But the mode in -which he speaks of experiments proves, what indeed is evident from the -general scheme of his system, that he had no due appreciation of the -place which observation must hold in real and natural philosophy. - - -7. _Picus, Agrippa, &c._--It had been seen in the later philosophical -history of Greece, how readily the ideas of the Platonic school lead -on to a system of unfathomable and unbounded mysticism. John Picus, -of Mirandula[99], added to the study of Plato and the Neoplatonists, -a mass of allegorical interpretations of the Scriptures, and the -dreams of the Cabbala, a Jewish system[100], which pretends to explain -how all things are an emanation of the Deity. To this his nephew, -Francis Picus, added a reference to inward illumination[101], by which -knowledge is obtained, independently of the progress of reasoning. -John Reuchlin, or Capnio, born 1455; John Baptist Helmont, born 1577; -Francis Mercurius Helmont, born 1618, and others, succeeded John Picus -in his admiration of the Cabbala: while others, as Jacob Bœhmen, -rested upon internal revelations like Francis Picus. And thus we have -a series of mystical writers, continued into modern times, who may -be considered as the successors of the Platonic school; and who all -exhibit views altogether erroneous with regard to the nature and origin -of knowledge. Among the various dreams of this school are certain wide -and loose analogies of terrestrial and spiritual things. Thus in the -writings of Cornelius Agrippa (who was born 1487, at Cologne) we have -such systems as the following[102]:--"Since there is a threefold world, -elemental, celestial, and intellectual, and each lower one is governed -by that above it, and receives the influence of its powers: so that -the very Archetype and Supreme Author transfuses the virtues of his -omnipotence into us through angels, heavens, stars, elements, animals, -plants, stones,--into us, I say, for whose service he has framed and -created all these things;--the Magi do not think it irrational that -we should be able to ascend by the same degrees, the same worlds, to -this Archetype of the world, the Author and First Cause of all, of whom -all things are, and from whom they proceed; and should not only avail -ourselves of those powers which exist in the nobler works of creation, -but also should be able to attract other powers, and add them to these." - -Agrippa's work, _De Vanitate Scientiarum_, may be said rather to -have a skeptical and cynical, than a Platonic, character. It is a -declamation[103], in a melancholy mood, against the condition of the -sciences in his time. His indignation at the worldly success of men -whom he considered inferior to himself, had, he says, metamorphosed him -into a dog, as the poets relate of Hecuba of Troy, so that his impulse -was to snarl and bark. His professed purpose, however, was to expose -the dogmatism, the servility, the self-conceit, and the neglect of -religious truth which prevailed in the reigning Schools of philosophy. -His views of the nature of science, and the modes of improving its -cultivation, are too imperfect and vague to allow us to rank him among -the reformers of science. - - -8. _Paracelsus, Fludd, &c._--The celebrated Paracelsus[104] put himself -forwards as a reformer in philosophy, and obtained no small number of -adherents. He was, in most respects, a shallow and impudent pretender; -and had small knowledge of the literature or science of his time: -but by the tone of his speaking and writing he manifestly belongs -to the mystical school of which we are now speaking. Perhaps by the -boldness with which he proposed new systems, and by connecting these -with the practical doctrines of medicine, he contributed something to -the introduction of a new philosophy. We have seen in the History of -Chemistry that he was the author of the system of Three Principles, -(salt, sulphur, and mercury,) which replaced the ancient doctrine of -Four Elements, and prepared the way for a true science of chemistry. -But the salt, sulphur, and mercury of Paracelsus were not, he tells his -disciples, the visible bodies which we call by those names, but certain -invisible, astral, or sidereal elements. The astral salt is the basis -of the solidity and incombustible parts in bodies; the astral sulphur -is the source of combustion and vegetation; the astral mercury is the -origin of fluidity and volatility. And again, these three elements are -analogous to the three elements of man,--Body, Spirit, and Soul. - -A writer of our own country, belonging to this mystical school, is -Robert Fludd, or De Fluctibus, who was born in 1571, in Kent, and -after pursuing his studies at Oxford, travelled for several years. -Of all the Theosophists and Mystics, he is by much the most learned; -and was engaged in various controversies with Mersenne, Gassendi, -Kepler, and others. He thus brings us in contact with the next class -of philosophers whom we have to consider, the practical reformers -of philosophy;--those who furthered the cause of science by making, -promulgating, or defending the great discoveries which now began -to occupy men. He adopted the principle, which we have noticed -elsewhere[105], of the analogy of the Macrocosm and Microcosm, the -world of nature and the world of man. His system contains such a -mixture and confusion of physical and metaphysical doctrines as might -be expected from his ground-plan, and from his school. Indeed his -object, the general object of mystical speculators, is to identify -physical with spiritual truths. Yet the influence of the practical -experimental philosophy which was now gaining ground in the world may -be traced in him. Thus he refers to experiments on distillation to -prove the existence and relation of the regions of water, air, and -fire, and of the spirits which correspond to them; and is conceived, by -some persons[106], to have anticipated Torricelli in the invention of -the Barometer. - -We need no further follow the speculations of this school. We see -already abundant reason why the reform of the methods of pursuing -science could not proceed from the Platonists. Instead of seeking -knowledge by experiment, they immersed themselves deeper than even the -Aristotelians had done in traditionary lore, or turned their eyes -inwards in search of an internal illumination. Some attempts were made -to remedy the defects of philosophy by a recourse to the doctrines -of other sects of antiquity, when men began to feel more distinctly -the need of a more connected and solid knowledge of nature than the -established system gave them. Among these attempts were those of -Berigard[107], Magernus, and especially Gassendi, to bring into repute -the philosophy of the Ionian school, of Democritus and of Epicurus. But -these endeavours were posterior in time to the new impulse given to -knowledge by Copernicus, Kepler, and Galileo, and were influenced by -views arising out of the success of these discoveries, and they must, -therefore, be considered hereafter. In the mean time, some independent -efforts (arising from speculative rather than practical reformers) -were made to cast off the yoke of the Aristotelian dogmatism, and to -apprehend the true form of that new philosophy which the most active -and hopeful minds saw to be needed; and we must give some account of -these attempts, before we can commit ourselves to the full stream of -progressive philosophy. - - -FOOTNOTES: - -[Footnote 86: Gratian published the _Decretals_ in the twelfth century; -and the Canon and Civil Law became a regular study in the universities -soon afterwards.] - -[Footnote 87: Tenneman, ix. 4.] - -[Footnote 88: Tenneman, ix. 25.] - -[Footnote 89: "Jam nobis manifestum est terram istam in veritate -moveri," &c.--_De Doctâ Ignorantiâ_, lib. ii. c. xii.] - -[Footnote 90: _De Doct. Ignor._ lib. i. c. i.] - -[Footnote 91: _De Conjecturis_, lib. i. c. iii. iv.] - -[Footnote 92: Born in 1433.] - -[Footnote 93: Born 1529, died 1597.] - -[Footnote 94: _Aristoteles Exotericus_, p. 50.] - -[Footnote 95: Tiraboschi, t. vii. pt. ii. p. 411.] - -[Footnote 96: "Franciscus Patricius, novam veram integram de universis -conditurus philosophiam, sequentia uti verissima prænuntiare est -ausus. Prænunciata ordine persecutus, divinis oraculis, geometricis -rationibus, clarissimisque experimentis comprobavit. - - Ante primum nihil, - Post primum omnia, - A principio omnia," &c. - -His other works are _Panaugia_, _Pancosmia_, _Dissertations -Peripateticæ_.] - -[Footnote 97: Tiraboschi, t. vii. pt. ii. p. 411.] - -[Footnote 98: _Dissert. Perip._ t. ii. lib. v. sub fin.] - -[Footnote 99: Tenneman, ix. 148.] - -[Footnote 100: Tenneman, ix. 167.] - -[Footnote 101: _Ibid._ 158.] - -[Footnote 102: Agrippa, _De Occult. Phil._ lib. i. c. l.] - -[Footnote 103: Written in 1526.] - -[Footnote 104: Philip Aurelius Theophrastus Bombastus von Hohenheim, -also called Paracelsus Eremita, born at Einsiedlen in Switzerland, in -1493.] - -[Footnote 105: _Hist. Sc. Id._ b. ix. c. 2. sect. 1. The Mystical -School of Biology.] - -[Footnote 106: Tenneman, ix. 221.] - -[Footnote 107: Tenneman, ix. 265.] - - - - -CHAPTER XIII. - -THE THEORETICAL REFORMERS OF SCIENCE. - - -We have already seen that Patricius, about the middle of the sixteenth -century, announced his purpose of founding anew the whole fabric -of philosophy; but that, in executing this plan, he ran into wide -and baseless hypotheses, suggested by _à priori_ conceptions rather -than by external observation; and that he was further misled by -fanciful analogies resembling those which the Platonic mystics loved -to contemplate. The same time, and the period which followed it, -produced several other essays which were of the same nature, with the -exception of their being free from the peculiar tendencies of the -Platonic school: and these insurrections against the authority of -the established dogmas, although they did not directly substitute a -better positive system in the place of that which they assailed, shook -the authority of the Aristotelian system, and led to its overthrow; -which took place as soon as these theoretical reformers were aided by -practical reformers. - - -1. _Bernardinus Telesius._--Italy, always, in modern times, fertile in -the beginnings of new systems, was the soil on which these innovators -arose. The earliest and most conspicuous of them is Bernardinus -Telesius, who was born in 1508, at Cosenza, in the kingdom of Naples. -His studies, carried on with great zeal and ability, first at Milan -and then at Rome, made him well acquainted with the knowledge of -his times; but his own reflections convinced him that the basis of -science, as then received, was altogether erroneous; and led him to -attempt a reform, with which view, in 1565, he published, at Rome, -his work[108], "_Bernardinus Telesius, of Cosenza, on the Nature of -Things, according to principles of his own_." In the preface of this -work he gives a short account[109] of the train of reflection by which -he was led to put himself in opposition to the Aristotelian philosophy. -This kind of autobiography occurs not unfrequently in the writings of -theoretical reformers; and shows how livelily they felt the novelty of -their undertaking. After the storm and sack of Rome in 1527, Telesius -retired to Padua, as a peaceful seat of the muses; and there studied -philosophy and mathematics, with great zeal, under the direction of -Jerome Amalthæus and Frederic Delphinus. In these studies he made great -progress; and the knowledge which he thus acquired threw a new light -upon his view of the Aristotelian philosophy. He undertook a closer -examination of the Physical Doctrines of Aristotle; and as the result -of this, he was astonished how it could have been possible that so -many excellent men, so many nations, and even almost the whole human -race, should, for so long a time, have allowed themselves to be carried -away by a blind reverence for a teacher, who had committed errors so -numerous and grave as he perceived to exist in "the philosopher." Along -with this view of the insufficiency of the Aristotelian philosophy, -arose, at an early period, the thought of erecting a better system in -its place. With this purpose he left Padua, when he had received the -degree of Doctor, and went to Rome, where he was encouraged in his -design by the approval and friendly exhortations of distinguished men -of letters, amongst whom were Ubaldino Bandinelli and Giovanni della -Casa. From Rome he went to his native place, when the incidents and -occupations of a married life for a while interrupted his philosophical -project. But after his wife was dead, and his eldest son grown to -manhood, he resumed with ardour the scheme of his youth; again studied -the works of Aristotle and other philosophers, and composed and -published the first two books of his treatise. The opening to this -work sufficiently exhibits the spirit in which it was conceived. Its -object is stated in the title to be to show, that "the construction -of the world, the magnitude and nature of the bodies contained in -it, are not to be investigated by reasoning, which was done by the -ancients, but are to be apprehended by the senses, and collected from -the things themselves." And the Proem is in the same strain. "They who -before us have inquired concerning the construction of this world and -of the things which it contains, seem indeed to have prosecuted their -examination with protracted vigils and great labour, but _never to have -looked at it_." And thus, he observes, they found nothing but error. -This he ascribes to their presumption. "For, as it were, attempting -to rival God in wisdom, and venturing to seek for the principles and -causes of the world by the light of their own reason, and thinking they -had found what they had only invented, they made an arbitrary world of -their own." "_We_ then," he adds, "not relying on ourselves, and of a -duller intellect than they, propose to ourselves to turn our regards to -the world itself and its parts." - -The execution of the work, however, by no means corresponds to the -announcement. The doctrines of Aristotle are indeed attacked; and the -objections to these, and to other received opinions, form a large -part of the work. But these objections are supported by _à priori_ -reasoning, and not by experiments. And thus, rejecting the Aristotelian -physics, he proposes a system at least equally baseless; although, no -doubt, grateful to the author from its sweeping and apparently simple -character. He assumes three principles, Heat, Cold, and Matter: Heat -is the principle of motion, Cold of immobility, and Matter is the -corporeal substratum, in which these incorporeal and active principles -produce their effects. It is easy to imagine that, by combining and -separating these abstractions in various ways, a sort of account of -many natural phenomena may be given; but it is impossible to ascribe -any real value to such a system. The merit of Telesius must be -considered to consist in his rejection of the Aristotelian errors, -in his perception of the necessity of a reform in the method of -philosophizing, and in his persuasion that this reform must be founded -on experiments rather than on reasoning. When he said[110], "We propose -to ourselves to turn our eyes to the world itself, and its parts, their -passions, actions, operations, and species," his view of the course to -be followed was right; but his purpose remained but ill fulfilled, by -the arbitrary edifice of abstract conceptions which his system exhibits. - -Francis Bacon, who, about half a century later, treated the subject -of a reform of philosophy in a far more penetrating and masterly -manner, has given us his judgment of Telesius. In his view, he takes -Telesius as the restorer of the Atomic philosophy, which Democritus -and Parmenides taught among the ancients; and according to his -custom, he presents an image of this philosophy in an adaptation of -a portion of ancient mythology[111]. The Celestial Cupid, who with -Cœlus, was the parent of the Gods and of the Universe, is exhibited -as a representation of matter and its properties, according to the -Democritean philosophy. "Concerning Telesius," says Bacon, "we think -well, and acknowledge him as a lover of truth, a useful contributor to -science, an amender of some tenets, the first of recent men. But we -have to do with him as the restorer of the philosophy of Parmenides, -to whom much reverence is due." With regard to this philosophy, -he pronounces a judgment which very truly expresses the cause of -its rashness and emptiness. "It is," he says, "such a system[112] -as naturally proceeds from the intellect, abandoned to its own -impulse, and not rising from experience to theory continuously and -successively." Accordingly, he says that, "Telesius, although learned -in the Peripatetic philosophy (if that were anything), which indeed, he -has turned against the teachers of it, is hindered by his affirmations, -and is more successful in destroying than in building." - -The work of Telesius excited no small notice, and was placed in the -_Index Expurgatorius_. It made many disciples, a consequence probably -due to its spirit of system-making, no less than to its promise of -reform, or its acuteness of argument; for till trial and reflection -have taught man modesty and moderation, he can never be content to -receive knowledge in the small successive instalments in which nature -gives it forth to him. It is the makers of large systems, arranged with -an _appearance_ of completeness and symmetry, who, principally, give -rise to Schools of philosophy. - - -2. (_Thomas Campanella_).--Accordingly, Telesius may be looked upon as -the founder of a School. His most distinguished successor was Thomas -Campanella, who was born in 1568, at Stilo, in Calabria. He showed -great talents at an early age, prosecuting his studies at Cosenza, -the birth-place of the great opponent of Aristotle and reformer of -philosophy. He, too, has given us an account[113] of the course of -thought by which he was led to become an innovator. "Being afraid -that not genuine truth, but falsehood in the place of truth, was the -tenant of the Peripatetic School, I examined all the Greek, Latin, -and Arabic commentators of Aristotle, and hesitated more and more, as -I sought to learn whether what they have said were also to be read -in the world itself, which I had been taught by learned men was the -living book of God. And as my doctors could not satisfy my scruples, -I resolved to read all the books of Plato, Pliny, Galen, the Stoics, -and the Democriteans, and especially those of Telesius; and to compare -them with that _first and original writing, the world_; that thus from -the primary autograph, I might learn if the copies contained anything -false." Campanella probably refers here to an expression of Plato, -who says, "the world is God's epistle to mankind." And this image, of -the natural world as an original manuscript, while human systems of -philosophy are but copies, and may be false ones, became a favourite -thought of the reformers, and appears repeatedly in their writings from -this time. "When I held my public disputation at Cosenza," Campanella -proceeds, "and still more, when I conversed privately with the brethren -of the monastery, I found little satisfaction in their answers; but -Telesius delighted me, on account of his freedom in philosophizing, -and because he rested upon the nature of things, and not upon the -assertions of men." - -With these views and feelings, it is not wonderful that Campanella, -at the early age of twenty-two (1590,) published a work remarkable -for the bold promise of its title: "_Thomas Campanella's Philosophy -demonstrated to the senses, against those who have philosophized in an -arbitrary and dogmatical manner, not taking nature for their guide; in -which the errors of Aristotle and his followers are refuted from their -own assertions and the laws of nature: and all the imaginations feigned -in the place of nature by the Peripatetics are altogether rejected; -with a true defence of Bernardin Telesius of Cosenza, the greatest -of philosophers; confirmed by the opinions of the ancients, here -elucidated and defended, especially those of the Platonists_." - -This work was written in answer to a book published against Telesius -by a Neapolitan professor named Marta; and it was the boast of the -young author that he had only employed eleven months in the composition -of his defence, while his adversary had been engaged eleven years -in preparing his attack. Campanella found a favourable reception in -the house of the Marchese Lavelli, and there employed himself in the -composition of an additional work, entitled _On the Sense of Things -and Magic_, and in other literary labours. These, however, are full -of the indications of an enthusiastic temper, inclined to mystical -devotion, and of opinions bearing the cast of pantheism. For instance, -the title of the book last quoted sets forth as demonstrated in the -course of the work, that "the world is the living and intelligent -statue of God; and that all its parts, and particles of parts, are -endowed some with a clearer, some with a more obscure sense, such -as suffices for the preservation of each and of the whole." Besides -these opinions, which could not fail to make him obnoxious to the -religious authorities, Campanella[114] engaged in schemes of political -revolution, which involved him in danger and calamity. He took part -in a conspiracy, of which the object was to cast off the tyranny of -Spain, and to make Calabria a republic. This design was discovered; and -Campanella, along with others, was thrown into prison and subjected to -torture. He was kept in confinement twenty-seven years; and at last -obtained his liberation by the interposition of Pope Urban VIII. He -was, however, still in danger from the Neapolitan Inquisition; and -escaped in disguise to Paris, where he received a pension from the -king, and lived in intercourse with the most eminent men of letters. He -died there in 1639. - -Campanella was a contemporary of Francis Bacon, whom we must consider -as belonging to an epoch to which the Calabrian school of innovators -was only a prelude. I shall not therefore further follow the connexion -of writers of this order. Tobias Adami, a Saxon writer, an admirer -of Campanella's works, employed himself, about 1620, in adapting -them to the German public, and in recommending them strongly to -German philosophers. Descartes, and even Bacon, may be considered as -successors of Campanella; for they too were theoretical reformers; but -they enjoyed the advantage of the light which had, in the mean time, -been thrown upon the philosophy of science, by the great practical -advances of Kepler, Galileo, and others. To these practical reformers -we must soon turn our attention: but we may first notice one or two -additional circumstances belonging to our present subject. - -Campanella remarks that both the Peripatetics and the Platonists -conducted the learner to knowledge by a long and circuitous path, which -he wished to shorten by setting out from the sense. Without speaking -of the methods which he proposed, we may notice one maxim[115] of -considerable value which he propounds, and to which we have already -been led. "We begin to reason from sensible objects, and definition -is the end and epilogue of science. It is not the beginning of our -knowing, but only of our teaching." - - -3. (_Andrew Cæsalpinus._)--The same maxim had already been announced -by Cæsalpinus, a contemporary of Telesius; (he was born at Arezzo in -1520, and died at Rome in 1603). Cæsalpinus is a great name in science, -though professedly an Aristotelian. It has been seen in the _History -of Science_[116], that he formed the first great epoch of the science -of botany by his systematic arrangement of plants, and that in this -task he had no successor for nearly a century. He also approached near -to the great discovery of the circulation of the blood[117]. He takes -a view of science which includes the remark that we have just quoted -from Campanella: "We reach perfect knowledge by three steps: Induction, -Division, Definition. By Induction, we collect likeness and agreement -from observation; by Division, we collect unlikeness and disagreement; -by Definition, we learn the proper substance of each object. Induction -makes universals from particulars, and offers to the mind all -intelligible matter; Division discovers the difference of universals, -and leads to species; Definition resolves species into their principles -and elements[118]." Without asserting this to be rigorously correct, it -is incomparably more true and philosophical than the opposite view, -which represents definition as the beginning of our knowledge; and -the establishment of such a doctrine is a material step in inductive -philosophy[119]. - - -4. (_Giordano Bruno._)--Among the Italian innovators of this time -we must notice the unfortunate Giordano Bruno, who was born at Nola -about 1550 and burnt at Rome in 1600. He is, however, a reformer of a -different school from Campanella; for he derives his philosophy from -Ideas and not from Observation. He represents himself as the author of -a new doctrine, which he terms the _Nolan Philosophy_. He was a zealous -promulgator and defender of the Copernican system of the universe, as -we have noticed in the _History of Science_[120]. Campanella also wrote -in defence of that system. - -It is worthy of remark that a thought which is often quoted from -Francis Bacon, occurs in Bruno's _Cena di Cenere_, published in -1584; I mean, the notion that the later times are more aged than -the earlier. In the course of the dialogue, the Pedant, who is one -of the interlocutors, says, "In antiquity is wisdom;" to which the -Philosophical Character replies, "If you knew what you were talking -about, you would see that your principle leads to the opposite result -of that which you wish to infer;--I mean, that _we_ are older, and have -lived longer, than our predecessors." He then proceeds to apply this, -by tracing the course of astronomy through the earlier astronomers up -to Copernicus. - - -5. (_Peter Ramus._)--I will notice one other reformer of this period, -who attacked the Aristotelian system on another side, on which it -was considered to be most impregnable. This was Peter Ramus,(born in -Picardy in 1515,) who ventured to denounce the _Logic_ of Aristotle as -unphilosophical and useless. After showing an extraordinary aptitude -for the acquirement of knowledge in his youth, when he proceeded to -the degree of Master of Arts, he astonished his examiners by choosing -for the subject of the requisite disputation the thesis[121], "that -what Aristotle has said is all wrong." This position, so startling in -1535, he defended for the whole day, without being defeated. This was, -however, only a formal academical exercise, which did not necessarily -imply any permanent conviction of the opinion thus expressed. But his -mind was really labouring to detect and remedy the errors which he -thus proclaimed. From him, as from the other reformers of this time, -we have an account of this mental struggle[122]. He says, in a work on -this subject, "I will candidly and simply explain how I was delivered -from the darkness of Aristotle. When, according to the laws of our -university, I had spent three years and a half in the Aristotelian -philosophy, and was now invested with the philosophical laurel as a -Master of Arts, I took an account of the time which I had consumed -in this study, and considered on what subjects I should employ this -logical art of Aristotle, which I had learnt with so much labour and -noise, I found it made me not more versed in history or antiquities, -more eloquent in discourse, more ready in verse, more wise in any -subject. Alas for me! how was I overpowered, how deeply did I groan, -how did I deplore my lot and my nature, how did I deem myself to be -by some unhappy and dismal fate and frame of mind abhorrent from the -Muses, when I found that I was one who, after all my pains, could -reap no benefit from that wisdom of which I heard so much, as being -contained in the Logic of Aristotle." He then relates that he was -led to the study of the Dialogues of Plato, and was delighted with -the kind of analysis of the subjects discussed which Socrates is -there represented as executing. "Well," he adds, "I began thus to -reflect within myself--(I should have thought it impious to say it to -another)--What, I pray you, prevents me from _socratizing_; and from -asking, without regard to Aristotle's authority, whether Aristotle's -Logic be true and correct? It may be that that philosopher leads -us wrong; and if so, no wonder that I cannot find in his books the -treasure which is not there. What if his dogmas be mere figments? Do -I not tease and torment myself in vain, trying to get a harvest from -a barren soil?" He convinced himself that the Aristotelian logic was -worthless: and constructed a new system of Logic, founded mainly on the -Platonic process of exhausting a subject by analytical classification -of its parts. Both works, his _Animadversions on Aristotle_, and his -_Logic_, appeared in 1543. The learned world was startled and shocked -to find a young man, on his first entrance into life, condemning -as faulty, fallacious, and useless, that part of Aristotle's works -which had always hitherto been held as a masterpiece of philosophical -acuteness, and as the Organon of scientific reasoning. And in truth, it -must be granted that Ramus does not appear to have understood the real -nature and object of Aristotle's Logic; while his own system could not -supply the place of the old one, and was not of much real value. This -dissent from the established doctrines was, however, not only condemned -but punished. The printing and selling of his books was forbidden -through France; and Ramus was stigmatized by a sentence[123] which -declared him rash, arrogant, impudent, and ignorant, and prohibited -from teaching logic and philosophy. He was, however, afterwards -restored to the office of professor: and though much attacked, -persisted in his plan of reforming, not only Logic but Physics and -Metaphysics. He made his position still more dangerous by adopting the -reformed religion; and during the unhappy civil wars of France, he was -deprived of his professorship, driven from Paris, and had his library -plundered. He endeavoured, but in vain, to engage a German professor, -Schegk, to undertake the reform of the Aristotelian Physics; a portion -of knowledge in which he felt himself not to be strong. Unhappily for -himself, he afterwards returned to Paris, where he perished in the -massacre of St. Bartholomew in 1572. - -Ramus's main objection to the Aristotelian Logic is, that it is not -the image of the natural process of thought; an objection which shows -little philosophical insight; for the course by which we obtain -knowledge may well differ from the order in which our knowledge, -when obtained, is exhibited. We have already seen that Ramus's -contemporaries, Cæsalpinus and Campanella, had a wiser view; placing -definition as the last step in knowing, but the first in teaching. -But the effect which Ramus produced was by no means slight. He aided -powerfully in turning the minds of men to question the authority of -Aristotle on all points; and had many followers, especially among the -Protestants. Among the rest, Milton, our great poet, published "Artis -Logicæ plenior Institutio _ad Petri Rami methodum concinnata_;" but -this work, appearing in 1672, belongs to a succeeding period. - - -6. (_The Reformers in general_).--It is impossible not to be struck -with the series of misfortunes which assailed the reformers of -philosophy of the period we have had to review. Roger Bacon was -repeatedly condemned and imprisoned; and, not to speak of others who -suffered under the imputation of magical arts, Telesius is said[124] to -have been driven from Naples to his native city by calumny and envy; -Cæsalpinus was accused of atheism[125]; Campanella was imprisoned for -twenty-seven years and tortured; Giordano Bruno was burnt at Rome as -a heretic; Ramus was persecuted during his life, and finally murdered -by his personal enemy Jacques Charpentier, in a massacre of which the -plea was religion. It is true, that for the most part these misfortunes -were not principally due to the attempts at philosophical reform, but -were connected rather with politics or religion. But we cannot doubt -that the spirit which led men to assail the received philosophy, might -readily incline them to reject some tenets of the established religion; -since the boundary line of these subjects is difficult to draw. And as -we have seen, there was in most of the persons of whom we have spoken, -not only a well-founded persuasion of the defects of existing systems, -but an eager spirit of change, and a sanguine anticipation of some -wide and lofty philosophy, which was soon to elevate the minds and -conditions of men. The most unfortunate were, for the most part, the -least temperate and judicious reformers. Patricius, who, as we have -seen, declared himself against the Aristotelian philosophy, lived and -died at Rome in peace and honour[126]. - - -7. (_Melancthon._)--It is not easy to point out with precision the -connexion between the efforts at a Reform in Philosophy, and the great -Reformation of Religion in the sixteenth century. The disposition to -assert (practically at least) a freedom of thinking, and to reject the -corruptions which tradition had introduced and authority maintained, -naturally extended its influence from one subject to another; and -especially in subjects so nearly connected as theology and philosophy. -The Protestants, however, did not reject the Aristotelian system; -they only reformed it, by going back to the original works of the -author, and by reducing it to a conformity with Scripture. In this -reform, Melancthon was the chief author, and wrote works on Logic, -Physics, Morals, and Metaphysics, which were used among Protestants. -On the subject of the origin of our knowledge, his views contained -a very philosophical improvement of the Aristotelian doctrines. He -recognized the importance of Ideas, as well as of Experience. "We could -not," he says[127], "proceed to reason at all, except there were by -nature innate in man certain fixed points, that is, principles of -science;--as Number, the recognition of Order and Proportion, logical, -geometrical, physical and moral Principles. Physical principles are -such as these,--everything which exists proceeds from a cause,--a body -cannot be in two places at once,--time is a continued series of things -or of motions,--and the like." It is not difficult to see that such -Principles partake of the nature of the Fundamental Ideas which we have -attempted to arrange and enumerate in a previous part of this work. - -Before we proceed to the next chapter, which treats of the Practical -Reformers of Scientific Method, let us for an instant look at the -strong persuasion implied in the titles of the works of this period, -that the time of a philosophical revolution was at hand. Telesius -published _De Rerum Natura juxta propria principia_; Francis Helmont, -_Philosophia vulgaris refutata_; Patricius, _Nova de Universis -Philosophia_; Campanella, _Philosophia sensibus demonstrata, adversus -errores Aristotelis_; Bruno professed himself the author of a _Nolan -Philosophy_; and Ramus of a _New Logic_. The age announced itself -pregnant; and the eyes of all who took an interest in the intellectual -fortunes of the race, were looking eagerly for the expected offspring. - - -FOOTNOTES: - -[Footnote 108: Bernardini Telesii Consentini _De Rerum Natura juxta -propria Principia_.] - -[Footnote 109: I take this account from Tenneman: this Proem was -omitted in subsequent editions of Telesius, and is not in the one which -I have consulted. Tenneman, _Gesch. d. Phil._ ix. 280.] - -[Footnote 110: Proem.] - -[Footnote 111: "De Principiis atque Originibus secundum fabulas -Cupidinis et Cœli: sive Parmenidis et Telesii et præcipuè Democriti -Philosophia tractata in Fabula de Cupidine."] - -[Footnote 112: "Talia sunt qualia possunt esse ea quæ ab intellectu -sibi permisso, nec ab experimentis continenter et gradatim sublevato, -profecta videntur."] - -[Footnote 113: Thom. Campanella _de Libris propriis_, as quoted in -Tenneman, ix. 291.] - -[Footnote 114: _Economisti Italiani_, t. i. p. xxxiii.] - -[Footnote 115: Tenneman, ix. 305.] - -[Footnote 116: _Hist. Ind. Sc._ b. xvi. c. iii. sect. 2.] - -[Footnote 117: _Ibid._ b. xvii. c. ii. sect. 1.] - -[Footnote 118: _Quæst. Peripat._ i. 1.] - -[Footnote 119: Tenneman, ix. 108.] - -[Footnote 120: _Hist. Ind. Sc._ b. v. c. iii. sect. 2.] - -[Footnote 121: Tenneman, ix. 420. "Quæcunque ab Aristotele dicta essent -commenticia esse." Freigius, _Vita Petri Rami_, p. 10.] - -[Footnote 122: Rami, _Animadv. Aristot._ i. iv.] - -[Footnote 123: See _Hist. Ind. Sc._ b. iv. c. iv. sect. 4.] - -[Footnote 124: Tenneman, ix. 230.] - -[Footnote 125: _Ibid._ 108.] - -[Footnote 126: Tenneman, ix. 246.] - -[Footnote 127: Melancthon, _De Anima_, p. 207, quoted in Tenneman, ix. -121.] - - - - -CHAPTER XIV. - -THE PRACTICAL REFORMERS OF SCIENCE. - - -1. _Character of the Practical Reformers._--We now come to a class -of speculators who had perhaps a greater share in bringing about the -change from stationary to progressive knowledge, than those writers who -so loudly announced the revolution. The mode in which the philosophers -of whom we now speak produced their impressions on men's minds, was -very different from the procedure of the theoretical reformers. What -these talked of, they did; what these promised, they performed. While -the theorists concerning knowledge proclaimed that great advances -were to be made, the practical discoverers went steadily forwards. -While one class spoke of a complete Reform of scientific Methods, the -other, boasting little, and often thinking little of Method, proved -the novelty of their instrument by obtaining new results. While the -metaphysicians were exhorting men to consult experience and the senses, -the physicists were examining nature by such means with unparalleled -success. And while the former, even when they did for a moment refer -to facts, soon rushed back into their own region of ideas, and tried -at once to seize the widest generalizations, the latter, fastening -their attention upon the phenomena, and trying to reduce them to -laws, were carried forwards by steps measured and gradual, such as no -conjectural view of scientific method had suggested; but leading to -truths as profound and comprehensive as any which conjecture had dared -to anticipate. The theoretical reformers were bold, self-confident, -hasty, contemptuous of antiquity, ambitious of ruling all future -speculations, as they whom they sought to depose had ruled the past. -The practical reformers were cautious, modest, slow, despising no -knowledge, whether borrowed from tradition or observation, confident in -the ultimate triumph of science, but impressed with the conviction that -each single person could contribute a little only to its progress. Yet -though thus working rather than speculating,--dealing with particulars -more than with generals,--employed mainly in adding to knowledge, and -not in defining what knowledge is, or how additions are to be made -to it,--these men, thoughtful, curious, and of comprehensive minds, -were constantly led to important views on the nature and methods of -science. And these views, thus suggested by reflections on their own -mental activity, were gradually incorporated with the more abstract -doctrines of the metaphysicians, and had a most important influence -in establishing an improved philosophy of science. The indications of -such views we must now endeavour to collect from the writings of the -discoverers of the times preceding the seventeenth century. - -Some of the earliest of these indications are to be found in those who -dealt with Art rather than with Science. I have already endeavoured -to show that the advance of the arts which give us a command over the -powers of nature, is generally prior to the formation of exact and -speculative knowledge concerning those powers. But Art, which is thus -the predecessor of Science, is, among nations of acute and active -intellects, usually its parent. There operates, in such a case, a -speculative spirit, leading men to seek for the reasons of that which -they find themselves able to do. How slowly, and with what repeated -deviations men follow this leading, when under the influence of a -partial and dogmatical philosophy, the late birth and slow growth of -sound physical theory shows. But at the period of which we now speak, -we find men, at length, proceeding in obedience to the impulse which -thus drives them from practice to theory;--from an acquaintance with -phenomena to a free and intelligent inquiry concerning their causes. - - -2. _Leonardo da Vinci._--I have already noted, in the History of -Science, that the Indistinctness of Ideas, which was long one main -impediment to the progress of science in the middle ages, was first -remedied among architects and engineers. These men, so far at least as -mechanical ideas were concerned, were compelled by their employments -to judge rightly of the relations and properties of the materials with -which they had to deal; and would have been chastised by the failure -of their works, if they had violated the laws of mechanical truth. It -was not wonderful, therefore, that these laws became known to _them_ -first. We have seen, in the _History_, that Leonardo da Vinci, the -celebrated painter, who was also an engineer, is the first writer in -whom we find the true view of the laws of equilibrium of the lever in -the most general case. This artist, a man of a lively and discursive -mind, is led to make some remarks[128] on the formation of our -knowledge, which may show the opinions on that subject that already -offered themselves at the beginning of the sixteenth century[129]. He -expresses himself as follows:--"Theory is the general, Experiments are -the soldiers. The interpreter of the artifices of nature is Experience: -she is never deceived. Our judgment sometimes is deceived, because it -expects effects which Experience refuses to allow." And again, "We -must consult Experience, and vary the circumstances till we have drawn -from them general rules; for it is she who furnishes true rules. But -of what use, you ask, are these rules; I reply, that they direct us in -the researches of nature and the operations of art. They prevent our -imposing upon ourselves and others by promising ourselves results which -we cannot obtain. - -"In the study of the sciences which depend on mathematics, those who do -not consult nature but authors, are not the children of nature, they -are only her grandchildren. She is the true teacher of men of genius. -But see the absurdity of men! They turn up their noses at a man who -prefers to learn from nature herself rather than from authors who are -only her clerks." - -In another place, in reference to a particular case, he says, "Nature -begins from the Reason and ends in Experience; but for all that, we -must take the opposite course; begin from the Experiment and try to -discover the Reason." - -Leonardo was born forty-six years before Telesius; yet we have here -an estimate of the value of experience far more just and substantial -than the Calabrian school ever reached. The expressions contained in -the above extracts, are well worthy our notice;--that experience is -never deceived;--that we must vary our experiments, and draw from them -general rules;--that nature is the original source of knowledge, and -books only a derivative substitute;--with a lively image of the sons -and grandsons of nature. Some of these assertions have been deemed, -and not without reason, very similar to those made by Bacon a century -later. Yet it is probable that the import of such expressions, in -Leonardo's mind, was less clear and definite than that which they -acquired by the progress of sound philosophy. When he says that theory -is the general and experiments the soldiers, he probably meant that -theory directs men what experiments to make; and had not in his mind -the notion of a theoretical Idea ordering and brigading the Facts. When -he says that Experience is the interpreter of Nature, we may recollect, -that in a more correct use of this image, Experience and Nature are the -writing, and the Intellect of man the interpreter. We may add, that -the clear apprehension of the importance of Experience led, in this as -in other cases, to an unjust depreciation of the value of what science -owed to books. Leonardo would have made little progress, if he had -attempted to master a complex science, astronomy for instance, by means -of observation alone, without the aid of books. - -But in spite of such criticism, Leonardo's maxims show extraordinary -sagacity and insight; and they appear to us the more remarkable, when -we see how rare such views are for a century after his time. - - -3. _Copernicus._--For we by no means find, even in those practical -discoverers to whom, in reality, the revolution in science, and -consequently in the philosophy of science, was due, this prompt and -vigorous recognition of the supreme authority of observation as a -ground of belief; this bold estimate of the probable worthlessness -of traditional knowledge; and this plain assertion of the reality of -theory founded upon experience. Among such discoverers, Copernicus must -ever hold a most distinguished place. The heliocentric theory of the -universe, established by him with vast labour and deep knowledge, was, -for the succeeding century, the field of discipline and exertion of all -the most active speculative minds. Men, during that time, proved their -freedom of thought, their hopeful spirit, and their comprehensive view, -by adopting, inculcating, and following out the philosophy which this -theory suggested. But in the first promulgation of the theory, in the -works of Copernicus himself, we find a far more cautious and reserved -temper. He does not, indeed, give up the reality of his theory, but -he expresses himself so as to avoid shocking those who might (as some -afterwards did) think it safe to speak of it as an _hypothesis_ rather -than a truth. In his preface addressed to the Pope[130], after speaking -of the difficulties in the old and received doctrines, by which he -was led to his own theory, he says, "Hence I began to think of the -mobility of the earth; and although the opinion seemed absurd, yet -because I knew that to others before me this liberty had been conceded, -of imagining any kinds of circles in order to explain the phenomena -of the stars, I thought it would also be readily granted me, that I -might try whether, by supposing the earth to be in motion, I might -not arrive at a better explanation than theirs, of the revolutions of -the celestial orbs." Nor does he anywhere assert that the seeming -absurdity had become a certain truth, or betray any feeling of triumph -over the mistaken belief of his predecessors. And, as I have elsewhere -shown, his disciples[131] indignantly and justly defended him from the -charge of disrespect towards Ptolemy and other ancient astronomers. Yet -Copernicus is far from compromising the value or evidence of the great -truths which he introduced to general acceptance; and from sinking in -his exposition of his discoveries below the temper which had led to -them. His quotation from Ptolemy, that "He who is to follow philosophy -must be a freeman in mind," is a grand and noble maxim, which it well -became him to utter. - - -4. _Fabricius._--In another of the great discoverers of this period, -though employed on a very different subject, we discern much of the -same temper. Fabricius of Acquapendente[132], the tutor and forerunner -of our Harvey, and one of that illustrious series of Paduan professors -who were the fathers of anatomy[133], exhibits something of the same -respect for antiquity, in the midst of his original speculations. -Thus in a dissertation[134] _On the Action of the Joints_, he quotes -Aristotle's Mechanical Problems to prove that in all animal motion -there must be some quiescent fulcrum; and finds merit even in -Aristotle's ignorance. "Aristotle," he says[135], "did not know that -motion was produced by the muscle; and after staggering about from one -supposition to another, at last is compelled by the facts themselves -to recur to an innate spirit, which, he conceives, is contrasted, and -which pulls and pushes. And here we cannot help admiring the genius of -Aristotle, who, though ignorant of the muscle, invents something which -produces nearly the same effect as the muscle, namely, contraction and -pulling." He then, with great acuteness, points out the distinction -between Aristotle's opinions, thus favourably interpreted, and those of -Galen. In all this, we see something of the wish to find all truths in -the writings of the ancients, but nothing which materially interferes -with freedom of inquiry. The anatomists have in all ages and countries -been practically employed in seeking knowledge from observation. Facts -have ever been to them a subject of careful and profitable study; while -the ideas which enter into the wider truths of the science, are, as we -have seen, even still involved in obscurity, doubt, and contest. - - -5. _Maurolycus._--Francis Maurolycus of Messana, whose mathematical -works were published in 1575, was one of the great improvers of the -science of optics in his time. In his Preface to his Treatise on -the Spheres, he speaks of previous writers on the same subject; and -observes that as they have not superseded one another, they have not -rendered it unfit for any one to treat the subject afresh. "Yet," he -says, "it is impossible to amend the errors of all who have preceded -us. This would be a task too hard for Atlas, although he supports the -heavens. Even Copernicus is tolerated, who makes the sun to be fixed, -and the earth to move round it in a circle, and who is more worthy -of a whip or a scourge than of a refutation." The mathematicians and -astronomers of that time were not the persons most sensible of the -progress of physical knowledge; for the basis of their science, and -a great part of its substance, were contained in the writings of the -ancients; and till the time of Kepler, Ptolemy's work was, very justly, -looked upon as including all that was essential in the science. - - -6. _Benedetti._--But the writers on Mechanics were naturally led to -present themselves as innovators and experimenters; for all that the -ancients had taught concerning the doctrine of motion was erroneous; -while those who sought their knowledge from experiment, were constantly -led to new truths. John Baptist Benedetti, a Venetian nobleman, in -1599, published his _Speculationum Liber_, containing, among other -matter, a treatise on Mechanics, in which several of the Aristotelian -errors were refuted. In the Preface to this Treatise, he says, "Many -authors have written much, and with great ability, on Mechanics; but -since nature is constantly bringing to light something either new, -or before unnoticed, I too wished to put forth a few things hitherto -unattempted, or not sufficiently explained." In the doctrine of motion -he distinctly and at some length condemns and argues against all the -Aristotelian doctrines concerning motion, weight, and many other -fundamental principles of physics. Benedetti is also an adherent of -the Copernican doctrine. He states[136] the enormous velocity which -the heavenly bodies must have, if the earth be the centre of their -motions; and adds, "which difficulty does not occur according to the -beautiful theory of the Samian Aristarchus, expounded in a divine -manner by Nicolas Copernicus; against which the reasons alleged by -Aristotle are of no weight." Benedetti throughout shows no want of the -courage or ability which were needed in order to rise in opposition -against the dogmas of the Peripatetics. He does not, however, refer to -experiment in a very direct manner; indeed most of the facts on which -the elementary truths of mechanics rest, were known and admitted by the -Aristotelians; and therefore could not be adduced as novelties. On the -contrary, he begins with _à priori_ maxims, which experience would not -have confirmed. "Since," he says[137], "we have undertaken the task -of proving that Aristotle is wrong in his opinions concerning motion, -there are certain absolute truths, the objects of the intellect known -of themselves, which we must lay down in the first place." And then, as -an example of these truths, he states this: "Any two bodies of equal -size and figure, but of different materials, will have their natural -velocities in the same proportion as their weights;" where by their -natural velocities, he means the velocities with which they naturally -fall downwards. - - -7. _Gilbert._--The greatest of these practical reformers of science -is our countryman, William Gilbert; if, indeed, in virtue of the -clear views of the prospects which were then opening to science, -and of the methods by which her future progress was to be secured, -while he exemplified those views by physical discoveries, he does not -rather deserve the still higher praise of being at the same time a -theoretical and a practical reformer. Gilbert's physical researches -and speculations were employed principally upon subjects on which the -ancients had known little or nothing; and on which therefore it could -not be doubtful whether tradition or observation was the source of -knowledge. Such was magnetism; for the ancients were barely acquainted -with the attractive property of the magnet. Its polarity, including -repulsion as well as attraction, its direction towards the north, -its limited variation from this direction, its declination from the -horizontal position, were all modern discoveries. Gilbert's work[138] -on the magnet and on the magnetism of the earth, appeared in 1600; -and in this, he repeatedly maintains the superiority of experimental -knowledge over the physical philosophy of the ancients. His preface -opens thus: "Since in making discoveries and searching out the hidden -causes of things, stronger reasons are obtained from trustworthy -experiments and demonstrable arguments, than from probable conjectures -and the dogmas of those who philosophize in the usual manner," he has, -he says, "endeavoured to proceed from common magnetical experiments to -the inward constitution of the earth." As I have stated in the History -of Magnetism[139], Gilbert's work contains all the fundamental facts -of that science, so fully stated, that we have, at this day, little to -add to them. He is not, however, by the advance which he thus made, -led to depreciate the ancients, but only to claim for himself the same -liberty of philosophizing which they had enjoyed[140]. "To those -ancient and first parents of philosophy, Aristotle, Theophrastus, -Ptolemy, Hippocrates, Galen, be all due honour; from them it was that -the stream of wisdom has been derived down to posterity. But our age -has discovered and brought to light many things which they, if they -were yet alive, would gladly embrace. Wherefore we also shall not -hesitate to expound, by probable hypotheses, those things which by long -experience we have ascertained." - -In this work the author not only adopts the Copernican doctrine of the -earth's motion, but speaks[141] of the contrary supposition as utterly -absurd, founding his argument mainly on the vast velocities which such -a supposition requires us to ascribe to the celestial bodies. Dr. -Gilbert was physician to Queen Elizabeth and to James the First, and -died in 1603. Some time after his death the executors of his brother -published another work of his, _De Mundo nostro Sublunari Philosophia -Nova_, in which similar views are still more comprehensively presented. -In this he says, "The two lords of philosophy, Aristotle and Galen, -are held in worship like gods, and rule the schools;--the former by -some destiny obtained a sway and influence among philosophers, like -that of his pupil Alexander among the kings of the earth;--Galen, with -like success, holds his triumph among the physicians of Europe." This -comparison of Aristotle to Alexander was also taken hold of by Bacon. -Nor is Gilbert an unworthy precursor of Bacon in the view he gives of -the History of Science, which occupies the first three chapters of his -Philosophy. He traces this history from "the simplicity and ignorance -of the ancients," through "the fabrication of the fable of the four -elements," to Aristotle and Galen. He mentions with due disapproval the -host of commentators which succeeded, the alchemists, the "shipwreck -of science in the deluge of the Goths," and the revival of letters -and genius in the time of "our grandfathers." "This later age," he -says, "has exploded the Barbarians, and restored the Greeks and Latins -to their pristine grace and honour. It remains, that if they have -written aught in error, this should be remedied by better and more -productive processes (_frugiferis_ institutis), not to be contemned -for their novelty; (for nothing which is true is really new, but is -perfect from eternity, though to weak man it may be unknown;) and that -thus Philosophy may bear her fruit." The reader of Bacon will not fail -to recognize, in these references to "fruit-bearing" knowledge, a -similarity of expression with the _Novum Organon_. - -Bacon does not appear to me to have done justice to his contemporary. -He nowhere recognizes in the labours of Gilbert a community of -purpose and spirit with his own. On the other hand, he casts upon -him a reflection which he by no means deserves. In the _Advancement -of Learning_[142], he says, "Another error is, that men have used to -infect their meditations, opinions, and doctrines, with some conceits -which they have most admired, or some sciences to which they have -most applied; and given all things else a tincture according to -them, utterly untrue and improper.... So have the alchemists made a -philosophy out of a few experiments of the furnace; and Gilbertus, -our countryman, hath made a philosophy out of the observations of a -loadstone," (in the Latin, philosophiam etiam e magnete elicuit). -And in the same manner he mentions him in the _Novum Organon_[143], -as affording an example of an empirical kind of philosophy, which -appears to those daily conversant with the experiments, probable, but -to other persons incredible and empty. But instead of blaming Gilbert -for disturbing and narrowing science by a too constant reference to -magnetical rules, we might rather censure Bacon, for not seeing how -important in all natural philosophy are those laws of attraction -and repulsion of which magnetical phenomena are the most obvious -illustration. We may find ground for such a judgment in another passage -in which Bacon speaks of Gilbert. In the Second Book[144] of the _Novum -Organon_, having classified motions, he gives, as one kind, what he -calls, in his figurative language, _motion for gain_, or _motion of -need_, by which a body shuns heterogeneous, and seeks cognate bodies. -And he adds, "The Electrical operation, concerning which Gilbert and -others since him have made up such a wonderful story, is nothing less -than the appetite of a body, which, excited by friction, does not well -tolerate the air, and prefers another tangible body if it be found -near." Bacon's notion of an appetite in the body is certainly much -less philosophical than Gilbert's, who speaks of light bodies as drawn -towards amber by certain material radii[145]; and we might perhaps -venture to say that Bacon here manifests a want of clear mechanical -ideas. Bacon, too, showed his inferior aptitude for physical research -in rejecting the Copernican doctrine which Gilbert adopted. In the -_Advancement of Learning_[146], suggesting a history of the opinions -of philosophers, he says that he would have inserted in it even recent -theories, as those of Paracelsus; of Telesius, who restored the -philosophy of Parmenides; or Patricius, who resublimed the fumes of -Platonism; or Gilbert, who brought back the dogmas of Philolaus. But -Bacon quotes[147] with pleasure Gilbert's ridicule of the Peripatetics' -definition of heat. They had said, that heat is that which separates -heterogeneous and unites homogeneous matter; which, said Gilbert, is -as if any one were to define _man_ as that which sows wheat and plants -vines. - -Galileo, another of Gilbert's distinguished contemporaries, had a -higher opinion of him. He says[148], "I extremely admire and envy this -author. I think him worthy of the greatest praise for the many new and -true observations which he has made, to the disgrace of so many vain -and fabling authors; who write, not from their own knowledge only, -but repeat everything they hear from the foolish and vulgar, without -attempting to satisfy themselves of the same by experience; perhaps -that they may not diminish the size of their books." - - -8. _Galileo._--Galileo was content with the active and successful -practice of experimental inquiry; and did not demand that such -researches should be made expressly subservient to that wider and -more ambitious philosophy, on which the author of the _Novum Organon_ -employed his powers. But still it now becomes our business to trace -those portions of Galileo's views which have reference to the theory, -as well as the practice, of scientific investigation. On this subject, -Galileo did not think more profoundly, perhaps, than several of his -contemporaries; but in the liveliness of expression and illustration -with which he recommended his opinions on such topics, he was -unrivalled. Writing in the language of the people, in the attractive -form of dialogue, with clearness, grace, and wit, he did far more than -any of his predecessors had done to render the new methods, results, -and prospects of science familiar to a wide circle of readers, first -in Italy, and soon, all over Europe. The principal points inculcated -by him were already becoming familiar to men of active and inquiring -minds; such as,--that knowledge was to be sought from observation, and -not from books;--that it was absurd to adhere to, and debate about, -the physical tenets of Aristotle and the rest of the ancients. On -persons who followed this latter course, Galileo fixed the epithet of -Paper Philosophers[149]; because, as he wrote in a letter to Kepler, -this sort of men fancied that philosophy was to be studied like the -_Æneid_ or _Odyssey_, and that the true reading of nature was to be -detected by the collation of texts. Nothing so much shook the authority -of the received system of Physics as the experimental discoveries, -directly contradicting it, which Galileo made. By experiment, as I -have elsewhere stated[150], he disproved the Aristotelian doctrine that -bodies fall quickly or slowly in proportion to their weight. And when -he had invented the telescope, a number of new discoveries of the most -striking kind (the inequalities of the moon's surface, the spots in -the sun, the moon-like phases of Venus, the satellites of Jupiter, the -ring of Saturn,) showed, by the evidence of the eyes, how inadequate -were the conceptions, and how erroneous the doctrines of the ancients, -respecting the constitution of the universe. How severe the blow was to -the disciples of the ancient schools, we may judge by the extraordinary -forms of defence in which they tried to intrench themselves. They would -not look through Galileo's glasses; they maintained that what was seen -was an illusion of witchcraft; and they tried, as Galileo says[151], -with logical arguments, as if with magical incantations, to charm the -new planets out of the sky. No one could be better fitted than Galileo -for such a warfare. His great knowledge, clear intellect, gaiety, and -light irony, (with the advantage of being in the right,) enabled him to -play with his adversaries as he pleased. Thus when an Aristotelian[152] -rejected the discovery of the irregularities in the moon's surface, -because, according to the ancient doctrine, her form was a perfect -sphere, and held that the apparent cavities were filled with an -invisible crystal substance, Galileo replied, that he had no objection -to assent to this, but that then he should require his adversary in -return to believe that there were on the same surface invisible crystal -mountains ten times as high as those visible ones which he had actually -observed and measured. - -We find in Galileo many thoughts which have since become established -maxims of modern philosophy. "Philosophy," he says[153], "is written -in that great book, I mean the Universe, which is constantly open -before our eyes; but it cannot be understood, unless we first know the -language and learn the characters in which it is written." With this -thought he combines some other lively images. One of his interlocutors -says concerning another, "Sarsi perhaps thinks that philosophy is -a book made up of the fancies of men, like the _Iliad_ or _Orlando -Furioso_, in which the matter of least importance is, that what is -written be true." And again, with regard to the system of authority, he -says, "I think I discover in him a firm belief that, in philosophizing, -it is necessary to lean upon the opinion of some celebrated author; -as if our mind must necessarily remain unfruitful and barren till it -be married to another man's reason."--"No," he says, "the case is not -so.--When we have the decrees of Nature, authority goes for nothing; -reason is absolute[154]." - -In the course of Galileo's controversies, questions of the logic of -science came under discussion. Vincenzio di Grazia objected to a proof -from induction which Galileo adduced, because _all_ the particulars -were not enumerated; to which the latter justly replies[155], that -if induction were required to pass through all the cases, it would -be either useless or impossible;--impossible when the cases are -innumerable; useless when they have each already been verified, since -then the general proposition adds nothing to our knowledge. - -One of the most novel of the characters which Science assumes in -Galileo's hands is, that she becomes cautious. She not only proceeds -leaning upon Experience, but she is content to proceed a little way -at a time. She already begins to perceive that she must rise to the -heights of knowledge by many small and separate steps. The philosopher -is desirous to know much, but resigned to be ignorant for a time of -that which cannot yet be known. Thus when Galileo discovered the true -law of the motion of a falling body[156], that the velocity increases -proportionally to the time from the beginning of the fall, he did -not insist upon immediately assigning the cause of this law. "The -cause of the acceleration of the motions of falling bodies is not," -he says, "a necessary part of the investigation." Yet the conception -of this acceleration, as the result of the continued action of the -force of gravity upon the falling body, could hardly fail to suggest -itself to one who had formed the idea of force. In like manner, the -truth that the velocities, acquired by bodies falling down planes of -equal heights, are all equal, was known to Galileo and his disciples, -long before he accounted for it[157], by the principle, apparently -so obvious, that the momentum generated is as the moving force which -generates it. He was not tempted to rush at once, from an experimental -truth to a universal system. Science had learnt that she must move step -by step; and the gravity of her pace already indicated her approaching -maturity and her consciousness of the long path which lay before her. - -But besides the genuine philosophical prudence which thus withheld -Galileo from leaping hastily from one inference to another, he had -perhaps a preponderating inclination towards facts; and did not feel, -so much as some other persons of his time, the need of reducing them to -ideas. He could bear to contemplate laws of motion without being urged -by an uncontrollable desire to refer them to conceptions of force. - - -9. _Kepler._--In this respect his friend Kepler differed from him; -for Kepler was restless and unsatisfied till he had reduced facts to -laws, and laws to causes; and never acquiesced in ignorance, though -he tested with the most rigorous scrutiny that which presented itself -in the shape of knowledge to fill the void. It may be seen in the -History of Astronomy[158] with what perseverance, energy, and fertility -of invention, Kepler pursued his labours, (enlivened and relieved by -the most curious freaks of fancy,) with a view of discovering the -rules which regulate the motions of the planet Mars. He represents -this employment under the image of a warfare; and describes[159] his -object to be "to triumph over Mars, and to prepare for him, as for one -altogether vanquished, tabular prisons and equated eccentric fetters;" -and when, "the enemy, left at home a despised captive, had burst all -the chains of the equations, and broken forth of the prisons of the -tables;"--when "it was buzzed here and there that the victory is vain, -and that the war is raging anew as violently as before;"--that is, when -the rules which he had proposed did not coincide with the facts;--he -by no means desisted from his attempts, but "suddenly sent into the -field a reserve of new physical reasonings on the rout and dispersion -of the veterans," that is, tried new suppositions suggested by such -views as he then entertained of the celestial motions. His efforts -to obtain the formal laws of the planetary motions resulted in some -of the most important discoveries ever made in astronomy; and if his -physical reasonings were for the time fruitless, this arose only from -the want of that discipline in mechanical ideas which the minds of -mathematicians had still to undergo; for the great discoveries of -Newton in the next generation showed that, in reality, the next step -of the advance was in this direction. Among all Kepler's fantastical -expressions, the fundamental thoughts were sound and true; namely, -that it was his business, as a physical investigator, to discover a -mathematical rule which governed and included all the special facts; -and that the rules of the motions of the planets must conform to some -conception of causation. - -The same characteristics,--the conviction of rule and cause, -perseverance in seeking these, inventiveness in devising hypotheses, -love of truth in trying and rejecting them, and a lively Fancy playing -with the Reason without interrupting her,--appear also in his work -on Optics; in which he tried to discover the exact law of optical -refraction[160]. In this undertaking he did not succeed entirely; -nor does he profess to have done so. He ends his numerous attempts by -saying, "Now, reader, you and I have been detained sufficiently long -while I have been attempting to _collect into one fagot_ the measures -of different refractions." - -In this and in other expressions, we see how clearly he apprehended -that _colligation of facts_ which is the main business of the practical -discoverer. And by his peculiar endowments and habits, Kepler exhibits -an essential portion of this process, which hardly appears at all in -Galileo. In order to bind together facts, theory is requisite as well -as observation,--the cord as well as the fagots. And the true theory -is often, if not always, obtained by trying several and selecting the -right. Now of this portion of the discoverer's exertions, Kepler is -a most conspicuous example. His fertility in devising suppositions, -his undaunted industry in calculating the results of them, his entire -honesty and candour in resigning them if these results disagreed with -the facts, are a very instructive spectacle; and are fortunately -exhibited to us in the most lively manner in his own garrulous -narratives. Galileo urged men by precept as well as example to begin -their philosophy from observation; Kepler taught them by his practice -that they must proceed from observation by means of hypotheses. The -one insisted upon facts; the other dealt no less copiously with ideas. -In the practical, as in the speculative portion of our history, this -antithesis shows itself; although in the practical part we cannot have -the two elements separated, as in the speculative we sometimes have. - -In the _History of Science_[161], I have devoted several pages to the -intellectual character of Kepler, inasmuch as his habit of devising so -great a multitude of hypotheses, so fancifully expressed, had led some -writers to look upon him as an inquirer who transgressed the most fixed -rules of philosophical inquiry. This opinion has arisen, I conceive, -among those who have forgotten the necessity of Ideas as well as Facts -for all theory; or who have overlooked the impossibility of selecting -and explicating our ideas without a good deal of spontaneous play of -the mind. It must, however, always be recollected that Kepler's genius -and fancy derived all their scientific value from his genuine and -unmingled love of truth. These qualities appeared, not only in the -judgment he passed upon hypotheses, but also in matters which more -immediately concerned his reputation. Thus when Galileo's discovery of -the telescope disproved several opinions which Kepler had published -and strenuously maintained, he did not hesitate a moment to retract -his assertions and range himself by the side of Galileo, whom he -vigorously supported in his warfare against those who were incapable of -thus cheerfully acknowledging the triumph of new facts over their old -theories. - - -10. _Tycho._--There remains one eminent astronomer, the friend and -fellow-labourer of Kepler, whom we must not separate from him as one -of the practical reformers of science. I speak of Tycho Brahe, who is, -I think, not justly appreciated by the literary world in general, in -consequence of his having made a retrograde step in that portion of -astronomical theory which is most familiar to the popular mind. Though -he adopted the Copernican view of the motion of the planets about the -sun, he refused to acknowledge the annual and diurnal motion of the -earth. But notwithstanding this mistake, into which he was led by his -interpretation of Scripture rather than of nature, Tycho must ever be -one of the greatest names in astronomy. In the philosophy of science -also, the influence of what he did is far from inconsiderable; and -especially its value in bringing into notice these two points:--that -not only are observations the beginning of science, but that the -progress of science may often depend upon the observer's pursuing his -task regularly and carefully for a long time, and with well devised -instruments; and again, that observed facts offer a _succession_ of -laws which we discover as our observations become better, and as our -theories are better adapted to the observations. With regard to the -former point, Tycho's observatory was far superior to all that had -preceded it[162], not only in the optical, but in the mechanical -arrangements; a matter of almost equal consequence. And hence it was -that his observations inspired in Kepler that confidence which led him -to all his labours and all his discoveries. "Since," he says[163], "the -divine goodness has given us in Tycho Brahe an exact observer, from -whose observations this error of eight minutes in the calculations of -the Ptolemaic hypothesis is detected, let us acknowledge and make use -of this gift of God: and since this error cannot be neglected, these -eight minutes alone have prepared the way for an entire reform of -Astronomy, and are to be the main subject of this work." - -With regard to Tycho's discoveries respecting the moon, it is to be -recollected that besides the first inequality of the moon's motion, -(the _equation of the centre_, arising from the elliptical form of her -orbit,) Ptolemy had discovered a second inequality, the _evection_, -which, as we have observed in the History of this subject[164], might -have naturally suggested the suspicion that there were still other -inequalities. In the middle ages, however, such suggestions, implying -a constant progress in science, were little attended to; and, we have -seen, that when an Arabian astronomer[165] had really discovered -another inequality of the moon, it was soon forgotten, because it had -no place in the established systems. Tycho not only rediscovered the -lunar inequality, (the _variation_,) thus once before won and lost, but -also two other inequalities; namely[166], the _change of inclination_ -of the moon's orbit as the line of nodes moves round, and an inequality -in the motion of the line of nodes. Thus, as I have elsewhere said, -it appeared that the discovery of a rule is a step to the discovery -of deviations from that rule, which require to be expressed in other -rules. It became manifest to astronomers, and through them to all -philosophers, that in the application of theory to observation, we -find, not only the stated phenomena, for which the theory does account, -but also _residual phenomena_, which are unaccounted for, and remain -over and above the calculation. And it was seen further, that these -residual phenomena might be, altogether or in part, exhausted by new -theories. - -These were valuable lessons; and the more valuable inasmuch as men -were now trying to lay down maxims and methods for the conduct of -science. A revolution was not only at hand, but had really taken place, -in the great body of real cultivators of science. The occasion now -required that this revolution should be formally recognized;--that -the new intellectual power should be clothed with the forms of -government;--that the new philosophical republic should be acknowledged -as a sister state by the ancient dynasties of Aristotle and Plato. -There was needed some great Theoretical Reformer, to speak in the name -of the Experimental Philosophy; to lay before the world a declaration -of its rights and a scheme of its laws. And thus our eyes are turned to -Francis Bacon, and others who like him attempted this great office. We -quit those august and venerable names of discoverers, whose appearance -was the prelude and announcement of the new state of things then -opening; and in doing so, we may apply to them the language which Bacon -applies to himself[167]:-- - - Χαίρετε Κήρυκες Διὸ ς ἄγγελοι ἠδὲ καὶ ἀνδρῶν. - - Hail, Heralds, Messengers of Gods and Men! - - -FOOTNOTES: - -[Footnote 128: His works have never been published, and exist in -manuscript in the library of the Institute at Paris. Some extracts were -published by Venturi, _Essai sur les Ouvrages de Leonard da Vinci_. -Paris, 1797.] - -[Footnote 129: Leonardo died in 1520, at the age of 78.] - -[Footnote 130: Paul III. in 1543.] - -[Footnote 131: _Hist. Ind. Sc._ b. v. c. ii.] - -[Footnote 132: Born 1537, died 1619.] - -[Footnote 133: _Hist. Ind. Sc._ b. xvii. c. ii. sect. 1.] - -[Footnote 134: Fabricius, _De Motu Locali_, p. 182.] - -[Footnote 135: p. 199.] - -[Footnote 136: _Speculationum Liber_, p. 195.] - -[Footnote 137: _Ibid._ p. 169.] - -[Footnote 138: Gulielmi Gilberti, _Colcestriensis, Medici Londinensis, -De Magnete, Magneticisque Corporibus, et de Magno Magnete Tellure, -Physiologia Nova, plurimis et Argumentis et Experimentis demonstrata_.] - -[Footnote 139: _Hist. Ind. Sc._ b. xii. c. i.] - -[Footnote 140: Pref.] - -[Footnote 141: _De Magnete_, lib. vi. c. 3, 4.] - -[Footnote 142: _Nov. Org._ b. i.] - -[Footnote 143: B. i. Aph. 64.] - -[Footnote 144: Vol. ix. 185.] - -[Footnote 145: _De Magnete_, p. 60.] - -[Footnote 146: B. iii. c. 4.] - -[Footnote 147: _Nov. Org._ b. ii. Aph. 48.] - -[Footnote 148: Drinkwater's _Life of Galileo_, p. 18.] - -[Footnote 149: _Life of Galileo_, p. 9.] - -[Footnote 150: _Hist. Ind. Sc._ b. vi. c. ii. sect. 5.] - -[Footnote 151: _Life of Galileo_, p. 29.] - -[Footnote 152: _Ibid._ p. 33.] - -[Footnote 153: _Il Saggiatore_, ii. 247.] - -[Footnote 154: _Il Saggiatore_, ii. 200.] - -[Footnote 155: _Ibid._ i. 501.] - -[Footnote 156: _Hist. Ind. Sc._ b. vi. c. ii. sect. 2.] - -[Footnote 157: _Hist. Ind. Sc._ b. vi. c. ii. sect. 4.] - -[Footnote 158: _Ibid._ b. v. c. iv. sect. 1.] - -[Footnote 159: _De Stell. Mart._ p. iv. c. 51 (1609); Drinkwater's -_Kepler_, p. 33.] - -[Footnote 160: Published 1604. _Hist. Ind. Sc._ b. ix. c. ii.] - -[Footnote 161: _Hist. Ind. Sc._ b. v. c. iv. sect. 1.] - -[Footnote 162: _Hist. Ind. Sc._ b. vii. c. vi. sect 1.] - -[Footnote 163: _De Stell. Mart._ p. 11. c. 19.] - -[Footnote 164: _Hist. Ind. Sc._ b. ii. c. iv. sect. 6.] - -[Footnote 165: _Ibid._ sect. 8.] - -[Footnote 166: Montucla, i. 566.] - -[Footnote 167: _De Augm._ lib. iv. c. 1.] - - - - -CHAPTER XV. - -FRANCIS BACON. - - -(I.) 1. _General Remarks._--It is a matter of some difficulty to speak -of the character and merits of this illustrious man, as regards his -place in that philosophical history with which we are here engaged. -If we were to content ourselves with estimating him according to the -office which, as we have just seen, he claims for himself[168], as -merely the harbinger and announcer of a sounder method of scientific -inquiry than that which was recognized before him, the task would -be comparatively easy. For we might select from his writings those -passages in which he has delivered opinions and pointed out processes, -then novel and strange, but since confirmed by the experience of -actual discoverers, and by the judgments of the wisest of succeeding -philosophers; and we might pass by, without disrespect, but without -notice, maxims and proposals which have not been found available for -use;--views so indistinct and vague, that we are even yet unable to -pronounce upon their justice;--and boundless anticipations, dictated -by the sanguine hopes of a noble and comprehensive intellect. But -if we thus reduce the philosophy of Bacon to that portion which the -subsequent progress of science has rigorously verified, we shall -have to pass over many of those declarations which have excited -most notice in his writings, and shall lose sight of many of those -striking thoughts which his admirers most love to dwell upon. For he -is usually spoken of, at least in this country, as a teacher who -not only commenced, but in a great measure completed, the Philosophy -of Induction. He is considered, not only as having asserted some -general principles, but laid down the special rules of scientific -investigation; as not only one of the Founders, but the supreme -Legislator of the modern Republic of Science; not only the Hercules who -slew the monsters that obstructed the earlier traveller, but the Solon -who established a constitution fitted for all future time. - - -2. Nor is it our purpose to deny that of such praise he deserves -a share which, considering the period at which he lived, is truly -astonishing. But it is necessary for us in this place to discriminate -and select that portion of his system which, bearing upon _physical_ -science, has since been confirmed by the actual history of science. -Many of Bacon's most impressive and captivating passages contemplate -the extension of the new methods of discovering truth to intellectual, -to moral, to political, as well as to physical science. And how far, -and how, the advantages of the inductive method may be secured for -those important branches of speculation, it will at some future time -be a highly interesting task to examine. But our plan requires us at -present to omit the consideration of these; for our purpose is to learn -what the genuine course of the formation of science is, by tracing it -in those portions of human knowledge, which, by the confession of all, -are most exact, most certain, most complete. Hence we must here deny -ourselves the dignity and interest which float about all speculations -in which the great moral and political concerns of men are involved. -It cannot be doubted that the commanding position which Bacon occupies -in men's estimation arises from his proclaiming a reform in philosophy -of so comprehensive a nature;--a reform which was to infuse a new -spirit into every part of knowledge. Physical Science has tranquilly -and noiselessly adopted many of his suggestions; which were, indeed, -her own natural impulses, not borrowed from him; and she is too deeply -and satisfactorily absorbed in contemplating her results, to talk much -about the methods of obtaining them which she has thus instinctively -pursued. But the philosophy which deals with mind, with manners, -with morals, with polity, is conscious still of much obscurity and -perplexity; and would gladly borrow aid from a system in which aid -is so confidently promised. The aphorisms and phrases of the _Novum -Organon_ are far more frequently quoted by metaphysical, ethical, and -even theological writers, than they are by the authors of works on -physics. - - -3. Again, even as regards physics, Bacon's fame rests upon something -besides the novelty of the maxims which he promulgated. That a -revolution in the method of scientific research was going on, all -the greatest physical investigators of the sixteenth century were -fully aware, as we have shown in the last chapter. But their writings -conveyed this conviction to the public at large somewhat slowly. Men of -letters, men of the world, men of rank, did not become familiar with -the abstruse works in which these views were published; and above all, -they did not, by such occasional glimpses as they took of the state of -physical science, become aware of the magnitude and consequences of -this change. But Bacon's lofty eloquence, wide learning, comprehensive -views, bold pictures of the coming state of things, were fitted to -make men turn a far more general and earnest gaze upon the passing -change. When a man of his acquirements, of his talents, of his rank and -position, of his gravity and caution, poured forth the strongest and -loftiest expressions and images which his mind could supply, in order -to depict the "Great Instauration" which he announced;--in order to -contrast the weakness, the blindness, the ignorance, the wretchedness, -under which men had laboured while they followed the long beaten track, -with the light, the power, the privileges, which they were to find in -the paths to which he pointed;--it was impossible that readers of all -classes should not have their attention arrested, their minds stirred, -their hopes warmed; and should not listen with wonder and with pleasure -to the strains of prophetic eloquence in which so great a subject -was presented. And when it was found that the prophecy was verified; -when it appeared that an immense change in the methods of scientific -research really _had_ occurred;--that vast additions to man's knowledge -and power had been acquired, in modes like those which had been spoken -of;--that further advances might be constantly looked for;--and that a -progress, seemingly boundless, was going on in the direction in which -the seer had thus pointed;--it was natural that men should hail him as -the leader of the revolution; that they should identify him with the -event which he was the first to announce; that they should look upon -him as the author of that which he had, as they perceived, so soon and -so thoroughly comprehended. - - -4. For we must remark, that although (as we have seen) he was not the -only, nor the earliest writer, who declared that the time was come -for such a change, he not only proclaimed it more emphatically, but -understood it, in its general character, much more exactly, than any -of his contemporaries. Among the maxims, suggestions and anticipations -which he threw out, there were many of which the wisdom and the novelty -were alike striking to his immediate successors;--there are many -which even now, from time to time, we find fresh reason to admire, -for their acuteness and justice. Bacon stands far above the herd of -loose and visionary speculators who, before and about his time, spoke -of the establishment of new philosophies. If we must select some one -philosopher as the Hero of the revolution in scientific method, beyond -all doubt Francis Bacon must occupy the place of honour. - -We shall, however, no longer dwell upon these general considerations, -but shall proceed to notice some of the more peculiar and -characteristic features of Bacon's philosophy; and especially those -views, which, occurring for the first time in his writings, have been -fully illustrated and confirmed by the subsequent progress of science, -and have become a portion of the permanent philosophy of our times. - - -(II.) 5. _A New Era announced._--The first great feature which -strikes us in Bacon's philosophical views is that which we have -already noticed;--his confident and emphatic announcement of a _New -Era_ in the progress of science, compared with which the advances of -former times were poor and trifling. This was with Bacon no loose and -shallow opinion, taken up on light grounds and involving only vague, -general notions. He had satisfied himself of the justice of such a -view by a laborious course of research and reflection. In 1605, at the -age of forty-four, he published his Treatise of the _Advancement of -Learning_, in which he takes a comprehensive and spirited survey of -the condition of all branches of knowledge which had been cultivated -up to that time. This work was composed with a view to that reform -of the existing philosophy which Bacon always had before his eyes; -and in the Latin edition of his works, forms the First Part of the -_Instauratio Magna_. In the Second Part of the Instauratio, the _Novum -Organon_, published in 1620, he more explicitly and confidently states -his expectations on this subject. He points out how slightly and -feebly the examination of nature had been pursued up to his time, and -with what scanty fruit. He notes the indications of this in the very -limited knowledge of the Greeks who had till then been the teachers -of Europe, in the complaints of authors concerning the subtilty and -obscurity of the secrets of nature, in the dissensions of sects, in -the absence of useful inventions resulting from theory, in the fixed -form which the sciences had retained for two thousand years. Nor, he -adds[169], is this wonderful; for how little of his thought and labour -has man bestowed upon science! Out of twenty-five centuries scarce six -have been favourable to the progress of knowledge. And even in those -favoured times, natural philosophy received the smallest share of man's -attention; while the portion so given was marred by controversy and -dogmatism; and even those who have bestowed a little thought upon -this philosophy, have never made it their main study, but have used it -as a passage or drawbridge to serve other objects. And thus, he says, -the great Mother of the Sciences is thrust down with indignity to the -offices of a handmaid; is made to minister to the labours of medicine -or mathematics, or to give the first preparatory tinge to the immature -minds of youth. For these and similar considerations of the errors of -past time, he draws hope for the future, employing the same argument -which Demosthenes uses to the Athenians: "That which is worst in the -events of the past, is the best as a ground of trust in the future. -For if you had done all that became you, and still had been in this -condition, your case might be desperate; but since your failure is the -result of your own mistakes, there is good hope that, correcting the -error of your course, you may reach a prosperity yet unknown to you." - - -(III.) 6. _A change of existing Method._--All Bacon's hope of -improvement indeed was placed in an entire _change of the Method_ by -which science was pursued; and the boldness, and at the same time (the -then existing state of science being considered), the definiteness of -his views of the change that was requisite, are truly remarkable. - -That all knowledge must begin with observation, is one great principle -of Bacon's philosophy; but I hardly think it necessary to notice the -inculcation of this maxim as one of his main services to the cause of -sound knowledge, since it had, as we have seen, been fully insisted -upon by others before him, and was growing rapidly into general -acceptance without his aid. But if he was not the first to tell men -that they must collect their knowledge from observation, he had no -rival in his peculiar office of teaching them _how_ science must thus -be gathered from experience. - -It appears to me that by far the most extraordinary parts of Bacon's -works are those in which, with extreme earnestness and clearness, he -insists upon a _graduated and successive induction_, as opposed to a -hasty transit from special facts to the highest generalizations. The -nineteenth Axiom of the First Book of the _Novum Organon_ contains a -view of the nature of true science most exact and profound, and, so -far as I am aware, at the time perfectly new. "There are two ways, and -can only be two, of seeking and finding truth. The one, from sense and -particulars, takes a flight to the most general axioms, and from those -principles and their truth, settled once for all, invents and judges of -intermediate axioms. The other method collects axioms from sense and -particulars, ascending _continuously and by degrees_, so that in the -end it arrives at the most general axioms; this latter way is the true -one, but hitherto untried." - -It is to be remarked, that in this passage Bacon employs the term -_axioms_ to express any propositions collected from facts by induction, -and thus fitted to become the starting-point of deductive reasonings. -How far propositions so obtained may approach to the character of -axioms in the more rigorous sense of the term, we have already in some -measure examined; but that question does not here immediately concern -us. The truly remarkable circumstance is to find this recommendation -of a continuous advance from observation, by limited steps, through -successive gradations of generality, given at a time when speculative -men in general had only just begun to perceive that they must begin -their course from experience in some way or other. How exactly this -description represents the general structure of the soundest and -most comprehensive physical theories, all persons who have studied -the progress of science up to modern times can bear testimony; but -perhaps this structure of science cannot in any other way be made so -apparent as by those Tables of successive generalizations in which we -have exhibited the history and constitution of some of the principal -physical sciences, in the Chapter of a preceding work which treats of -the Logic of Induction. And the view which Bacon thus took of the true -progress of science was not only new, but, so far as I am aware, has -never been adequately illustrated up to the present day. - - -7. It is true, as I observed in the last chapter, that Galileo had been -led to see the necessity, not only of proceeding from experience in the -pursuit of knowledge, but of proceeding cautiously and gradually; and -he had exemplified this rule more than once, when, having made one step -in discovery, he held back his foot, for a time, from the next step, -however tempting. But Galileo had not reached this wide and commanding -view of the successive subordination of many steps, all leading up at -last to some wide and simple general truth. In catching sight of this -principle, and in ascribing to it its due importance, Bacon's sagacity, -so far as I am aware, wrought unassisted and unrivalled. - - -8. Nor is there any wavering or vagueness in Bacon's assertion of this -important truth. He repeats it over and over again; illustrates it by -a great number of the most lively metaphors and emphatic expressions. -Thus he speaks of the successive _floors_ (_tabulata_) of induction; -and speaks of each science as a _pyramid_[170] which has observation -and experience for its basis. No images can better exhibit the relation -of general and particular truths, as our own Inductive Tables may serve -to show. - - -(IV.) 9. _Comparison of the New and Old Method._ Again; not less -remarkable is his contrasting this true Method of Science (while it was -almost, as he says, yet untried) with the ancient and _vicious Method_, -which began, indeed, with facts of observation, but rushed at once -and with no gradations, to the most general principles. For this was -the course which had been actually followed by all those speculative -reformers who had talked so loudly of the necessity of beginning our -philosophy from experience. All these men, if they attempted to frame -physical doctrines at all, had caught up a few facts of observation, -and had erected a universal theory upon the suggestions which these -offered. This process of illicit generalization, or, as Bacon terms -it, Anticipation of Nature (_anticipatio naturæ_), in opposition to -the Interpretation of Nature, he depicts with singular acuteness, in -its character and causes. "These two ways," he says[171], "both begin -from sense and particulars; but their discrepancy is immense. The one -merely skims over experience and particulars in a cursory transit; the -other deals with them in a due and orderly manner. The one, at its very -outset, frames certain general abstract principles, but useless; the -other gradually rises to those principles which have a real existence -in nature." - -"The former path," he adds[172], "that of illicit and hasty -generalization, is one which the intellect follows when abandoned to -its own impulse; and this it does from the requisitions of logic. For -the mind has a yearning which makes it dart forth to generalities, that -it may have something to rest in; and after a little dallying with -experience, becomes weary of it; and all these evils are augmented by -logic, which requires these generalities to make a show with in its -disputations." - -"In a sober, patient, grave intellect," he further adds, "the mind, by -its own impulse, (and more especially if it be not impelled by the sway -of established opinions) attempts in some measure that other and true -way, of gradual generalization; but this it does with small profit; -for the intellect, except it be regulated and aided, is a faculty of -unequal operation, and altogether unapt to master the obscurity of -things." - -The profound and searching wisdom of these remarks appears more -and more, as we apply them to the various attempts which men have -made to obtain knowledge; when they begin with the contemplation of -a few facts, and pursue their speculations, as upon most subjects -they have hitherto generally done; for almost all such attempts have -led immediately to some process of illicit generalization, which -introduces an interminable course of controversy. In the physical -sciences, however, we have the further inestimable advantage of seeing -the other side of the contrast exemplified: for many of them, as our -inductive Tables show us, have gone on according to the most rigorous -conditions of gradual and successive generalization; and in consequence -of this circumstance in their constitution, possess, in each part of -their structure, a solid truth, which is always ready to stand the -severest tests of reasoning and experiment. - -We see how justly and clearly Bacon judged concerning the mode in which -facts are to be employed in the construction of science. This, indeed, -has ever been deemed his great merit: insomuch that many persons appear -to apprehend the main substance of his doctrine to reside in the maxim -that facts of observation, and such facts alone, are the essential -elements of all true science. - - -(V.) 10. _Ideas are necessary._--Yet we have endeavoured to establish -the doctrine that facts are but one of two ingredients of knowledge -both equally necessary;--that _Ideas_ are no less indispensable than -facts themselves; and that except these be duly unfolded and applied, -facts are collected in vain. Has Bacon then neglected this great -portion of his subject? Has he been led by some partiality of view, or -some peculiarity of circumstances, to leave this curious and essential -element of science in its pristine obscurity? Was he unaware of its -interest and importance? - -We may reply that Bacon's philosophy, in its effect upon his readers -in general, does _not_ give due weight or due attention to the ideal -element of our knowledge. He is considered as peculiarly and eminently -the asserter of the value of experiment and observation. He is always -understood to belong to the experiential, as opposed to the ideal -school. He is held up in contrast to Plato and others who love to dwell -upon that part of knowledge which has its origin in the intellect of -man. - - -11. Nor can it be denied that Bacon has, in the finished part of his -_Novum Organon_, put prominently forwards the necessary dependence of -all our knowledge upon Experience, and said little of its dependence, -equally necessary, upon the Conceptions which the intellect itself -supplies. It will appear, however, on a close examination, that he -was by no means insensible or careless of this internal element of -all connected speculation. He held the balance, with no partial or -feeble hand, between phenomena and ideas. He urged the Colligation of -Facts, but he was not the less aware of the value of the Explication of -Conceptions. - - -12. This appears plainly from some remarkable Aphorisms in the _Novum -Organon_. Thus, in noticing the causes of the little progress then -made by science[173], he states this:--"In the current Notions, all is -unsound, whether they be logical or physical. _Substance_, _quality_, -_action_, _passion_, even _being_, are not good Conceptions; still less -are _heavy_, _light_, _dense_, _rare_, _moist_, _dry_, _generation_, -_corruption_, _attraction_, _repulsion_, _element_, _matter_, _form_, -and others of that kind; all are fantastical and ill-defined." And in -his attempt to exemplify his own system, he hesitates[174] in accepting -or rejecting the notions of _elementary_, _celestial_, _rare_, as -belonging to fire, since, as he says, they are vague and ill-defined -notions (_notiones vagæ nec bene terminatæ_). In that part of his work -which appears to be completed, there is not, so far as I have noticed, -any attempt to fix and define any notions thus complained of as loose -and obscure. But yet such an undertaking appears to have formed part -of his plan; and in the _Abecedarium Naturæ_[175], which consists of -the heads of various portions of his great scheme, marked by letters -of the alphabet, we find the titles of a series of dissertations "On -the Conditions of Being," which must have had for their object the -elucidation of divers Notions essential to science, and which would -have been contributions to the Explication of Conceptions, such as -we have attempted in a former part of this work. Thus some of the -subjects of these dissertations are;--Of Much and Little;--Of Durable -and Transitory;--Of Natural and Monstrous;--Of Natural and Artificial. -When the philosopher of induction came to discuss these, considered as -_conditions of existence_, he could not do otherwise than develope, -limit, methodize, and define the Ideas involved in these Notions, -so as to make them consistent with themselves, and a fit basis of -demonstrative reasoning. His task would have been of the same nature -as ours has been, in that part of this work which treats of the -Fundamental Ideas of the various classes of sciences. - - -13. Thus Bacon, in his speculative philosophy, took firmly hold of -both the handles of science; and if he had completed his scheme, would -probably have given due attention to Ideas, no less than to Facts, as -an element of our knowledge; while in his view of the general method -of ascending from facts to principles, he displayed a sagacity truly -wonderful. But we cannot be surprised, that in attempting to exemplify -the method which he recommended, he should have failed. For the method -could be exemplified only by some important discovery in physical -science; and great discoveries, even with the most perfect methods, do -not come at command. Moreover, although the general structure of his -scheme was correct, the precise import of some of its details could -hardly be understood, till the actual progress of science had made men -somewhat familiar with the kind of steps which it included. - - -(VI.) 14. _Bacon's Example._--Accordingly, Bacon's _Inquisition into -the Nature of Heat_, which is given in the Second Book of the _Novum -Organon_ as an example of the mode of interrogating Nature, cannot be -looked upon otherwise than as a complete failure. This will be evident -if we consider that, although the exact nature of heat is still an -obscure and controverted matter, the science of Heat now consists of -many important truths; and that to none of these truths is there any -approximation in Bacon's essay. From his process he arrives at this, -as the "forma or true definition" of heat;--"that it is an expansive, -restrained motion, modified in certain ways, and exerted in the -smaller particles of the body." But the steps by which the science of -Heat really advanced were (as may be seen in the history[176] of the -subject) these;--The discovery of a _measure_ of heat or temperature -(the thermometer); the establishment of the _laws_ of conduction -and radiation; of the _laws_ of specific heat, latent heat, and the -like. Such steps have led to Ampère's _hypothesis_[177], that heat -consists in the vibrations of an imponderable fluid; and to Laplace's -_hypothesis_, that temperature consists in the internal radiation of -such a fluid. These hypotheses cannot yet be said to be even probable; -but at least they are so modified as to include some of the preceding -laws which are firmly established; whereas Bacon's hypothetical motion -includes no laws of phenomena, explains no process, and is indeed -itself an example of illicit generalization. - - -15. One main ground of Bacon's ill fortune in this undertaking appears -to be, that he was not aware of an important maxim of inductive -science, that we must first obtain the _measure_ and ascertain the -_laws_ of phenomena, before we endeavour to discover their _causes_. -The whole history of thermotics up to the present time has been -occupied with the _former_ step, and the task is not yet completed: -it is no wonder, therefore, that Bacon failed entirely, when he so -prematurely attempted the _second_. His sagacity had taught him that -the progress of science must be gradual; but it had not led him to -judge adequately how gradual it must be, nor of what different kinds -of inquiries, taken in due order, it must needs consist, in order to -obtain success. - -Another mistake, which could not fail to render it unlikely that Bacon -should really exemplify his precepts by any actual advance in science, -was, that he did not justly appreciate the sagacity, the inventive -genius, which all discovery requires. He conceived that he could -supersede the necessity of such peculiar endowments. "Our method of -discovery in science," he says[178], "is of such a nature, that there -is not much left to acuteness and strength of genius, but all degrees -of genius and intellect are brought nearly to the same level." And he -illustrates this by comparing his method to a pair of compasses, by -means of which a person with no manual skill may draw a perfect circle. -In the same spirit he speaks of proceeding by _due rejections_; and -appears to imagine that when we have obtained a collection of facts, if -we go on successively rejecting what is false, we shall at last find -that we have, left in our hands, that scientific truth which we seek. -I need not observe how far this view is removed from the real state of -the case. The necessity of a _conception_ which must be furnished by -the mind in order to bind together the facts, could hardly have escaped -the eye of Bacon, if he had cultivated more carefully the ideal side -of his own philosophy. And any attempts which he could have made to -construct such conceptions by mere rule and method, must have ended -in convincing him that nothing but a peculiar inventive talent could -supply that which was thus not contained in the facts, and yet was -needed for the discovery. - - -(VII.) 16. _His Failure._--Since Bacon, with all his acuteness, had not -divined circumstances so important in the formation of science, it is -not wonderful that his attempt to reduce this process to a _Technical -Form_ is of little value. In the first place, he says[179], we must -prepare a natural and experimental history, good and sufficient; in the -next place, the instances thus collected are to be arranged in Tables -in some orderly way; and then we must apply a legitimate and true -induction. And in his example[180], he first collects a great number -of cases in which heat appears under various circumstances, which he -calls "a Muster of Instances before the intellect," (_comparentia -instantiarum ad intellectum_,) or a _Table of the Presence_ of the -thing sought. He then adds a _Table of its Absence_ in proximate cases, -containing instances where heat does not appear; then a _Table of -Degrees_, in which it appears with greater or less intensity. He then -adds[181], that we must try to exclude several obvious suppositions, -which he does by reference to some of the instances he has collected; -and this step he calls the _Exclusive_, or the _Rejection of Natures_. -He then observes, (and justly,) that whereas truth emerges more easily -from error than from confusion, we may, after this preparation, _give -play to the intellect_, (fiat permissio intellectus,) and make an -attempt at induction, liable afterwards to be corrected; and by this -step, which he terms his _First Vindemiation_, or _Inchoate Induction_, -he is led to the proposition concerning heat, which we have stated -above. - - -17. In all the details of his example he is unfortunate. By proposing -to himself to examine at once into the _nature_ of heat, instead -of the laws of special classes of phenomena, he makes, as we have -said, a fundamental mistake; which is the less surprising since he -had before him so few examples of the right course in the previous -history of science. But further, his collection of instances is very -loosely brought together; for he includes in his list the _hot_ taste -of aromatic plants, the _caustic_ effects of acids, and many other -facts which cannot be ascribed to heat without a studious laxity in -the use of the word. And when he comes to that point where he permits -his intellect its range, the conception of _motion_ upon which it at -once fastens, appears to be selected with little choice or skill, the -suggestion being taken from flame[182], boiling liquids, a blown fire, -and some other cases. If from such examples we could imagine heat -to be motion, we ought at least to have some gradation to cases of -heat where no motion is visible, as in a red-hot iron. It would seem -that, after a large collection of instances had been looked at, the -intellect, even in its first attempts, ought not to have dwelt upon -such an hypothesis as this. - - -18. After these steps, Bacon speaks of several classes of instances -which, singling them out of the general and indiscriminate collection -of facts, he terms _Instances with Prerogative_: and these he points -out as peculiar aids and guides to the intellect in its task. These -Instances with Prerogative have generally been much dwelt upon by those -who have commented on the _Novum Organon_. Yet, in reality, such a -classification, as has been observed by one of the ablest writers of -the present day[183], is of little service in the task of induction. -For the instances are, for the most part, classed, not according to -the ideas which they involve, or to any obvious circumstance in the -facts of which they consist, but according to the extent or manner of -their influence upon the inquiry in which they are employed. Thus we -have Solitary Instances, Migrating Instances, Ostensive Instances, -Clandestine Instances, so termed according to the degree in which -they exhibit, or seem to exhibit, the property whose nature we would -examine. We have Guide-Post Instances, (_Instantiæ Crucis_,) Instances -of the Parted Road, of the Doorway, of the Lamp, according to the -guidance they supply to our advance. Such a classification is much of -the same nature as if, having to teach the art of building, we were to -describe tools with reference to the amount and place of the work which -they must do, instead of pointing out their construction and use:--as -if we were to inform the pupil that we must have tools for lifting a -stone up, tools for moving it sideways, tools for laying it square, -tools for cementing it firmly. Such an enumeration of ends would convey -little instruction as to the means. Moreover, many of Bacon's classes -of instances are vitiated by the assumption that the "form," that is, -the general law and cause of the property which is the subject of -investigation, is to be looked for directly in the instances; which, as -we have seen in his inquiry concerning heat, is a fundamental error. - - -19. Yet his phraseology in some cases, as in the _instantia crucis_, -serves well to mark the place which certain experiments hold in our -reasonings: and many of the special examples which he gives are full -of acuteness and sagacity. Thus he suggests swinging a pendulum in a -mine, in order to determine whether the attraction of the earth arises -from the attraction of its parts; and observing the tide at the same -moment in different parts of the world, in order to ascertain whether -the motion of the water is expansive or progressive; with other -ingenious proposals. These marks of genius may serve to counterbalance -the unfavourable judgment of Bacon's aptitude for physical science -which we are sometimes tempted to form, in consequence of his false -views on other points; as his rejection of the Copernican system, and -his undervaluing Gilbert's magnetical speculations. Most of these -errors arose from a too ambitious habit of intellect, which would not -be contented with any except very wide and general truths; and from an -indistinctness of mechanical, and perhaps, in general, of mathematical -ideas:--defects which Bacon's own philosophy was directed to remedy, -and which, in the progress of time, it has remedied in others. - - -(VIII.) 20. _His Idols._--Having thus freely given our judgment -concerning the most exact and definite portion of Bacon's precepts, -it cannot be necessary for us to discuss at any length the value -of those more vague and general _Warnings_ against prejudice and -partiality, against intellectual indolence and presumption, with which -his works abound. His advice and exhortations of this kind are always -expressed with energy and point, often clothed in the happiest forms -of imagery; and hence it has come to pass, that such passages are -perhaps more familiar to the general reader than any other part of -his writings. Nor are Bacon's counsels without their importance, when -we have to do with those subjects in which prejudice and partiality -exercise their peculiar sway. Questions of politics and morals, -of manners, taste, or history, cannot be subjected to a scheme of -rigorous induction; and though on such matters we venture to assert -general principles, these are commonly obtained with some degree of -insecurity, and depend upon special habits of thought, not upon mere -logical connexion. Here, therefore, the intellect may be perverted, -by mixing, with the pure reason, our gregarious affections, or our -individual propensities; the false suggestions involved in language, -or the imposing delusions of received theories. In these dim and -complex labyrinths of human thought, _the Idol of the Tribe_, or _of -the Den_, _of the Forum_, or _of the Theatre_, may occupy men's minds -with delusive shapes, and may obscure or pervert their vision of truth. -But in that Natural Philosophy with which we are here concerned, there -is little opportunity for such influences. As far as a physical theory -is completed through all the steps of a just induction, there is a -clear daylight diffused over it which leaves no lurking-place for -prejudice. Each part can be examined separately and repeatedly; and -the theory is not to be deemed perfect till it will bear the scrutiny -of all sound minds alike. Although, therefore, Bacon, by warning men -against the idols of fallacious images above spoken of, may have -guarded them from dangerous error, his precepts have little to do with -Natural Philosophy: and we cannot agree with him when he says[184], -that the doctrine concerning these idols bears the same relation to -the interpretation of nature as the doctrine concerning sophistical -paralogisms bears to common logic. - - -(IX.) 21. _His Aim, Utility._--There is one very prominent feature in -Bacon's speculations which we must not omit to notice; it is a leading -and constant object with him to apply his knowledge to _Use_. The -insight which he obtains into nature, he would employ in commanding -nature for the service of man. He wishes to have not only principles -but works. The phrase which best describes the aim of his philosophy is -his own[185], "Ascendendo ad _axiomata_, descendendo ad _opera_." This -disposition appears in the first aphorism of the _Novum Organon_, and -runs through the work. "Man, the _minister_ and interpreter of nature, -_does_ and understands, so far as he has, in fact or in thought, -observed the course of nature; and he cannot know or _do_ more than -this." It is not necessary for us to dwell much upon this turn of mind; -for the whole of our present inquiry goes upon the supposition that an -acquaintance with the laws of nature is worth our having for its own -sake. It may be universally true, that Knowledge is Power; but we have -to do with it not as Power, but as Knowledge. It is the formation of -Science, not of Art, with which we are here concerned. It may give a -peculiar interest to the history of science, to show how it constantly -tends to provide better and better for the wants and comforts of the -body; but _that_ is not the interest which engages us in our present -inquiry into the nature and course of philosophy. The consideration -of the means which promote man's material well-being often appears to -be invested with a kind of dignity, by the discovery of general laws -which it involves; and the satisfaction which rises in our minds at -the contemplation of such cases, men sometimes ascribe, with a false -ingenuity, to the love of mere bodily enjoyment. But it is never -difficult to see that this baser and coarser element is not the real -source of our admiration. Those who hold that it is the main business -of science to construct instruments for the uses of life, appear -sometimes to be willing to accept the consequence which follows from -such a doctrine, that the first shoemaker was a philosopher worthy of -the highest admiration[186]. But those who maintain such paradoxes, -often, by a happy inconsistency, make it their own aim, not to devise -some improved covering for the feet, but to delight the mind with acute -speculations, exhibited in all the graces of wit and fancy. - -It has been said[187] that the key of the Baconian doctrine consists in -two words, Utility and Progress. With regard to the latter point, we -have already seen that the hope and prospect of a boundless progress in -human knowledge had sprung up in men's minds, even in the early times -of imperial Rome; and were most emphatically expressed by that very -Seneca who disdained to reckon the worth of knowledge by its value in -food and clothing. And when we say that Utility was the great business -of Bacon's philosophy, we forget one-half of his characteristic phrase: -"Ascendendo ad aximomata," no less than "descendendo ad opera," was, -he repeatedly declared, the scheme of his path. He constantly spoke, -we are told by his secretary[188], of two kinds of experiments, -_experimenta fructifera_, and _experimenta lucifera_. - -Again; when we are told by modern writers that Bacon merely recommended -such induction as all men instinctively practise, we ought to recollect -his own earnest and incessant declarations to the contrary. The -induction hitherto practised is, he says, of no use for obtaining solid -science. There are two ways[189], "hæc via in usu est," "altera vera, -sed intentata." Men have constantly been employed in _anticipation_; -in illicit induction. The intellect left to itself rushes on in this -road[190]; the conclusions so obtained are persuasive[191]; far more -persuasive than inductions made with due caution[192]. But still this -method must be rejected if we would obtain true knowledge. We shall -then at length have ground of good hope for science when we proceed -in another manner[193]. We must rise, not by a leap, but by small -steps, by successive advances, by a gradation of ascents, trying our -facts, and clearing our notions at every interval. The scheme of true -philosophy, according to Bacon, is not obvious and simple, but long and -technical, requiring constant care and self-denial to follow it. And we -have seen that, in this opinion, his judgment is confirmed by the past -history and present condition of science. - -Again; it is by no means a just view of Bacon's character to place -him in contrast to Plato. Plato's philosophy was the philosophy of -Ideas; but it was not left for Bacon to set up the philosophy of -Facts in opposition to that of Ideas. That had been done fully by the -speculative reformers of the sixteenth century. Bacon had the merit of -showing that Facts and Ideas must be combined; and not only so, but of -divining many of the special rules and forms of this combination, when -as yet there were no examples of them, with a sagacity hitherto quite -unparalleled. - - -(X.) 22. _His Perseverance._--With Bacon's unhappy political life we -have here nothing to do. But we cannot but notice with pleasure how -faithfully, how perseveringly, how energetically he discharged his -great philosophical office of a Reformer of Methods. He had conceived -the purpose of making this his object at an early period. When -meditating the continuation of his _Novum Organon_, and speaking of -his reasons for trusting that his work will reach some completeness -of effect, he says[194], "I am by two arguments thus persuaded. -First, I think thus from the zeal and constancy of my mind, which has -not waxed old in this design, nor, after so many years, grown cold -and indifferent; I remember that about forty years ago I composed -a juvenile work about these things, which with great contrivance -and a pompous title I called _temporis partum maximum_, or the most -considerable birth of time; Next, that on account of its usefulness, -it may hope the Divine blessing." In stating the grounds of hope for -future progress in the sciences, he says[195]: "Some hope may, we -conceive, be ministered to men by our own example: and this we say, not -for the sake of boasting, but because it is useful to be said. If any -despond, let them look at me, a man among all others of my age most -occupied with civil affairs, nor of very sound health, (which brings a -great loss of time;) also in this attempt the first explorer, following -the footsteps of no man, nor communicating on these subjects with any -mortal; yet, having steadily entered upon the true road and made my -mind submit to things themselves, one who has, in this undertaking, -made, (as we think,) some progress." He then proceeds to speak of what -may be done by the combined and more prosperous labours of others, -in that strain of noble hope and confidence, which rises again and -again, like a chorus, at intervals in every part of his writings. In -the _Advancement of Learning_ he had said, "I could not be true and -constant to the argument I handle, if I were not willing to go beyond -others, but yet not more willing than to have others go beyond me -again." In the Preface to the _Instauratio Magna_, he had placed among -his postulates those expressions which have more than once warmed the -breast of a philosophical reformer[196]. "Concerning ourselves we -speak not; but as touching the matter which we have in hand, this we -ask;--that men be of good hope, neither feign and imagine to themselves -this our Reform as something of infinite dimension and beyond the grasp -of mortal man, when in truth it is the end and true limit of infinite -error; and is by no means unmindful of the condition of mortality and -humanity, not confiding that such a thing can be carried to its perfect -close in the space of a single age, but assigning it as a task to a -succession of generations." In a later portion of the _Instauratio_ he -says: "We bear the strongest love to the _human republic_ our common -country; and we by no means abandon the hope that there will arise and -come forth some man among posterity, who will be able to receive and -digest all that is best in what we deliver; and whose care it will be -to cultivate and perfect such things. Therefore, by the blessing of the -Deity, to tend to this object, to open up the fountains, to discover -the useful, to gather guidance for the way, shall be our task; and from -this we shall never, while we remain in life, desist." - - -(XI.) 23. _His Piety._--We may add, that the spirit of piety as well as -of hope which is seen in this passage, appears to have been habitual -to Bacon at all periods of his life. We find in his works several -drafts of portions of his great scheme, and several of them begin with -a prayer. One of these entitled, in the edition of his works, "The -Student's Prayer," appears to me to belong probably to his early youth. -Another, entitled "The Writer's Prayer," is inserted at the end of -the Preface of the _Instauratio_, as it was finally published. I will -conclude my notice of this wonderful man by inserting here these two -prayers. - -"To God the Father, God the Word, God the Spirit, we pour forth most -humble and hearty supplications; that he, remembering the calamities -of mankind, and the pilgrimage of this our life, in which we wear out -days few and evil, would please to open to us new refreshments out of -the fountains of his goodness for the alleviating of our miseries. -This also we humbly and earnestly beg, that human things may not -prejudice such as are divine; neither that, from the unlocking of the -gates of sense, and the kindling of a greater natural light, anything -of incredulity, or intellectual night, may arise in our minds towards -divine mysteries. But rather, that by our mind thoroughly cleansed and -purged from fancy and vanities, and yet subject and perfectly given up -to the Divine oracles, there may be given unto faith the things that -are faith's." - -"Thou, O Father, who gavest the visible light as the first-born of -thy creatures, and didst pour into man the intellectual light as the -top and consummation of thy workmanship, be pleased to protect and -govern this work, which coming from thy goodness, returneth to thy -glory. Thou, after thou hadst reviewed the works which thy hands had -made, beheldest that everything was very good, and thou didst rest -with complacency in them. But man, reflecting on the works which he -had made, saw that all was vanity and vexation of spirit, and could by -no means acquiesce in them. Wherefore, if we labour in thy works with -the sweat of our brows, thou wilt make us partakers of thy vision and -thy Sabbath. We humbly beg that this mind may be steadfastly in us; -and that thou, by our hands, and also by the hands of others on whom -thou shalt bestow the same spirit, wilt please to convey a largess -of new alms to thy family of mankind. These things we commend to thy -everlasting love, by our Jesus, thy Christ, God with us. Amen." - - -FOOTNOTES: - -[Footnote 168: And in other passages: thus, "Ego enim buccinator tantum -pugnam non ineo." _Nov. Org._ lib. iv. c. i.] - -[Footnote 169: Lib. 1. Aphor. 78 _et seq._] - -[Footnote 170: _Aug. Sc._ Lib. iii. c. 4. p. 194. So in other places, -as _Nov. Org._ i. Aph. 104. "De scientiis tum demum bene sperandum est -quando per scalam veram et per gradus continuos, et non intermissos aut -hiulcos a particularibus ascendetur ad axiomata minora, et deinde ad -media, alia aliis superiora, et postremo demum ad generalissima."] - -[Footnote 171: _Nov. Org._ 1. Aph. 22.] - -[Footnote 172: _Ib._ Aph. 20.] - -[Footnote 173: 1 Ax. 15.] - -[Footnote 174: _Nov. Org._ lib. ii. Aph. 19.] - -[Footnote 175: _Inst. Mag._ par. iii. (vol. viii. p. 244).] - -[Footnote 176: _Hist. Ind. Sc._ b. x. c. i.] - -[Footnote 177: _Ib._ c. iv.] - -[Footnote 178: _Nov. Org._ lib. i. Aph. 61.] - -[Footnote 179: _Nov. Org._ lib. ii. Aph. 10.] - -[Footnote 180: Aph. 11.] - -[Footnote 181: Aph. 15, p. 105.] - -[Footnote 182: Page 110.] - -[Footnote 183: Herschel, _On the Study of Nat. Phil._ Art. 192.] - -[Footnote 184: _Nov. Org._ lib. i. Aph. 40.] - -[Footnote 185: _Nov. Org._ lib. i. Ax. 103.] - -[Footnote 186: _Edinb. Rev._ No. cxxxii. p. 65.] - -[Footnote 187: _Ib._] - -[Footnote 188: Pref. to the _Nat. Hist._ i. 243.] - -[Footnote 189: _Nov. Org._ lib. i. Aph. 19.] - -[Footnote 190: _Ibid._ lib. i. Aph. 20.] - -[Footnote 191: Aph. 27.] - -[Footnote 192: _Ib._ 28.] - -[Footnote 193: Aph. 104. So Aph. 105. "In constituendo axiomate forma -_inductionis_ alia quam adhuc in usu fuit excogitanda est," &c.] - -[Footnote 194: _Ep. ad P. Fulgentium._ _Op._ x. 330.] - -[Footnote 195: _Nov. Org._ i. Aph. 113.] - -[Footnote 196: See the motto to Kant's _Kritik der Reinen Vernunft_.] - - - - -CHAPTER XVI. - -ADDITIONAL REMARKS ON FRANCIS BACON. - - -Francis Bacon and his works have recently been discussed and examined -by various writers in France and Germany as well as England[197]. Not -to mention smaller essays, M. Bouillet has published a valuable edition -of his philosophical works; Count Joseph de Maistre wrote a severe -critique of his philosophy, which has been published since the death of -the author; M. Charles Remusat has written a lucid and discriminating -Essay on the subject; and in England we have had a new edition of the -works published, with a careful and thoughtful examination of the -philosophy which they contain, written by one of the editors: a person -especially fitted for such an examination by an acute intellect, great -acquaintance with philosophical literature, and a wide knowledge of -modern science. Robert Leslie Ellis, the editor of whom I speak, died -during the publication of the edition, and before he had done full -justice to his powers; but he had already written various dissertations -on Bacon's philosophy, which accompany the different Treatises in the -new edition. - -Mr. Ellis has given a more precise view than any of his predecessors -had done of the nature of Bacon's induction and of his philosophy of -discovery. Bacon's object was to discover the 'natures' or essences -of things, in order that he might reproduce these natures or essences -at will; he conceived that these natures were limited in number, and -manifested in various combinations in the bodies which exist in the -universe; so that by accumulating observations of them in a multitude -of cases, we may learn by induction in what they do and in what -they do not consist; the _Induction_ which is to be used for this -purpose consists in a great measure of _excluding_ the cases which -do not exhibit the 'nature' in question; and by such exclusion, duly -repeated, we have at last left in our hands the elements of which the -proposed nature consists. And the knowledge which is thus obtained may -be applied to reproduce the things so analysed. As exhibiting this -view clearly we may take a passage in the _Sylva Sylvarum_: "Gold has -these natures: greatness of weight, closeness of parts, fixation, -pliantness or softness, immunity from rust, colour or tincture of -yellow. Therefore the sure way, though most about, to make gold, is to -know the causes of the several natures before rehearsed, and the axioms -concerning the same. For if a man can make a metal, that hath all these -properties, let men dispute whether it be gold or no." He means that -however they dispute, it is gold for all practical purposes. - -For such an Induction as this, Bacon claims the merit both of -being certain, and of being nearly independent of the ingenuity of -the inquirer. It is a method which enables all men to make exact -discoveries, as a pair of compasses enables all men to draw an exact -circle. - -Now it is necessary for us, who are exploring the progress of the true -philosophy of discovery, to say plainly that this part of Bacon's -speculation is erroneous and valueless. No scientific discovery ever -has been made in this way. Men have not obtained truths concerning -the natural world by seeking for the natures of things, and by -extracting them from phenomena by rejecting the cases in which they -were not. On the contrary, they have begun by ascertaining the _laws -of the phenomena_; and have then gone on, not by a mechanical method -which levels all intellect, but by special efforts of the brightest -intellects to catch hold of the ideas by which these laws of phenomena -might be interpreted and expressed in more general terms. These two -steps, the finding the laws of phenomena, and finding the conceptions -by which those laws can be expressed, are really the course of -discovery, as the history of science exhibits it to us. - -Bacon, therefore, according to the view now presented, was wrong both -as to his object and as to his method. He was wrong in taking for his -object the essences of things,--the causes of abstract properties: -for these man cannot, or can very rarely discover; and all Bacon's -ingenuity in enumerating and classifying these essences and abstract -properties has led, and could lead, to no result. The vast results -of modern science have been obtained, not by seeking and finding the -essences of things, but by exploring the laws of phenomena and the -causes of those laws. - -And Bacon's method, as well as his object, is vitiated by a pervading -error:--the error of supposing that to be done by method which must -be done by mind;--that to be done by rule which must be done by a -flight beyond rule;--that to be mainly negative which is eminently -positive;--that to depend on other men which must depend on the -discoverer himself;--that to be mere prose which must have a dash of -poetry;--that to be a work of mere labour which must be also a work of -genius. - -Mr. Ellis has seen very clearly and explained very candidly that this -method thus recommended by Bacon has not led to discovery. "It is," he -says, "neither to the technical part of his method nor to the details -of his view of the nature and progress of science, that his great fame -is justly owing. His merits are of another kind. They belong to the -spirit rather than to the positive precepts of his philosophy." - -As the reader of the last chapter will see, this amounts to much the -same as the account which I had given of the positive results of -Bacon's method, and the real value of that portion of his philosophy -which he himself valued most. But still there remain, as I have also -noted, portions of Bacon's speculations which have a great and enduring -value, namely, his doctrine that Science is the Interpretation of -Nature, his distinction of this Interpretation of Nature from the -vicious and premature Anticipation of Nature which had generally -prevailed till then; and the recommendation of a graduated and -successive induction by which alone the highest and most general -truths were to be reached. These are points which he urges with great -clearness and with great earnestness; and these are important points in -the true philosophy of discovery. - -I may add that Mr. Ellis agrees with me in noting the invention of -the conception by which the laws of phenomena are interpreted as -something additional to _Induction_, both in the common and in the -Baconian sense of the word. He says (General Preface, Art. 9), "In -all cases this process [scientific discovery] involves an element to -which nothing corresponds in the Tables of Comparence and Exclusion; -namely the application to the facts of a _principle_ of arrangement, -an _idea_, existing in the mind of the discoverer antecedently to the -act of induction." It may be said that this principle or idea is aimed -at in the Baconian analysis. "And this is in one sense true: but it -must be added, that this _analysis_, if it be thought right to call it -so, is of the essence of the discovery which results from it. To take -for granted that it has been already effected is simply a _petitio -principii_. In most cases the mere act of induction follows as a matter -of course as soon as the _appropriate idea_ has been introduced." And -as an example he takes Kepler's invention of the ellipse, as the idea -by which Mars's motions could be reduced to law; making the same use of -this example which we have repeatedly made of it. - -Mr. Ellis may at first sight appear to express himself more favourably -than I have done, with regard to the value of Bacon's _Inquisitio in -Naturam Calidi_ in the Second Book of the _Novum Organon_. He says of -one part of it[198]: "Bacon here anticipates not merely the essential -character of the most recent theory of heat, but also the kind of -evidence by which it has been established.... The merit of having -perceived the true significance of the production of heat by friction -belongs of right to Bacon." - -But notwithstanding this, Mr. Ellis's general judgment on this specimen -of Bacon's application of his own method does not differ essentially -from mine. He examines the _Inquisitio_ at some length, and finally -says: "If it were affirmed that Bacon, after having had a glimpse of -the truth suggested by some obvious phenomena, had then recourse, as he -himself expresses it, to certain 'differentiæ inanes' in order to save -the phenomena, I think it would be hard to dispute the truth of the -censure." - - -Another of the Editors of this edition (Mr. Spedding) fixes his -attention upon another of the features of the method of discovery -proposed by Bacon, and is disposed to think that the proposed method -has never yet had justice done it, because it has not been tried in the -way and on the scale that Bacon proposes[199]. Bacon recommended that -a great collection of facts should be at once made and accumulated, -regarding every branch of human knowledge; and conceived that, when -this had been done by common observers, philosophers might extract -scientific truths from this mass of facts by the application of a right -method. This separation of the offices of the observer and discoverer, -Mr. Spedding thinks is shown to be possible by such practical examples -as meteorological observations, made by ordinary observers, and -reduced to tables and laws by a central calculator; by hydrographical -observations made by ships provided with proper instructions, and -reduced to general laws by the man of science in his study; by -magnetical observations made by many persons in every part of the -world, and reduced into subservience to theory by mathematicians at -home. - -And to this our reply will be, in the terms which the history of -all the Sciences has taught us, that such methods of procedure as -this do not belong to the _Epoch of Discovery_, but to the Period of -_verification_ and _application_ of the discovery which follows. When a -theory has been established in its general form, our knowledge of the -distribution of its phenomena in time and space can be much promoted -by ordinary observers scattered over the earth, and succeeding each -other in time, provided they are furnished with instruments and methods -of observation, duly constructed on the principles of science; but -such observers cannot in any degree supersede the discoverer who is -first to establish the theory, and to introduce into the facts a new -principle of order. When the laws of nature have been caught sight -of, much may be done, even by ordinary observers, in verifying and -exactly determining them; but when a real discovery is to be made, -this separation of the observer and the theorist is not possible. In -those cases, the questioning temper, the busy suggestive mind, is -needed at every step, to direct the operating hand or the open gaze. -No possible accumulation of facts about mixture and heat, collected in -the way of blind trial, could have led to the doctrines of chemistry, -or crystallography, or the atomic theory, or voltaic and chemical -and magnetic polarity, or physiology, or any other science. Indeed -not only is an existing theory requisite to supply the observer with -instruments and methods, but without theory he cannot even describe his -observations. He says that he mixes an acid and an alkali; but what -is an acid? What is an alkali? How does he know them? He classifies -crystals according to their forms: but till he has learnt what is -distinctive in the form of a crystal, he cannot distinguish a cube -from a square prism, even if he had a goniometer and could use it. And -the like impossibility hangs over all the other subjects. To report -facts for scientific purposes without some aid from theory, is not only -useless, but impossible. - -When Mr. Spedding says, "I could wish that men of science would apply -themselves earnestly to the solution of this practical problem: -What measures are to be taken in order that the greatest variety of -judicious observations of nature all over the world may be carried on -in concert upon a common plan and brought to a common centre:"--he is -urging upon men of science to do what they have always done, so far -as they have had any power, and in proportion as the state of science -rendered such a procedure possible and profitable to science. In -Astronomy, it has been done from the times of the Greeks and even of -the Chaldeans, having been begun _as soon as_ the heavens were reduced -to law at all. In meteorology, it has been done extensively, though to -little purpose, because the weather has _not yet_ been reduced to rule. -Men of science have shown how barometers, thermometers, hygrometers, -and the like, may be constructed; and these may be now read by any one -as easily as a clock; but of ten thousand meteorological registers -thus kept by ordinary observers, what good has come to science? -Again: The laws of the tides have been in a great measure determined -by observations in all parts of the globe, _because_ theory pointed -out what was to be observed. In like manner the facts of terrestrial -magnetism were ascertained with tolerable completeness by extended -observations, _then_, and then only, when a most recondite and profound -branch of mathematics had pointed out what was to be observed, and most -ingenious instruments had been devised by men of science for observing. -And even with these, it requires an education to use the instruments. -But in many cases no education in the use of instruments devised by -others can supersede the necessity of a theoretical and suggestive -spirit in the inquirer himself. He must devise his own instruments -and his own methods, if he is to make any discovery. What chemist, or -inquirer about polarities, or about optical laws yet undiscovered, can -make any progress by using another man's experiments and observations? -He must invent at every step of his observation; and the observer and -theorist can no more be dissevered, than the body and soul of the -inquirer. - -That persons of moderate philosophical powers may, when duly -educated, make observations which may be used by greater discoverers -than themselves, is true. We have examples of such a subordination -of scientific offices in astronomy, in geology, and in many other -departments. But still, as I have said, a very considerable degree of -scientific education is needed even for the subordinate labourers in -science; and the more considerable in proportion as science advances -further and further; since every advance implies a knowledge of what -has already been done, and requires a new precision or generality in -the new points of inquiry. - - -FOOTNOTES: - -[Footnote 197: _Œuvres Philosophiques de Bacon, &c._ par M. N. -Bouillet, 3 Tomes. - -_Examen de la Philosophie de Bacon_ (_Œuvres Posthumes_ du Comte J. de -Maistre). - -_Bacon, sa Vie, son Temps, sa Philosophie_, par Charles de Remusat. - -_Histoire de la Vie et des Ouvrages de François Bacon_, par J. B. de -Vaugelles. - -_Franz Baco von Verulam_, von Kuno Fischer. - -_The Works of Francis Bacon_, collected and edited by James Spedding, -Robert Leslie Ellis, and Douglas Denon Heath.] - -[Footnote 198: Note to Aph. xviii.] - -[Footnote 199: Pref. to the _Parasceue_, Vol. i. p. 382.] - - - - -CHAPTER XVII. - -FROM BACON TO NEWTON. - - -1. _Harvey._--We have already seen that Bacon was by no means the -first mover or principal author of the revolution in the method of -philosophizing which took place in his time; but only the writer who -proclaimed in the most impressive and comprehensive manner, the scheme, -the profit, the dignity, and the prospects of the new philosophy. -Those, therefore, who after him, took up the same views are not to be -considered as his successors, but as his fellow-labourers; and the -line of historical succession of opinions must be pursued without -special reference to any one leading character, as the principal figure -of the epoch. I resume this line, by noticing a contemporary and -fellow-countryman of Bacon, Harvey, the discoverer of the circulation -of the blood. This discovery was not published and generally accepted -till near the end of Bacon's life; but the anatomist's reflections -on the method of pursuing science, though strongly marked with the -character of the revolution that was taking place, belong to a very -different school from the Chancellor's. Harvey was a pupil of Fabricius -of Acquapendente, whom we noticed among the practical reformers of the -sixteenth century. He entertained, like his master, a strong reverence -for the great names which had ruled in philosophy up to that time, -Aristotle and Galen; and was disposed rather to recommend his own -method by exhibiting it as the true interpretation of ancient wisdom, -than to boast of its novelty. It is true, that he assigns, as his -reason for publishing some of his researches[200], "that by revealing -the method I use in searching into things, I might propose to studious -men, a new and (if I mistake not) a surer path to the attainment of -knowledge[201];" but he soon proceeds to fortify himself with the -authority of Aristotle. In doing this, however, he has the very great -merit of giving a living and practical character to truths which exist -in the Aristotelian works, but which had hitherto been barren and empty -professions. We have seen that Aristotle had asserted the importance -of experience as one root of knowledge; and in this had been followed -by the schoolmen of the middle ages: but this assertion came with very -different force and effect from a man, the whole of whose life had been -spent in obtaining, by means of experience, knowledge which no man had -possessed before. In Harvey's general reflections, the necessity of -both the elements of knowledge, sensations and ideas, experience and -reason, is fully brought into view, and rightly connected with the -metaphysics of Aristotle. He puts the antithesis of these two elements -with great clearness. "Universals are chiefly known to us, for science -is begot by reasoning from universals to particulars; yet that very -comprehension of universals in the understanding springs from the -perception of singulars in our sense." Again, he quotes Aristotle's -apparently opposite assertions:--that made in his _Physics_[202], -"that we must advance from things which are first known to us, though -confusedly, to things more distinctly intelligible in themselves; -from the whole to the part; from the universal to the particular;" -and that made in the _Analytics_[203]; that "Singulars are more known -to us and do first exist according to sense: for nothing is in the -understanding which was not before in the sense." Both, he says, are -true, though at first they seem to clash: for "though in knowledge -we begin with sense, sensation itself is a universal thing." This he -further illustrates; and quotes Seneca, who says, that "Art itself is -nothing but the _reason_ of the work, implanted in the Artist's mind:" -and adds, "the same way by which we gain an Art, by the very same way -we attain any kind of science or knowledge whatever; for as Art is -a habit whose object is something to be done, so Science is a habit -whose object is something to be known; and as the former proceedeth -from the imitation of examples, so this latter, from the knowledge of -things natural. The source of both is from sense and experience; since -[but?] it is impossible that Art should be rightly purchased by the one -or Science by the other without a direction from ideas." Without here -dwelling on the relation of Art and Science, (very justly stated by -Harvey, except that ideas exist in a very different form in the mind -of the Artist and the Scientist) it will be seen that this doctrine, -of science springing from experience with a direction from ideas, is -exactly that which we have repeatedly urged, as the true view of the -subject. From this view, Harvey proceeds to infer the importance of a -reference to sense in his own subject, not only for first discovering, -but for receiving knowledge: "Without experience, not other men's but -our own, no man is a proper disciple of any part of natural knowledge; -without experimental skill in anatomy, he will no better apprehend -what I shall deliver concerning generation, than a man born blind can -judge of the nature and difference of colours, or one born deaf, of -sounds." "If we do otherwise, we may get a humid and floating opinion, -but never a solid and infallible knowledge: as is happenable to those -who see foreign countries only in maps, and the bowels of men falsely -described in anatomical tables. And hence it comes about, that in this -rank age, we have many sophisters and bookwrights, but few wise men -and philosophers." He had before declared "how unsafe and degenerate a -thing it is, to be tutored by other men's commentaries, without making -trial of the things themselves; especially since Nature's book is so -open and legible." We are here reminded of Galileo's condemnation -of the "paper philosophers." The train of thought thus expressed by -the practical discoverers, spread rapidly with the spread of the -new knowledge that had suggested it, and soon became general and -unquestioned. - - -2. _Descartes._--Such opinions are now among the most familiar and -popular of those which are current among writers and speakers; but -we should err much if we were to imagine that after they were once -propounded they were never resisted or contradicted. Indeed, even in -our own time, not only are such maxims very often practically neglected -or forgotten, but the opposite opinions, and views of science quite -inconsistent with those we have been explaining, are often promulgated -and widely accepted. The philosophy of pure ideas has its commonplaces, -as well as the philosophy of experience. And at the time of which -we speak, the former philosophy, no less than the latter, had its -great asserter and expounder; a man in his own time more admired than -Bacon, regarded with more deference by a large body of disciples all -over Europe, and more powerful in stirring up men's minds to a new -activity of inquiry. I speak of Descartes, whose labours, considered -as a philosophical system, were an endeavour to revive the method -of obtaining knowledge by reasoning from our own ideas only, and to -erect it in opposition to the method of observation and experiment. -The Cartesian philosophy contained an attempt at a counter-revolution. -Thus in this author's _Principia Philosophiæ_[204], he says that "he -will give a short account of the principal phenomena of the world, -not that he may use them as reasons to prove anything; for," adds he, -"we desire to deduce effects from causes, not causes from effects; -but only in order that out of the innumerable effects which we learn -to be capable of resulting from the same causes, we may determine our -mind to consider some rather than others." He had before said, "The -principles which we have obtained [by pure _à priori_ reasoning] are so -vast and so fruitful, that many more consequences follow from them than -we see contained in this visible world, and even many more than our -mind can ever take a full survey of." And he professes to apply this -method in detail. Thus in attempting to state the three fundamental -laws of motion, he employs only _à priori_ reasonings, and is in fact -led into error in the third law which he thus obtains[205]. And in -his _Dioptrics_[206] he pretends to deduce the laws of reflection -and refraction of light from certain comparisons (which are, in -truth, arbitrary,) in which the radiation of light is represented -by the motion of a ball impinging upon the reflecting or refracting -body. It might be represented as a curious instance of the caprice -of fortune, which appears in scientific as in other history, that -Kepler, professing to derive all his knowledge from experience, and -exerting himself with the greatest energy and perseverance, failed in -detecting the law of refraction; while Descartes, who professed to be -able to despise experiment, obtained the true law of sines. But as we -have stated in the _History_[207], Descartes appears to have learnt -this law from Snell's papers. And whether this be so or not, it is -certain that notwithstanding the profession of independence which his -philosophy made, it was in reality constantly guided and instructed by -experience. Thus in explaining the Rainbow (in which his portion of -the discovery merits great praise) he speaks[208] of taking a globe -of glass, allowing the sun to shine on one side of it, and noting the -colours produced by rays after two refractions and one reflection. -And in many other instances, indeed in all that relates to physics, -the reasonings and explanations of Descartes and his followers were, -consciously or unconsciously, directed by the known facts, which they -had observed themselves or learnt from others. - -But since Descartes thus, speculatively at least, set himself in -opposition to the great reform of scientific method which was going -on in his time, how, it may be asked, did he acquire so strong an -influence over the most active minds of his time? How is it that he -became the founder of a large and distinguished school of philosophers? -How is it that he not only was mainly instrumental in deposing -Aristotle from his intellectual throne, but for a time appeared to have -established himself with almost equal powers, and to have rendered the -Cartesian school as firm a body as the Peripatetic had been? - -The causes to be assigned for this remarkable result are, I conceive, -the following. In the first place, the physicists of the Cartesian -school did, as I have just stated, found their philosophy upon -experiment, and did not practically, or indeed, most of them, -theoretically, assent to their master's boast of showing what the -phenomena _must be_, instead of looking to see what they _are_. And -as Descartes had really incorporated in his philosophy all the chief -physical discoveries of his own and preceding times, and had delivered, -in a more general and systematic shape than any one before him, the -principles which he thus established, the physical philosophy of his -school was in reality far the best then current; and was an immense -improvement upon the Aristotelian doctrines, which had not yet been -displaced as a system. Another circumstance which gained him much -favour, was the bold and ostentatious manner in which he professed -to begin his philosophy by liberating himself from all preconceived -prejudice. The first sentence of his philosophy contains this -celebrated declaration: "Since," he says, "we begin life as infants, -and have contracted various judgments concerning sensible things before -we possess the entire use of our reason, we are turned aside from the -knowledge of truth by many prejudices: from which it does not appear -that we can be any otherwise delivered, than if once in our life we -make it our business to doubt of everything in which we discern the -smallest suspicion of uncertainty." In the face of this sweeping -rejection or unhesitating scrutiny of all preconceived opinions, -the power of the ancient authorities and masters in philosophy must -obviously shrink away; and thus Descartes came to be considered as -the great hero of the overthrow of the Aristotelian dogmatism. But -in addition to these causes, and perhaps more powerful than all in -procuring the assent of men to his doctrines, came the deductive and -systematic character of his philosophy. For although all knowledge of -the external world is in reality only to be obtained from observation, -by inductive steps,--minute, perhaps, and slow, and many, as Galileo -and Bacon had already taught;--the human mind conforms to these -conditions reluctantly and unsteadily, and is ever ready to rush to -general principles, and then to employ itself in deducing conclusions -from these by synthetical reasonings; a task grateful, from the -distinctness and certainty of the result, and the accompanying feeling -of our own sufficiency. Hence men readily overlooked the precarious -character of Descartes' fundamental assumptions, in their admiration -of the skill with which a varied and complex Universe was evolved out -of them. And the complete and systematic character of this philosophy -attracted men no less than its logical connexion. I may quote here -what a philosopher[209] of our own time has said of another writer: -"He owed his influence to various causes; at the head of which may be -placed that genius for system which, though it cramps the growth of -knowledge, perhaps finally atones for that mischief by the zeal and -activity which it rouses among followers and opponents, who discover -truth by accident when in pursuit of weapons for their warfare. A -system which attempts a task so hard as that of subjecting vast -provinces of human knowledge to one or two principles, if it presents -some striking instances of conformity to superficial appearances, is -sure to delight the framer; and for a time to subdue and captivate the -student too entirely for sober reflection and rigorous examination. In -the first instance consistency passes for truth. When principles in -some instances have proved sufficient to give an unexpected explanation -of facts, the delighted reader is content to accept as true all other -deductions from the principles. Specious premises being assumed to be -true, nothing more can be required than logical inference. Mathematical -forms pass current as the equivalent of mathematical certainty. The -unwary admirer is satisfied with the completeness and symmetry of the -plan of his house, unmindful of the need of examining the firmness of -the foundation and the soundness of the materials. The system-maker, -like the conqueror, long dazzles and overawes the world; but when their -sway is past, the vulgar herd, unable to measure their astonishing -faculties, take revenge by trampling on fallen greatness." Bacon -showed his wisdom in his reflections on this subject, when he said -that "Method, carrying a show of total and perfect knowledge, hath a -tendency to generate acquiescence." - -The main value of Descartes' physical doctrines consisted in their -being arrived at in a way inconsistent with his own professed method, -namely, by a reference to observation. But though he did in reality -begin from facts, his system was nevertheless a glaring example -of that error which Bacon had called _Anticipation_; that illicit -generalization which leaps at once from special facts to principles -of the widest and remotest kind; such, for instance, as the Cartesian -doctrine, that the world is an absolute _plenum_, every part being -full of matter of some kind, and that all natural effects depend on -the laws of motion. Against this fault, to which the human mind is -so prone, Bacon had lifted his warning voice in vain, so far as the -Cartesians were concerned; as indeed, to this day, one theorist after -another pursues his course, and turns a deaf ear to the Verulamian -injunctions; perhaps even complacently boasts that he founds his theory -upon observation; and forgets that there are, as the aphorism of the -_Novum Organon_ declares, two ways by which this may be done;--the one -hitherto in use and suggested by our common tendencies, but barren and -worthless; the other almost untried, to be pursued only with effort and -self-denial, but alone capable of producing true knowledge. - - -3. _Gassendi._--Thus the lessons which Bacon taught were far from being -generally accepted and applied at first. The amount of the influence of -these two men, Bacon and Descartes, upon their age, has often been a -subject of discussion. The fortunes of the Cartesian school have been -in some measure traced in the History of Science. But I may mention the -notice taken of these two philosophers by Gassendi, a contemporary and -countryman of Descartes. Gassendi, as I have elsewhere stated[210], -was associated with Descartes in public opinion, as an opponent of the -Aristotelian dogmatism; but was not in fact a follower or profound -admirer of that writer. In a Treatise on Logic, Gassendi gives an -account of the Logic of various sects and authors; treating, in order, -of the Logic of Zeno (the Eleatic), of Euclid (the Megarean), of -Plato, of Aristotle, of the Stoics, of Epicurus, of Lullius, of Ramus; -and to these he adds the Logic of Verulam, and the Logic of Cartesius. -"We must not," he says, "on account of the celebrity it has obtained, -pass over the Organon or Logic of Francis Bacon Lord Verulam, High -Chancellor of England, whose noble purpose in our time it has been, to -make an Instauration of the Sciences." He then gives a brief account -of the _Novum Organon_, noticing the principal features in its rules, -and especially the distinction between the vulgar induction which leaps -at once from particular experiments to the more general axioms, and -the chastised and gradual induction, which the author of the _Organon_ -recommends. In his account of the Cartesian Logic, he justly observes, -that "He too imitated Verulam in this, that being about to build up a -new philosophy from the foundation, he wished in the first place to lay -aside all prejudice: and having then found some solid principle, to -make that the groundwork of his whole structure. But he proceeds by a -very different path from that which Verulam follows; for while Verulam -seeks aid from things, to perfect the cogitation of the intellect, -Cartesius conceives, that when we have laid aside all knowledge of -things, there is, in our thoughts alone, such a resource, that the -intellect may by its own power arrive at a perfect knowledge of all, -even the most abstruse things." - -The writings of Descartes have been most admired, and his method -most commended, by those authors who have employed themselves upon -metaphysical rather than physical subjects of inquiry. Perhaps we might -say that, in reference to such subjects, this method is not so vicious -as at first, when contrasted with the Baconian induction, it seems to -be: for it might be urged that the _thoughts_ from which Descartes -begins his reasonings are, in reality, _experiments_ of the kind which -the subject requires us to consider: each such thought is a fact in -the intellectual world; and of such facts, the metaphysician seeks to -discover the laws. I shall not here examine the validity of this plea; -but shall turn to the consideration of the actual progress of physical -science, and its effect on men's minds. - - -4. _Actual progress in Science._--The practical discoverers were indeed -very active and very successful during the seventeenth century, which -opened with Bacon's survey and exhortations. The laws of nature, of -which men had begun to obtain a glimpse in the preceding century, were -investigated with zeal and sagacity, and the consequence was that the -foundations of most of the modern physical sciences were laid. That -mode of research by experiment and observation, which had, a little -time ago, been a strange, and to many, an unwelcome innovation, was now -become the habitual course of philosophers. The revolution from the -philosophy of tradition to the philosophy of experience was completed. -The great discoveries of Kepler belonged to the preceding century. -They are not, I believe, noticed, either by Bacon or by Descartes; but -they gave a strong impulse to astronomical and mechanical speculators, -by showing the necessity of a sound science of motion. Such a science -Galileo had already begun to construct. At the time of which I speak, -his disciples[211] were still labouring at this task, and at other -problems which rapidly suggested themselves. They had already convinced -themselves that air had weight; in 1643 Torricelli proved this -practically by the invention of the Barometer; in 1647 Pascal proved -it still further by sending the Barometer to the top of a mountain. -Pascal and Boyle brought into clear view the fundamental laws of fluid -equilibrium; Boyle and Mariotte determined the law of the compression -of air as regulated by its elasticity. Otto Guericke invented the -air-pump, and by his "Madgeburg Experiments" on a vacuum, illustrated -still further the effects of the air. Guericke pursued what Gilbert -had begun, the observation of electrical phenomena; and these two -physicists made an important step, by detecting repulsion as well as -attraction in these phenomena. Gilbert had already laid the foundations -of the science of Magnetism. The law of refraction, at which Kepler -had laboured in vain, was, as we have seen, discovered by Snell (about -1621), and published by Descartes. Mersenne had discovered some of -the more important parts of the theory of Harmonics. In sciences of -a different kind, the same movement was visible. Chemical doctrines -tended to assume a proper degree of generality, when Sylvius in 1679 -taught the opposition of acid and alkali, and Stahl, soon after, -the phlogistic theory of combustion. Steno had remarked the most -important law of crystallography in 1669, that the angles of the same -kind of crystals are always equal. In the sciences of classification, -about 1680, Ray and Morison in England resumed the attempt to form a -systematic botany, which had been interrupted for a hundred years, from -the time of the memorable essay of Cæsalpinus. The grand discovery of -the circulation of the blood by Harvey about 1619, was followed in 1651 -by Pecquet's discovery of the course of the chyle. There could now no -longer be any question whether science was progressive, or whether -observation could lead to new truths. - -Among these cultivators of science, such sentiments as have been -already quoted became very familiar;--that knowledge is to be sought -from nature herself by observation and experiment;--that in such -matters tradition is of no force when opposed to experience, and that -mere reasonings without facts cannot lead to solid knowledge. But I -do not know that we find in these writers any more special rules of -induction and scientific research which have since been confirmed -and universally adopted. Perhaps too, as was natural in so great a -revolution, the writers of this time, especially the second-rate -ones, were somewhat too prone to disparage the labours and talents -of Aristotle and the ancients in general, and to overlook the ideal -element of our knowledge, in their zealous study of phenomena. They -urged, sometimes in an exaggerated manner, the superiority of modern -times in all that regards science, and the supreme and sole importance -of facts in scientific investigations. There prevailed among them also -a lofty and dignified tone of speaking of the condition and prospects -of science, such as we are accustomed to admire in the Verulamian -writings; for this, in a less degree, is epidemic among those who a -little after his time speak of the new philosophy. - - -5. _Otto Guericke, &c._--I need not illustrate these characteristics -at any great length. I may as an example notice Otto Guericke's -Preface to his _Experimenta Magdeburgica_ (1670). He quotes a passage -from Kircher's Treatise on the Magnetic Art, in which the author -says, "Hence it appears how all philosophy, except it be supported by -experiments, is empty, fallacious, and useless; what monstrosities -philosophers, in other respects of the highest and subtlest genius, -may produce in philosophy by neglecting experiment. Thus Experience -alone is the Dissolver of Doubts, the Reconciler of Difficulties, the -sole Mistress of Truth, who holds a torch before us in obscurity, -unties our knots, teaches us the true causes of things." Guericke -himself reiterates the same remark, adding that "philosophers, -insisting upon their own thoughts and arguments merely, cannot come -to any sound conclusion respecting the natural constitution of the -world." Nor were the Cartesians slow in taking up the same train of -reflection. Thus Gilbert Clark who, in 1660, published[212] a defence -of Descartes' doctrine of a _plenum_ in the universe, speaks in a -tone which reminds us of Bacon, and indeed was very probably caught -from him: "Natural philosophy formerly consisted entirely of loose -and most doubtful controversies, carried on in high-sounding words, -fit rather to delude than to instruct men. But at last (by the favour -of the Deity) there shone forth some more divine intellects, who -taking as their counsellors reason and experience together, exhibited -a new method of philosophizing. Hence has been conceived a strong hope -that philosophers may embrace, not a shadow or empty image of Truth, -but Truth herself: and that Physiology (Physics) scattering these -controversies to the winds, will contract an alliance with Mathematics. -Yet this is hardly the work of one age; still less of one man. Yet let -not the mind despond, or doubt not that, one party of investigators -after another following the same method of philosophizing, at last, -under good auguries, the mysteries of nature being daily unlocked as -far as human feebleness will allow, Truth may at last appear in full, -and these nuptial torches may be lighted." - -As another instance of the same kind, I may quote the preface to the -First volume of the Transactions of the Academy of Sciences at Paris: -"It is only since the present century," says the writer, "that we can -reckon the revival of Mathematics and Physics. M. Descartes and other -great men have laboured at this work with so much success, that in this -department of literature, the whole face of things has been changed. -Men have quitted a sterile system of physics, which for several -generations had been always at the same point; the reign of words -and terms is passed; men will have things; they establish principles -which they understand, they follow those principles; and thus they -make progress. Authority has ceased to have more weight than Reason: -that which was received without contradiction because it had been -long received, is now examined, and often rejected: and philosophers -have made it their business to consult, respecting natural things, -Nature herself rather than the Ancients." These had now become the -commonplaces of those who spoke concerning the course and method of the -Sciences. - - -6. _Hooke._--In England, as might be expected, the influence of -Francis Bacon was more directly visible. We find many writers, about -this time, repeating the truths which Bacon had proclaimed, and in -almost every case showing the same imperfections in their views -which we have noticed in him. We may take as an example of this -Hooke's Essay, entitled "A General Scheme or Idea of the present -state of Natural Philosophy, and how its defects may be remedied by -a Methodical proceeding in the making Experiments and collecting -Observations; whereby to compile a Natural History as a solid basis -for the superstructure of true Philosophy." This Essay may be looked -upon as an attempt to adapt the _Novum Organon_ to the age which -succeeded its publication. We have in this imitation, as in the -original, an enumeration of various mistakes and impediments which had -in preceding times prevented the progress of knowledge; exhortations -to experiment and observation as the only solid basis of Science; very -ingenious suggestions of trains of inquiry, and modes of pursuing them; -and a promise of obtaining scientific truths when facts have been -duly accumulated. This last part of his scheme the author calls _a -Philosophical Algebra_; and he appears to have imagined that it might -answer the purpose of finding unknown causes from known facts, by means -of certain regular processes, in the same manner as Common Algebra -finds unknown from known quantities. But this part of the plan appears -to have remained unexecuted. The suggestion of such a method was a -result of the Baconian notion that invention in a discoverer might be -dispensed with. We find Hooke adopting the phrases in which this notion -is implied: thus he speaks of the understanding as "being very prone to -run into the affirmative way of judging, and wanting patience to follow -and prosecute the negative way of inquiry, by rejection of disagreeing -natures." And he follows Bacon also in the error of attempting at -once to obtain from the facts the discovery of a "nature," instead of -investigating first the measures and the laws of phenomena. I return to -more general notices of the course of men's thoughts on this subject. - - -7. _Royal Society._--Those who associated themselves together for the -prosecution of science quoted Bacon as their leader, and exulted in the -progress made by the philosophy which proceeded upon his principles. -Thus in Oldenburg's Dedication of the Transactions of the Royal Society -of London for 1670, to Robert Boyle, he says; "I am informed by such as -well remember the best and worst days of the famous Lord Bacon, that -though he wrote his _Advancement of Learning_ and his _Instauratio -Magna_ in the time of his greatest power, yet his greatest reputation -rebounded first from the most intelligent foreigners in many parts -of Christendom:" and after speaking of his practical talents and his -public employments, he adds, "much more justly still may we wonder how, -without any great skill in Chemistry, without much pretence to the -Mathematics or Mechanics, without optic aids or other engines of late -invention, he should so much transcend the philosophers then living, -in judicious and clear instructions, in so many useful observations -and discoveries, I think I may say beyond the records of many ages." -And in the end of the Preface to the same volume, he speaks with -great exultation of the advance of science all over Europe, referring -undoubtedly to facts then familiar. "And now let envy snarl, it -cannot stop the wheels of active philosophy, in no part of the known -world;--not in France, either in Paris or in Caen;--not in Italy, -either in Rome, Naples, Milan, Florence, Venice, Bononia or Padua;--in -none of the Universities either on this or on that side of the seas, -Madrid and Lisbon, all the best spirits in Spain and Portugal, and -the spacious and remote dominions to them belonging;--the Imperial -Court and the Princes of Germany; the Northern Kings and their best -luminaries; and even the frozen Muscovite and Russian have all taken -the operative ferment: and it works high and prevails every way, to the -encouragement of all sincere lovers of knowledge and virtue." - -Again, in the Preface for 1672, he pursues the same thought into -detail: "We must grant that in the last age, when operative philosophy -began to recover ground, and to tread on the heels of triumphant -Philology; emergent adventures and great successes were encountered by -dangerous oppositions and strong obstructions. Galilæus and others in -Italy suffered extremities for their celestial discoveries; and here -in England Sir Walter Raleigh, when he was in his greatest lustrous, -was notoriously slandered to have erected a school of atheism, because -he gave countenance to chemistry, to practical arts, and to curious -mechanical operations, and designed to form the best of them into -a college. And Queen Elizabeth's Gilbert was a long time esteemed -extravagant for his magnetisms; and Harvey for his diligent researches -in pursuance of the circulation of the blood. But when our renowned -Lord Bacon had demonstrated the methods for a perfect restoration -of all parts of real knowledge; and the generous and philosophical -Peireskius had, soon after, agitated in all parts to redeem the most -instructive antiquities, and to excite experimental essays and fresh -discoveries; the success became on a sudden stupendous; and effective -philosophy began to sparkle, and even to flow into beams of shining -light all over the world." - -The formation of the Royal Society of London and of the Academy -of Sciences of Paris, from which proceeded the declamations just -quoted, were among many indications, belonging to this period, of -the importance which states as well as individuals had by this time -begun to attach to the cultivation of science. The English Society was -established almost immediately when the restoration of the monarchy -appeared to give a promise of tranquillity to the nation (in 1660), and -the French Academy very soon afterwards (in 1666). These measures were -very soon followed by the establishment of the Observatories of Paris -and Greenwich (in 1667 and 1675); which may be considered to be a kind -of public recognition of the astronomy of observation, as an object -on which it was the advantage and the duty of nations to bestow their -wealth. - - -8. _Bacon's New Atalantis._--When philosophers had their attention -turned to the boundless prospect of increase to the knowledge and -powers and pleasures of man which the cultivation of experimental -philosophy seemed to promise, it was natural that they should think of -devising institutions and associations by which such benefits might be -secured. Bacon had drawn a picture of a society organized with a view -to such purpose, in his fiction of the "New Atalantis." The imaginary -teacher who explains this institution to the inquiring traveller, -describes it by the name of _Solomon's House_; and says[213], "The end -of our foundation is the knowledge of causes and secret motions of -things; and the enlarging the bounds of the human empire to effecting -of things possible." And, as parts of this House, he describes caves -and wells, chambers and towers, baths and gardens, parks and pools, -dispensatories and furnaces, and many other contrivances, provided -for the purpose of making experiments of many kinds. He describes -also the various employments of the Fellows of this College, who take -a share in its researches. There are _merchants of light_, who bring -books and inventions from foreign countries; _depredators_, who gather -the experiments which exist in books; _mystery-men_, who collect the -experiments of the mechanical arts; _pioneers_ or _miners_, who invent -new experiments; and _compilers_, "who draw the experiments of the -former into titles and tables, to give the better light for the drawing -of observations and axioms out of them." There are also _dowry-men_ or -_benefactors_, that cast about how to draw out of the experiments of -their fellows things of use and practice for man's life; _lamps_, that -direct new experiments of a more penetrating light than the former; -_inoculators_, that execute the experiments so directed. Finally, there -are the _interpreters of nature_, that raise the former discoveries by -experiments into greater observations (that is, more general truths), -axioms and aphorisms. Upon this scheme we may remark, that fictitious -as it undisguisedly is, it still serves to exhibit very clearly some of -the main features of the author's philosophy:--namely, his steady view -of the necessity of ascending from facts to the most general truths -by several stages;--an exaggerated opinion of the aid that could be -derived in such a task from technical separation of the phenomena and a -distribution of them into tables;--a belief, probably incorrect, that -the offices of experimenter and interpreter may be entirely separated, -and pursued by different persons with a certainty of obtaining -success!--and a strong determination to make knowledge constantly -subservient to the uses of life. - - -9. _Cowley._--Another project of the same kind, less ambitious but -apparently more directed to practice, was published a little later -(1657) by another eminent man of letters in this country. I speak of -Cowley's "Proposition for the Advancement of Experimental Philosophy." -He suggests that a College should be established at a short distance -from London, endowed with a revenue of four thousand pounds, and -consisting of twenty professors with other members. The objects of the -labours of these professors he describes to be, first, to examine all -knowledge of nature delivered to us from former ages and to pronounce -it sound or worthless; second, to recover the lost inventions of the -ancients; third, to improve all arts that we now have; lastly, to -discover others that we yet have not. In this proposal we cannot help -marking the visible declension from Bacon's more philosophical view. -For we have here only a very vague indication of improving old arts -and discovering new, instead of the two clear Verulamian antitheses, -Experiments and Axioms deduced from them, on the one hand, and on the -other an ascent to general Laws, and a derivation, from these, of Arts -for daily use. Moreover the prominent place which Cowley has assigned -to the verifying the knowledge of former ages and recovering "the lost -inventions and drowned lands of the ancients," implies a disposition to -think too highly of traditionary knowledge; a weakness which Bacon's -scheme shows _him_ to have fully overcome. And thus it has been up to -the present day, that with all Bacon's mistakes, in the philosophy of -scientific method few have come up to him, and perhaps none have gone -beyond him. - -Cowley exerted himself to do justice to the new philosophy in verse as -well as prose, and his Poem to the Royal Society expresses in a very -noble manner those views of the history and prospects of philosophy -which prevailed among the men by whom the Royal Society was founded. -The fertility and ingenuity of comparison which characterize Cowley's -poetry are well known; and these qualities are in this instance largely -employed for the embellishment of his subject. Many of the comparisons -which he exhibits are apt and striking. Philosophy is a ward whose -estate (human knowledge) is, in his nonage, kept from him by his -guardians and tutors; (a case which the ancient rhetoricians were fond -of taking as a subject of declamation;) and these wrong-doers retain -him in unjust tutelage and constraint for their own purposes; until - - Bacon at last, a mighty man, arose, - (Whom a wise King, and Nature, chose - Lord Chancellor of both their laws,) - And boldly undertook the injured pupil's cause. - -Again, Bacon is one who breaks a scarecrow Priapus which stands in the -garden of knowledge. Again, Bacon is one who, instead of a picture of -painted grapes, gives us real grapes from which we press "the thirsty -soul's refreshing wine." Again, Bacon is like Moses, who led the -Hebrews forth from the barren wilderness, and ascended Pisgah;-- - - Did on the very border stand - Of the blest promised land, - And from the mountain's top of his exalted wit - Saw it himself and showed us it. - -The poet however adds, that Bacon discovered, but did not conquer -this new world; and that the men whom he addresses must subdue these -regions. These "champions" are then ingeniously compared to Gideon's -band: - - Their old and empty pitchers first they brake, - And with their hands then lifted up the light. - -There were still at this time some who sneered at or condemned the new -philosophy; but the tide of popular opinion was soon strongly in its -favour. I have elsewhere[214] noticed a pasquinade of the poet Boileau -in 1682, directed against the Aristotelians. At this time, and indeed -for long afterwards, the philosophers of France were Cartesians. The -English men of science, although partially and for a time they accepted -some of Descartes' opinions, for the most part carried on the reform -independently, and in pursuance of their own views. And they very soon -found a much greater leader than Descartes to place at their head, and -to take as their authority, so far as they acknowledged authority, -in their speculations. I speak of Newton, whose influence upon the -philosophy of science I must now consider. - - -10. _Barrow._--I will, however, first mention one other writer who may, -in more than one way, be regarded as the predecessor of Newton. I speak -of Isaac Barrow, whom Newton succeeded as Professor of Mathematics in -the University of Cambridge, and who in his mathematical speculations -approached very near to Newton's method of Fluxions. He afterwards -(in 1673) became Master of Trinity College, which office he held -till his death in 1677. But the passages which I shall quote belong -to an earlier period, (when Barrow was about 22 years old,) and may -be regarded as expressions of the opinions which were then current -among active-minded and studious young men. They manifest a complete -familiarity with the writings both of Bacon and of Descartes, and a -very just appreciation of both. The discourse of which I speak is -an academical exercise delivered in 1652, on the thesis _Cartesiana -hypothesis haud satisfacit præcipuis naturæ phænomenis_. By the -"Cartesian hypothesis," he does not mean the hypothesis that the -planets are moved by vortices of etherial matter: I believe that this -Cartesian tenet never had any disciples in England; it certainly -never took any hold of Cambridge. By the Cartesian hypothesis, Barrow -means the doctrine that all the phenomena of nature can be accounted -for by matter and motion; and allowing that the motions of the planets -are to be so accounted for, (which is Newtonian as well as Cartesian -doctrine,) he denies that the Cartesian hypothesis accounts for "the -generations, properties, and specific operations of animals, plants, -minerals, stones, and other natural bodies," in doing which he shows -a sound philosophical judgment. But among the parts of this discourse -most bearing on our present purpose are those where he mentions Bacon. -"Against Cartesius," he says, "I pit the chymists and others, but -especially as the foremost champion of this battle, our Verulam, a man -of great name and of great judgment, who condemned this philosophy -before it was born." "He," adds Barrow, "several times in his -_Organon_, warned men against all hypotheses of this kind, and noticed -beforehand that there was not much to be expected from those principles -which are brought into being by violent efforts of argumentation from -the brains of particular men: for that, as upon the phenomena of the -stars, various constructions of the heavens may be devised, so also -upon the phenomena of the Universe, still more dogmas may be founded -and constructed; and yet all such are mere inventions: and as many -philosophies of this kind as are or shall be extant, so many fictitious -and theatrical worlds are made." The reference is doubtless to Aphorism -LXII. of the First Book of the _Novum Organon_, in which Bacon is -speaking of his "Idols of the Theatre." After making the remark which -Barrow has adopted, Bacon adds, "Such theatrical fables have also -this in common with those of dramatic poets, that the dramatic story -is more regular and elegant than true histories are, and is made so -as to be agreeable." Barrow, having this in his mind, goes on to say: -"And though Cartesius has dressed up the stage of his theatre more -prettily than any other person, and made his drama more like history, -still he is not exempt from the like censure." And he then refers to -Cartesius's own declaration, that he did not learn his system from -things themselves, but tried to impose his own laws upon things; thus -inverting the order of true philosophy. - -Other parts of Bacon's work to which Barrow refers are those where -he speaks of the Form, or Formal Cause of a body, and says that in -comparison with that, the Efficient Cause and the Material Cause are -things unimportant and superficial, and contribute little to true and -active science[215]. And again, his classification of the various -kinds of motions[216],--the motus libertatis, motus nexus, motus -continuitatis, motus ad lucrum, fugæ, unionis, congregationis; and the -explanation of electrical attraction (about which Gilbert and others -had written) as _motus ad lucrum_. - -These passages show that Barrow had read the _Novum Organon_ in a -careful and intelligent manner, and presumed his Cambridge hearers to -be acquainted with the work. Nor is his judgment of Descartes less wise -and philosophical. He rejects, as we have seen, his system as a true -scheme of the universe, and condemns altogether his _à priori_ mode -of philosophizing; but this does not prevent his accepting Descartes' -real discoveries, and admiring the boldness and vigour of his attempts -to reform philosophy. There is, in Barrow's works, academic verse, as -well as prose, on the subject of the Cartesian hypothesis. In this, -Descartes himself is highly praised, though his doctrines are very -partially accepted. The writer says: "Pardon us, great Cartesius, if -the Muse resists you. Pardon! We follow you, Inquiring Spirit that you -are, while we reject your system. As you have taught us free thought, -and broken down the rule of tyranny, we undauntedly speculate, even in -opposition to you." - -Descartes is even yet spoken of, especially by French writers, as the -person who first asserted and established the freedom of inquiry which -is the boast of modern philosophy; but this is said with reference to -metaphysics, not to physics. In physical philosophy, though he caught -hold of some of the discoveries which were then coming into view, the -method in which he reasoned or professed to reason was altogether -vicious; and was, as I have already said, an attempt to undo what -the reformers, both theoretical and practical, had been doing:--to -discredit the philosophy of experience, and to restore the reign of _à -priori_ systems. - -It was, however, now, too late to make any such attempt; and nothing -came of it to interrupt the progress of a better philosophy of -discovery. - - -FOOTNOTES: - -[Footnote 200: _Anatomical Exercitations concerning the Generation of -Living Creatures_, 1653. Preface.] - -[Footnote 201: He used similar expressions in conversation. George Ent, -who edited his _Generation of Animals_, visited him, "at that time -residing not far from the city; and found him very intent upon the -perscrutation of nature's works, and with a countenance as cheerful, -as mind unperturbed; Democritus-like, chiefly searching into the cause -of natural things." In the course of conversation the writer said, "It -hath always been your choice about the secrets of Nature, to consult -Nature herself." "'Tis true," replied he; "and I have constantly been -of opinion that from thence we might acquire not only the knowledge -of those less considerable secrets of Nature, but even a certain -admiration of that Supreme Essence, the Creator. And though I have -ever been ready to acknowledge, that many things have been discovered -by learned men of former times; yet do I still believe that the number -of those which remain yet concealed in the darkness of impervestigable -Nature is much greater. Nay, I cannot forbear to wonder, and sometimes -smile at those, who persuade themselves, that all things were so -consummately and absolutely delivered by Aristotle, Galen, or some -other great name, as that nothing was left to the superaddition of any -that succeeded."] - -[Footnote 202: Lib. i. c. 2, 3.] - -[Footnote 203: _Anal. Post._ ii.] - -[Footnote 204: Pars iii. p. 45.] - -[Footnote 205: See _Hist. Ind. Sc._ b. vi. c. ii.] - -[Footnote 206: Cap. i. ii.] - -[Footnote 207: _Hist. Ind. Sc._ b. ix. c. ii.] - -[Footnote 208: _Meteorum_, c. viii. p. 187.] - -[Footnote 209: Mackintosh, _Dissertation on Ethical Science_.] - -[Footnote 210: _Hist. Ind. Sc._ b. vii. c. i.] - -[Footnote 211: Castelli, Torricelli, Viviani, Baliani, Gassendi, -Mersenne, Borelli, Cavalleri.] - -[Footnote 212: _De Plenitudine Mundi, in qua defenditur Cartesiana -Philosophia contra sententias Francisci Baconi, Th. Hobbii et Sethi -Wardi._] - -[Footnote 213: Bacon's _Works_, vol. ii. 111.] - -[Footnote 214: _Hist. Ind. Sc._ b. vii. c. i.] - -[Footnote 215: _Nov. Org._ lib. ii. Aph. 2.] - -[Footnote 216: _Ib._ lib. ii. Aph. 45.] - - - - -CHAPTER XVIII. - -NEWTON. - - -1. Bold and extensive as had been the anticipations of those whose -minds were excited by the promise of the new philosophy, the -discoveries of Newton respecting the mechanics of the universe, -brought into view truths more general and profound than those earlier -philosophers had hoped or imagined. With these vast accessions to human -knowledge, men's thoughts were again set in action; and philosophers -made earnest and various attempts to draw, from these extraordinary -advances in science, the true moral with regard to the conduct and -limits of the human understanding. They not only endeavoured to verify -and illustrate, by these new portions of science, what had recently -been taught concerning the methods of obtaining sound knowledge; -but they were also led to speculate concerning many new and more -interesting questions relating to this subject. They saw, for the first -time, or at least far more clearly than before, the distinction between -the inquiry into the _laws_, and into the _causes_ of phenomena. They -were tempted to ask, how far the discovery of causes could be carried; -and whether it would soon reach, or clearly point to, the ultimate -cause. They were driven to consider whether the properties which they -discovered were essential properties of all matter, necessarily and -primarily involved in its essence, though revealed to us at a late -period by their derivative effects. These questions even now agitate -the thoughts of speculative men. Some of them have already, in this -work, been discussed, or arranged in the places which our view of the -philosophy of these subjects assigns to them. But we must here notice -them as they occurred to Newton himself and his immediate followers. - - -2. The general Baconian notion of the method of philosophizing,--that -it consists in ascending from phenomena, through various stages of -generalization, to truths of the highest order,--received, in Newton's -discovery of the universal mutual gravitation of every particle of -matter, that pointed actual exemplification, for want of which it had -hitherto been almost overlooked, or at least very vaguely understood. -That great truth, and the steps by which it was established, afford, -even now, by far the best example of the successive ascent, from one -scientific truth to another,--of the repeated transition from less to -more general propositions,--which we can yet produce; as may be seen -in the Table which exhibits the relation of these steps in Book II. of -the _Novum Organon Renovatum_. Newton himself did not fail to recognize -this feature in the truths which he exhibited. Thus he says[217], "By -the way of Analysis we proceed from compounds to ingredients, as from -motions to the forces producing them; and in general, from effects -to their causes, and from particular causes to more general ones, -till the argument ends in the most general." And in like manner in -another Query[218]: "The main business of natural philosophy is to -argue from phenomena without feigning hypotheses, and to deduce causes -from effects, till we come to the First Cause, which is certainly not -mechanical." - - -3. Newton appears to have had a horror of the term _hypothesis_, -which probably arose from his acquaintance with the rash and illicit -general assumptions of Descartes. Thus in the passage just quoted, -after declaring that gravity must have some other cause than matter, -he says, "Later philosophers banish the consideration of such a cause -out of Natural Philosophy, feigning hypotheses for explaining all -things mechanically, and referring other causes to metaphysics." In the -celebrated Scholium at the end of the _Principia_ he says, "Whatever -is not deduced from the phenomena, is to be termed _hypothesis_; -and hypotheses, whether metaphysical or physical, or occult causes, -or mechanical, have no place in experimental philosophy. In this -philosophy, propositions are deduced from phenomena, and rendered -general by induction." And in another place, he arrests the course -of his own suggestions, saying, "Verum hypotheses non fingo." I have -already attempted to show that this is, in reality, a superstitious and -self-destructive spirit of speculation. Some hypotheses are necessary, -in order to connect the facts which are observed; some new principle -of unity must be applied to the phenomena, before induction can be -attempted. What is requisite is, that the hypothesis should be close -to the facts, and not connected with them by the intermediation of -other arbitrary and untried facts; and that the philosopher should be -ready to resign it as soon as the facts refuse to confirm it. We have -seen in the _History_[219], that it was by such a use of hypotheses, -that both Newton himself, and Kepler, on whose discoveries those of -Newton were based, made their discoveries. The suppositions of a force -tending to the sun and varying inversely as the square of the distance; -of a mutual force between all the bodies of the solar system; of the -force of each body arising from the attraction of all its parts; not to -mention others, also propounded by Newton,--were all hypotheses before -they were verified as theories. It is related that when Newton was -asked how it was that he saw into the laws of nature so much further -than other men, he replied, that if it were so, it resulted from his -keeping his thoughts steadily occupied upon the subject which was to be -thus penetrated. But what is this occupation of the thoughts, if it be -not the process of keeping the phenomena clearly in view, and trying, -one after another, all the plausible hypotheses which seem likely to -connect them, till at last the true law is discovered? Hypotheses so -used are a necessary element of discovery. - - -4. With regard to the details of the process of discovery, Newton -has given us some of his views, which are well worthy of notice, on -account of their coming from him; and which are real additions to the -philosophy of this subject. He speaks repeatedly of the _analysis_ -and _synthesis_ of observed facts; and thus marks certain steps in -scientific research, very important, and not, I think, clearly pointed -out by his predecessors. Thus he says[220], "As in Mathematics, so -in Natural Philosophy, the investigation of difficult things by the -method of analysis ought ever to precede the method of composition. -This analysis consists in making experiments and observations, and -in drawing general conclusions from them by induction, and admitting -of no objections against the conclusions, but such as are taken from -experiments or other certain truths. And although the arguing from -experiments and observations by induction be no demonstration of -general conclusions; yet it is the best way of arguing which the nature -of things admits of, and may be looked upon as so much the stronger, -by how much the induction is more general." And he then observes, as -we have quoted above, that by this way of analysis we proceed from -compounds to ingredients, from motions to forces, from effects to -causes, and from less to more general causes. The _analysis_ here -spoken of includes the steps which in _our_ Novum Organon we call the -_decomposition_ of facts, the exact _observation_ and _measurement_ -of the phenomena, and the _colligation_ of facts; the necessary -intermediate step, the _selection_ and _explication_ of the appropriate -conception, being passed over by Newton, in the fear of seeming to -encourage the fabrication of hypotheses. The _synthesis_ of which -Newton here speaks consists of those steps of _deductive reasoning_, -proceeding from the conception once assumed, which are requisite for -the comparison of its consequences with the observed facts. This, his -statement of the process of research, is, as far as it goes, perfectly -exact. - - -5. In speaking of Newton's precepts on the subject, we are naturally -led to the celebrated "Rules of Philosophizing," inserted in the second -edition of the _Principia_. These rules have generally been quoted and -commented on with an almost unquestioning reverence. Such Rules, coming -from such an authority, cannot fail to be highly interesting to us; but -at the same time, we cannot here evade the necessity of scrutinizing -their truth and value, according to the principles which our survey of -this subject has brought into view. The Rules stand at the beginning of -that part of the _Principia_ (the Third Book) in which he infers the -mutual gravitation of the sun, moon, planets, and all parts of each. -They are as follows: - -"Rule I. We are not to admit other causes of natural things than such -as both are true, and suffice for explaining their phenomena. - -"Rule II. Natural effects of the same kind are to be referred to the -same causes, as far as can be done. - -"Rule III. The qualities of bodies which cannot be increased or -diminished in intensity, and which belong to all bodies in which we -can institute experiments, are to be held for qualities of all bodies -whatever. - -"Rule IV. In experimental philosophy, propositions collected from -phenomena by induction, are to be held as true either accurately -or approximately, notwithstanding contrary hypotheses; till other -phenomena occur by which they may be rendered either more accurate or -liable to exception." - -In considering these Rules, we cannot help remarking, in the first -place, that they are constructed with an intentional adaptation to -the case with which Newton has to deal,--the induction of Universal -Gravitation; and are intended to protect the reasonings before which -they stand. Thus the first Rule is designed to strengthen the inference -of gravitation from the celestial phenomena, by describing it as a -_vera causa_, a true cause; the second Rule countenances the doctrine -that the planetary motions are governed by mechanical forces, as -terrestrial motions are; the third rule appears intended to justify the -assertion of gravitation, as a _universal_ quality of bodies; and the -fourth contains, along with a general declaration of the authority of -induction, the author's usual protest against hypotheses, levelled at -the Cartesian hypotheses especially. - - -6. _Of the First Rule._--We, however, must consider these Rules in -their general application, in which point of view they have often been -referred to, and have had very great authority allowed them. One of the -points which has been most discussed, is that maxim which requires that -the causes of phenomena which we assign should be true causes, _veræ -causæ_. Of course this does not mean that they should be _the_ true -or right cause; for although it is the philosopher's aim to discover -such causes, he would be little aided in his search of truth, by being -told that it is truth which he is to seek. The rule has generally -been understood to prescribe that in attempting to account for any -class of phenomena, we must assume such causes only, as _from other -considerations_, we know to exist. Thus gravity, which was employed in -explaining the motions of the moon and planets, was already known to -exist and operate at the earth's surface. - -Now the Rule thus interpreted is, I conceive, an injurious limitation -of the field of induction. For it forbids us to look for a cause, -except among the causes with which we are already familiar. But if we -follow this rule, how shall we ever become acquainted with any new -cause? Or how do we know that the phenomena which we contemplate do -really arise from some cause which we already truly know? If they do -not, must we still insist upon making them depend upon some of our -known causes; or must we abandon the study of them altogether? Must we, -for example, resolve to refer the action of radiant heat to the air, -rather than to any peculiar fluid or ether, because the former is known -to exist, the latter is merely assumed for the purpose of explanation? -But why should we do this? Why should we not endeavour to learn the -cause from the effects, even if it be not already known to us? We -can infer causes, which are new when we first become acquainted with -them. Chemical Forces, Optical Forces, Vital Forces, are known to us -only by chemical and optical and vital phenomena; must we, therefore, -reject their existence or abandon their study? They do not conform to -the double condition, that they shall be sufficient and _also_ real: -they are true, only so far as they explain the facts, but are they, -therefore, unintelligible or useless? Are they not highly important -and instructive subjects of speculation? And if the gravitation which -rules the motions of the planets had not existed at the earth's -surface;--if it had been there masked and concealed by the superior -effect of magnetism, or some other extraneous force,--might not Newton -still have inferred, from Kepler's laws, the tendency of the planets to -the sun; and from their perturbations, their tendency to each other? -His discoveries would still have been immense, if the cause which he -assigned had not been a _vera causa_ in the sense now contemplated. - - -7. But what do we mean by calling gravity a "true cause"? How do -we learn its reality? Of course, by its effects, with which we are -familiar;--by the weight and fall of bodies about us. These strike even -the most careless observer. No one can fail to see that all bodies -which we come in contact with are heavy;--that gravity acts in our -neighbourhood here upon earth. Hence, it may be said, this cause is at -any rate a true cause, whether it explains the celestial phenomena or -not. - -But if this be what is meant by a _vera causa_, it appears strange to -require that in all cases we should find such a one to account for -all classes of phenomena. Is it reasonable or prudent to demand that -we shall reduce every set of phenomena, however minute, or abstruse, -or complicated, to causes so obviously existing as to strike the most -incurious, and to be familiar among men? How can we expect to find -_such veræ causæ_ for the delicate and recondite phenomena which -an exact and skilful observer detects in chemical, or optical, or -electrical experiments? The facts themselves are too fine for vulgar -apprehension; their relations, their symmetries, their measures require -a previous discipline to understand them. How then can their causes be -found among those agencies with which the common unscientific herd of -mankind are familiar? What likelihood is there that causes held for -real by such persons, shall explain facts which such persons cannot see -or cannot understand? - -Again: if we give authority to such a rule, and require that the causes -by which science explains the facts which she notes and measures and -analyses, shall be causes which men, without any special study, have -already come to believe in, from the effects which they casually -see around them, what is this, except to make our first rude and -unscientific persuasions the criterion and test of our most laborious -and thoughtful inferences? What is it, but to give to ignorance and -thoughtlessness the right of pronouncing upon the convictions of -intense study and long-disciplined thought? "Electrical atmospheres" -surrounding electrized bodies, were at one time held to be a "true -cause" of the effects which such bodies produce. These atmospheres, it -was said, are obvious to the senses; we feel them like a spider's web -on the hands and face. Æpinus had to answer such persons, by proving -that there are no atmospheres, no effluvia, but only repulsion. He -thus, for a _true cause_ in the vulgar sense of the term, substituted -an _hypothesis_; yet who doubts that what he did was an advance in the -science of electricity? - - -8. Perhaps some persons may be disposed to say, that Newton's Rule -does not enjoin us to take those causes only which we clearly know, or -suppose we know, to be really existing and operating, but only causes -_of such kinds_ as we have already satisfied ourselves do exist in -nature. It may be urged that we are entitled to infer that the planets -are governed in their motions by an attractive force, because we find, -in the bodies immediately subject to observation and experiment, -that such motions are produced by attractive forces, for example, by -that of the earth. It may be said that we might on similar grounds -infer forces which unite particles of chemical compounds, or deflect -particles of light, because we see adhesion and deflection produced by -forces. - -But it is easy to show that the Rule, thus laxly understood, loses all -significance. It prohibits no hypothesis; for all hypotheses suppose -causes _such as_, in some case or other, we have seen in action. No -one would think of explaining phenomena by referring them to forces -and agencies altogether different from any which are known; for on -this supposition, how could he pretend to reason about the effects -of the assumed causes, or undertake to prove that they would explain -the facts? Some close similarity with some known kind of cause is -requisite, in order that the hypothesis may have the appearance of -an explanation. No forces, or virtues, or sympathies, or fluids, or -ethers, would be excluded by _this_ interpretation of _veræ causæ_. -Least of all, would such an interpretation reject the Cartesian -hypothesis of vortices; which undoubtedly, as I conceive, Newton -intended to condemn by his Rule. For that _such_ a case as a whirling -fluid, carrying bodies round a centre in orbits, does occur, is too -obvious to require proof. Every eddying stream, or blast that twirls -the dust in the road, exhibits examples of such action, and would -justify the assumption of the vortices which carry the planets in their -courses; as indeed, without doubt, such facts suggested the Cartesian -explanation of the solar system. The vortices, in this mode of -considering the subject, are at the least as _real_ a cause of motion -as gravity itself. - - -9. Thus the Rule which enjoins "true causes," is nugatory, if we take -_veræ causæ_ in the extended sense of any causes of a real _kind_, -and unphilosophical, if we understand the term of _those very_ causes -which we familiarly suppose to exist. But it may be said that we are to -designate as "true causes," not those which are collected in a loose, -confused and precarious manner, by undisciplined minds, from obvious -phenomena, but those which are justly and rigorously inferred. Such -a cause, it may be added, gravity is; for the facts of the downward -pressures and downward motions of bodies at the earth's surface lead -us, by the plainest and strictest induction, to the assertion of such -a force. Now to this interpretation of the Rule there is no objection; -but then, it must be observed, that on this view, terrestrial gravity -is inferred by the same process as celestial gravitation; and the -cause is no more entitled to be called "true," because it is obtained -from the former, than because it is obtained from the latter class of -facts. We thus obtain an intelligible and tenable explanation of a -_vera causa_; but then, by this explanation, its _verity_ ceases to be -distinguishable from its other condition, that it "suffices for the -explanation of the phenomena." The assumption of universal gravitation -accounts for the fall of a stone; it also accounts for the revolutions -of the Moon or of Saturn; but since both these explanations are of the -same kind, we cannot with justice make the one a criterion or condition -of the admissibility of the other. - - -10. But still, the Rule, so understood, is so far from being unmeaning -or frivolous, that it expresses one of the most important tests which -can be given of a sound physical theory. It is true, the explanation of -one set of facts may be of the same nature as the explanation of the -other class: but then, that the cause explains _both_ classes, gives it -a very different claim upon our attention and assent from that which -it would have if it explained one class only. The very circumstance -that the two explanations coincide, is a most weighty presumption in -their favour. It is the testimony of two witnesses in behalf of the -hypothesis; and in proportion as these two witnesses are separate -and independent, the conviction produced by their agreement is more -and more complete. When the explanation of two kinds of phenomena, -distinct, and not apparently connected, leads us to the same cause, -such a coincidence does give a reality to the cause, which it has -not while it merely accounts for those appearances which suggested -the supposition. This coincidence of propositions inferred from -separate classes of facts, is exactly what we noticed in the _Novum -Organon Renovatum_ (b. ii. c. 5, sect. 3), as one of the most decisive -characteristics of a true theory, under the name of _Consilience of -Inductions_. - -That Newton's First Rule of Philosophizing, so understood, authorizes -the inferences which he himself made, is really the ground on which -they are so firmly believed by philosophers. Thus when the doctrine -of a gravity varying inversely as the square of the distance from -the body, accounted at the same time for the relations of times and -distances in the planetary orbits and for the amount of the moon's -deflection from the tangent of her orbit, such a doctrine became most -convincing: or again, when the doctrine of the universal gravitation of -all parts of matter, which explained so admirably the inequalities of -the moon's motions, also gave a satisfactory account of a phenomenon -utterly different, the precession of the equinoxes. And of the same -kind is the evidence in favour of the undulatory theory of light, when -the assumption of the length of an undulation, to which we are led by -the colours of thin plates, is found to be identical with that length -which explains the phenomena of diffraction; or when the hypothesis of -transverse vibrations, suggested by the facts of polarization, explains -also the laws of double refraction. When such a convergence of two -trains of induction points to the same spot, we can no longer suspect -that we are wrong. Such an accumulation of proof really persuades us -that we have to do with a _vera causa_. And if this kind of proof be -multiplied;--if we again find other facts of a sort uncontemplated in -framing our hypothesis, but yet clearly accounted for when we have -adopted the supposition;--we are still further confirmed in our belief; -and by such accumulation of proof we may be so far satisfied, as to -believe without conceiving it possible to doubt. In this case, when the -validity of the opinion adopted by us has been repeatedly confirmed by -its sufficiency in unforeseen cases, so that all doubt is removed and -forgotten, the theoretical cause takes its place among the realities -of the world, and becomes _a true cause_. - - -11. Newton's Rule then, to avoid mistakes, might be thus expressed: -That "we may, provisorily, assume such hypothetical cause as will -account for any given class of natural phenomena; but that when two -different classes of facts lead us to the same hypothesis, we may hold -it to be a _true cause_." And this Rule will rarely or never mislead -us. There are no instances, in which a doctrine recommended in this -manner has afterwards been discovered to be false. There have been -hypotheses which have explained many phenomena, and kept their ground -long, and have afterwards been rejected. But these have been hypotheses -which explained only one class of phenomena; and their fall took place -when another kind of facts was examined and brought into conflict with -the former. Thus the system of eccentrics and epicycles accounted -for all the observed _motions_ of the planets, and was the means of -expressing and transmitting all astronomical knowledge for two thousand -years. But then, how was it overthrown? By considering the _distances_ -as well as motions of the heavenly bodies. Here was a second class of -facts; and when the system was adjusted so as to agree with the one -class, it was at variance with the other. These cycles and epicycles -could not be true, because they could not be made a just representation -of the facts. But if the measures of distance as well as of position -had conspired in pointing out the cycles and epicycles, as the paths of -the planets, the paths so determined could not have been otherwise than -their real paths; and the epicyclical theory would have been, at least -geometrically, true. - - -12. _Of the Second Rule._--Newton's Second Rule directs that "natural -events of the _same kind_ are to be referred to the _same causes_, so -far as can be done." Such a precept at first appears to help us but -little; for all systems, however little solid, profess to conform to -such a rule. When any theorist undertakes to explain a class of facts, -he assigns causes which, according to him, will by their natural -action, as seen in other cases, produce the effects in question. The -events which he accounts for by his hypothetical cause, are, he holds, -of the same kind as those which such a cause is known to produce. -Kepler, in ascribing the planetary motions to magnetism, Descartes, in -explaining them by means of vortices, held that they were referring -celestial motions to the causes which give rise to terrestrial motions -of the same kind. The question is, _Are_ the effects of the same kind? -This once settled, there will be no question about the propriety of -assigning them to the same cause. But the difficulty is, to determine -_when_ events are of the same kind. Are the motions of the planets of -the same kind with the motion of a body moving freely in a curvilinear -path, or do they not rather resemble the motion of a floating body -swept round by a whirling current? The Newtonian and the Cartesian -answered this question differently. How then can we apply this Rule -with any advantage? - - -13. To this we reply, that there is no way of escaping this uncertainty -and ambiguity, but by obtaining a clear possession of the ideas which -our hypothesis involves, and by reasoning rigorously from them. Newton -asserts that the planets move in free paths, acted on by certain -forces. The most exact calculation gives the closest agreement of -the results of this hypothesis with the facts. Descartes asserts -that the planets are carried round by a fluid. The more rigorously -the conceptions of force and the laws of motion are applied to this -hypothesis, the more signal is its failure in reconciling the facts -to one another. Without such calculation, we can come to no decision -between the two hypotheses. If the Newtonian hold that the motions -of the planets are _evidently_ of the _same kind_ as those of a body -describing a curve in free space, and therefore, like that, to be -explained by a force acting upon the body; the Cartesian denies that -the planets do move in free space. They are, he maintains, immersed -in a plenum. It is only when it appears that comets pass through this -plenum in all directions with no impediment, and that no possible form -and motion of its whirlpools can explain the forces and motions which -are observed in the solar system, that he is compelled to allow the -Newtonian's classification of events of the _same kind_. - -Thus it does not appear that this Rule of Newton can be interpreted in -any distinct and positive manner, otherwise than as enjoining that, in -the task of induction, we employ clear ideas, rigorous reasoning, and -close and fair comparison of the results of the hypothesis with the -facts. These are, no doubt, important and fundamental conditions of a -just induction; but in this injunction we find no peculiar or technical -criterion by which we may satisfy ourselves that we are right, or -detect our errors. Still, of such general prudential rules, none can be -more wise than one which thus, in the task of connecting facts by means -of ideas, recommends that the ideas be clear, the facts, correct, and -the chain of reasoning which connects them, without a flaw. - - -14. _Of the Third Rule._--The Third Rule, that "qualities which are -observed without exception be held to be universal," as I have already -said, seems to be intended to authorize the assertion of gravitation -as a universal attribute of matter. We formerly stated, in treating of -Mechanical Ideas[221], that this application of such a Rule appears -to be a mode of reasoning far from conclusive. The assertion of the -universality of any property of bodies must be grounded upon the -reason of the case, and not upon any arbitrary maxim. Is it intended -by this Rule to prohibit any further examination how far gravity is -an original property of matter, and how far it may be resolved into -the result of other agencies? We know perfectly well that this was not -Newton's intention; since the cause of gravity was a point which he -proposed to himself as a subject of inquiry. It would certainly be very -unphilosophical to pretend, by this Rule of Philosophizing, to prejudge -the question of such hypotheses as that of Mosotti, That gravity is -the excess of the electrical attraction over electrical repulsion, and -yet to adopt this hypothesis, would be to suppose electrical forces -more truly universal than gravity; for according to the hypothesis, -gravity, being the inequality of the attraction and repulsion, is only -an accidental and partial relation of these forces. Nor would it be -allowable to urge this Rule as a reason of assuming that double stars -are attracted to each other by a force varying according to the inverse -square of the distance; without examining, as Herschel and others have -done, the orbits which they really describe. But if the Rule is not -available in such cases, what is its real value and authority? and in -what cases are they exemplified? - - -15. In a former work[222], it was shown that the fundamental laws of -motion, and the properties of matter which these involve, are, after a -full consideration of the subject, unavoidably assumed as universally -true. It was further shown, that although our knowledge of these laws -and properties be gathered from experience, we are strongly impelled, -(some philosophers think, authorized,) to look upon these as not only -universally, but necessarily true. It was also stated, that the law -of gravitation, though its universality may be deemed probable, does -not apparently involve the same necessity as the fundamental laws of -motion. But it was pointed out that these are some of the most abstruse -and difficult questions of the whole of philosophy; involving the -profound, perhaps insoluble, problem of the identity or diversity of -Ideas and Things. It cannot, therefore, be deemed philosophical to -cut these Gordian knots by peremptory maxims, which encourage us to -decide without rendering a reason. Moreover, it appears clear that -the reason which is rendered for this Rule by the Newtonians is quite -untenable; namely, that we know extension, hardness, and inertia, to -be universal qualities of bodies by experience alone, and that we have -the same evidence of experience for the universality of gravitation. -We have already observed that we cannot, with any propriety, say that -we _find_ by experience all bodies are extended. This could not be a -just assertion, unless we conceive the possibility of our finding the -contrary. But who can conceive our finding by experience some bodies -which are not extended? It appears, then, that the reason given for -the Third Rule of Newton involves a mistake respecting the nature and -authority of experience. And the Rule itself cannot be applied without -attempting to decide, by the casual limits of observation, questions -which necessarily depend upon the relations of ideas. - - -16. _Of the Fourth Rule._--Newton's Fourth Rule is, that "Propositions -collected from phenomena by induction, shall be held to be true, -notwithstanding contrary hypotheses; but shall be liable to be rendered -more accurate, or to have their exceptions pointed out, by additional -study of phenomena." This Rule contains little more than a general -assertion of the authority of induction, accompanied by Newton's usual -protest against hypotheses. - -The really valuable part of the Fourth Rule is that which implies -that a constant verification, and, if necessary, rectification, -of truths discovered by induction, should go on in the scientific -world. Even when the law is, or appears to be, most certainly exact -and universal, it should be constantly exhibited to us afresh in the -form of experience and observation. This is necessary, in order to -discover exceptions and modifications if such exist: and if the law be -rigorously true, the contemplation of it, as exemplified in the world -of phenomena, will best give us that clear apprehension of its bearings -which may lead us to see the ground of its truth. - -The concluding clause of this Fourth Rule appears, at first, to -imply that all inductive propositions are to be considered as merely -provisional and limited, and never secure from exception. But to judge -thus would be to underrate the stability and generality of scientific -truths; for what man of science can suppose that we shall hereafter -discover exceptions to the universal gravitation of all parts of the -solar system? And it is plain that the author did not intend the -restriction to be applied so rigorously; for in the Third Rule, as -we have just seen, he authorizes us to infer universal properties of -matter from observation, and carries the liberty of inductive inference -to its full extent. The Third Rule appears to encourage us to assert a -law to be universal, even in cases in which it has not been tried; the -Fourth Rule seems to warn us that the law may be inaccurate, even in -cases in which it has been tried. Nor is either of these suggestions -erroneous; but both the universality and the rigorous accuracy of our -laws are proved by reference to Ideas rather than to Experience; a -truth, which, perhaps, the philosophers of Newton's time were somewhat -disposed to overlook. - - -17. The disposition to ascribe all our knowledge to Experience, appears -in Newton and the Newtonians by other indications; for instance, it -is seen in their extreme dislike to the ancient expressions by which -the principles and causes of phenomena were described, as the _occult -causes_ of the Schoolmen, and the _forms_ of the Aristotelians, which -had been adopted by Bacon. Newton says[223], that the particles of -matter not only possess inertia, but also active principles, as -gravity, fermentation, cohesion; he adds, "These principles I consider -not as Occult Qualities, supposed to result from the Specific Forms of -things, but as General Laws of Nature, by which the things themselves -are formed: their truth appearing to us by phenomena, though their -causes be not yet discovered. For these are manifest qualities, and -their causes only are occult. And the Aristotelians gave the name of -_occult qualities_, not to manifest qualities, but to such qualities -only as they supposed to lie hid in bodies, and to the unknown causes -of manifest effects: such as would be the causes of gravity, and of -magnetick and electrick attractions, and of fermentations, if we -should suppose that these forces or actions arose from qualities -unknown to us, and incapable of being discovered and made manifest. -Such occult qualities put a stop to the improvement of Natural -Philosophy, and therefore of late years have been rejected. To tell -us that every species of things is endowed with an occult specific -quality by which it acts and produces manifest effects, is to tell us -nothing: but to derive two or three general principles of motion from -phenomena, and afterwards to tell us how the properties and actions -of all corporeal things follow from these manifest principles, would -be a great step in philosophy, though the causes of those principles -were not yet discovered: and therefore I scruple not to propose the -principles of motion above maintained, they being of very general -extent, and leave their causes to be found out." - - -18. All that is here said is highly philosophical and valuable; but we -may observe that the investigation of _specific forms_ in the sense in -which some writers had used the phrase, was by no means a frivolous -or unmeaning object of inquiry. Bacon and others had used _form_ as -equivalent to _law_[224]. If we could ascertain that arrangement of -the particles of a crystal from which its external crystalline form -and other properties arise, this arrangement would be the _internal -form_ of the crystal. If the undulatory theory be true, the _form_ of -light is transverse vibrations: if the emission theory be maintained, -the _form_ of light is particles moving in straight lines, and -deflected by various forces. Both the terms, _form_ and _law_, imply -an ideal connexion of sensible phenomena; form supposes matter which -is moulded to the form; law supposes objects which are governed by -the law. The former term refers more precisely to existences, the -latter to occurrences. The latter term is now the more familiar, and -is, perhaps, the better metaphor: but the former also contains the -essential antithesis which belongs to the subject, and might be used in -expressing the same conclusions. - -But occult causes, employed in the way in which Newton describes, -had certainly been very prejudicial to the progress of knowledge, by -stopping inquiry with a mere word. The absurdity of such pretended -explanations had not escaped ridicule. The pretended physician in the -comedy gives an example of an occult cause or virtue. - - Mihi demandatur - A doctissimo Doctore - _Quare_ Opium facit dormire: - Et ego respondeo, - _Quia_ est in eo - _Virtus dormitiva_, - Cujus natura est sensus assoupire. - - -19. But the most valuable part of the view presented to us in -the quotation just given from Newton is the distinct separation, -already noticed as peculiarly brought into prominence by him, of the -determination of the _laws_ of phenomena, and the investigation of -their _causes_. The maxim, that the former inquiry must precede the -latter, and that if the general laws of facts be discovered, the result -is highly valuable, although the causes remain unknown, is extremely -important; and had not, I think, ever been so strongly and clearly -stated, till Newton both repeatedly promulgated the precept, and added -to it the weight of the most striking examples. - -We have seen that Newton, along with views the most just and important -concerning the nature and methods of science, had something of the -tendency, prevalent in his time, to suspect or reject, at least -speculatively, all elements of knowledge except observation. This -tendency was, however, in him so corrected and restrained by his own -wonderful sagacity and mathematical habits, that it scarcely led to -any opinion which we might not safely adopt. But we must now consider -the cases in which this tendency operated in a more unbalanced manner, -and led to the assertion of doctrines which, if consistently followed, -would destroy the very foundations of all general and certain knowledge. - - -FOOTNOTES: - -[Footnote 217: _Optics_, qu. 31, near the end.] - -[Footnote 218: Qu. 28.] - -[Footnote 219: _Hist. Ind. Sc._ b. v. and b. vii.] - -[Footnote 220: _Optics_, qu. 31.] - -[Footnote 221: _History of Ideas_, b. iii. c. x.] - -[Footnote 222: _Ibid._ b. iii. c. ix. x. xi.] - -[Footnote 223: _Opticks_, qu. 31.] - -[Footnote 224: _Nov. Org._ l. ii. Aph. 2. "Licet enim in natura nihil -existet præter corpora individua, edentia actus puros individuos -ex lege; in doctrinis tamen illa ipsa lex, ejusque inquisitio, et -inventio, et explicatio, pro fundamento est tam ad sciendum quam ad -operandum. Eam autem _legem_, ejusque _paragraphos, formarum_ nomine -intelligimus; præsertim cum hoc vocabulum invaluerit, et familiariter -occurrat." - -Aph. 17. "Eadem res est _forma_ calidi vel _forma_ luminis, et _lex_ -calidi aut _lex_ luminis."] - - - - -CHAPTER XIX. - -LOCKE AND HIS FRENCH FOLLOWERS. - - -1. In the constant opposition and struggle of the schools of -philosophy, which consider our Senses and our Ideas respectively, -as the principal sources of our knowledge, we have seen that at the -period of which we now treat, the tendency was to exalt the external -and disparage the internal element. The disposition to ascribe our -knowledge to observation alone, had already, in Bacon's time, led him -to dwell to a disproportionate degree upon that half of his subject; -and had tinged Newton's expressions, though it had not biassed his -practice. But this partiality soon assumed a more prominent shape, -becoming extreme in Locke, and extravagant in those who professed to -follow him. - -Indeed Locke appears to owe his popularity and influence as a popular -writer mainly to his being one of the first to express, in a plain and -unhesitating manner, opinions which had for some time been ripening -in the minds of a large portion of the cultivated public. Hobbes had -already promulgated the main doctrines which Locke afterwards urged, on -the subject of the origin and nature of our knowledge: but in him these -doctrines were combined with offensive opinions on points of morals, -government, and religion, so that their access to general favour was -impeded: and it was to Locke that they were indebted for the extensive -influence which they soon after obtained. Locke owed this authority -mainly to the intellectual circumstances of the time. Although a writer -of great merit, he by no means possesses such metaphysical acuteness or -such philosophical largeness of view, or such a charm of writing, as -must necessarily give him the high place he has held in the literature -of Europe. But he came at a period when the reign of Ideas was -tottering to its fall. All the most active and ambitious spirits had -gone over to the new opinions, and were prepared to follow the fortunes -of the Philosophy of Experiment, then in the most prosperous and -brilliant condition, and full of still brighter promise. There were, -indeed, a few learned and thoughtful men who still remained faithful -to the empire of Ideas; partly, it may be, from a too fond attachment -to ancient systems; but partly, also, because they knew that there -were subjects of vast importance, in which experience did not form the -whole foundation of our knowledge. They knew, too, that many of the -plausible tenets of the new philosophy were revivals of fallacies which -had been discussed and refuted in ancient times. But the advocates of -mere experience came on with a vast store of weighty truth among their -artillery, and with the energy which the advance usually bestows. The -ideal system of philosophy could, for the present, make no effectual -resistance; Locke, by putting himself at the head of the assault, -became the hero of his day: and his name has been used as the watchword -of those who adhere to the philosophy of the senses up to our own times. - - -2. Locke himself did not assert the exclusive authority of the senses -in the extreme unmitigated manner in which some who call themselves -his disciples have done. But this is the common lot of the leaders -of revolutions, for they are usually bound by some ties of affection -and habit to the previous state of things, and would not destroy all -traces of that condition: while their followers attend, not to their -inconsistent wishes, but to the meaning of the revolution itself; -and carry out, to their genuine and complete results, the principles -which won the victory, and which have been brought out more sharp from -the conflict. Thus Locke himself does not assert that all our ideas -are derived from Sensation, but from Sensation _and Reflection_. But -it was easily seen that, in this assertion, two very heterogeneous -elements were conjoined: that while to pronounce Sensation the origin -of ideas, is a clear decided tenet, the acceptance or rejection of -which determines the general character of our philosophy; to make the -same declaration concerning Reflection, is in the highest degree vague -and ambiguous; since reflection may either be resolved into a mere -modification of sensation, as was done by one school, or may mean all -that the opposite school opposes to sensation, under the name of Ideas. -Hence the clear and strong impression which fastened upon men's minds, -and which does in fact represent all the systematic and consistent part -of Locke's philosophy, was, that in it all our ideas are represented as -derived from Sensation. - - -3. We need not spend much time in pointing out the inconsistencies into -which Locke fell; as all must fall into inconsistencies who recognize -no source of knowledge except the senses. Thus he maintains that our -Idea of Space is derived from the senses of sight and touch; our Idea -of Solidity from the touch alone. Our Notion of Substance is an unknown -support of unknown qualities, and is illustrated by the Indian fable -of the tortoise which supports the elephant, which supports the world. -Our Notion of Power or Cause is in like manner got from the senses. -And yet, though these ideas are thus mere fragments of our experience, -Locke does not hesitate to ascribe to them necessity and universality -when they occur in propositions. Thus he maintains the necessary truth -of geometrical properties: he asserts that the resistance arising from -solidity is absolutely insurmountable[225]; he conceives that nothing -short of Omnipotence can annihilate a particle of matter[226]; and he -has no misgivings in arguing upon the axiom that Every thing must have -a cause. He does not perceive that, upon his own account of the origin -of our knowledge, we can have no right to make any of these assertions. -If our knowledge of the truths which concern the external world were -wholly derived from experience, all that we could venture to say would -be,--that geometrical properties of figures are true _as far as we have -tried them_;--that we have seen _no example_ of a solid body being -reduced to occupy less space by pressure, or of a material substance -annihilated by natural means;--and that _wherever we have examined_, -we have found that every change has had a cause. Experience can never -entitle us to declare that what she has not seen is impossible; still -less, that things which she can not see are certain. Locke himself -intended to throw no doubt upon the certainty of either human or -divine knowledge; but his principles, when men discarded the temper in -which he applied them, and the checks to their misapplication which -he conceived that he had provided, easily led to a very comprehensive -skepticism. His doctrines tended to dislodge from their true bases the -most indisputable parts of knowledge; as, for example, pure and mixed -mathematics. It may well be supposed, therefore, that they shook the -foundations of many other parts of knowledge in the minds of common -thinkers. - -It was not long before these consequences of the overthrow of -ideas showed themselves in the speculative world. I have already -in a previous work[227] mentioned Hume's skeptical inferences from -Locke's maxim, that we have no ideas except those which we acquire -by experience; and the doctrines set up in opposition to this by -the metaphysicians of Germany. I might trace the progress of the -sensational opinions in Britain till the reaction took place here -also: but they were so much more clearly and decidedly followed out in -France, that I shall pursue their history in that country. - - -4. _The French Followers of Locke, Condillac, &c._--Most of the -French writers who adopted Locke's leading doctrines, rejected the -"Reflection," which formed an anomalous part of his philosophy, and -declared that Sensation alone was the source of ideas. Among these -writers, Condillac was the most distinguished. He expressed the leading -tenet of their school in a clear and pointed manner by saying that "All -ideas are transformed sensations." We have already considered this -phrase[228], and need not here dwell upon it. - -Opinions such as these tend to annihilate, as we have seen, one of the -two co-ordinate elements of our knowledge. Yet they were far from being -so prejudicial to the progress of science, or even of the philosophy -of science, as might have been anticipated. One reason of this was, -that they were practically corrected, especially among the cultivators -of Natural Philosophy, by the study of mathematics; for that study did -really supply all that was requisite on the ideal side of science, so -far as the ideas of space, time, and number, were concerned, and partly -also with regard to the idea of cause and some others. And the methods -of discovery, though the philosophy of them made no material advance, -were practically employed with so much activity, and in so many various -subjects, that a certain kind of prudence and skill in this employment -was very widely diffused. - - -5. _Importance of Language._--In one respect this school of -metaphysicians rendered a very valuable service to the philosophy of -science. They brought into prominent notice the great importance of -_words_ and _terms_ in the formation and progress of knowledge, and -pointed out that the office of language is not only to convey and -preserve our thoughts, but to perform the analysis in which reasoning -consists. They were led to this train of speculation, in a great -measure, by taking pure mathematical science as their standard example -of substantial knowledge. Condillac, rejecting, as we have said, almost -all those ideas on which universal and demonstrable truths must be -based, was still not at all disposed to question the reality of human -knowledge; but was, on the contrary, a zealous admirer of the evidence -and connexion which appear in those sciences which have the ideas of -space and number for their foundation, especially the latter. He looked -for the grounds of the certainty and reality of the knowledge which -these sciences contain; and found them, as he conceived, in the nature -of the _language_ which they employ. The _Signs_ which are used in -arithmetic and algebra enable us to keep steadily in view the identity -of the same quantity under all the forms which, by composition and -decomposition, it may be made to assume; and these Signs also not only -express the operations which are performed, but suggest the extension -of the operations according to analogy. Algebra, according to him, -is only a very perfect language; and language answers its purpose of -leading us to truth, by possessing the characteristics of algebra. -Words are the symbols of certain groups of impressions or facts; they -are so selected and applied as to exhibit the analogies which prevail -among these facts; and these analogies are the truths of which our -knowledge consists. "Every language is an analytical method; every -analytical method is a language[229];" these were the truths "alike new -and simple," as he held, which he conceived that he had demonstrated. -"The art of speaking, the art of writing, the art of reasoning, the -art of thinking, are only, at bottom, one and the same art[230]." Each -of these operations consists in a succession of analytical operations; -and words are the marks by which we are able to fix our minds upon the -steps of this analysis. - - -6. The analysis of our impressions and notions does in reality lead -to truth, not only in virtue of the identity of the whole with its -parts, as Condillac held, but also in virtue of certain Ideas which -govern the synthesis of our sensations, and which contain the elements -of universal truths, as we have all along endeavoured to show. But -although Condillac overlooked or rejected this doctrine, the importance -of words, as marking the successive steps of this synthesis and -analysis, is not less than he represented it to be. Every truth, once -established by induction from facts, when it is become familiar under -a brief and precise form of expression, becomes itself a fact; and is -capable of being employed, along with other facts of a like kind, as -the materials of fresh inductions. In this successive process, the -term, like the cord of a fagot, both binds together the facts which it -includes, and makes it possible to manage the assemblage as a single -thing. On occasion of most discoveries in science, the selection of a -technical term is an essential part of the proceeding. In the _History -of Science_, we have had numerous opportunities of remarking this; and -the List of technical terms given as an Index to that work, refers us, -by almost every word, to one such occasion. And these terms, which -thus have had so large a share in the formation of science, and which -constitute its language, do also offer the means of analyzing its -truths, each into its constituent truths; and these into facts more -special, till the original foundations of our most general propositions -are clearly exhibited. The relations of general and particular truths -are most evidently represented by the Inductive Tables given in -Book II. of the _Novum Organon Renovatum_. But each step in each of -these Tables has its proper form of expression, familiar among the -cultivators of science; and the analysis which our Tables display, is -commonly performed in men's minds, when it becomes necessary, by fixing -the attention successively upon a series of words, not upon the lines -of a Table. Language offers to the mind such a scale or ladder as the -Table offers to the eye; and since such Tables present to us, as we -have said, the Logic of Induction, that is, the formal conditions of -the soundness of our reasoning from facts, we may with propriety say -that a just analysis of the meaning of words is an essential portion of -Inductive Logic. - -In saying this, we must not forget that a decomposition of general -truths into ideas, as well as into facts, belongs to our philosophy; -but the point we have here to remark, is the essential importance of -words to the latter of these processes. And this point had not ever -had its due weight assigned to it till the time of Condillac and other -followers of Locke, who pursued their speculations in the spirit I have -just described. The doctrine of the importance of terms is the most -considerable addition to the philosophy of science which has been made -since the time of Bacon[231]. - - -7. _The French Encyclopedists._--The French _Encyclopédie_, published -in 1751, of which Diderot and Dalembert were the editors, may be -considered as representing the leading characters of European -philosophy during the greater part of the eighteenth century. The -writers in this work belong for the most part to the school of Locke -and Condillac; and we may make a few remarks upon them, in order to -bring into view one or two points in addition to what we have already -said of that school. The _Discours Préliminaire_, written by Dalembert, -is celebrated as containing a view of the origin of our knowledge, and -the connexion and classification of the sciences. - -A tendency of the speculations of the Encyclopedists, as of the School -of Locke in general, is to reject all ideal principles of connexion -among facts, as something which experience, the only source of true -knowledge, does not give. Hence all certain knowledge consists only -in the recognition of the same thing under different aspects, or -different forms of expression. Axioms are not the result of an original -relation of ideas, but of the use, or it may be the abuse[232], of -words. In like manner, the propositions of Geometry are a series of -modifications,--of distortions, so to speak,--of one original truth; -much as if the proposition were stated in the successive forms of -expression presented by a language which was constantly growing more -and more artificial. Several of the sciences which rest upon physical -principles, that is, (says the writer,) truths of experience or simple -hypotheses, have only an experimental or hypothetical certainty. -Impenetrability added to the idea of extent is a mystery in addition: -the nature of motion is a riddle for philosophers: the metaphysical -principle of the laws of percussion is equally concealed from them. The -more profoundly they study the idea of matter and of the properties -which represent it, the more obscure this idea becomes; the more -completely does it escape them. - - -8. This is a very common style of reflection, even down to our own -times. I have endeavoured to show that concerning the Fundamental Ideas -of space, of force and resistance, of substance, external quality, and -the like, we know enough to make these Ideas the grounds of certain -and universal truths;--enough to supply us with axioms from which we -can demonstratively reason. If men wish for any other knowledge of -the nature of matter than that which ideas, and facts conformable to -ideas, give them, undoubtedly their desire will be frustrated, and -they will be left in a mysterious vacancy; for it does not appear -how such knowledge as they ask for could be knowledge at all. But in -reality, this complaint of our ignorance of the real nature of things -proceeds from the rejection of ideas, and the assumption of the senses -alone as the ground of knowledge. "Observation and calculation are -the only sources of truth:" this is the motto of the school of which -we now speak. And its import amounts to this:--that they reject all -ideas except the idea of number, and recognize the modifications which -parts undergo by addition and subtraction as the only modes in which -true propositions are generated. The laws of nature are assemblages of -facts: the truths of science are assertions of the identity of things -which are the same. "By the avowal of almost all philosophers," says -a writer of this school[233], "the most sublime truths, when once -simplified and reduced to their lowest terms, are converted into facts, -and thenceforth present to the mind only this proposition; the white is -white, the black is black." - -These statements are true in what they positively assert, but they -involve error in the denial which by implication they convey. It -is true that observation and demonstration are the only sources of -scientific truth; but then, demonstration may be founded on other -grounds besides the elementary properties of number. It is true that -the theory of gravitation is but the assertion of a general fact; but -this is so, not because a sound theory does not involve ideas, but -because our apprehension of a fact does. - - -9. Another characteristic indication of the temper of the -Encyclopedists and of the age to which they belong, is the importance -by them assigned to those practical _Arts_ which minister to man's -comfort and convenience. Not only, in the body of the Encyclopedia, are -the Mechanical Arts placed side by side with the Sciences, and treated -at great length; but in the Preliminary Discourse, the preference -assigned to the liberal over the mechanical Arts is treated as a -prejudice[234], and the value of science is spoken of as measured -by its utility. "The discovery of the Mariner's Compass is not less -advantageous to the human race than the explanation of its properties -would be to physics.--Why should we not esteem those to whom we owe -the fusee and the escapement of watches as much as the inventors of -Algebra?" And in the classification of sciences which accompanies the -Discourse, the labours of artisans of all kinds have a place. - -This classification of the various branches of science contained -in the Dissertation is often spoken of. It has for its basis the -classification proposed by Bacon, in which the parts of human knowledge -are arranged according to the faculties of the mind in which they -originate; and these faculties are taken, both by Bacon and by -Dalembert, as Memory, Reason, and Imagination. The insufficiency of -Bacon's arrangement as a scientific classification is so glaring, that -the adoption of it, with only superficial modifications, at the period -of the Encyclopedia, is a remarkable proof of the want of original -thought and real philosophy at the time of which we speak. - - -10. We need not trace further the opinion which derives all our -knowledge from the senses in its application to the philosophy of -Science. Its declared aim is to reduce all knowledge to the knowledge -of Facts; and it rejects all inquiries which involve the Idea of Cause, -and similar Ideas, describing them as "metaphysical," or in some other -damnatory way. It professes, indeed, to discard all Ideas; but, as we -have long ago seen, some Ideas or other are inevitably included even -in the simplest Facts. Accordingly the speculations of this school -are compelled to retain the relations of Position, Succession, Number -and Resemblance, which are rigorously ideal relations. The philosophy -of Sensation, in order to be consistent, ought to reject these Ideas -along with the rest, and to deny altogether the possibility of general -knowledge. - -When the opinions of the Sensational School had gone to an extreme -length, a Reaction naturally began to take place in men's minds. Such -have been the alternations of opinion, from the earliest ages of human -speculation. Man may perhaps have existed in an original condition in -which he was only aware of the impressions of Sense; but his first -attempts to analyse his perceptions brought under his notice Ideas as -a separate element, essential to the existence of knowledge. Ideas -were thenceforth almost the sole subject of the study of philosophers; -of Plato and his disciples, professedly; of Aristotle, and still more -of the followers and commentators of Aristotle, practically. And this -continued till the time of Galileo, when the authority of the Senses -again began to be asserted; for it was shown by the great discoveries -which were then made, that the Senses had at least some share in -the promotion of knowledge. As discoveries more numerous and more -striking were supplied by Observation, the world gradually passed -over to the opinion that the share which had been ascribed to Ideas in -the formation of real knowledge was altogether a delusion, and that -Sensation alone was true. But when this was asserted as a general -doctrine, both its manifest falsity and its alarming consequences -roused men's minds, and made them recoil from the extreme point to -which they were approaching. Philosophy again oscillated back towards -Ideas; and over a great part of Europe, in the clearest and most -comprehensive minds, this regression from the dogmas of the Sensational -School is at present the prevailing movement. We shall conclude our -review by noticing a few indications of this state of things. - - -FOOTNOTES: - -[Footnote 225: _Essay_, b. xi. c. iv. sect. 3.] - -[Footnote 226: _Ibid._ c. xiii. sect. 22.] - -[Footnote 227: _History of Ideas_, b. iii. c. iii. Modern Opinions -respecting the Idea of Cause.] - -[Footnote 228: _Ibid._ b. i. c. iv.] - -[Footnote 229: _Langue des Calculs_, p. 1.] - -[Footnote 230: _Grammaire_, p. xxxvi.] - -[Footnote 231: Since the selection and construction of terms is thus -a matter of so much consequence in the formation of science, it is -proper that systematic rules, founded upon sound principles, should be -laid down for the performance of this operation. Some such rules are -accordingly suggested in b. iv. of the _Nov. Org. Ren._] - -[Footnote 232: _Disc. Prélim._ p. viii.] - -[Footnote 233: Helvetius _Sur l'Homme_, c. xxiii.] - -[Footnote 234: P. xiii.] - - - - -CHAPTER XX. - -THE REACTION AGAINST THE SENSATIONAL SCHOOL. - - -1. When Locke's _Essay_ appeared, it was easily seen that its tendency -was to urge, in a much more rigorous sense than had previously been -usual, the ancient maxim of Aristotle, adopted by the schoolmen of -the middle ages, that "nothing exists in the intellect but what has -entered by the senses." Leibnitz expressed in a pointed manner the -limitation with which this doctrine had always been understood. "Nihil -est in intellectu quod non prius fuerit in sensu;--_nempe_," he added, -"_nisi intellectus ipse_." To this it has been objected[235], that we -cannot say that the intellect is _in_ the intellect. But this remark -is obviously frivolous; for the faculties of the understanding (which -are what the argument against the Sensational School requires us to -reserve) may be said to be _in_ the understanding, with as much justice -as we may assert there are _in_ it the impressions derived from sense. -And when we take account of these faculties, and of the Ideas to which, -by their operation, we necessarily subordinate our apprehension of -phenomena, we are led to a refutation of the philosophy which makes -phenomena, unconnected by Ideas, the source of all knowledge. The -succeeding opponents of the Lockian school insisted upon and developed -in various ways this remark of Leibnitz, or some equivalent view. - - -2. It was by inquiries into the foundations of Morals that English -philosophers were led to question the truth of Locke's theory. Dr. -Price, in his _Review of the Principal Questions in Morals_, first -published in 1757, maintained that we cannot with propriety assert -all our ideas to be derived from sensation and reflection. He pointed -out, very steadily, the other source. "The power, I assert, that -_understands_, or the faculty within us that discerns _truth_, and that -compares all the objects of thought and _judges_ of them, is a spring -of new ideas[236]." And he exhibits the antithesis in various forms. -"Were not _sense_ and _knowledge_ entirely different, we should rest -satisfied with sensible impressions, such as light, colours and sounds, -and inquire no further about them, at least when the impressions are -strong and vigorous: whereas, on the contrary, we necessarily desire -some further acquaintance with them, and can never be satisfied -till we have subjected them to the survey of reason. Sense presents -_particular_ forms to the mind, but cannot rise to any _general_ ideas. -It is the intellect that examines and compares the presented forms, -that rises above individuals to universal and abstract ideas; and -thus looks downward upon objects, takes in at one view an infinity of -particulars, and is capable of discovering general truths. Sense sees -only the outside of things, reason acquaints itself with their natures. -Sensation is only a mode of feeling in the mind; but knowledge implies -an active and vital energy in the mind[237]." - - -3. The necessity of refuting Hume's inferences from the mere sensation -system led other writers to limit, in various ways, their assent to -Locke. Especially was this the case with a number of intelligent -metaphysicians in Scotland, as Reid, Beattie, Dugald Stewart, and -Thomas Brown. Thus Reid asserts[238], "that the account which Mr. -Locke himself gives of the Idea of Power cannot be reconciled to -his favourite doctrine, that all our simple ideas have their origin -from sensation or reflection." Reid remarks, that our memory and our -reasoning power come in for a share in the origin of this idea: and -in speaking of reasoning, he obviously assumes the axiom that every -event must have a cause. By succeeding writers of this school, the -assumption of the fundamental principles, to which our nature in such -cases irresistibly directs us, is more clearly pointed out. Thus -Stewart defends the form of expression used by Price[239]: "A variety -of intuitive judgments might be mentioned, involving simple ideas, -which it is impossible to trace to any origin but to the power which -enables us to form these judgments. Thus it is surely an intuitive -truth that the sensations of which I am conscious, and all those I -remember, belong to one and the same being, which I call _myself_. Here -is an intuitive judgment involving the simple idea of _Identity_. In -like manner, the changes which I perceive in the universe impress me -with a conviction that some cause must have operated to produce them. -Here is an intuitive judgment involving the simple Idea of _Causation_. -When we consider the adjacent angles made by a straight line standing -upon another, and perceive that their sum is equal to two right angles, -the judgment we form involves a simple idea of _Equality_. To say, -therefore, that the Reason or the Understanding is a source of new -ideas, is not so exceptionable a mode of speaking as has been sometimes -supposed. According to Locke, _Sense_ furnishes our ideas, and Reason -perceives their agreements and disagreements. But the truth is, that -these agreements and disagreements are in many instances, simple -ideas, of which no analysis can be given; and of which the origin must -therefore be referred to Reason, according to Locke's own doctrine." -This view, according to which the Reason or Understanding is the source -of certain simple ideas, such as Identity, Causation, Equality, which -ideas are necessarily involved in the intuitive judgments which we -form, when we recognize fundamental truths of science, approaches very -near in effect to the doctrine which in several works I have presented, -of Fundamental Ideas belonging to each science, and manifesting -themselves in the axioms of the science. It may be observed, however, -that by attempting to enumerate these ideas and axioms, so as to -lay the foundations of the whole body of physical science, and by -endeavouring, as far as possible, to simplify and connect each group -of such Ideas, I have at least given a more systematic form to this -doctrine. I have, moreover, traced it into many consequences to which -it necessarily leads, but which do not appear to have been contemplated -by the metaphysicians of the Scotch school. But I gladly acknowledge -my obligations to the writers of that school; and I trust that in the -near agreement of my views on such points with theirs, there is ground -for believing the system of philosophy which I have presented, to be -that to which the minds of thoughtful men, who have meditated on such -subjects, are generally tending. - - -4. As a further instance that such a tendency is at work, I may make -a quotation from an eminent English philosophical writer of another -school. "If you will be at the pains," says Archbishop Whately[240], -"carefully to analyze the simplest description you hear of any -transaction or state of things, you will find that the process which -almost invariably takes place is, in logical language, this: that each -individual _has in his mind_ certain major premises or principles -relative to the subject in question;--that observation of what actually -presents itself to the senses, supplies minor premises; and that -the statement given (and which is reported as a thing experienced) -consists, in fact, of the _conclusions_ drawn from the combinations of -these premises." The major premises here spoken of are the Fundamental -Ideas, and the Axioms and Propositions to which they lead; and whatever -is regarded as a fact of observation is necessarily a conclusion in -which these propositions are assumed; for these contain, as we have -said, the conditions of our experience. Our experience conforms to -these axioms and their consequences, whether or not the connexion be -stated in a logical manner, by means of premises and a conclusion. - - -5. The same persuasion is also suggested by the course which the study -of metaphysics has taken of late years in France. In that country, -as we have seen, the Sensational System, which was considered as the -necessary consequence of the revolution begun by Locke, obtained a more -complete ascendancy than it did in England; and in that country too, -the reaction, among metaphysical and moral writers, when its time came, -was more decided and rapid than it was among Locke's own countrymen. -It would appear that M. Laromiguière was one of the first to give -expression to this feeling, of the necessity of a modification of the -sensational philosophy. He began by professing himself the disciple -of Condillac, even while he was almost unconsciously subverting the -fundamental principles of that writer. And thus, as M. Cousin justly -observes[241], his opinions had the more powerful effect from being -presented, not as thwarting and contradicting, but as sharing and -following out the spirit of his age. M. Laromiguière's work, entitled -_Essai sur les Facultés de l'Ame_, consists of lectures given to the -Faculty of Letters of the Academy of Paris, in the years 1811, 1812 -and 1813. In the views which these lectures present, there is much -which the author has in common with Condillac. But he is led by his -investigation to assert[242], that it is not true that sensation is -the sole fundamental element of our thoughts and our understanding. -_Attention_ also is requisite: and here we have an element of quite -another kind. For sensation is passive; attention is active. Attention -does not spring out of sensation; the passive principle is not the -reason of the active principle. Activity and passivity are two facts -entirely different. Nor can this activity be defined or derived; being, -as the author says, a fundamental idea. The distinction is manifest -by its own nature; and we may find evidence of it in the very forms of -language. To _look_ is more than to _see_; to _hearken_ is more than -to _hear_. The French language marks this distinction with respect to -other senses also. "On _voit_, et l'on _regarde_; on _entend_, et l'on -_écoute_; on _sent_, et l'on _flaire_; on _goûte_, et l'on _savoure_." -And thus the mere sensation, or capacity of feeling, is only the -occasion on which the attention is exercised; while the attention is -the foundation of all the operations of the understanding. - -The reader of my works will have seen how much I have insisted upon the -activity of the mind, as the necessary basis of all knowledge. In all -observation and experience, the mind is active, and by its activity -apprehends all sensations in subordination to its own ideas; and thus -it becomes capable of collecting knowledge from phenomena, since -ideas involve general relations and connexions, which sensations of -themselves cannot involve. And thus we see that, in this respect also, -our philosophy stands at that point to which the speculations of the -most reflecting men have of late constantly been verging. - - -6. M. Cousin himself, from whom we have quoted the above account -of Laromiguière, shares in this tendency, and has argued very -energetically and successfully against the doctrines of the Sensational -School. He has made it his office once more to bring into notice among -his countrymen, the doctrine of ideas as the sources of knowledge; and -has revived the study of Plato, who may still be considered as one of -the great leaders of the ideal school. But the larger portion of M. -Cousin's works refers to questions out of the reach of our present -review, and it would be unsuitable to dwell longer upon them in this -place. - - -7. We turn to speculations more closely connected with our present -subject. M. Ampère, a French man of science, well entitled by his -extensive knowledge, and large and profound views, to deal with the -philosophy of the sciences, published in 1834, his _Essai sur la -Philosophie des Sciences, ou Exposition analytique d'une Classification -Naturelle de toutes les Connaissances Humaines_. In this remarkable -work we see strong evidence of the progress of the reaction against -the system which derives our knowledge from sensation only. The -author starts from a maxim, that in classing the sciences, we must -not only regard the nature of the objects about which each science is -concerned, but also the point of view under which it considers them: -that is, the _ideas_ which each science involves. M. Ampère also gives -briefly his views of the intellectual constitution of man; a subject -on which he had long and sedulously employed his thoughts; and these -views are far from belonging to the Sensational School. Human thought, -he says, is composed of phenomena and of conceptions. Phenomena are -external, or _sensitive_; and internal, or _active_. Conceptions are -of four kinds; _primitive_, as space and motion, duration and cause; -_objective_, as our idea of matter and substance; _onomatic_, or those -which we associate with the general terms which language presents to -us; and _explicative_, by which we ascend to causes after a comparative -study of phenomena. He teaches further, that in deriving ideas from -sensation, the mind is not passive; but exerts an action which, when -voluntary, is called _attention_, but when it is, as it often is, -involuntary, may be termed _reaction_. - -I shall not dwell upon the examination of these opinions[243]; but I -may remark, that both in the recognition of conceptions as an original -and essential element of the mind, and in giving a prominent place to -the active function of the mind, in the origin of our knowledge, this -view approaches to that which I have presented in preceding works; -although undoubtedly with considerable differences. - - -8. The classification of the sciences which M. Ampère proposes, is -founded upon a consideration of the sciences themselves; and is, -the author conceives, in accordance with the conditions of natural -classifications, as exhibited in Botany and other sciences. It is of -a more symmetrical kind, and exhibits more steps of subordination, -than that to which I have been led; it includes also practical Art as -well as theoretical Science; and it is extended to moral and political -as well as physical Sciences. It will not be necessary for me here -to examine it in detail: but I may remark, that it is throughout a -_dichotomous_ division, each higher member being subdivided into two -lower ones, and so on. In this way, M. Ampère obtains sciences of -the First Order, each of which is divided into two sciences of the -Second, and four of the Third Order. Thus Mechanics is divided into -_Cinematics_, _Statics_, _Dynamics_, and _Molecular Mechanics_; Physics -is divided into _Experimental Physics_, _Chemistry_, _Stereometry_, -and _Atomology_; Geology is divided into _Physical Geography_, -_Mineralogy_, _Geonomy_, and _Theory of the Earth_. Without here -criticizing these divisions or their principle, I may observe that -_Cinematics_, the doctrine of motion without reference to the force -which produces it, is a portion of knowledge which our investigation -has led us also to see the necessity of erecting into a separate -science; and which we have termed _Pure Mechanism_. Of the divisions of -Geology, _Physical Geography_, especially as explained by M. Ampère, is -certainly a part of the subject, both important and tolerably distinct -from the rest. _Geonomy_ contains what we have termed in the History, -_Descriptive Geology_;--the exhibition of the facts separate from the -inquiry into their causes; while our _Physical Geology_ agrees with M. -Ampère's _Theory of the Earth_. _Mineralogy_ appears to be placed by -him in a different place from that which it occupies in our scheme: -but in fact, he uses the term for a different science; he applies -it to the classification not of _simple minerals_, but of _rocks_, -which is a science auxiliary to geology, and which has sometimes been -called _Petralogy_. What we have termed _Mineralogy_, M. Ampère unites -with _Chemistry_. "It belongs," he says[244], "to Chemistry, and not -to Mineralogy, to inquire how many atoms of silicium and of oxygen -compose silica; to tell us that its primitive form is a rhombohedron of -certain angles, that it is called _quartz_, &c.; leaving, on one hand, -to Molecular Geometry the task of explaining the different secondary -forms which may result from the primitive form; and on the other hand, -leaving to Mineralogy the office of describing the different varieties -of quartz, and the rocks in which they occur, according as the quartz -is crystallized, transparent, coloured, amorphous, solid, or in sand." -But we may remark, that by adopting this arrangement, we separate from -Mineralogy almost all the knowledge, and absolutely all the general -knowledge, which books professing to treat of that science have -usually contained. The consideration of Mineralogical Classifications, -which, as may be seen in the _History of Science_, is so curious and -instructive, is forced into the domain of Chemistry, although many of -the persons who figure in it were not at all properly chemists. And we -lose, in this way, the advantage of that peculiar office which, in our -arrangement, Mineralogy fills; of forming a rigorous transition from -the sciences of classification to those which consider the mathematical -properties of bodies; and connecting the external characters and the -internal constitution of bodies by means of a system of important -general truths. I conceive, therefore, that our disposition of this -science, and our mode of applying the name, are far more convenient -than those of M. Ampère. - - -9. We have seen the reaction against the pure sensational doctrines -operating very powerfully in England and in France. But it was in -Germany that these doctrines were most decidedly rejected; and systems -in extreme opposition to these put forth with confidence, and received -with applause. Of the authors who gave this impulse to opinions in that -country, Kant was the first, and by far the most important. I have in -the _History of Ideas_ (b. iii. c. 3), endeavoured to explain how he -was aroused, by the skepticism of Hume, to examine wherein the fallacy -lay which appeared to invalidate all reasonings from effect to cause; -and how this inquiry terminated in a conviction that the foundations -of our reasonings on this and similar points were to be sought in -the mind, and not in the phenomena;--in the _subject_, and not in -the _object_. The revolution in the customary mode of contemplating -human knowledge which Kant's opinions involved, was most complete. -He himself, with no small justice, compares[245] it with the change -produced by Copernicus's theory of the solar system. "Hitherto," he -says, "men have assumed that all our knowledge must be regulated by -the objects of it; yet all attempts to make out anything concerning -objects _à priori_ by means of our conceptions," (as for instance their -geometrical properties) "must, on this foundation, be unavailing. Let -us then try whether we cannot make out something more in the problems -of metaphysics, by assuming that objects must be regulated by our -knowledge, since this agrees better with that supposition, which we are -prompted to make, that we can know something of them _à priori_. This -thought is like that of Copernicus, who, when he found that nothing -was to be made of the phenomena of the heavens so long as everything -was supposed to turn about the spectator, tried whether the matter -might not be better explained if he made the spectator turn, and left -the stars at rest. We may make the same essay in metaphysics, as to -what concerns our intuitive knowledge respecting objects. If our -apprehension of objects must be regulated by the properties of the -objects, I cannot comprehend how we can possibly know anything about -them _à priori_. But if the object, as apprehended by us, be regulated -by the constitution of our faculties of apprehension, I can readily -conceive this possibility." From this he infers that our experience -must be regulated by our conceptions. - - -10. This view of the nature of knowledge soon superseded entirely -the doctrines of the Sensational School among the metaphysicians of -Germany. These philosophers did not gradually modify and reject the -dogmas of Locke and Condillac, as was done in England and France[246]; -nor did they endeavour to ascertain the extent of the empire of Ideas -by a careful survey of its several provinces, as we have been doing in -this series of works. The German metaphysicians saw at once that Ideas -and Things, the Subjective and the Objective elements of our knowledge, -were, by Kant's system, brought into opposition and correlation, as -equally real and equally indispensable. Seeing this, they rushed at -once to the highest and most difficult problem of philosophy,--to -determine what this correlation is;--to discover how Ideas and Things -are at the same time opposite and identical;--how the world, while it -is distinct from and independent of us, is yet, as an object of our -knowledge, governed by the conditions of our thoughts. The attempts -to solve this problem, taken in the widest sense, including the forms -which it assumes in Morals, Politics, the Arts, and Religion, as well -as in the Material Sciences, have, since that time, occupied the most -profound speculators of Germany; and have given rise to a number of -systems, which, rapidly succeeding each other, have, each in its day, -been looked upon as a complete solution of the problem. To trace the -characters of these various systems, does not belong to the business of -the present chapter: my task is ended when I have shown, as I have now -done, how the progress of thought in the philosophical world, followed -from the earliest up to the present time, has led to that recognition -of the co-existence and joint necessity of the two opposite elements -of our knowledge; and when I have pointed out processes adapted to -the extension of our knowledge, which a true view of its nature has -suggested or may suggest. - -The latter portion of this task occupies the Third Book of the _Novum -Organon Renovatum_. With regard to the recent succession of German -systems of philosophy, I shall add something in a subsequent chapter: -and I shall also venture to trace further than I have yet done, the -bearing of the philosophy of science upon the theological view of the -universe and the moral and religious condition of man. - - -FOOTNOTES: - -[Footnote 235: See Mr. Sharpe's _Essays_.] - -[Footnote 236: Price's _Essays_, p. 16.] - -[Footnote 237: P. 18.] - -[Footnote 238: Reid, _Essays on the Powers of the Human Mind_, iii. 31.] - -[Footnote 239: Stewart, _Outlines of Moral Phil._ p. 138.] - -[Footnote 240: Whately, _Polit. Econ._ p. 76.] - -[Footnote 241: Cousin, _Fragmens Philosophiques_, i. 53.] - -[Footnote 242: _Ibid._ i. 67.] - -[Footnote 243: See also the vigorous critique of Locke's _Essay_, by -Lemaistre, _Soirées de St. Petersbourg_.] - -[Footnote 244: Ampère, _Essai_, p. 210.] - -[Footnote 245: _Kritik der Reinen Vernunft_, Pref. p. xv.] - -[Footnote 246: The sensational system never acquired in Germany the -ascendancy which it obtained in England and France; but I am compelled -here to pass over the history of philosophy in Germany, except so far -as it affects ourselves.] - - - - -CHAPTER XXI. - -FURTHER ADVANCE OF THE SENSATIONAL SCHOOL. - -M. AUGUSTE COMTE. - - -I shall now take the liberty of noticing the views published by a -contemporary writer; not that it forms part of my design to offer -any criticism upon the writings of all those who have treated of -those subjects on which we are now employed; but because we can -more distinctly in this manner point out the contrasts and ultimate -tendencies of the several systems of opinion which have come under -our survey: and since from among these systems we have endeavoured to -extract and secure the portion of truth which remains in each, and -to reject the rest, we are led to point out the errors on which our -attention is thus fixed, in recent as well as older writers. - -M. Auguste Comte published in 1830 the first, and in 1835 the second -volume of his _Cours de Philosophie Positive_; of which the aim is not -much different from that of the present work, since as he states (p. -viii.) such a title as the _Philosophy of the Sciences_ would describe -a part of his object, and would be inappropriate only by excluding that -portion (not yet published) which refers to speculations concerning -social relations. - - -1. _M. Comte on Three States of Science._--By employing the term -_Philosophie Positive_, he wishes to distinguish the philosophy -involved in the present state of our sciences from the previous forms -of human knowledge. For according to him, each branch of knowledge -passes, in the course of man's history, through three different states; -it is first _theological_, then _metaphysical_, then _positive_. By -the latter term he implies a state which includes nothing but general -representations of facts;--phenomena _arranged according_ to relations -of succession and resemblance. This "positive philosophy" rejects all -inquiry after causes, which inquiry he holds to be void of sense[247] -and inaccessible. All such conceptions belong to the "metaphysical" -state of science which deals with abstract forces, real entities, -and the like. Still more completely does he reject, as altogether -antiquated and absurd, the "theological" view of phenomena. Indeed he -conceives[248] that any one's own consciousness of what passes within -himself is sufficient to convince him of the truth of the law of the -three phases through which knowledge must pass. "Does not each of us," -he says, "in contemplating his own history, recollect that he has been -successively a _theologian_ in his infancy, a _metaphysician_ in his -youth, and a _physicist_ in his ripe age? This may easily be verified -for all men who are up to the level of their time." - -It is plain from such statements, and from the whole course of his -work, that M. Comte holds, in their most rigorous form, the doctrines -to which the speculations of Locke and his successors led; and which -tended, as we have seen, to the exclusion of all ideas except those -of number and resemblance. As M. Comte refuses to admit into his -philosophy the fundamental idea of Cause, he of course excludes most of -the other ideas, which are, as we endeavoured to show, the foundations -of science; such as the ideas of Media by which secondary qualities are -made known to us; the ideas of Chemical Attraction, of Polar Forces, -and the like. He would reduce all science to the mere expression of -laws of phenomena, expressed in formulæ of space, time, and number; and -would condemn as unmeaning, and as belonging to an obsolete state of -science, all endeavours to determine the causes of phenomena, or even -to refer them to any of the other ideas just mentioned. - - -2. _M. Comte rejects the Search of Causes._--In a previous work[249] -I have shown, I trust decisively, that it is the genuine office -of science to inquire into the causes as well as the laws of -phenomena;--that such an inquiry cannot be avoided; and that it has -been the source of almost all the science we possess. I need not here -repeat the arguments there urged; but I may make a remark or two upon -M. Comte's hypothesis, that all science is first "metaphysical" and -then "positive;" since it is in virtue of this hypothesis that he -rejects the investigation of causes, as worthy only of the infancy -of science. All discussions concerning ideas, M. Comte would condemn -as "metaphysical," and would consider as mere preludes to positive -philosophy. Now I venture to assert, on the contrary, that discussions -concerning ideas, and real discoveries, have in every science gone -hand in hand. There is no science in which the pretended order of -things can be pointed out. There is no science in which the discoveries -of the laws of phenomena, when once begun, have been carried on -independently of discussions concerning ideas. There is no science -in which the expression of the laws of phenomena can at this time -dispense with ideas which have acquired their place in science in -virtue of metaphysical considerations. There is no science in which -the most active disquisitions concerning ideas did not come _after_, -not _before_, the first discovery of laws of phenomena. In Astronomy, -the discovery of the phenomenal laws of the epicyclical motions of the -heavens led to assumptions of the metaphysical principle of equable -circular motions: Kepler's discoveries would never have been made -but for his metaphysical notions. These discoveries of the laws of -phenomena did not lead immediately to Newton's theory, _because_ a -century of metaphysical discussions was requisite as a preparation. -Newton then discovered, not merely a law of phenomena, but a _cause_; -and _therefore_ he was the greatest of discoverers. The same is the -case in Optics; the ancients possessed some share of our knowledge -of facts; but meddled little with the metaphysical reasonings of the -subject. In modern times when men began to inquire into the _nature_ -of light, they soon extended their knowledge of its _laws_. When this -series of discoveries had come to a pause, a new series of brilliant -discoveries of laws of phenomena went on, inseparably connected with a -new series of views of the nature and cause of light. In like manner, -the most modern discoveries in chemistry involve indispensably the idea -of polar forces. The metaphysics (in M. Comte's sense) of each subject -advances in a parallel line with the knowledge of physical laws. The -Explication of Conceptions must go on, as we have already shown, at the -same rate as the Colligation of Facts. - -M. Comte will say[250] that Newton's discovery of gravitation only -consists in exhibiting the astronomical phenomena of the universe -as one single fact under different points of view. But this _fact_ -involves the idea of _force_, that is, of _cause_. And that this idea -is not a mere modification of the ideas of time and space, we have -shown: if it were so, how could it lead to the axiom that attraction -is mutual, an indispensable part of the Newtonian theory? M. Comte -says[251] that we do not know what attraction is, since we can only -define it by identical phrases: but this is just as true of space, -or time, or motion; and is in fact exactly the characteristic of a -fundamental idea. We do not obtain such ideas from definitions, but we -possess them not the less truly because we cannot define them. - -That M. Comte's hypothesis is historically false, is obvious by such -examples as I have mentioned. Metaphysical discussions have been -essential steps in the progress of each science. If we arbitrarily -reject all these portions of scientific history as useless trifling, -belonging to the first rude attempts at knowledge, we shall not only -distort the progress of things, but pervert the plainest facts. Of -this we have an example in M. Comte's account of Kepler's mechanical -speculations. We have seen, in the History of Physical Astronomy, that -Kepler's second law, (that the planets describe areas about the sun -proportional to the times,) was proved by him, by means of calculations -founded on the observations of Tycho; but that the mechanical reason -of it was not assigned till a later period, when it appeared as the -first proposition of Newton's _Principia_. It is plain from the -writings of Kepler, that it was impossible for him to show how this -law resulted from the forces which were in action; since the forces -which he considered were not those tending to the centre, which really -determine the property in question, but forces exerted by the sun _in -the direction of the planet's motion_, without which forces Kepler -conceived that the motion could not go on. In short, the state of -mechanical science in Kepler's time was such that no demonstration of -the law could be given. The terms in which such a demonstration must -be expressed had not at that time acquired a precise significance; and -it was in virtue of many subsequent _metaphysical_ discussions (as M. -Comte would term them) that these terms became capable of expressing -sound mechanical reasoning. Kepler did indeed pretend to assign what -he called a "physical proof" of his law, depending upon this, that the -sun's force is less at greater distances; a condition which does not -at all influence the result. Thus Kepler's reason for his law proves -nothing but the confusion of thought in which he was involved on such -subjects. Yet M. Comte assigns to Kepler the credit of having proved -this law by sound mechanical reasoning, as well as established it as -a matter of fact[252]. "This discovery by Kepler," he adds, "is the -more remarkable, inasmuch as it occurred before the science of dynamics -had really been created by Galileo." We may remark that inasmuch as M. -Comte perceived this incongruity in the facts as he stated them, it is -the more remarkable that he did not examine them more carefully. - - -3. _Causes in Physics._--The condemnation of the inquiry into causes -which is conveyed in M. Comte's notion of the three stages of Science, -he again expresses more in detail, in stating[253] what he calls his -_Fundamental theory of hypotheses_. This "theory" is, that we may -employ hypotheses in our natural philosophy, but these hypotheses -must always be such as admit of a positive verification. We must have -no suppositions concerning the agents by which effects are produced. -All such suppositions have an anti-scientific character, and can only -impede the real progress of physics. There can be no use in the ethers -and imaginary fluids to which some persons refer the phenomena of heat, -light, electricity and magnetism. And in agreement with this doctrine, -M. Comte in his account[254] of the Science of Optics, condemns, as -utterly unphilosophical and absurd, both the theory of emission and -that of undulation. - -To this we reply, that theory of one kind or other is indispensable -to the expression of the phenomena; and that when the laws are -expressed, and apparently explained, by means of a theory, to forbid -us to inquire whether it be really true or false, is a pedantic and -capricious limitation of our knowledge, to which the intellect of man -neither can nor should submit. If any one holds the adoption of one or -other of these theories to be indifferent, let him express the _laws -of phenomena_ of diffraction in terms of the theory of emission[255]. -If any one rejects the doctrine of undulation, let him point out some -other way of connecting double refraction with polarization. And -surely no man of science will contend that the beautiful branch of -science which refers to that connexion is not a portion of our positive -knowledge. - -M. Comte's contempt for the speculations of the undulationists seems -to have prevented his acquainting himself with their reasonings, and -even with the laws of phenomena on which they have reasoned, although -these form by far the most striking and beautiful addition which -Science has received in modern times. He adduces, as an insuperable -objection to the undulatory theory, a difficulty which is fully -removed by calculation in every work on the subject:--the existence -of shadow[256]. He barely mentions the subject of diffraction, and -Young's law of interferences;--speaks of Fresnel as having applied this -principle to the phenomena of coloured rings, "on which the ingenious -labours of Newton left much to desire;" as if Fresnel's labours on -this subject had been the supplement of those of Newton: and after -regretting that "this principle of interferences has not yet been -distinctly disentangled from chemical conceptions on the nature of -light," concludes his chapter. He does not even mention the phenomena -of dipolarization, of circular and elliptical polarization, or of the -optical properties of crystals; discoveries of laws of phenomena quite -as remarkable as any which can be mentioned. - -M. Comte's favourite example of physical research is Thermotics, and -especially Fourier's researches with regard to heat. It is shown[257] -in the History of Thermotics, that the general phenomena of radiation -required the assumption of a fluid to express them; as appears in the -_theory of exchanges_[258]. And the explanation of the principal laws -of radiation, which Fourier gives, depends upon the conception of -material molecular radiation. The _flux_ of caloric, of which Fourier -speaks, cannot be conceived otherwise than as implying a material -flow. M. Comte apologizes[259] for this expression, as too figurative, -and says that it merely indicates a _fact_. But what is the flow of a -current of fluid except a fact? And is it not evident that without such -expressions, and the ideas corresponding to them, Fourier could neither -have conveyed nor conceived his theory? - -In concluding this discussion it must be recollected, that though -it is a most narrow and untenable rule to say that we will admit no -agency of ethers and fluids into philosophy; yet the reality of such -agents is only to be held in the way, and to the extent, which the laws -of phenomena indicate. It is not only allowable, but inevitable to -assume, as the vehicle of heat and light, a medium possessing some of -the properties of more familiar kinds of matter. But the idea of such -a medium, which we possess, and on which we cannot but reason, can be -fully developed only by an assiduous study of the cases in which it is -applicable. It may be, that as science advances, all our knowledge may -converge to one general and single aspect of the universe. We abandon -and reject this hope, if we refuse to admit those ideas which must -be our stepping-stones in advancing to such a point: and we no less -frustrate such an expectation, if we allow ourselves to imagine that -from our present position we can stride at once to the summit. - - -4. _Causes in other Sciences._--But if it is, in the sciences just -mentioned, impracticable to reduce our knowledge to laws of phenomena -alone, without referring to causes, media, and other agencies; how much -more plainly is it impossible to confine our thoughts to phenomena, -and to laws of succession and resemblance, in other sciences, as -chemistry, physiology, and geology? Who shall forbid us, or why should -we be forbidden, to inquire whether chemical and galvanic forces are -identical; whether irritability is a peculiar vital power; whether -geological causes have been uniform or paroxysmal? To exclude such -inquiries, would be to secure ourselves from the poison of error by -abstaining from the banquet of truth:--it would be to attempt to feed -our minds with the meagre diet of space and number, because we may find -too delightful a relish in such matters as cause and end, symmetry and -affinity, organization and development. - -Thus M. Comte's arrangement of the progress of science as successively -metaphysical and positive, is contrary to history in fact, and contrary -to sound philosophy in principle. Nor is there any better foundation -for his statement that theological views are to be found only in the -rude infantine condition of human knowledge, and vanish as science -advances. Even in material sciences this is not the case. We have -shown in the chapter on Final Causes, that physiologists have been -directed in their remarks by the conviction of a purpose in every -part of the structure of animals; and that this idea, which had its -rise _after_ the first observations, has gone on constantly gaining -strength and clearness, so that it is now the basis of a large portion -of the science. We have seen, too, in the Book on the palætiological -sciences, that the researches of that class do by no means lead us to -reject an origin of the series of events, nor to suppose this origin -to be included in the series of natural laws. Science has not at all -shown any reason for denying either the creation or the purpose of the -universe. - -This is true of those aspects of the universe which have become the -subjects of rigorous science: but how small a portion of the whole do -they form! Especially how minute a proportion does our knowledge bear -to our ignorance, if we admit into science, as M. Comte advises, only -the laws of phenomena! Even in the best explored fields of science, how -few such laws do we know! Meteorology, climate, terrestrial magnetism, -the colours and other properties of bodies, the conditions of musical -and articulate sound, and a thousand other facts of physics, are not -defined by any known laws. In physiology we may readily convince -ourselves how little we know of laws, since we can hardly study one -species without discovering some unguessed property, or apply the -microscope without seeing some new structure in the best known organs. -And when we go on to social and moral and political matters, we may -well doubt whether any one single rigorous rule of phenomena has ever -been stated, although on such subjects man's ideas have been busily -and eagerly working ever since his origin. What a wanton and baseless -assumption it would be, then, to reject those suggestions of a Governor -of the universe which we derive from man's moral and spiritual nature, -and from the institutions of society, because we fancy we see in the -small field of our existing "positive knowledge" a tendency to exclude -"theological views!" Because we can explain the motion of the stars by -a general Law which seems to imply no hyperphysical agency, and can -trace a few more limited laws in other properties of matter, we are -exhorted to reject convictions irresistibly suggested to us by our -bodies and our souls, by history and antiquities, by conscience and -human law. - - -5. _M. Comte's practical philosophy._--It is not merely as a -speculative doctrine that M. Comte urges the necessity of our thus -following the guidance of "positive philosophy." The fevered and -revolutionary condition of human society at present arises, according -to him[260], from the simultaneous employment of three kinds of -philosophy radically incompatible;--theological, metaphysical, and -positive philosophy. The remedy for the evil is to reject the two -former, and to refer everything to that positive philosophy, of which -the destined triumph cannot be doubtful. In like manner, our European -education[261], still essentially theological, metaphysical, and -literary, must be replaced by a _positive_ education, suited to the -spirit of our epoch. - -With these practical consequences of M. Comte's philosophy we are not -here concerned: but the notice of them may serve to show how entirely -the rejection of the theological view pervades his system; and how -closely this rejection is connected with the principles which lead -him also to reject the fundamental ideas of the sciences as we have -presented them. - - -6. _M. Comte on Hypotheses._--In the detail of M. Comte's work, I do -not find any peculiar or novel remarks on the induction by which the -sciences are formed; except we may notice, as such, his permission of -hypotheses to the inquirer, already referred to. "There can only be," -he says[262], "two general modes fitted to reveal to us, in a direct -and entirely rational manner, the true law of any phenomenon;--either -the immediate analysis of this phenomenon, or its exact and evident -relation to some more extended law, previously established;--in a word, -_induction_, or _deduction_. But both these ways would certainly be -insufficient, even with regard to the simplest phenomenon, in the eyes -of any one who fully comprehends the essential difficulties of the -intimate study of nature, if we did not often begin by anticipating -the result, and making a provisory supposition, at first essentially -conjectural, even with respect to some of the notions which constitute -the final object of inquiry. Hence the introduction, which is strictly -indispensable, of hypotheses in natural philosophy." We have already -seen that the "permissio intellectus" had been noticed as a requisite -step in discovery, as long before as the time of Bacon. - - -7. _M. Comte's Classification of Sciences._--I do not think it -necessary to examine in detail M. Comte's views of the philosophy of -the different sciences; but it may illustrate the object of the present -work, to make a remark upon his attempt to establish a distinction -between physical and chemical science. This distinction he makes to -consist in three points[263];--that Physics considers general and -Chemistry special properties;--that Physics considers masses and -Chemistry molecules;--that in Physics the mode of arrangement of -the molecules remains constant, while in Chemistry this arrangement -is necessarily altered. M. Comte however allows that these lines -of distinction are vague and insecure; for, among many others, -magnetism, a special property, belongs to physics, and breaks down -his first criterion; and molecular attractions are a constant subject -of speculation in physics, so that the second distinction cannot be -insisted on. To which we may add that the greater portion of chemistry -does not attend at all to the arrangement of the molecules, so that -the third character is quite erroneous. The real distinction of -these branches of science is, as we have seen, the fundamental ideas -which they employ. Physics deals with relations of space, time, and -number, media, and scales of qualities, according to intensity and -other differences; while chemistry has for its subject elements and -attractions as shown in composition; and polarity, though in different -senses, belongs to both. The failure of this attempt of M. Comte at -distinguishing these provinces of science by their objects, may be -looked upon as an illustration of the impossibility of establishing a -philosophy of the sciences on any other ground than the ideas which -they involve. - -We have thus traced to its extreme point, so far as the nature -of science is concerned, one of those two antagonistic opinions, -of which the struggle began in the outset of philosophy, and has -continued during the whole of her progress;--namely, the opinions -which respectively make our sensations and our ideas the origin of our -knowledge. The former, if it be consistent with itself, must consider -all knowledge of causes as impossible, since no sensation can give us -the idea of cause. And when this opinion is applied to science, it -reduces it to the mere investigation of laws of phenomena, according -to relations of space, time, and number. I purposely abstain, as far -as possible, from the consideration of the other consequences, not -strictly belonging to the physical sciences, which were drawn from -the doctrine that all our ideas are only transformed sensations. The -materialism, the atheism, the sensualist morality, the anarchical -polity, which some of the disciples of the Sensational School erected -upon the fundamental dogmas of their sect, do not belong to our -present subject, and are matters too weighty to be treated of as mere -accessories. - - * * * * * - -The above Remarks were written before I had seen the third volume of M. -Comte's work, or the subsequent volumes. But I do not find, in anything -which those volumes contain, any ground for altering what I have -written. Indeed they are occupied altogether with subjects which do not -come within the field of my present speculations. - - -FOOTNOTES: - -[Footnote 247: i. p. 14.] - -[Footnote 248: i. p. 7.] - -[Footnote 249: _Hist. Ind. Sc._ b. xi. c. vii.] - -[Footnote 250: P. 15.] - -[Footnote 251: P. 16.] - -[Footnote 252: M. Comte's statement is so entirely at variance with the -fact that I must quote it here. (_Phil. Pos._ vol. i. p. 705.) - -"Le second théorème général de dynamique consiste dans le célèbre et -important _principe des aires_, dont le première idée est due à Kepler, -qui découvrit et démontra forte simplement cette propriété pour le cas -du mouvement d'une molecule unique, ou en d'autres terms, d'un corps -dont tous les points se meuvent identiquement. Kepler établit, par les -considérations les plus élémentaires, qui si la force accélératrice -totale dont une molecule est animée tend constamment vers un point -fixé, le rayon vecteur du mobile décrit autour de ce point des aires -égales en temps egaux, de telle sorte que l'aire décrite au bout d'un -temps quelconque croît proportionellement à ce temps. Il fit voir en -outre que réciproquement, si une semblable relation a été vérifiée -dans le mouvement d'un corps par rapport à un certain point, c'est une -preuve suffisante de l'action sur le corps d'un force dirigée sans -cesse vers ce point." - -There is not a trace of the above propositions in the work _De Stellâ -Martis_, which contains Kepler's discovery of his law, nor, I am -convinced, in any other of Kepler's works. He is everywhere constant to -his conceptions of the _magnetic_ virtue residing in the sun, by means -of which the sun, revolving on his axis, carries the planets round with -him. M. Comte's statement so exactly expresses _Newton's_ propositions, -that one is led to suspect some extraordinary mistake, by which what -should have been said of the one was transferred to the other.] - -[Footnote 253: Vol. ii. p. 433.] - -[Footnote 254: Vol. ii. 640.] - -[Footnote 255: I venture to offer this problem;--to express the -_laws of the phenomena_ of diffraction without the hypothesis of -undulations;--as a challenge to any one who holds such hypothesis to be -unphilosophical.] - -[Footnote 256: ii. p. 641.] - -[Footnote 257: ii. p. 673.] - -[Footnote 258: _Hist. Ind. Sc._ ii. 489, b. x. c. i.] - -[Footnote 259: ii. p. 561.] - -[Footnote 260: i. 50.] - -[Footnote 261: i. 41.] - -[Footnote 262: ii. 433.] - -[Footnote 263: _Phil. Pos._ ii. 392-398.] - - - - -CHAPTER XXII. - -MR. MILL'S LOGIC[264]. - - -The _History of the Inductive Sciences_ was published in 1837, and -the _Philosophy of the Inductive Sciences_ in 1840. In 1843 Mr. Mill -published his _System of Logic_, in which he states that without the -aid derived from the facts and ideas in my volumes, the corresponding -portion of his own would most probably not have been written, and -quotes parts of what I have said with commendation. He also, however, -dissents from me on several important and fundamental points, and -argues against what I have said thereon. I conceive that it may tend -to bring into a clearer light the doctrines which I have tried to -establish, and the truth of them, if I discuss some of the differences -between us, which I shall proceed to do[265]. - -Mr. Mill's work has had, for a work of its abstruse character, a -circulation so extensive, and admirers so numerous and so fervent, that -it needs no commendation of mine. But if my main concern at present -had not been with the points in which Mr. Mill _differs_ from me, I -should have had great pleasure in pointing out passages, of which there -are many, in which Mr. Mill appears to me to have been very happy in -promoting or in expressing philosophical truth. - -There is one portion of his work indeed which tends to give it an -interest of a wider kind than belongs to that merely scientific truth -to which I purposely and resolutely confined my speculations in the -works to which I have referred. Mr. Mill has introduced into his work -a direct and extensive consideration of the modes of dealing with -moral and political as well as physical questions; and I have no doubt -that this part of his book has, for many of his readers, a more lively -interest than any other. Such a comprehensive scheme seems to give to -doctrines respecting science a value and a purpose which they cannot -have, so long as they are restricted to mere material sciences. I still -retain the opinion, however, upon which I formerly acted, that the -philosophy of science is to be extracted from the portions of science -which are universally allowed to be most certainly established, and -that those are the physical sciences. I am very far from saying, or -thinking, that there is no such thing as Moral and Political Science, -or that no method can be suggested for its promotion; but I think that -by attempting at present to include the Moral Sciences in the same -formulæ with the Physical, we open far more controversies than we -close; and that in the moral as in the physical sciences, the first -step towards showing how truth is to be discovered, is to study some -portion of it which is assented to so as to be beyond controversy. - - -1. _What is Induction?_--1. Confining myself, then, to the material -sciences, I shall proceed to offer my remarks on Induction with -especial reference to Mr. Mill's work. And in order that we may, as -I have said, proceed as intelligibly as possible, let us begin by -considering what we mean by _Induction_, as a mode of obtaining truth; -and let us note whether there is any difference between Mr. Mill and me -on this subject. - -"For the purposes of the present inquiry," Mr. Mill says (i. 347[266]), -"Induction may be defined the operation of discovering and forming -general propositions:" meaning, as appears by the context, the -discovery of them from particular facts. He elsewhere (i. 370) terms -it "generalization from experience:" and again he speaks of it with -greater precision as the inference of a more general proposition from -less general ones. - -2. Now to these definitions and descriptions I assent as far as they -go; though, as I shall have to remark, they appear to me to leave -unnoticed a feature which is very important, and which occurs in all -cases of Induction, so far as we are concerned with it. Science, then, -consists of general propositions, inferred from particular facts, or -from less general propositions, by Induction; and it is our object to -discern the nature and laws of _Induction_ in this sense. That the -propositions are general, or are more general than the facts from which -they are inferred, is an indispensable part of the notion of Induction, -and is essential to any discussion of the process, as the mode of -arriving at Science, that is, at a body of general truths. - -3. I am obliged therefore to dissent from Mr. Mill when he includes, in -his notion of Induction, the process by which we arrive _at individual -facts_ from other facts _of the same order of particularity_. - -Such inference is, at any rate, not Induction _alone_; if it be -Induction at all, it is Induction applied to an example. - -For instance, it is a general law, obtained by Induction from -particular facts, that a body falling vertically downwards from rest, -describes spaces proportional to the squares of the times. But that a -particular body will fall through 16 feet in one second and 64 feet in -two seconds, is not an induction simply, it is a result obtained by -applying the inductive law to a particular case. - -But further, such a process is often not induction _at all_. That a -ball striking another ball directly will communicate to it as much -momentum as the striking ball itself loses, is a law established -by induction: but if, from habit or practical skill, I make one -billiard-ball strike another, so as to produce the velocity which -I wish, without knowing or thinking of the general law, the term -_Induction_ cannot then be rightly applied. If I _know the law_ and -act upon it, I have in my mind both the general induction and its -particular application. But if I act by the ordinary billiard-player's -skill, without thinking of momentum or law, there is no Induction in -the case. - -4. This distinction becomes of importance, in reference to Mr. Mill's -doctrine, because he has extended his use of the term _Induction_, not -only to the cases in which the general induction is consciously applied -to a particular instance; but to the cases in which the particular -instance is dealt with by means of experience, in that rude sense in -which _experience_ can be asserted of brutes; and in which, of course, -we can in no way imagine that the law is possessed or understood, as a -general proposition. He has thus, as I conceive, overlooked the broad -and essential difference between speculative knowledge and practical -action; and has introduced cases which are quite foreign to the idea -of science, alongside with cases from which we may hope to obtain some -views of the nature of science and the processes by which it must be -formed. - -5. Thus (ii. 232) he says, "This inference of one particular fact from -another is a case of induction. It is of this sort of induction that -brutes are capable." And to the same purpose he had previously said (i. -251), "He [the burnt child who shuns the fire] is not generalizing: -he is inferring a particular from particulars. In the same way also, -brutes reason ... not only the burnt child, but the burnt dog, dreads -the fire." - -6. This confusion, (for such it seems to me,) of knowledge with -practical tendencies, is expressed more in detail in other places. Thus -he says (i. 118), "I cannot dig the ground unless I have an idea of the -ground and of a spade, and of all the other things I am operating upon." - -7. This appears to me to be a use of words which can only tend to -confuse our idea of knowledge by obliterating all that is distinctive -in _human_ knowledge. It seems to me quite false to say that I cannot -dig the ground, unless I have an idea of the ground and of my spade. -Are we to say that we cannot _walk_ the ground, unless we have an idea -of the ground, and of our feet, and of our shoes, and of the muscles of -our legs? Are we to say that a mole cannot dig the ground, unless he -has an idea of the ground and of the snout and paws with which he digs -it? Are we to say that a pholas cannot perforate a rock, unless he have -an idea of the rock, and of the acid with which he corrodes it? - -8. This appears to me, as I have said, to be a line of speculation -which can lead to nothing but confusion. The knowledge concerning which -I wish to inquire is _human_ knowledge. And in order that I may have -any chance of success in the inquiry, I find it necessary to single -out that kind of knowledge which is especially and distinctively -human. Hence, I pass by, in this part of my investigation, all the -_knowledge_, if it is to be so called, which man has in no other way -than brutes have it;--all that merely shows itself in action. For -though action may be modified by habit, and habit by experience, in -animals as well as in men, such experience, so long as it retains -that merely practical form, is no part of the materials of science. -Knowledge in a _general_ form, is alone knowledge for that purpose; -and to _that_, therefore, I must confine my attention; at least till -I have made some progress in ascertaining its nature and laws, and am -thus prepared to compare such knowledge,--_human knowledge_ properly so -called,--with mere animal tendencies to action; or even with practical -skill which does not include, as for the most part practical skill does -not include, speculative knowledge. - -9. And thus, I accept Mr. Mill's definition of Induction only in its -first and largest form; and reject, as useless and mischievous for our -purposes, his extension of the term to the practical influence which -experience of one fact exercises upon a creature dealing with similar -facts. Such influence cannot be resolved into _ideas_ and _induction_, -without, as I conceive, making all our subsequent investigation vague -and heterogeneous, indefinite and inconclusive. If we must speak of -animals as _learning_ from experience, we may at least abstain from -applying to them terms which imply that they learn, in the same way -in which men learn astronomy from the stars, and chemistry from the -effects of mixture and heat. And the same may be said of the language -which is to be used concerning what _men_ learn, when their _learning_ -merely shows itself in action, and does not exist as a general thought. -_Induction_ must not be applied to such cases. _Induction_ must be -confined to cases where we have in our minds general propositions, in -order that the sciences, which are our most instructive examples of the -process we have to consider, may be, in any definite and proper sense, -_Inductive_ Sciences. - -10. Perhaps some persons may be inclined to say that this difference -of opinion, as to the extent of meaning which is to be given to the -term _Induction_, is a question merely of words; a matter of definition -only. This is a mode in which men in our time often seem inclined to -dispose of philosophical questions; thus evading the task of forming -an opinion upon such questions, while they retain the air of looking -at the subject from a more comprehensive point of view. But as I have -elsewhere said, such questions of definition are never questions -of definition merely. A proposition is always implied along with -the definition; and the truth of the proposition depends upon the -settlement of the definition. This is the case in the present instance. -We are speaking of _Induction_, and we mean that kind of Induction -by which the sciences now existing among men have been constructed. -On this account it is, that we cannot include, in the meaning of the -term, mere practical tendencies or practical habits; for science is not -constructed of these. No accumulation of these would make up any of the -acknowledged sciences. The elements of such sciences are something of a -kind different from practical habits. The elements of such sciences are -principles which we _know_; truths which can be contemplated as being -_true_. Practical habits, practical skill, instincts and the like, -appear in action, and in action only. Such endowments or acquirements -show themselves when the occasion for action arrives, and then, show -themselves in the act; without being put, or being capable of being -put, in the form of truths contemplated by the intellect. But the -elements and materials of Science are necessary truths contemplated by -the intellect. It is by consisting of such elements and such materials, -that Science _is_ Science. Hence a use of the term _Induction_ which -requires us to obliterate this distinction, must make it impossible for -us to arrive at any consistent and intelligible view of the nature of -Science, and of the mental process by which Sciences come into being. -We must, for the purpose which Mr. Mill and I have in common, retain -his larger and more philosophical definition of Induction,--that it is -the inference of a more general proposition from less general ones. - -11. Perhaps, again, some persons may say, that practical skill and -practical experience _lead_ to science, and may therefore be included -in the term _Induction_, which describes the formation of science. But -to this we reply, that these things lead to science as occasions only, -and do not form part of science; and that science begins then only -when we look at the facts in a general point of view. This distinction -is essential to the philosophy of science. The rope-dancer may, by -his performances, suggest, to himself or to others, properties of -the center of gravity; but this is so, because man has a tendency to -speculate and to think of general truths, as well as a tendency to -dance on a rope on special occasions, and to acquire skill in such -dancing by practice. The rope-dancer does not dance by Induction, -any more than the dancing dog does. To apply the terms Science and -Induction to such cases, carries us into the regions of metaphor; -as when we call birds of passage "wise meteorologists," or the bee -"a natural chemist, who turns the flower-dust into honey." This is -very well in poetry: but for our purposes we must avoid recognizing -these cases as really belonging to the sciences of meteorology and -chemistry,--as really cases of Induction. Induction for us is general -propositions, _contemplated as such_, derived from particulars. - -Science may result _from_ experience and observation _by_ Induction; -but Induction is not therefore the same thing as experience and -observation. Induction is experience or observation _consciously_ -looked at in a _general_ form. This consciousness and generality are -necessary parts of that knowledge which is science. And accordingly, -on the other hand, science cannot result from mere Instinct, as -distinguished from Reason; because Instinct by its nature is not -conscious and general, but operates blindly and unconsciously in -particular cases, the actor not seeing or thinking of the rule which he -obeys. - -12. A little further on I shall endeavour to show that not only a -general _thought_, but a general _word_ or phrase is a requisite -element in Induction. This doctrine, of course, still more decidedly -excludes the case of animals, and of mere practical knowledge in man. -A burnt child dreads the fire; but reason must be unfolded, before the -child learns to understand the words "fire will hurt you." The burnt -dog never thus learns to understand words. And this difference points -to an entirely different state of thought in the two cases: or rather, -to a difference between a state of rational thought on the one hand, -and of mere practical instinct on the other. - -13. Besides this difference of speculative thought and practical -instinct which thus are, as appears to me, confounded in Mr. Mill's -philosophy, in such a way as tends to destroy all coherent views of -human knowledge, there is another set of cases to which Mr. Mill -applies the term _Induction_, and to which it appears to me to be -altogether inapplicable. He employs it to describe the mode in which -superstitious men, in ignorant ages, were led to the opinion that -striking natural events presaged or accompanied calamities. Thus he -says (i. 389), "The opinion so long prevalent that a comet or any -other unusual appearance in the heavenly regions was the precursor of -calamities to mankind, or at least to those who witnessed it; the -belief in the oracles of Delphi and Dodona; the reliance on astrology, -or on the weather-prophecies in almanacs; were doubtless inductions -supposed to be grounded on experience;" and he speaks of these -insufficient inductions being extinguished by the stronger inductions -subsequently obtained by scientific inquiry. And in like manner, -he says in another place (i. 367), "Let us now compare different -predictions: the first, that eclipses will occur whenever one planet -or satellite is so situated as to cast its shadow upon another: the -second, that they will occur whenever some great calamity is impending -over mankind." - -14. Now I cannot see how anything but confusion can arise from -applying the term _Induction_ to superstitious fancies like those -here mentioned. They are not imperfect truths, but entire falsehoods. -Of that, Mr. Mill and I are agreed: how then can they exemplify the -progress towards truth? They were not collected from the facts by -seeking a law of their occurrence; but were suggested by an imagination -of the anger of superior powers shown by such deviations from the -ordinary course of nature. If we are to speak of _inductions_ to any -purpose, they must be such inductions as represent the facts, in some -degree at least. It is not meant, I presume, that these opinions are in -any degree true: to what purpose then are they adduced? If I were to -hold that my dreams predict or conform to the motions of the stars or -of the clouds, would this be an induction? It would be so, as much one -as those here so denominated: yet what but confusion could arise from -classing it among scientific truths? Mr. Mill himself has explained -(ii. 389) the way in which such delusions as the prophecies of -almanac-makers, and the like, obtain credence; namely, by the greater -effect which the positive instances produce on ordinary minds in -comparison with the negative, when the rule has once taken possession -of their thoughts. And this being, as he says, the recognized -explanation of such cases, why should we not leave them to their due -place, and not confound and perplex the whole of our investigation by -elevating them to the rank of "inductions"? The very condemnation of -such opinions is that they are not at all inductive. When we have made -any progress in our investigation of the nature of science, to attempt -to drive us back to the wearisome discussion of such elementary points -as these, is to make progress hopeless. - - -II. _Induction or Description?_--15. In the cases hitherto noticed, Mr. -Mill extends the term _Induction_, as I think, too widely, and applies -it to cases to which it is not rightly applicable. I have now to notice -a case of an opposite kind, in which he does not apply it where I do, -and condemns me for using it in such a case. I had spoken of Kepler's -discovery of the Law, that the planets move round the sun in ellipses, -as an example of Induction. The separate facts of any planet (Mars, for -instance,) being in certain places at certain times, are all included -in the general proposition which Kepler discovered, that Mars describes -an ellipse of a certain form and position. This appears to me a very -simple but a very distinct example of the operation of discovering -general propositions; general, that is, with reference to particular -facts; which operation Mr. Mill, as well as myself, says is Induction. -But Mr. Mill denies this operation in this case to be Induction at -all (i. 357). I should not have been prepared for this denial by the -previous parts of Mr. Mill's book, for he had said just before (i. -350), "such facts as the magnitudes of the bodies of the solar system, -their distances from each other, the figure of the earth and its -rotation ... are proved indirectly, by the aid of inductions founded -on other facts which we can more easily reach." If the figure of the -earth and its rotation are proved by Induction, it seems very strange, -and is to me quite incomprehensible, how the figure of the earth's -orbit and its revolution (and of course, of the figure of Mars's orbit -and his revolution in like manner,) are not also proved by Induction. -No, says Mr. Mill, Kepler, in putting together a number of places of -the planet into one figure, only performed an act of _description_. -"This descriptive operation," he adds (i. 359), "Mr. Whewell, by an -aptly chosen expression, has termed Colligation of Facts." He goes on -to commend my observations concerning this process, but says that, -according to the old and received meaning of the term, it is not -Induction at all. - -16. Now I have already shown that Mr. Mill himself, a few pages -earlier, had applied the term _Induction_ to cases undistinguishable -from this in any essential circumstance. And even in this case, he -allows that Kepler did really perform an act of Induction (i. 358), -"namely, in concluding that, because the observed places of Mars were -correctly represented by points in an imaginary ellipse, therefore Mars -would continue to revolve in that same ellipse; and even in concluding -that the position of the planet during the time which had intervened -between the two observations must have coincided with the intermediate -points of the curve." Of course, in Kepler's Induction, of which I -speak, I include all this; all this is included in speaking of the -_orbit_ of Mars: a continuous line, a periodical motion, are implied -in the term _orbit_. I am unable to see what would remain of Kepler's -discovery, if we take from it these conditions. It would not only not -be an induction, but it would not be a description, for it would not -recognize that Mars moved in an orbit. Are particular positions to be -conceived as points in a curve, without thinking of the intermediate -positions as belonging to the same curve? If so, there is no law at -all, and the facts are not bound together by any intelligible tie. - -In another place (ii. 209) Mr. Mill returns to his distinction of -Description and Induction; but without throwing any additional light -upon it, so far as I can see. - -17. The only meaning which I can discover in this attempted distinction -of Description and Induction is, that when particular facts are bound -together by their relation in _space_, Mr. Mill calls the discovery -of the connexion _Description_, but when they are connected by other -general relations, as time, cause and the like, Mr. Mill terms the -discovery of the connexion _Induction_. And this way of making a -distinction, would fall in with the doctrine of other parts of Mr. -Mill's book, in which he ascribes very peculiar attributes to space -and its relations, in comparison with other Ideas, (as I should call -them). But I cannot see any ground for this distinction, of connexion -according to space and other connexions of facts. - -To stand upon such a distinction, appears to me to be the way to miss -the general laws of the formation of science. For example: The ancients -discovered that the planets revolved in recurring periods, and thus -connected the observations of their motions according to the Idea of -_Time_. Kepler discovered that they revolved in ellipses, and thus -connected the observations according to the Idea of _Space_. Newton -discovered that they revolved in virtue of the Sun's attraction, and -thus connected the motions according to the Idea of _Force_. The first -and third of these discoveries are recognized on all hands as processes -of Induction. Why is the second to be called by a different name? or -what but confusion and perplexity can arise from refusing to class it -with the other two? It is, you say, Description. But such Description -is a kind of Induction, and must be spoken of as Induction, if we are -to speak of Induction as the process by which Science is formed: for -the three steps are all, the second in the same sense as the first -and third, in co-ordination with them, steps in the formation of -astronomical science. - -18. But, says Mr. Mill (i. 363), "it is a fact surely that the planet -does describe an ellipse, and a fact which we could see if we had -adequate visual organs and a suitable position." To this I should -reply: "Let it be so; and it is a fact, surely, that the planet does -move periodically: it is a fact, surely, that the planet is attracted -by the sun. Still, therefore, the asserted distinction fails to find a -ground." Perhaps Mr. Mill would remind us that the elliptical form of -the orbit is a fact which we could see if we had adequate visual organs -and a suitable position: but that force is a thing which we cannot -see. But this distinction also will not bear handling. Can we not see -a tree blown down by a storm, or a rock blown up by gunpowder? Do we -not here see force:--see it, that is, by its effects, the only way in -which we need to see it in the case of a planet, for the purposes of -our argument? Are not such operations of force, Facts which may be the -objects of sense? and is not the operation of the sun's Force a Fact -of the same kind, just as much as the elliptical form of orbit which -results from the action? If the latter be "surely a Fact," the former -is a Fact no less surely. - -19. In truth, as I have repeatedly had occasion to remark, all attempts -to frame an argument by the exclusive or emphatic appropriation of -the term _Fact_ to particular cases, are necessarily illusory and -inconclusive. There is no definite and stable distinction between Facts -and Theories; Facts and Laws; Facts and Inductions. Inductions, Laws, -Theories, which are true, _are_ Facts. Facts involve Inductions. It is -a fact that the moon is attracted by the earth, just as much as it is a -Fact that an apple falls from a tree. That the former fact is collected -by a more distinct and conscious Induction, does not make it the less -a Fact. That the orbit of Mars is a Fact--a true Description of the -path--does not make it the less a case of Induction. - -20. There is another argument which Mr. Mill employs in order to -show that there is a difference between mere colligation which is -description, and induction in the more proper sense of the term. He -notices with commendation a remark which I had made (i. 364), that -at different stages of the progress of science the facts had been -successfully connected by means of very different conceptions, while -yet the later conceptions have not contradicted, but included, so far -as they were true, the earlier: thus the ancient Greek representation -of the motions of the planets by means of epicycles and eccentrics, -was to a certain degree of accuracy true, and is not negatived, though -superseded, by the modern representation of the planets as describing -ellipses round the sun. And he then reasons that this, which is thus -true of Descriptions, cannot be true of Inductions. He says (i. 367), -"Different descriptions therefore may be all true: but surely not -different explanations." He then notices the various explanations of -the motions of the planets--the ancient doctrine that they are moved -by an inherent virtue; the Cartesian doctrine that they are moved by -impulse and by vortices; the Newtonian doctrine that they are governed -by a central force; and he adds, "Can it be said of these, as was said -of the different descriptions, that they are all true as far as they -go? Is it not true that one only can be true in any degree, and that -the other two must be altogether false?" - -21. And to this questioning, the history of science compels me to reply -very distinctly and positively, in the way which Mr. Mill appears to -think extravagant and absurd. I am obliged to say, Undoubtedly, all -these explanations _may_ be true and consistent with each other, and -would be so if each had been followed out so as to show in what manner -it could be made consistent with the facts. And this was, in reality, -in a great measure done[267]. The doctrine that the heavenly bodies -were moved by vortices was successively modified, so that it came to -coincide in its results with the doctrine of an inverse-quadratic -centripetal force, as I have remarked in the _History_[268]. When this -point was reached, the vortex was merely a machinery, well or ill -devised, for producing such a centripetal force, and therefore did not -contradict the doctrine of a centripetal force. Newton himself does -not appear to have been averse to explaining gravity by impulse. So -little is it true that if the one theory be true the other must be -false. The attempt to explain gravity by the impulse of streams of -particles flowing through the universe in all directions, which I have -mentioned in the _Philosophy_[269] so far from being inconsistent -with the Newtonian theory, that it is founded entirely upon it. And -even with regard to the doctrine, that the heavenly bodies move by -an inherent virtue; if this doctrine had been maintained in any such -way that it was brought to agree with the facts, the inherent virtue -must have had its laws determined; and then, it would have been found -that the virtue had a reference to the central body; and so, the -"inherent virtue" must have coincided in its effect with the Newtonian -force; and then, the two explanations would agree, except so far as -the word "inherent" was concerned. And if such a part of an earlier -theory as this word _inherent_ indicates, is found to be untenable, -it is of course rejected in the transition to later and more exact -theories, in Inductions of this kind, as well as in what Mr. Mill calls -Descriptions. There is therefore still no validity discoverable in the -distinction which Mr. Mill attempts to draw between "descriptions" like -Kepler's law of elliptical orbits, and other examples of induction. - -22. When Mr. Mill goes on to compare what he calls different -predictions--the first, the true explanation of eclipses by the shadows -which the planets and satellites cast upon one another, and the -other, the belief that they will occur whenever some great calamity -is impending over mankind, I must reply, as I have stated already, -(Art. 17), that to class such superstitions as the last with cases of -Induction, appears to me to confound all use of words, and to prevent, -as far as it goes, all profitable exercise of thought. What possible -advantage can result from comparing (as if they were alike) the -relation of two descriptions of a phenomenon, each to a certain extent -true, and therefore both consistent, with the relation of a scientific -truth to a false and baseless superstition? - -23. But I may make another remark on this example, so strangely -introduced. If, under the influence of fear and superstition, men -may make such mistakes with regard to laws of nature, as to imagine -that eclipses portend calamities, are they quite secure from mistakes -in _description_? Do not the very persons who tell us how eclipses -predict disasters, also describe to us fiery swords seen in the air, -and armies fighting in the sky? So that even in this extreme case, -at the very limit of the rational exercise of human powers, there is -nothing to distinguish Description from Induction. - -I shall now leave the reader to judge whether this feature in the -history of science,--that several views which appear at first quite -different are yet all true,--which Mr. Mill calls a curious and -interesting remark of mine, and which he allows to be "strikingly true" -of the Inductions which he calls _Descriptions_, (i. 364) is, as he -says, "unequivocally false" of other Inductions. And I shall confide -in having general assent with me, when I continue to speak of Kepler's -_Induction_ of the elliptical orbits. - -I now proceed to another remark. - - -III. _In Discovery a new Conception is introduced._-- - -24. There is a difference between Mr. Mill and me in our view of the -essential elements of this Induction of Kepler, which affects all other -cases of Induction, and which is, I think, the most extensive and -important of the differences between us. I must therefore venture to -dwell upon it a little in detail. - -I conceive that Kepler, in discovering the law of Mars's motion, -and in asserting that the planet moved in an ellipse, did this;--he -bound together particular observations of separate places of Mars -by the notion, or, as I have called it, the _conception_, of an -_ellipse_, which was supplied by his own mind. Other persons, and he -too, before he made this discovery, had present to their minds the -facts of such separate successive positions of the planet; but could -not bind them together rightly, because they did not apply to them -this conception of an _ellipse_. To supply this conception, required -a special preparation, and a special activity in the mind of the -discoverer. He, and others before him, tried other ways of connecting -the special facts, none of which fully succeeded. To discover such -a connexion, the mind must be conversant with certain relations of -space, and with certain kinds of figures. To discover the right figure -was a matter requiring research, invention, resource. To hit upon -the right conception is a difficult step; and when this step is once -made, the facts assume a different aspect from what they had before: -that done, they are seen in a new point of view; and the catching -this point of view, is a special mental operation, requiring special -endowments and habits of thought. Before this, the facts are seen as -detached, separate, lawless; afterwards, they are seen as connected, -simple, regular; as parts of one general fact, and thereby possessing -innumerable new relations before unseen. Kepler, then, I say, bound -together the facts by superinducing upon them the _conception_ of an -_ellipse_; and this was an essential element in his Induction. - -25. And there is the same essential element in all Inductive -discoveries. In all cases, facts, before detached and lawless, are -bound together by a new thought. They are reduced to law, by being -seen in a new point of view. To catch this new point of view, is an -act of the mind, springing from its previous preparation and habits. -The facts, in other discoveries, are brought together according to -other relations, or, as I have called them, _Ideas_;--the Ideas of -Time, of Force, of Number, of Resemblance, of Elementary Composition, -of Polarity, and the like. But in all cases, the mind performs the -operation by an apprehension of some such relations; by singling out -the one true relation; by combining the apprehension of the true -relation with the facts; by applying to them the Conception of such a -relation. - -26. In previous writings, I have not only stated this view generally, -but I have followed it into detail, exemplifying it in the greater part -of the History of the principal Inductive Sciences in succession. I -have pointed out what are the Conceptions which have been introduced in -every prominent discovery in those sciences; and have noted to which of -the above Ideas, or of the like Ideas, each belongs. The performance -of this task is the office of the greater part of my _Philosophy -of the Inductive Sciences_. For that work is, in reality, no less -historical than the _History_ which preceded it. The _History of the -Inductive Sciences_ is the history of the discoveries, mainly so far -as concerns the _Facts_ which were brought together to form sciences. -The _Philosophy_ is, in the first ten Books, the history of the _Ideas_ -and _Conceptions_, by means of which the facts were connected, so as -to give rise to scientific truths. It would be easy for me to give a -long list of the Ideas and Conceptions thus brought into view, but -I may refer any reader who wishes to see such a list, to the Tables -of Contents of the _History_, and of the first ten Books of the -_Philosophy_. - -27. That these Ideas and Conceptions are really distinct elements of -the scientific truths thus obtained, I conceive to be proved beyond -doubt, not only by considering that the discoveries never were made, -nor could be made, till the right Conception was obtained, and by -seeing how difficult it often was to obtain this element; but also, by -seeing that the Idea and the Conception itself, as distinct from the -Facts, was, in almost every science, the subject of long and obstinate -controversies;--controversies which turned upon the possible relations -of Ideas, much more than upon the actual relations of Facts. The first -ten Books of the _Philosophy_ to which I have referred, contain the -history of a great number of these controversies. These controversies -make up a large portion of the history of each science; a portion quite -as important as the study of the facts; and a portion, at every stage -of the science, quite as essential to the progress of truth. Men, in -seeking and obtaining scientific knowledge, have always shown that they -found the formation of right conceptions in their own minds to be an -essential part of the process. - -28. Moreover, the presence of a Conception of the mind as a special -element of the inductive process, and as the tie by which the -particular facts are bound together, is further indicated, by there -being some special new _term_ or _phrase_ introduced in every -induction; or at least some term or phrase thenceforth steadily -applied to the facts, which had not been applied to them before; as -when Kepler asserted that Mars moved round the sun in an _elliptical -orbit_, or when Newton asserted that the planets _gravitate_ towards -the sun; these new terms, _elliptical orbit_, and _gravitate_, mark -the new conceptions on which the inductions depend. I have in the -_Philosophy_[270] further illustrated this application of "technical -terms," that is, fixed and settled terms, in every inductive discovery; -and have spoken of their use in enabling men to proceed from each such -discovery to other discoveries more general. But I notice these terms -here, for the purpose of showing the existence of a conception in the -discoverer's mind, corresponding to the term thus introduced; which -conception, the term is intended to convey to the minds of those to -whom the discovery is communicated. - -29. But this element of discovery,--right conceptions supplied by -the mind in order to bind the facts together,--Mr. Mill denies to be -an element at all. He says, of Kepler's discovery of the elliptical -orbit (i. 363), "It superadded nothing to the particular facts -which it served to bind together;" yet he adds, "except indeed the -knowledge that a resemblance existed between the planetary orbit -and other ellipses;" that is, except the knowledge that it _was_ an -ellipse;--precisely the circumstance in which the discovery consisted. -Kepler, he says, "asserted as a fact that the planet moved in an -ellipse. But this fact, which Kepler did not add to, but found in the -motion of the planet ... was the very fact, the separate parts of -which had been separately observed; it was the sum of the different -observations." - -30. That the fact of the elliptical motion was not merely the _sum_ of -the different observations, is plain from this, that other persons, and -Kepler himself before his discovery, did not find it by adding together -the observations. The fact of the elliptical orbit was not the sum of -the observations _merely_; it was the sum of the observations, _seen -under a new point of view_, which point of view Kepler's mind supplied. -Kepler found it in the facts, because it was there, no doubt, for one -reason; but also, for another, because he had, in his mind, those -relations of thought which enabled him to find it. We may illustrate -this by a familiar analogy. We too find the law in Kepler's book; but -if we did not understand Latin, we should not find it there. We must -learn Latin in order to find the law in the book. In like manner, a -discoverer must know the language of science, as well as look at the -book of nature, in order to find scientific truth. All the discussions -and controversies respecting Ideas and Conceptions of which I have -spoken, may be looked upon as discussions and controversies respecting -the grammar of the language in which nature speaks to the scientific -mind. Man is the _Interpreter_ of Nature; not the Spectator merely, -but the Interpreter. The study of the language, as well as the mere -sight of the characters, is requisite in order that we may read the -inscriptions which are written on the face of the world. And this -study of the language of nature, that is, of the necessary coherencies -and derivations of the relations of phenomena, is to be pursued by -examining Ideas, as well as mere phenomena;--by tracing the formation -of Conceptions, as well as the accumulation of Facts. And this is what -I have tried to do in the books already referred to. - -31. Mr. Mill has not noticed, in any considerable degree, what I have -said of the formation of the Conceptions which enter into the various -sciences; but he has, in general terms, denied that the Conception is -anything different from the facts themselves. "If," he says (i. 301), -"the facts are rightly classed under the conceptions, it is because -there is in the facts themselves, something of which the conception -is a copy." But it is a copy which cannot be made by a person without -peculiar endowments; just as a person cannot copy an ill-written -inscription, so as to make it convey sense, unless he understand the -language. "Conceptions," Mr. Mill says (ii. 217), "do not develope -themselves from within, but are impressed from without." But what comes -from without is not enough: they must have both origins, or they cannot -make knowledge. "The conception," he says again (ii. 221), "is not -furnished _by_ the mind till it has been furnished _to_ the mind." But -it is furnished to the mind by its own activity, operating according to -its own laws. No doubt, the conception may be formed, and in cases of -discovery, must be formed, by the suggestion and excitement which the -facts themselves produce; and must be so moulded as to agree with the -facts. But this does not make it superfluous to examine, out of what -_materials_ such conceptions are formed, and _how_ they are capable of -being moulded so as to express laws of nature; especially, when we see -how large a share this part of discovery--the examination how our ideas -can be modified so as to agree with nature,--holds, in the history of -science. - -32. I have already (Art. 28) given, as evidence that the conception -enters as an element in every induction, the constant introduction -in such cases, of a new fixed term or phrase. Mr. Mill (ii. 282) -notices this introduction of a new phrase in such cases as important, -though he does not appear willing to allow that it is necessary. Yet -the necessity of the conception at least, appears to result from the -considerations which he puts forward. "What darkness," he says, "would -have been spread over geometrical demonstration, if wherever the word -_circle_ is used, the definition of a circle was inserted instead of -it." "If we want to make a particular combination of ideas permanent -in the mind, there is nothing which clenches it like a name specially -devoted to express it." In my view, the new conception is the _nail_ -which connects the previous notions, and the name, as Mr. Mill says, -_clenches_ the junction. - -33. I have above (Art. 30) referred to the difficulty of getting -hold of the right conception, as a proof that induction is not a -mere juxtaposition of facts. Mr. Mill does not dispute that it is -often difficult to hit upon the right conception. He says (i. 360), -"that a conception of the mind is introduced, is indeed most certain, -and Mr. Whewell has rightly stated elsewhere, that to hit upon the -right conception is often a far more difficult, and more meritorious -achievement, than to prove its applicability when obtained. But," he -adds, "a conception implies and corresponds to something conceived; and -although the conception itself is not in the facts, but in our mind, it -must be a conception of something which really is in the facts." But to -this I reply, that its being really in the facts, does not help us at -all towards knowledge, if we cannot see it there. As the poet says, - - It is the mind that sees: the outward eyes - Present the object, but the mind descries. - -And this is true of the sight which produces knowledge, as well as of -the sight which produces pleasure and pain, which is referred to in the -Tale. - -34. Mr. Mill puts his view, as opposed to mine, in various ways, but, -as will easily be understood, the answers which I have to offer are -in all cases nearly to the same effect. Thus, he says (ii. 216), "the -tardy development of several of the physical sciences, for example, -of Optics, Electricity, Magnetism, and the higher generalizations of -Chemistry, Mr. Whewell ascribes to the fact that mankind had not yet -possessed themselves of the idea of Polarity, that is, of opposite -properties in opposite directions. But what was there to suggest such -an idea, until by a separate examination of several of these different -branches of knowledge it was shown that the facts of each of them did -present, in some instances at least, the curious phenomena of opposite -properties in opposite directions?" But on this I observe, that these -facts did not, nor do yet, present this conception to ordinary minds. -The opposition of properties, and even the opposition of directions, -which are thus apprehended by profound cultivators of science, are -of an abstruse and recondite kind; and to conceive any one kind of -polarity in its proper generality, is a process which few persons -hitherto appear to have mastered; still less, have men in general -come to conceive of them all as modifications of a general notion of -Polarity. The description which I have given of Polarity in general, -"opposite properties in opposite directions," is of itself a very -imperfect account of the manner in which corresponding antitheses are -involved in the portions of science into which Polar relations enter. -In excuse of its imperfection, I may say, that I believe it is the -first attempt to define Polarity in general; but yet, the conception -of Polarity has certainly been strongly and effectively present in the -minds of many of the sagacious men who have discovered and unravelled -polar phenomena. They attempted to convey this conception, each in his -own subject, sometimes by various and peculiar expressions, sometimes -by imaginary mechanism by which the antithetical results were produced; -their mode of expressing themselves being often defective or imperfect, -often containing what was superfluous; and their meaning was commonly -very imperfectly apprehended by most of their hearers and readers. -But still, the conception was there, gradually working itself into -clearness and distinctness, and in the mean time, directing their -experiments, and forming an essential element of their discoveries. So -far would it be from a sufficient statement of the case to say, that -they conceived polarity because they saw it;--that they saw it as soon -as it came into view;--and that they described it as they saw it. - -35. The way in which such conceptions acquire clearness and -distinctness is often by means of Discussions of Definitions. To define -well a thought which already enters into trains of discovery, is often -a difficult matter. The business of such definition is a part of the -business of discovery. These, and other remarks connected with these, -which I had made in the _Philosophy_, Mr. Mill has quoted and adopted -(ii. 242). They appear to me to point very distinctly to the doctrine -to which he refuses his assent,--that there is a special process in the -mind, in addition to the mere observation of facts, which is necessary -at every step in the progress of knowledge. The Conception must be -_formed_ before it can be _defined_. The Definition gives the last -stamp of distinctness to the Conception; and enables us to express, in -a compact and lucid form, the new scientific propositions into which -the new Conception enters. - -36. Since Mr. Mill assents to so much of what has been said in the -_Philosophy_, with regard to the process of scientific discovery, how, -it may be asked, would he express these doctrines so as to exclude that -which he thinks erroneous? If he objects to our saying that when we -obtain a new inductive truth, we connect phenomena by applying to them -a new Conception which fits them, in what terms would he describe the -process? If he will not agree to say, that in order to discover the law -of the facts, we must find an appropriate Conception, what language -would he use instead of this? This is a natural question; and the -answer cannot fail to throw light on the relation in which his views -and mine stand to each other. - -Mr. Mill would say, I believe, that when we obtain a new inductive law -of facts, we find something in which the facts _resemble each other_; -and that the business of making such discoveries is the business of -discovering such resemblances. Thus, he says (of me,) (ii. 211), -"his Colligation of Facts by means of appropriate Conceptions, is -but the ordinary process of finding by a comparison of phenomena, in -what consists their agreement or resemblance." And the Methods of -experimental Inquiry which he gives (i. 450, &c.), proceed upon the -supposition that the business of discovery may be thus more properly -described. - -37. There is no doubt that when we discover a law of nature by -induction, we find some point in which all the particular facts agree. -All the orbits of the planets agree in being ellipses, as Kepler -discovered; all falling bodies agree in being acted on by a uniform -force, as Galileo discovered; all refracted rays agree in having -the sines of incidence and refraction in a constant ratio, as Snell -discovered; all the bodies in the universe agree in attracting each -other, as Newton discovered; all chemical compounds agree in being -constituted of elements in definite proportions, as Dalton discovered. -But it appears to me a most scanty, vague, and incomplete account of -these steps in science, to say that the authors of them discovered -something in which the facts in each case agreed. The point in which -the cases agree, is of the most diverse kind in the different cases--in -some, a relation of space, in others, the action of a force, in others, -the mode of composition of a substance;--and the point of agreement, -visible to the discoverer alone, does not come even into his sight, -till after the facts have been connected by thoughts of his own, and -regarded in points of view in which he, by his mental acts, places -them. It would seem to me not much more inappropriate to say, that an -officer, who disciplines his men till they move together at the word of -command, does so by finding something in which they agree. If the power -of consentaneous motion did not exist in the individuals, he could not -create it: but that power being there, he finds it and uses it. Of -course I am aware that the parallel of the two cases is not exact; but -in the one case, as in the other, that in which the particular things -are found to agree, is something formed in the mind of him who brings -the agreement into view. - - -IV. _Mr. Mill's Four Methods of Inquiry._--38. Mr. Mill has not only -thus described the business of scientific discovery; he has also given -rules for it, founded on this description. It may be expected that we -should bestow some attention upon the methods of inquiry which he thus -proposes. I presume that they are regarded by his admirers as among the -most valuable parts of his book; as certainly they cannot fail to be, -if they describe methods of scientific inquiry in such a manner as to -be of use to the inquirer. - -Mr. Mill enjoins four methods of experimental inquiry, which he calls -_the Method of Agreement_, _the Method of Difference_, _the Method -of Residues_, and _the Method of Concomitant Variations_[271]. They -are all described by formulæ of this kind:--Let there be, in the -observed facts, combinations of antecedents, _ABC_, _BC_, _ADE_, &c. -and combinations of corresponding consequents, _abc_, _bc_, _ade_, &c.; -and let the object of inquiry be, the consequence of some cause _A_, or -the cause of some consequence _a_. The Method of Agreement teaches us, -that when we find by experiment such facts as _abc_ the consequent of -_ABC_, and _ade_ the consequent of _ADE_, then _a_ is the consequent of -_A_. The Method of Difference teaches us that when we find such facts -as _abc_ the consequent of _ABC_, and _bc_ the consequent of _BC_, then -_a_ is the consequent of _A_. The Method of Residues teaches us, that -if _abc_ be the consequent of _ABC_, and if we have already ascertained -that the effect of _A_ is _a_, and the effect of _B_ is _b_, then we -may infer that the effect of _C_ is _c_. The Method of Concomitant -Variations teaches us, that if a phenomenon _a_ varies according as -another phenomenon _A_ varies, there is some connexion of causation -direct or indirect, between _A_ and _a_. - -39. Upon these methods, the obvious thing to remark is, that they take -for granted the very thing which is most difficult to discover, the -reduction of the phenomena to formulæ such as are here presented to -us. When we have any set of complex facts offered to us; for instance, -those which were offered in the cases of discovery which I have -mentioned,--the facts of the planetary paths, of falling bodies, of -refracted rays, of cosmical motions, of chemical analysis; and when, in -any of these cases, we would discover the law of nature which governs -them, or, if any one chooses so to term it, the feature in which all -the cases agree, where are we to look for our _A_, _B_, _C_ and _a_, -_b_, _c_? Nature does not present to us the cases in this form; and -how are we to reduce them to this form? You say, _when_ we find the -combination of _ABC_ with _abc_ and _ABD_ with _abd_, then we may -draw our inference. Granted: but when and where are we to find such -combinations? Even now that the discoveries are made, who will point -out to us what are the _A_, _B_, _C_ and _a_, _b_, _c_ elements of the -cases which have just been enumerated? Who will tell us which of the -methods of inquiry those historically real and successful inquiries -exemplify? Who will carry these formulæ through the history of the -sciences, as they have really grown up; and show us that these four -methods have been operative in their formation; or that any light is -thrown upon the steps of their progress by reference to these formulæ? - -40. Mr. Mill's four methods have a great resemblance to Bacon's -"Prerogatives of Instances;" for example, the Method of Agreement to -the _Instantiæ Ostensivæ_; the Method of Differences to the _Instantiæ -Absentiæ in Proximo_, and the _Instantiæ Crucis_; the Method of -Concomitant Variations to the _Instantiæ Migrantes_. And with regard to -the value of such methods, I believe all study of science will convince -us more and more of the wisdom of the remarks which Sir John Herschel -has made upon them[272]. - -"It has always appeared to us, we must confess, that the help which -the classification of instances under their different titles of -prerogative, affords to inductions, however just such classification -may be in itself, is yet more apparent than real. The force of the -instance must be felt in the mind before it can be referred to -its place in the system; and before it can be either referred or -appreciated it must be known; and when it _is_ appreciated, we are -ready enough to weave our web of induction, without greatly troubling -ourselves whence it derives the weight we acknowledge it to have in our -decisions.... No doubt such instances as these are highly instructive; -but the difficulty in physics is to find such, not to perceive their -force when found." - - -V. _His Examples._--41. If Mr. Mill's four methods had been applied by -him in his book to a large body of conspicuous and undoubted examples -of discovery, well selected and well analysed, extending along the -whole history of science, we should have been better able to estimate -the value of these methods. Mr. Mill has certainly offered a number -of examples of his methods; but I hope I may say, without offence, -that they appear to me to be wanting in the conditions which I have -mentioned. As I have to justify myself for rejecting Mr. Mill's -criticism of doctrines which I have put forward, and examples which I -have adduced, I may, I trust, be allowed to offer some critical remarks -in return, bearing upon the examples which he has given, in order to -illustrate his doctrines and precepts. - -42. The first remark which I have to make is, that a large proportion -of his examples (i. 480, &c.) is taken from one favourite author; -who, however great his merit may be, is too recent a writer to have -had his discoveries confirmed by the corresponding investigations and -searching criticisms of other labourers in the same field, and placed -in their proper and permanent relation to established truths; these -alleged discoveries being, at the same time, principally such as deal -with the most complex and slippery portions of science, the laws of -vital action. Thus Mr. Mill has adduced, as examples of discoveries, -Prof. Liebig's doctrine--that death is produced by certain metallic -poisons through their forming indecomposable compounds; that the effect -of respiration upon the blood consists in the conversion of peroxide -of iron into protoxide--that the antiseptic power of salt arises from -its attraction for moisture--that chemical action is contagious; and -others. Now supposing that we have no doubt of the truth of these -discoveries, we must still observe that they cannot wisely be cited, -in order to exemplify the nature of the progress of knowledge, till -they have been verified by other chemists, and worked into their places -in the general scheme of chemistry; especially, since it is tolerably -certain that in the process of verification, they will be modified and -more precisely defined. Nor can I think it judicious to take so large -a proportion of our examples from a region of science in which, of all -parts of our material knowledge, the conceptions both of ordinary -persons, and even of men of science themselves, are most loose and -obscure, and the genuine principles most contested; which is the case -in physiology. It would be easy, I think, to point out the vague and -indeterminate character of many of the expressions in which the above -examples are propounded, as well as their doubtful position in the -scale of chemical generalization; but I have said enough to show why I -cannot give much weight to these, as cardinal examples of the method -of discovery; and therefore I shall not examine in detail how far they -support Mr. Mill's methods of inquiry. - -43. Mr. Liebig supplies the first and the majority of Mr. Mill's -examples in chapter IX. of his Book on Induction. The second is -an example for which Mr. Mill states himself to be indebted to -Mr. Alexander Bain; the law established being this, that (i. 487) -electricity cannot exist in one body without the simultaneous -excitement of the opposite electricity in some neighbouring body, which -Mr. Mill also confirms by reference to Mr. Faraday's experiments on -voltaic wires. - -I confess I am quite at a loss to understand what there is in the -doctrine here ascribed to Mr. Bain which was not known to the -electricians who, from the time of Franklin, explained the phenomena of -the Leyden vial. I may observe also that the mention of an "electrified -atmosphere" implies a hypothesis long obsolete. The essential point in -all those explanations was, that each electricity produced by induction -the opposite electricity in neighbouring bodies, as I have tried to -make apparent in the _History_[273]. Faraday has, more recently, -illustrated this universal co-existence of opposite electricities with -his usual felicity. - -But the conjunction of this fact with voltaic phenomena, implies a -non-recognition of some of the simplest doctrines of the subject. -"Since," it is said (i. 488), "common or machine electricity, and -voltaic electricity may be considered for the present purpose to be -identical, Faraday wished to know, &c." I think Mr. Faraday would be -much astonished to learn that he considered electricity in equilibrium, -and electricity in the form of a voltaic current, to be, for any -purpose, identical. Nor do I conceive that he would assent to the -expression in the next page, that "from the nature of a voltaic charge, -the two opposite currents necessary to the existence of each other are -both accommodated in one wire." Mr. Faraday has, as it appears to me, -studiously avoided assenting to this hypothesis. - -44. The next example is the one already so copiously dwelt upon by Sir -John Herschel, Dr. Wells's researches on the production of Dew. I have -already said[274] that "this investigation, although it has sometimes -been praised as an original discovery, was in fact only resolving the -phenomenon into principles already discovered namely, the doctrine of a -_constituent temperature_ of vapour, the different conducting power of -different bodies, and the like. And this agrees in substance with what -Mr. Mill says (i. 497); that the discovery, when made, was corroborated -by deduction from the known laws of aqueous vapour, of conduction, and -the like. Dr. Wells's researches on Dew tended much in this country -to draw attention to the general principles of Atmology; and we may -see, in this and in other examples which Mr. Mill adduces, that the -explanation of special phenomena by means of general principles, -already established, has, for common minds, a greater charm, and -is more complacently dwelt on, than the discovery of the general -principles themselves. - -45. The next example, (i. 502) is given in order to illustrate the -Method of Residues, and is the discovery by M. Arago that a disk -of copper affects the vibrations of the magnetic needle. But this -apparently detached fact affords little instruction compared with the -singularly sagacious researches by which Mr. Faraday discovered the -cause of this effect to reside in the voltaic currents which the motion -of the magnetic needle developed in the copper. I have spoken of this -discovery in the _History_[275]. Mr. Mill however is quoting Sir John -Herschel in thus illustrating the Method of Residues. He rightly gives -the Perturbations of the Planets and Satellites as better examples of -the method[276]. - -46. In the next chapter (c. x.) Mr. Mill speaks of Plurality of causes -and of the Intermixture of effects, and gives examples of such cases. -He here teaches (i. 517) that chemical synthesis and analysis, (as when -oxygen and hydrogen compose water, and when water is resolved into -oxygen and hydrogen,) is properly _transformation_, but that because we -find that the weight of the compound is equal to the sum of the weights -of the elements, we take up the notion of chemical _composition_. I -have endeavoured to show[277] that the maxim, that the sum of the -weights of the elements is equal to the weight of the compound, was, -historically, not _proved_ from experiment, but _assumed_ in the -reasonings upon experiments. - -47. I have now made my remarks upon nearly all the examples which Mr. -Mill gives of scientific inquiry, so far as they consist of knowledge -which has really been obtained. I may mention, as points which -appear to me to interfere with the value of Mr. Mill's references to -examples, expressions which I cannot reconcile with just conceptions -of scientific truth; as when he says (i. 523), "some other force which -_impinges on_ the first force;" and very frequently indeed, of the -"tangential _force_," as co-ordinate with the centripetal force. - -When he speaks (ii. 20, Note) of "the doctrine now universally received -that the earth is a great natural magnet with two poles," he does not -recognize the recent theory of Gauss, so remarkably coincident with a -vast body of facts[278]. Indeed in his statement, he rejects no less -the earlier views proposed by Halley, theorized by Euler, and confirmed -by Hansteen, which show that we are compelled to assume at least _four_ -poles of terrestrial magnetism; which I had given an account of in the -first edition of the _History_. - -There are several other cases which he puts, in which, the knowledge -spoken of not having been yet acquired, he tells us how he would -set about acquiring it; for instance, if the question were (i. 526) -whether mercury be a cure for a given disease; or whether the brain be -a voltaic pile (ii. 21); or whether the moon be inhabited (ii. 100); -or whether all crows are black (ii. 124); I confess that I have no -expectation of any advantage to philosophy from discussions of this -kind. - -48. I will add also, that I do not think any light can be thrown upon -scientific methods, at present, by grouping along with such physical -inquiries as I have been speaking of, speculations concerning the -human mind, its qualities and operations. Thus he speaks (i. 508) of -human characters, as exemplifying the effect of plurality of causes; -of (i. 518) the phenomena of our mental nature, which are analogous to -chemical rather than to dynamical phenomena; of (i. 518) the reason why -susceptible persons are imaginative; to which I may add, the passage -where he says (i. 444), "let us take as an example of a phenomenon -which we have no means of fabricating artificially, a human mind." -These, and other like examples, occur in the part of his work in which -he is speaking of scientific inquiry in general, not in the Book on the -Logic of the Moral Sciences; and are, I think, examples more likely to -lead us astray than to help our progress, in discovering the laws of -Scientific Inquiry, in the ordinary sense of the term. - - -VI. _Mr. Mill against Hypothesis._--49. I will now pass from Mr. Mill's -methods, illustrated by such examples as those which I have been -considering, to the views respecting the conditions of Scientific -Induction to which I have been led, by such a survey as I could -make, of the whole history of the principal Inductive Sciences; and -especially, to those views to which Mr. Mill offers his objections[279]. - -Mr. Mill thinks that I have been too favourable to the employment -of hypotheses, as means of discovering scientific truth; and that -I have countenanced a laxness of method, in allowing hypotheses to -be established, merely in virtue of the accordance of their results -with the phenomena. I believe I should be as cautious as Mr. Mill, in -accepting mere hypothetical explanations of phenomena, in any case in -which we had the phenomena, and their relations, placed before both of -us in an equally clear light. I have not accepted the Undulatory theory -of Heat, though recommended by so many coincidences and analogies[280]. -But I see some grave reasons for not giving any great weight to Mr. -Mill's admonitions;--reasons drawn from the language which he uses on -the subject, and which appears to me inconsistent with the conditions -of the cases to which he applies it. Thus, when he says (ii. 22) that -the condition of a hypothesis accounting for all the known phenomena -is "often fulfilled equally well by two conflicting hypotheses," I can -only say that I know of no such case in the history of Science, where -the phenomena are at all numerous and complicated; and that if such -a case were to occur, one of the hypotheses might always be resolved -into the other. When he says, that "this evidence (the agreement of the -results of the hypothesis with the phenomena) cannot be of the smallest -value, because we cannot have in the case of such an hypothesis the -assurance that if the hypothesis be false it must lead to results at -variance with the true facts," we must reply, with due submission, that -we have, in the case spoken of, the most complete evidence of this; -for any change in the hypothesis would make it incapable of accounting -for the facts. When he says that "if we give ourselves the license -of inventing the causes as well as their laws, a person of fertile -imagination might devise a hundred modes of accounting for any given -fact;" I reply, that the question is about accounting for a large and -complex series of facts, of which the laws have been ascertained: and -as a test of Mr. Mill's assertion, I would propose as a challenge to -any person of fertile imagination to devise any _one_ other hypothesis -to account for the perturbations of the moon, or the coloured fringes -of shadows, besides the hypothesis by which they have actually been -explained with such curious completeness. This challenge has been -repeatedly offered, but never in any degree accepted; and I entertain -no apprehension that Mr. Mill's supposition will ever be verified by -such a performance. - -50. I see additional reason for mistrusting the precision of Mr. Mill's -views of that accordance of phenomena with the results of a hypothesis, -in several others of the expressions which he uses (ii. 23). He speaks -of a hypothesis being a "_plausible_ explanation of all or most of the -phenomena;" but the case which we have to consider is where it gives an -_exact_ representation of all the phenomena in which its results can be -traced. He speaks of its being certain that the laws of the phenomena -are "_in some measure analogous_" to those given by the hypothesis; the -case to be dealt with being, that they are in every way identical. He -speaks of this analogy being certain, from the fact that the hypothesis -can be "for a moment _tenable_;" as if any one had recommended a -hypothesis which is tenable only while a small part of the facts -are considered, when it is inconsistent with others which a fuller -examination of the case discloses. I have nothing to say, and have said -nothing, in favour of hypotheses which are _not_ tenable. He says there -are many such "_harmonies_ running through the laws of phenomena in -other respects radically distinct;" and he gives as an instance, the -laws of light and heat. I have never alleged such harmonies as grounds -of theory, unless they should amount to identities; and if they should -do this, I have no doubt that the most sober thinkers will suppose -the causes to be of the same kind in the two harmonizing instances. -If chlorine, iodine and brome, or sulphur and phosphorus, have, as -Mr. Mill says, analogous properties, I should call these substances -_analogous_: but I can see no temptation to frame an hypothesis that -they are _identical_ (which he seems to fear), so long as Chemistry -proves them distinct. But any hypothesis of an analogy in the -constitution of these elements (suppose, for instance, a resemblance -in their atomic form or composition) would seem to me to have a fair -claim to trial; and to be capable of being elevated from one degree of -probability to another by the number, variety, and exactitude of the -explanations of phenomena which it should furnish. - - -VII. _Against prediction of Facts._--51. These expressions of Mr. -Mill have reference to a way in which hypotheses may be corroborated, -in estimating the value of which, it appears that he and I differ. -"It seems to be thought," he says (ii. 23), "that an hypothesis of -the sort in question is entitled to a more favourable reception, if, -besides accounting for the facts previously known, it has led to the -anticipation and prediction of others which experience afterwards -verified." And he adds, "Such predictions and their fulfilment are -indeed well calculated to strike the ignorant vulgar;" but it is -strange, he says, that any considerable stress should be laid upon such -a coincidence by scientific thinkers. However strange it may seem to -him, there is no doubt that the most scientific thinkers, far more than -the ignorant vulgar, have allowed the coincidence of results predicted -by theory with fact afterwards observed, to produce the strongest -effects upon their conviction; and that all the best-established -theories have obtained their permanent place in general acceptance -in virtue of such coincidences, more than of any other evidence. It -was not the ignorant vulgar alone, who were struck by the return of -Halley's comet, as an evidence of the Newtonian theory. Nor was it the -ignorant vulgar, who were struck with those facts which did so much -strike men of science, as curiously felicitous proofs of the undulatory -theory of light,--the production of darkness by two luminous rays -interfering in a special manner; the refraction of a single ray of -light into a conical pencil; and other complex yet precise results, -predicted by the theory and verified by experiment. It must, one would -think, strike all persons in proportion to their thoughtfulness, that -when Nature thus does our bidding, she acknowledges that we have learnt -her true language. If we can predict new facts which we have not seen, -as well as explain those which we have seen, it must be because our -explanation is not a mere formula of observed facts, but a truth of a -deeper kind. Mr. Mill says, "If the laws of the propagation of light -agree with those of the vibrations of an elastic fluid in so many -respects as is necessary to make the hypothesis a plausible explanation -of all or most of the phenomena known at the time, it is nothing -strange that they should accord with each other in one respect more." -Nothing strange, if the theory be true; but quite unaccountable, -if it be not. If I copy a long series of letters of which the last -half-dozen are concealed, and if I guess those aright, as is found to -be the case when they are afterwards uncovered, this must be because -I have made out the import of the inscription. To say, that because I -have copied all that I could see, it is nothing strange that I should -guess those which I cannot see, would be absurd, without supposing such -a ground for guessing. The notion that the discovery of the laws and -causes of phenomena is a loose haphazard sort of guessing, which gives -"plausible" explanations, accidental coincidences, casual "harmonies," -laws, "in some measure analogous" to the true ones, suppositions -"tenable" for a time, appears to me to be a misapprehension of the -whole nature of science; as it certainly is inapplicable to the case to -which it is principally applied by Mr. Mill. - -52. There is another kind of evidence of theories, very closely -approaching to the verification of untried predictions, and to which, -apparently, Mr. Mill does not attach much importance, since he has -borrowed the term by which I have described it, _Consilience_, but -has applied it in a different manner (ii. 530, 563, 590). I have -spoken, in the _Philosophy_[281], of the _Consilience of Inductions_, -as one of the _Tests of Hypotheses_, and have exemplified it by many -instances; for example, the theory of universal gravitation, obtained -by induction from the motions of the planets, was found to explain -also that peculiar motion of the spheroidal earth which produces the -Precession of the Equinoxes. This, I have said, was a striking and -surprising coincidence which gave the theory a stamp of truth beyond -the power of ingenuity to counterfeit. I may compare such occurrences -to a case of interpreting an unknown character, in which two different -inscriptions, deciphered by different persons, had given the same -alphabet. We should, in such a case, believe with great confidence -that the alphabet was the true one; and I will add, that I believe the -history of science offers no example in which a theory supported by -such consiliences, had been afterwards proved to be false. - -53. Mr. Mill accepts (ii. 21) a rule of M. Comte's, that we may apply -hypotheses, provided they are capable of being afterwards verified as -facts. I have a much higher respect for Mr. Mill's opinion than for -M. Comte's[282]; but I do not think that this rule will be found of -any value. It appears to me to be tainted with the vice which I have -already noted, of throwing the whole burthen of explanation upon the -unexplained word _fact_--unexplained in any permanent and definite -opposition to theory. As I have said, the Newtonian theory _is_ a -fact. Every true theory is a fact. Nor does the distinction become -more clear by Mr. Mill's examples. "The vortices of Descartes would -have been," he says, "a perfectly legitimate hypothesis, if it had -been possible by any mode of explanation which we could entertain -the hope of possessing, to bring the question whether such vortices -exist or not, within the reach of our observing faculties." But this -was possible, and was done. The free passage of comets through the -spaces in which these vortices should have been, convinced men that -these vortices did not exist. In like manner Mr. Mill rejects the -hypothesis of a luminiferous ether, "because it can neither be seen, -heard, smelt, tasted, or touched." It is a strange complaint to make of -the vehicle of light, that it cannot be heard, smelt, or tasted. Its -vibrations _can_ be seen. The fringes of shadows for instance, show its -vibrations, just as the visible lines of waves near the shore show the -undulations of the sea. Whether this can be touched, that is, whether -it resists motion, is hardly yet clear. I am far from saying there are -not difficulties on this point, with regard to _all_ theories which -suppose a _medium_. But there are no more difficulties of this kind in -the undulatory theory of light, than there are in Fourier's theory of -heat, which M. Comte adopts as a model of scientific investigation; or -in the theory of voltaic _currents_, about which Mr. Mill appears to -have no doubt; or of electric _atmospheres_, which, though generally -obsolete, Mr. Mill appears to favour; for though it had been said that -we _feel_ such atmospheres, no one had said that they have the other -attributes of matter. - - -VIII. _Newton's Vera Causa._--54. Mr. Mill conceives (ii. 17) that his -own rule concerning hypotheses coincides with Newton's Rule, that the -cause assumed must be a _vera causa_. But he allows that "Mr. Whewell -... has had little difficulty in showing that his (Newton's) conception -was neither precise nor consistent with itself." He also allows that -"Mr. Whewell is clearly right in denying it to be necessary that the -cause assigned should be a cause already known; else how could we ever -become acquainted with new causes?" These points being agreed upon, I -think that a little further consideration will lead to the conviction -that Newton's Rule of philosophizing will best become a valuable guide, -if we understand it as asserting that when the explanation of two or -more different kinds of phenomena (as the revolutions of the planets, -the fall of a stone, and the precession of the equinoxes,) lead us to -_the same_ cause, such a coincidence gives a reality to the cause. We -have, in fact, in such a case, a Consilience of Inductions. - -55. When Mr. Mill condemns me (ii. 24) (using, however, expressions of -civility which I gladly acknowledge,) for having recognized no mode of -Induction except that of trying hypothesis after hypothesis until one -is found which fits the phenomena, I must beg to remind the readers of -our works, that Mr. Mill himself allows (i. 363) that the process of -finding a conception which binds together observed facts "is tentative, -that it consists of a succession of guesses, many being rejected until -one at last occurs fit to be chosen." I must remind them also that I -have given a Section upon the _Tests of Hypotheses_, to which I have -just referred,--that I have given various methods of Induction, as -the _Method of Gradation_, the _Method of Natural Classification_, -the _Method of Curves_, the _Method of Means_, the _Method of Least -Squares_, the _Method of Residues_: all which I have illustrated by -conspicuous examples from the History of Science; besides which, I -conceive that what I have said of the Ideas belonging to each science, -and of the construction and explication of conceptions, will point -out in each case, in what region we are to look for the Inductive -Element in order to make new discoveries. I have already ventured to -say, elsewhere, that the methods which I have given, are as definite -and practical as any others which have been proposed, with the -great additional advantage of being the methods by which all great -discoveries in science have really been made. - - -IX. _Successive Generalizations._--56. There is one feature in the -construction of science which Mr. Mill notices, but to which he does -not ascribe, as I conceive, its due importance: I mean, that process by -which we not only ascend from particular facts to a general law, but -when this is done, ascend from the first general law to others more -general; and so on, proceeding to the highest point of generalization. -This character of the scientific process was first clearly pointed -out by Bacon, and is one of the most noticeable instances of his -philosophical sagacity. "There are," he says, "two ways, and can -be only two, of seeking and finding truth. The one from sense and -particulars, takes a flight to the most general axioms, and from these -principles and their truth, settled once for all, invents and judges of -intermediate axioms. The other method collects axioms from sense and -particulars, ascending _continuously and by degrees_, so that in the -end it arrives at the most general axioms:" meaning by _axioms_, laws -or principles. The structure of the most complete sciences consists -of several such steps,--_floors_, as Bacon calls them, of successive -generalization; and thus this structure may be exhibited as a kind -of scientific pyramid. I have constructed this pyramid in the case -of the science of Astronomy[283]: and I am gratified to find that -the illustrious Humboldt approves of the design, and speaks of it as -executed with complete success[284]. The capability of being exhibited -in this form of successive generalizations, arising from particulars -upward to some very general law, is the condition of all tolerably -perfect sciences; and the steps of the successive generalizations are -commonly the most important events in the history of the science. - -57. Mr. Mill does not reject this process of generalization; but he -gives it no conspicuous place, making it only one of three modes of -reducing a law of causation into other laws. "There is," he says (i. -555), "the _subsumption_ of one law under another; ... the gathering up -of several laws into one more general law which includes them all. He -adds afterwards, that the general law is the _sum_ of the partial ones -(i. 557), an expression which appears to me inadequate, for reasons -which I have already stated. The general law is not the mere sum of -the particular laws. It is, as I have already said, their amount _in a -new point of view_. A new conception is introduced; thus, Newton did -not merely add together the laws of the motions of the moon and of the -planets, and of the satellites, and of the earth; he looked at them -altogether as the result of a universal force of mutual gravitation; -and therein consisted his generalization. And the like might be pointed -out in other cases. - -58. I am the more led to speak of Mr. Mill as not having given due -importance to this process of successive generalization, by the way in -which he speaks in another place (ii. 525) of this doctrine of Bacon. -He conceives Bacon "to have been radically wrong when he enunciates, -as a universal rule, that induction should proceed from the lowest to -the middle principles, and from those to the highest, never reversing -that order, and consequently, leaving no room for the discovery of new -principles by way of deduction[285] at all." - -59. I conceive that the Inductive Table of Astronomy, to which I have -already referred, shows that in that science,--the most complete which -has yet existed,--the history of the science has gone on, as to its -general movement, in accordance with the view which Bacon's sagacity -enjoined. The successive generalizations, _so far as they were true_, -were made by successive generations. I conceive also that the Inductive -Table of Optics shows the same thing; and this, without taking for -granted the truth of the Undulatory Theory; for with regard to all the -steps of the progress of the science, lower than that highest one, -there is, I conceive, no controversy. - -60. Also, the Science of Mechanics, although Mr. Mill more especially -refers to it, as a case in which the highest generalizations (for -example the Laws of Motion) were those earliest ascertained with any -scientific exactness, will, I think, on a more careful examination of -its history, be found remarkably to confirm Bacon's view. For, in that -science, we have, in the first place, very conspicuous examples of the -vice of the method pursued by the ancients in flying to the highest -generalizations first; as when they made their false distinctions of -the laws of _natural_ and _violent_ motions, and of _terrestrial_ -and _celestial_ motions. Many erroneous laws of motion were asserted -through neglect of facts or want of experiments. And when Galileo and -his school had in some measure succeeded in discovering some of the -true laws of the motions of terrestrial bodies, they did not at once -assert them as general: for they did not at all apply those laws to -the celestial motions. As I have remarked, all Kepler's speculations -respecting the causes of the motions of the planets, went upon the -supposition that the First Law of terrestrial Motion did not apply to -celestial bodies; but that, on the contrary, some continual force was -requisite to keep up, as well as to originate, the planetary motions. -Nor did Descartes, though he enunciated the Laws of Motion with more -generality than his predecessors, (but not with exactness,) venture -to trust the planets to those laws; on the contrary, he invented his -machinery of Vortices in order to keep up the motions of the heavenly -bodies. Newton was the first who extended the laws of terrestrial -motion to the celestial spaces; and in doing so, he used all the laws -of the celestial motions which had previously been discovered by -more limited inductions. To these instances, I may add the gradual -generalization of the Third Law of motion by Huyghens, the Bernoullis, -and Herman, which I have described in the _History_[286] as preceding -that Period of Deduction, to which the succeeding narrative[287] is -appropriated. In Mechanics, then, we have a cardinal example of the -historically gradual and successive ascent of science from particulars -to the most general laws. - -61. The Science of Hydrostatics may appear to offer a more favourable -example of the ascent to the most general laws, without going through -the intermediate particular laws; and it is true, with reference -to this science, as I have observed[288], that it does exhibit the -_peculiarity_ of our possessing the most general principles on which -the phenomena depend, and from which many cases of special facts are -explained by deduction; while other cases cannot be so explained, -from the want of principles intermediate between the highest and the -lowest. And I have assigned, as the reason of this peculiarity, that -the general principles of the Mechanics of Fluids were not obtained -with reference to the science itself, but by extension from the sister -science of the Mechanics of Solids. The two sciences are parts of the -same Inductive Pyramid; and having reached the summit of this Pyramid -on one side, we are tempted to descend on the other from the highest -generality to more narrow laws. Yet even in this science, the best -part of our knowledge is mainly composed of inductive laws, obtained -by inductive examination of particular classes of facts. The mere -mathematical investigations of the laws of waves, for instance, have -not led to any results so valuable as the experimental researches of -Bremontier, Emy, the Webers, and Mr. Scott Russell. And in like manner -in Acoustics, the Mechanics of Elastic Fluids[289], the deductions of -mathematicians made on general principles have not done so much for -our knowledge, as the cases of vibrations of plates and pipes examined -experimentally by Chladni, Savart, Mr. Wheatstone and Mr. Willis. We -see therefore, even in these sciences, no reason to slight the wisdom -which exhorts us to ascend from particulars to intermediate laws, -rather than to hope to deduce these latter better from the more general -laws obtained once for all. - -62. Mr. Mill himself indeed, notwithstanding that he slights Bacon's -injunction to seek knowledge by proceeding from less general to more -general laws, has given a very good reason why this is commonly -necessary and wise. He says (ii. 526), "Before we attempt to explain -deductively, from more general laws, any new class of phenomena, it is -desirable to have gone as far as is practicable in ascertaining the -empirical laws of these phenomena; so as to compare the results of -deduction, not with one individual instance after another, but with -general propositions expressive of the points of agreement which have -been found among many instances. For," he adds with great justice, -"if Newton had been obliged to verify the theory of gravitation, not -by deducing from it Kepler's laws, but by deducing all the observed -planetary positions which had served Kepler to establish those laws, -the Newtonian theory would probably never have emerged from the state -of an hypothesis." To which we may add, that it is certain, from the -history of the subject, that in that case the hypothesis would never -have been framed at all. - - -X. _Mr. Mill's Hope from Deduction._--63. Mr. Mill expresses a hope -of the efficacy of Deduction, rather than Induction, in promoting -the future progress of Science; which hope, so far as the physical -sciences are concerned, appears to me at variance with all the lessons -of the history of those sciences. He says (i. 579), "that the advances -henceforth to be expected even in physical, and still more in mental -and social science, will be chiefly the result of deduction, is evident -from the general considerations already adduced:" these considerations -being, that the phenomena to be considered are very complex, and are -the result of many known causes, of which we have to disentangle the -results. - -64. I cannot but take a very different view from this. I think that -any one, looking at the state of physical science, will see that there -are still a vast mass of cases, in which we do not at all know the -causes, at least, in their full generality; and that the knowledge of -new causes, and the generalization of the laws of those already known, -can only be obtained by new _inductive_ discoveries. Except by new -Inductions, equal, in their efficacy for grouping together phenomena -in new points of view, to any which have yet been performed in the -history of science, how are we to solve such questions as those which, -in the survey of what we already know, force themselves upon our minds? -Such as, to take only a few of the most obvious examples--What is the -nature of the connexion of heat and light? How does heat produce the -expansion, liquefaction and vaporization of bodies? What is the nature -of the connexion between the optical and the chemical properties of -light? What is the relation between optical, crystalline and chemical -polarity? What is the connexion between the atomic constitution and -the physical qualities of bodies? What is the tenable definition of a -mineral species? What is the true relation of the apparently different -types of vegetable life (monocotyledons, dicotyledons, and cryptogamous -plants)? What is the relation of the various types of animal life -(vertebrates, articulates, radiates, &c.)? What is the number, and -what are the distinctions of the Vital Powers? What is the internal -constitution of the earth? These, and many other questions of equal -interest, no one, I suppose, expects to see solved by deduction from -principles already known. But we can, in many of them, see good hope of -progress by a large use of induction; including, of course, copious and -careful experiments and observations. - -65. With such questions before us, as have now been suggested, I -can see nothing but a most mischievous narrowing of the field and -enfeebling of the spirit of scientific exertion, in the doctrine that -"Deduction is the great scientific work of the present and of future -ages;" and that "A revolution is peaceably and progressively effecting -itself in philosophy the reverse of that to which Bacon has attached -his name." I trust, on the contrary, that we have many new laws of -nature still to discover; and that our race is destined to obtain a -sight of wider truths than any we yet discern, including, as cases, the -general laws we now know, and obtained from these known laws as they -must be, by Induction. - -66. I can see, however, reasons for the comparatively greater favour -with which Mr. Mill looks upon Deduction, in the views to which he has -mainly directed his attention. The explanation of remarkable phenomena -by known laws of Nature, has, as I have already said, a greater charm -for many minds than the discovery of the laws themselves. In the case -of such explanations, the problem proposed is more definite, and the -solution more obviously complete. For the process of induction includes -a mysterious step, by which we pass from particulars to generals, -of which step the reason always seems to be inadequately rendered -by any words which we can use; and this step to most minds is not -demonstrative, as to few is it given to perform it on a great scale. -But the process of explanation of facts by known laws is deductive, -and has at every step a force like that of demonstration, producing -a feeling peculiarly gratifying to the clear intellects which are -most capable of following the process. We may often see instances in -which this admiration for deductive skill appears in an extravagant -measure; as when men compare Laplace with Newton. Nor should I think -it my business to argue against such a preference, unless it were -likely to leave us too well satisfied with what we know already, to -chill our hope of scientific progress, and to prevent our making any -further strenuous efforts to ascend, higher than we have yet done, the -mountain-chain which limits human knowledge. - -67. But there is another reason which, I conceive, operates in leading -Mr. Mill to look to Deduction as the principal means of future progress -in knowledge, and which is a reason of considerable weight in the -subjects of research which, as I conceive, he mainly has in view. In -the study of our own minds and of the laws which govern the history of -society, I do not think that it is very likely that we shall hereafter -arrive at any wider principles than those of which we already possess -some considerable knowledge; and this, for a special reason; namely, -that our knowledge in such cases is not gathered by mere external -observation of a collection of external facts; but acquired by -attention to internal facts, our own emotions, thoughts, and springs of -action; facts are connected by ties existing in our own consciousness, -and not in mere observed juxtaposition, succession, or similitude. -How the character, for instance, is influenced by various causes, (an -example to which Mr. Mill repeatedly refers, ii. 518, &c.), is an -inquiry which may perhaps be best conducted by considering what we know -of the influence of education and habit, government and occupation, -hope and fear, vanity and pride, and the like, upon men's characters, -and by tracing the various effects of the intermixture of such -influences. Yet even here, there seems to be room for the discovery -of laws in the way of experimental inquiry: for instance, what share -race or family has in the formation of character; a question which can -hardly be solved to any purpose in any other way than by collecting -and classing instances. And in the same way, many of the principles -which regulate the material wealth of states, are obtained, if not -exclusively, at least most clearly and securely, by induction from -large surveys of facts. Still, however, I am quite ready to admit that -in Mental and Social Science, we are much less likely than in Physical -Science, to obtain new truths by any process which can be distinctively -termed _Induction_; and that in those sciences, what may be called -_Deductions_ from principles of thought and action of which we are -already conscious, or to which we assent when they are felicitously -picked out of our thoughts and put into words, must have a large share; -and I may add, that this observation of Mr. Mill appears to me to be -important, and, in its present connexion, new. - - -XI. _Fundamental opposition of our doctrines._--68. I have made nearly -all the remarks which I now think it of any consequence to make upon -Mr. Mill's _Logic_, so far as it bears upon the doctrines contained -in my _History_ and _Philosophy_. And yet there remains still -untouched one great question, involving probably the widest of all the -differences between him and me. I mean the question whether geometrical -axioms, (and, as similar in their evidence to these, _all_ axioms,) be -truths derived from experience, or be necessary truths in some deeper -sense. This is one of the fundamental questions of philosophy; and all -persons who take an interest in metaphysical discussions, know that the -two opposite opinions have been maintained with great zeal in all ages -of speculation. To me it appears that there are _two_ distinct elements -in our knowledge, Experience, without, and the Mind, within. Mr. Mill -derives all our knowledge from Experience _alone_. In a question thus -going to the root of all knowledge, the opposite arguments must needs -cut deep on both sides. Mr. Mill cannot deny that our knowledge of -geometrical axioms and the like, _seems_ to be _necessary_. I cannot -deny that our knowledge, axiomatic as well as other, _never is_ -acquired _without experience_. - -69. Perhaps ordinary readers may despair of following our reasonings, -when they find that they can only be made intelligible by supposing, -on the one hand, a person who thinks distinctly and yet has never seen -or felt any external object; and on the other hand, a person who is -transferred, as Mr. Mill supposes (ii. 117), to "distant parts of the -stellar regions where the phenomena may be entirely unlike those with -which we are acquainted," and where even the axiom, that every effect -must have a cause, does not hold good. Nor, in truth, do I think it -necessary here to spend many words on this subject. Probably, for those -who take an interest in this discussion, most of the arguments on each -side have already been put forwards with sufficient repetition. I have, -in an "Essay on the Fundamental Antithesis of Philosophy," and in some -accompanying "Remarks," printed[290] at the end of the second edition -of my _Philosophy_, given my reply to what has been said on this -subject, both by Mr. Mill, and by the author of a very able critique on -my _History_ and _Philosophy_ which appeared in the _Quarterly Review_ -in 1841: and I will not here attempt to revive the general discussion. - -70. Perhaps I may be allowed to notice, that in one part of Mr. Mill's -work where this subject is treated, there is the appearance of one of -the parties to the controversy pronouncing judgment in his own cause. -This indeed is a temptation which it is especially difficult for an -author to resist, who writes a treatise upon _Fallacies_, the subject -of Mr. Mill's fifth Book. In such a treatise, the writer has an easy -way of disposing of adverse opinions by classing them as "Fallacies," -and putting them side by side with opinions universally acknowledged to -be false. In this way, Mr. Mill has dealt with several points which are -still, as I conceive, matters of controversy (ii. 357, &c.). - -71. But undoubtedly, Mr. Mill has given his argument against my -opinions with great distinctness in another place (i. 319). In order -to show that it is merely habitual association which gives to an -experimental truth the character of a necessary truth, he quotes -the case of the laws of motion, which were really discovered from -experiment, but are now looked upon as the only conceivable laws; and -especially, what he conceives as "the _reductio ad absurdum_ of the -theory of inconceivableness," an opinion which I had ventured to throw -out, that if we could conceive the Composition of bodies distinctly, -we might be able to see that it is necessary that the modes of their -composition should be definite. I do not think that readers in general -will see anything absurd in the opinion, that the laws of Mechanics, -and even the laws of the Chemical Composition of bodies, may depend -upon principles as necessary as the properties of space and number; and -that this necessity, though not at all perceived by persons who have -only the ordinary obscure and confused notions on such subjects, may -be evident to a mind which has, by effort and discipline, rendered its -ideas of Mechanical Causation, Elementary Composition and Difference of -Kind, clear and precise. It may easily be, I conceive, that while such -necessary principles are perceived to be necessary only by a few minds -of highly cultivated insight, such principles as the axioms of Geometry -and Arithmetic may be perceived to be necessary by _all_ minds which -have any habit of abstract thought at all: and I conceive also, that -though these axioms are brought into distinct view by a certain degree -of intellectual cultivation, they may still be much better described -as conditions of experience, than as results of experience:--as laws -of the mind and of its activity, rather than as facts impressed upon a -mind merely passive. - - -XII. _Absurdities in Mr. Mill's Logic._--72. I will not pursue the -subject further: only, as the question has arisen respecting the -absurdities to which each of the opposite doctrines leads, I will point -out opinions connected with this subject, which Mr. Mill has stated in -various parts of his book. - -He holds (i. 317) that it is merely from habit that we are unable to -conceive the _last point_ of space or the _last instant_ of time. -He holds (ii. 360) that it is strange that any one should rely upon -the _à priori_ evidence that space or extension is infinite, or that -nothing can be made of nothing. He holds (i. 304) that the first law -of _motion_ is _rigorously true_, but that the axioms respecting -the _lever_ are only _approximately_ true. He holds (ii. 110) that -there may be sidereal firmaments in which events succeed each other -at random, without obeying any laws of causation; although one might -suppose that even if space and cause are both to have their limits, -still they might terminate together: and then, even on this bold -supposition, we should no _where_ have a world in which events were -_casual_. He holds (ii. 111) that the axiom, that every event must -have a cause, is established by means of an "induction by simple -enumeration:" and in like manner, that the principles of number and -of geometry are proved by this method of simple enumeration alone. He -ascribes the proof (i. 162) of the axiom, "things which are equal to -the same are equal to each other," to the fact that this proposition -has been perpetually _found_ true and never false. He holds (i. 338) -that "In all propositions concerning numbers, a condition is implied, -without which none of them would be true; and that condition is an -assumption which _may be false_. _The condition is that_ 1 = 1." - -73. Mr. Mill further holds (i. 309), that it is a characteristic -property of geometrical forms, that they are capable of being painted -in the imagination with a distinctness equal to reality:--that our -ideas of forms exactly resemble our sensations: which, it is implied, -is not the case with regard to any other class of our ideas;--that we -thus may have mental pictures of all possible combinations of lines -and angles, which are as fit subjects of geometrical experimentation -as the realities themselves. He says, that "we know that the imaginary -lines exactly resemble real ones;" and that we obtain this knowledge -respecting the characteristic property of the idea of space by -experience; though it does not appear _how_ we can compare our _ideas_ -with the _realities_, since we know the realities only _by_ our ideas; -or why this property of their resemblance should be confined to _one -class_ of ideas alone. - -74. I have now made such remarks as appear to me to be necessary, on -the most important parts of Mr. Mill's criticism of my _Philosophy_. I -hope I have avoided urging any thing in a contentious manner; as I have -certainly written with no desire of controversy, but only with a view -to offer to those who may be willing to receive it, some explanation of -portions of my previous writings. I have already said, that if this had -not have been my especial object, I could with pleasure have noted the -passages of Mr. Mill's _Logic_ which I admire, rather than the points -in which we differ. I will in a very few words refer to some of these -points, as the most agreeable way of taking leave of the dispute. - -I say then that Mr. Mill appears to me especially instructive in -his discussion of the nature of the proof which is conveyed by the -syllogism; and that his doctrine, that the force of the syllogism -consists in an _inductive assertion, with an interpretation added -to it_, solves very happily the difficulties which baffle the -other theories of this subject. I think that this doctrine of his -is made still more instructive, by his excepting from it the cases -of Scriptural Theology and of Positive Law (i. 260), as cases in -which general propositions, not particular facts, are our original -data. I consider also that the recognition of _Kinds_ (i. 166) as -classes in which we have, not a finite but an _inexhaustible_ body of -resemblances among individuals, and as groups made by nature, not by -mere definition, is very valuable, as stopping the inroad to an endless -train of false philosophy. I conceive that he takes the right ground -in his answer to Hume's argument against miracles (ii. 183): and I -admire the acuteness with which he has criticized Laplace's tenets on -the Doctrine of Chances, and the candour with which he has, in the -second edition, acknowledged oversights on this subject made in the -first. I think that much, I may almost say all, which he says on the -subject of Language, is very philosophical; for instance, what he says -(ii. 238) of the way in which words acquire their meaning in common -use. I especially admire the acuteness and force with which he has -shown (ii. 255) how moral principles expressed in words degenerate into -formulas, and yet how the formula cannot be rejected without a moral -loss. This "perpetual oscillation in spiritual truths," as he happily -terms it, has never, I think, been noted in the same broad manner, -and is a subject of most instructive contemplation. And though I have -myself refrained from associating moral and political with physical -science in my study of the subject, I see a great deal which is full of -promise for the future progress of moral and political knowledge in Mr. -Mill's sixth Book, "On the Logic of the Moral and Political Sciences." -Even his arrangement of the various methods which have been or may -be followed in "the Social Science,"--"the Chemical or Experimental -Method," "the Geometrical or Abstract Method," "the Physical or -Concrete Deductive Method," "the Inverse Deductive or Historical -Method," though in some degree fanciful and forced, abounds with -valuable suggestions; and his estimate of "the interesting philosophy -of the Bentham school," the main example of "the geometrical method," -is interesting and philosophical. On some future occasion, I may, -perhaps, venture into the region of which Mr. Mill has thus essayed -to map the highways: for it is from no despair either of the great -progress to be made in such truth as that here referred to, or of the -effect of philosophical method in arriving at such truth, that I have, -in what I have now written, confined myself to the less captivating but -more definite part of the subject. - - -FOOTNOTES: - -[Footnote 264: [_A System of Logic, Ratiocinative and Inductive, being -a connected view of the Principles of Evidence, and of the Methods of -Scientific Investigation._ By John Stuart Mill.]] - -[Footnote 265: These Remarks were published in 1849, under the title -_Of Induction, with especial reference to Mr. J. S. Mill's System of -Logic_.] - -[Footnote 266: My references are throughout (except when otherwise -expressed) to the volume and the page of Mr. Mill's first edition of -his _Logic_.] - -[Footnote 267: On this subject see an Essay _On the Transformation of -Hypotheses_, given in the Appendix.] - -[Footnote 268: B. vii. c. iii. sect. 3.] - -[Footnote 269: B. iii. c. ix. art. 7.] - -[Footnote 270: B. i. c. iii.] - -[Footnote 271: B. iii. c. viii.] - -[Footnote 272: _Discourse_, Art. 192.] - -[Footnote 273: B. xi. c. xi.] - -[Footnote 274: _Phil._ b. xiii. c. ix. art. 7.] - -[Footnote 275: B. xiii. c. viii.] - -[Footnote 276: Given also in the _Phil. Ind. Sc._ b. xiii. c. vii. -sect. 17.] - -[Footnote 277: _Ibid._ b. vi. c. iv.] - -[Footnote 278: See _Hist. Ind. Sc._ b. xii. note D, in the second -edition.] - -[Footnote 279: There are some points in my doctrines on the subject -of the Classificatory Sciences to which Mr. Mill objects, (ii. 314, -&c.), but there is nothing which I think it necessary to remark here, -except one point. After speaking of Classification of organized beings -in general, Mr. Mill notices (ii. 321) as an additional subject, the -arrangement of natural groups into a Natural Series; and he says, that -"all who have attempted a theory of natural arrangement, including -among the rest Mr. Whewell, have stopped short of this: all except M. -Comte." On this I have to observe, that I stopped short of, or rather -passed by, the doctrine of a Series of organized beings, because I -thought it bad and narrow philosophy: and that I sufficiently indicated -that I did this. In the _History_ (b. xvi. c. vi.) I have spoken of the -doctrine of Circular Progression propounded by Mr. Macleay, and have -said, "so far as this view _negatives_ a mere _linear_ progression in -nature, which would place each genus in contact with the preceding and -succeeding ones, and so far as it requires us to attend to the more -varied and ramified resemblances, there can be no doubt that it is -supported by the result of all the attempts to form natural systems." -And with regard to the difference between Cuvier and M. de Blainville, -to which Mr. Mill refers (ii. 321), I certainly cannot think that M. -Comte's suffrage can add any weight to the opinion of either of those -great naturalists.] - -[Footnote 280: _Hist. Ind. Sc._ b. x. note (VA) in the second edition.] - -[Footnote 281: B. xi. c. v. art. 11.] - -[Footnote 282: I have given elsewhere (see last chapter) reasons why I -cannot assign to M. Comte's _Philosophie Positive_ any great value as a -contribution to the philosophy of science. In this judgment I conceive -that I am supported by the best philosophers of our time. M. Comte -owes, I think, much of the notice which has been given to him to his -including, as Mr. Mill does, the science of society and of human nature -in his scheme, and to his boldness in dealing with these. He appears -to have been received with deference as a mathematician: but Sir John -Herschel has shown that a supposed astronomical discovery of his is a -mere assumption. I conceive that I have shown that his representation -of the history of science is erroneous, both in its details and in its -generalities. His distinction of the three stages of sciences, the -theological, metaphysical, and positive, is not at all supported by the -facts of scientific history. Real discoveries always involve what he -calls _metaphysics_; and the doctrine of final causes in physiology, -the main element of science which can properly be called _theological_, -is retained at the end, as well as the beginning of the science, by all -except a peculiar school.] - -[Footnote 283: I have also, in the same place, given the Inductive -Pyramid for the science of Optics. These Pyramids are necessarily -inverted in their form, in order that, in reading in the ordinary way, -we may proceed _to_ the vertex. _Phil. Ind. Sc._ b. xi. c. vi.] - -[Footnote 284: _Cosmos_, vol. ii. note 35.] - -[Footnote 285: The reader will probably recollect that as _Induction_ -means the inference of general propositions from particular cases, -_Deduction_ means the inference by the application of general -propositions to particular cases, and by combining such applications; -as when from the most general principles of Geometry or of Mechanics, -we prove some less general theorem; for instance, the number of the -possible regular solids, or the principle of _vis viva_.] - -[Footnote 286: B. vi. c. v.] - -[Footnote 287: c. vi.] - -[Footnote 288: _Hist._ b. vi. c. vi. sect. 13.] - -[Footnote 289: _Hist. Ind. Sc._ b. viii.] - -[Footnote 290: Reprinted in the Appendix to this volume.] - - - - -CHAPTER XXIII. - -POLITICAL ECONOMY AS AN INDUCTIVE SCIENCE. - - -(_Moral Sciences._)--1. Both M. Comte and Mr. Mill, in speaking of the -methods of advancing science, aim, as I have said, at the extension of -their methods to moral subjects, and aspire to suggest means for the -augmentation of our knowledge of ethical, political, and social truths. -I have not here ventured upon a like extension of my conclusions, -because I wished to confine my views of the philosophy of discovery -to the cases in which all allow that solid and permanent discoveries -have been made. Moreover in the case of moral speculations, we have -to consider not only observed external facts and the ideas by which -they are colligated, but also internal facts, in which the instrument -of observation is consciousness, and in which observations and ideas -are mingled together, and act and react in a peculiar manner. It may -therefore be doubted whether the methods which have been effectual -in the discovery of physical theories will not require to be greatly -modified, or replaced by processes altogether different, when we would -make advances in ethical, political, or social knowledge. In ethics, at -least, it seems plain that we must take our starting-point not without -but within us. Our mental powers, our affections, our reason, and any -other faculties which we have, must be the basis of our convictions. -And in this field of knowledge, the very form of our highest -propositions is different from what it is in the physical sciences. In -Physics we examine what _is_, in a form more or less general: in Ethics -we seek to determine what OUGHT _to be_, as the highest rule, which is -supreme over all others. In this case we cannot expect the methods of -physical discovery to aid us. - -But others of the subjects which I have mentioned, though strongly -marked and influenced by this ethical element, are still of a mixed -character, and require also observation of external facts of human, -individual, and social conduct, and generalizations derived from -such observations. The facts of political constitutions and social -relations in communities of men, and the histories of such communities, -afford large bodies of materials for political and social science; -and it seems not at all unlikely that such science may be governed, -in its formation and progress, by laws like those which govern the -physical sciences, and may be steered clear of errors and directed -towards truths by an attention to the forms which error and truth have -assumed in the most stable and certain sciences. The different forms -of society, and the principal motives which operate upon men regarded -in masses, may be classified as facts; and though our consciousness of -what we ourselves are and the affections which we ourselves feel are -always at work in our interpretations of such facts, yet the knowledge -which we thus obtain may lead us to bodies of knowledge which we may -call _Sciences_, and compare with the other sciences as to their form -and maxims. - - -(_Political Economy._)--2. Among such bodies of knowledge, I may notice -as a specimen, the science of _Political Economy_, and may compare it -with other sciences in the respects which have been referred to. - -M. Comte has given a few pages to the discussion of this science of -Political Economy[291]; but what he has said amounts only to a few -vague remarks on Adam Smith and Destutt de Tracy; his main object -being, it would seem, to introduce his usual formula, and to condemn -all that has hitherto been done (with which there is no evidence that -he is adequately acquainted) as worthless, because it is "theological," -"metaphysical," "literary," and not "_positive_." - -Mr. Mill has much more distinctly characterized the plan and form -of Political Economy in his system[292]. He regards this science as -that which deals with the results which take place in human society -in consequence of the desire of wealth. He explains, however, that -it is only for the sake of convenience that one of the motives which -operate upon man is thus insulated and treated as if it were the only -one:--that there are other principles, for instance, the principles on -which the progress of population depends, which co-operate with the -main principle, and materially modify its results: and he gives reasons -why this mode of simplifying the study of social phenomena tends to -promote the progress of systematic knowledge. - -Instead of discussing these reasons, I will notice the way in which the -speculations of political economists have exemplified tendencies to -error, and corrections of those tendencies, of the same nature as those -which we have already noticed in speaking of other sciences. - - -(_Wages, Profits, and Rent._)--3. We may regard as one of the first -important steps in this science, Adam Smith's remark, that the value -or price of any article bought and sold consists of three elements, -_Wages_, _Profits_, and _Rent_. Some of the most important of -subsequent speculations were attempts to determine the laws of each of -these three elements. At first it might be supposed that there ought to -be added to them a fourth element, _Materials_. But upon consideration -it will be seen that materials, as an element of price, resolves itself -into wages and rent; for all materials derive their value from the -labour which is bestowed upon them. The iron of the ploughshare costs -just what it costs to sink the mine, dig up and smelt the iron. The -wood of the frame costs what it costs to cut down the tree, together -with the rent of the ground on which it grows. - - -(_Premature Generalizations._)--4. But what determines Wages?--The -amount of persons seeking work, that is, speaking loosely, the -population; and the amount of money which is devoted to the payment of -wages. And what determines the population? It was replied,--the means -of subsistence. And how does the population tend to increase?--In a -geometrical ratio. And how does the subsistence tend to increase?--At -most in an arithmetical ratio. And hence it was inferred that the -population tends constantly to run beyond the means of subsistence, -and will be limited by a threatened deficiency of these means. And -the wages paid must be such as to form this limit. And therefore the -wages paid will always be such as just to keep up the population in its -ordinary state of progress. Here was one general proposition which was -gathered from summary observations of society. - -Again: as to Rent: Adam Smith had treated Rent as if it were a monopoly -price--the result of a monopoly of the land by the landowners. But -subsequent writers acutely remarked that land is of various degrees of -fertility, and there is some land which barely pays the cultivator, if -cultivating it he pay no rent. And rent can be afforded for other land -only in so far as it is better than this bad land. And thus, there was -obtained another general proposition; that the Rent of good land was -just equal to the excess of its produce over the worst cultivable land. - -Now these two propositions are examples of a hasty and premature -generalization, like that from which the sweeping physical systems -of antiquity were derived. They were examples of that process which -Francis Bacon calls _anticipation_; in which we leap at once from a few -facts to propositions of the highest generality; and supposing these -to be securely established, proceed to draw a body of conclusions from -them, and thus frame a system. - -And what is the sounder and wiser mode of proceeding in order to obtain -a science of such things? We must classify the facts which we observe, -and take care that we do not ascribe to the facts in our immediate -neighbourhood or specially under our notice, a generality of prevalence -which does not belong to them. We must proceed by the ladder of -Induction, and be sure we have obtained the narrower generalizations, -before we aspire to the widest. - - -(_Correction of them by Induction. Rent._)--5. For instance; in the -case of the latter of the above two propositions--that Rent is the -excess of the produce of good soils over the worst--that is the case -in England and Scotland; but is it the case in other countries? Let us -see. Why is it the case in England? Because if the rent demanded for -good land were _more_ than the excess of the produce over bad land, the -farmer would prefer the bad land as more gainful. If the rent demanded -for good land were _less_ than the excess, the bad land would be -abandoned by the farmer. - -But all this goes upon the supposition that the farmer can remove from -good land to bad, or from bad to good, or apply his capital in some -other way than farming, according as it is more gainful. This is true -in England; but is it true all over the world? - -By no means. It is true in scarcely any other part of the world. In -almost every other part of the world the cultivator is bound to the -land, so that he cannot remove himself and his capital from it; and -cannot, because he is not satisfied with his position upon it, seek and -find a position and a subsistence elsewhere. On the contrary, he is -bound by the laws and customs of the country, by constitution, history -and character, so that he cannot, or can only with great difficulty, -change his plan and mode of life. And thus over great part of the world -the fundamental supposition on which rests the above generalization -respecting Rent is altogether false. - -An able political economist[293] has taken the step, which as we have -said, sound philosophy would have prescribed: he has classified the -states of society which exist or have existed on the earth, as they -bear on this point, the amount of Rent. He has classified the modes -in which the produce is, in different countries and different stages -of society, divided between the cultivator and the proprietor: and he -finds that the natural divisions are these:--_Serf Rents_, that is, -labour rents paid by the Cultivator to the Landowner, as in Russia: -_Métayer Rents_, where the produce is divided between the Cultivator -and the Landowner, as in Central Europe: _Ryot Rents_, where a portion -of the produce is paid to the Sovereign as Landlord, as in India: -_Cottier Rents_, where a money-rent is paid by a Cultivator who raises -his own subsistence from the soil; and _Farmers' Rents_, where a -covenanted Rent is paid by a person employing labourers. In this last -case alone is it true that the Rent is equal to the excess of good over -bad soils. - -The error of the conclusion, in this case, arises from assuming the -mobility of capital and labour in cases in which it is not moveable: -which is much as if mechanicians had reasoned respecting rigid bodies, -supposing them to be fluid bodies. - -But the error of method was in not classifying the facts of societies -before jumping to a conclusion which was to be applicable to all -societies. - - -(_Wages._)--6. And in like manner there is an error of the same kind -in the assertion of the other general principles:--that wages are -determined by the capital which is forthcoming for the payment of -wages; and that population is determined in its progress by wages. For -there is a vast mass of population on the surface of the earth which -does not live upon wages: and though in England the greater part of the -people lives upon wages, in the rest of the world the part that does so -is small. And in this case, as in the other, we must class these facts -as they exist in different nations, before we can make assertions of -any wide generality. - -Mr. Jones[294] classed the condition of labourers in different -countries in the same inductive manner in which he classed the tenure -of land. He pointed out that there are three broad distinct classes -of them: _Unhired Labourers_, who cultivate the ground which they -occupy, and live on _self-produced wages_; _Paid Dependants_, who are -paid out of the _revenue_ or income of their employers, as the military -retainers and domestic artizans of feudal times in Europe, and the -greater part of the people of Asia at the present day; and _Hired -Labourers_, who are paid wages from _capital_. - -This last class, though taken as belonging to the normal condition of -society by many political economists, is really the exceptional case, -taking the world at large; and no propositions concerning the structure -and relations of ranks in society can have any wide generality which -are founded on a consideration of this case alone. - - -(_Population._)--7. And again: with regard to the proposition that -the progress of population depends merely on the rate of wages, a -very little observation of different communities, and of the same -communities at different times, will show that this is a very rash and -hasty generalization. When wages rise, whether or not population shall -undergo a corresponding increase depends upon many other circumstances -besides this single fact of the increase of wages. The effect of a -rise of wages upon population is affected by the form of the wages, -the time occupied by the change, the institutions of the society -under consideration, and other causes: and a due classification of -the conditions of the society according to these circumstances, is -requisite in order to obtain any general proposition concerning the -effect of a rise or fall of wages upon the progress of the population. - -And thus those precepts of the philosophy of discovery which we have -repeated so often, which are so simple, and which seem so obvious, -have been neglected or violated in the outset of Political Economy as -in so many other sciences:--namely, the precepts that we must classify -our facts before we generalize, and seek for narrower generalizations -and inductions before we aim at the widest. If these maxims had been -obeyed, they would have saved the earlier speculators on this subject -from some splendid errors; but, on the other hand, it may be said, that -if these earlier speculators had not been thus bold, the science could -not so soon have assumed that large and striking form which made it so -attractive, and to which it probably owes a large part of its progress. - - -FOOTNOTES: - -[Footnote 291: _Phil. Pos._ t. iv. p. 264.] - -[Footnote 292: _Logic_, b. vi. c. 3.] - -[Footnote 293: Jones, _On Rent_, 1833.] - -[Footnote 294: _Literary Remains_, 1859.] - - - - -CHAPTER XXIV. - -MODERN GERMAN PHILOSOPHY[295]. - - -I. _Science is the Idealization of Facts._ - -1. I have spoken, a few chapters back, of the Reaction against the -doctrines of the Sensational School in England and France. In Germany -also there was a Reaction against these doctrines;--but there, this -movement took a direction different from its direction in other -countries. Omitting many other names, Kant, Fichte, Schelling and Hegel -may be regarded as the writers who mark, in a prominent manner, this -Germanic line of speculation. The problem of philosophy, in the way in -which they conceived it, may best be explained by reference to that -Fundamental Antithesis of which I had occasion to speak in the _History -of Scientific Ideas_[296]. And in order to characterize the steps taken -by these modern German philosophers, I must return to what I have said -concerning the Fundamental Antithesis. - -This Antithesis, as I have there remarked, is stated in various -ways:--as the Antithesis of Thoughts and Things; of Ideas and -Sensations; of Theory and Facts; of Necessary Truth and Experience; of -the Subjective and Objective elements of our knowledge; and in other -phrases. I have further remarked that the elements thus spoken of, -though opposed, are inseparable. We cannot have the one without the -other. We cannot have thoughts without thinking of Things: we cannot -have things before us without thinking of them. - -Further, it has been shown, I conceive, that our knowledge derives -from the former of these two elements, namely our Ideas, its form -and character of knowledge; our ideas being the necessary _Forms_ of -knowledge, while the _Matter_ of our knowledge in each case is supplied -by the appropriate perception or outward experience. - -Thus our Ideas of Space and Time are the necessary Forms of our -geometrical and arithmetical knowledge; and no sensations or experience -are needed as the matter of such knowledge, except in so far as -sensation and experience are needed to evoke our Ideas in any degree. -And hence these sciences are sometimes called _Formal_ sciences. All -other Sciences involve, along with the experience and observation -appropriate to each, a development of the ideal conditions of knowledge -existing in our minds; and I have given the history, both of this -development of ideas and of the matter derived from experience, in two -former works, the _History of Scientific Ideas_, and the _History of -the Inductive Sciences_. I have there traced this history through the -whole body of the physical sciences. - -But though Ideas and Perceptions are thus separate elements in our -philosophy, they cannot in fact be distinguished and separated, but are -different aspects of the same thing. And the only way in which we can -approach to truth is by gradually and successively, in one instance -after another, advancing from the perception to the idea; from the fact -to the theory. - -2. I would now further observe, that in this progression from fact -to theory, we advance (when the theory is complete and completely -possessed by the mind) from the apprehension of truths as _actual_ to -the apprehension of them as _necessary_; and thus Facts which were -originally observed merely as Facts become the consequences of theory, -and are thus brought within the domain of Ideas. That which was a part -of the objective world becomes also a part of the subjective world; a -necessary part of the thoughts of the theorist. And in this way the -progress of true theory is the _Idealization of Facts_. - -Thus the Progress of Science consists in a perpetual reduction of Facts -to Ideas. Portions are perpetually transferred from one side to another -of the Fundamental Antithesis: namely, from the Objective to the -Subjective side. The Centre or Fulcrum of the Antithesis is shifted by -every movement which is made in the advance of science, and is shifted -so that the ideal side gains something from the real side. - -3. I will proceed to illustrate this Proposition a little further. -Necessary Truths belong to the Subjective, Observed Facts to the -Objective side of our knowledge. Now in the progress of that exact -speculative knowledge which we call Science, Facts which were at a -previous period merely Observed Facts, come to be known as Necessary -Truths; and the attempts at new advances in science generally introduce -the representation of known truths of fact, as included in higher and -wider truths, and therefore, so far, necessary. - -We may exemplify this progress in the history of the science of -Mechanics. Thus the property of the lever, the inverse proportion of -the weights and arms, was known as a fact before the time of Aristotle, -and known as no more; for he gives many fantastical and inapplicable -reasons for the fact. But in the writings of Archimedes we find this -fact brought within the domain of necessary truth. It was there -transferred from the empirical to the ideal side of the Fundamental -Antithesis; and thus a progressive step was made in science. In like -manner, it was at first taken by Galileo as a mere fact of experience, -that in a falling body, the velocity increases in proportion to the -time; but his followers have seen in this the necessary effect of the -uniform force of gravity. In like manner, Kepler's empirical Laws were -shown by Newton to be necessary results of a central force attracting -inversely as the square of the distance. And if it be still, even at -present, doubtful whether this is the _necessary_ law of a central -force, as some philosophers have maintained that it is, we cannot doubt -that if now or hereafter, those philosophers could establish their -doctrine as certain, they would make an important step in science, in -addition to those already made. - -And thus, such steps in science are made, whenever empirical facts -are discerned to be necessary laws; or, if I may be allowed to use a -briefer expression, whenever _facts are idealized_. - -4. In order to show how widely this statement is applicable, I will -exemplify it in some of the other sciences. - -In Chemistry, not to speak of earlier steps in the science, which -might be presented as instances of the same general process, we may -remark that the analyses of various compounds into their elements, -according to the quantity of the elements, form a vast multitude of -facts, which were previously empirical only, but which are reduced -to a law, and therefore to a certain kind of ideal necessity, by the -discovery of their being compounded according to definite and multiple -proportions. And again, this very law of definite proportions, which -may at first be taken as a law given by experience only, it has been -attempted to make into a necessary truth, by asserting that bodies -must necessarily consist of atoms, and atoms must necessarily combine -in definite small numbers. And however doubtful this Atomic Theory may -at present be, it will not be questioned that any chemical philosopher -who could establish it, or any other Theory which would produce an -equivalent change in the aspect of the science, would make a great -scientific advance. And thus, in this Science also, the Progress of -Science consists in the transfer of facts from the empirical to the -necessary side of the antithesis; or, as it was before expressed, in -the idealization of facts. - -5. We may illustrate the same process in the Natural History -Sciences. The discovery of the principle of Morphology in plants -was the reduction of a vast mass of Facts to an _Idea_; as Schiller -said to Göthe when he explained the discovery; although the latter, -cherishing a horror of the term _Idea_, which perhaps is quite as -common in England as in Germany, was extremely vexed at being told -that he possessed such furniture in his mind. The applications of this -Principle to special cases, for instance, to Euphorbia by Brown, to -Reseda by Lindley, have been attempts to idealize the facts of these -special cases. - -6. We may apply the same view to steps in Science which are still -under discussion;--the question being, whether an advance has really -been made in science or not. For instance, in Astronomy, the Nebular -Hypothesis has been propounded, as an explanation of many of the -observed phenomena of the Universe. If this Hypothesis could be -conceived ever to be established as a true Theory, this must be done -by its taking into itself, as necessary parts of the whole Idea, many -Facts which have already been observed; such as the various form of -nebulæ;--many Facts which it must require a long course of years to -observe, such as the changes of nebulæ from one form to another;--and -many facts which, so far as we can at present judge, are utterly -at variance with the Idea, such as the motions of satellites, the -relations of the material elements of planets, the existence of -vegetable and animal life upon their surfaces. But if all these Facts, -when fully studied, should appear to be included in the general Idea -of Nebular Condensation according to the Laws of Nature, the Facts -so idealized would undoubtedly constitute a very remarkable advance -in science. But then, we are to recollect that we are not to suppose -that the Facts will agree with the Idea, merely because the Idea, -considered by itself, and without carefully attending to the Facts, -is a large and striking Idea. And we are also to recollect that the -Facts may be compared with another Idea, no less large and striking; -and that if we take into our account, (as, in forming an Idea of the -Course of the Universe, we must do,) not only vegetable and animal, -but also _human_ life, this other Idea appears likely to take into it -a far larger portion of the known Facts, than the Idea of the Nebular -Hypothesis. The other Idea which I speak of is the Idea of Man as the -principal Object in the Creation; to whose sustenance and development -the other parts of the Universe are subservient as means to an end; and -although, in our attempts to include all known Facts in this Idea, we -again meet with many difficulties, and find many trains of Facts which -have no apparent congruity with the Idea; yet we may say that, taking -into account the Facts of man's intellectual and moral condition, and -his history, as well as the mere Facts of the material world, the -difficulties and apparent incongruities are far less when we attempt -to idealize the Facts by reference to this Idea, of Man as the End of -Creation, than according to the other Idea, of the World as the result -of Nebular Condensation, without any conceivable End or Purpose. I am -now, of course, merely comparing these two views of the Universe, as -supposed steps in science, according to the general notion which I -have just been endeavouring to explain, that a step in science is some -Idealization of Facts. - -7. Perhaps it will be objected, that what I have said of the -Idealization of Facts, as the manner in which the progress of science -goes on, amounts to no more than the usual expressions, that the -progress of science consists in reducing Facts to Theories. And to this -I reply, that the advantage at which I aim, by the expression which -I have used, is this, to remind the reader, that Fact and Theory, in -every subject, are not marked by separate and prominent features of -difference, but only by their present opposition, which is a transient -relation. They are related to each other no otherwise than as the poles -of the fundamental antithesis: the point which separates those poles -shifts with every advance of science; and then, what was Theory becomes -Fact. As I have already said elsewhere, a true Theory is a Fact; a Fact -is a familiar Theory. If we bear this in mind, we express the view -on which I am now insisting when we say that the progress of science -consists in reducing Facts to Theories. But I think that speaking of -_Ideas_ as opposed to Facts, we express more pointedly the original -Antithesis, and the subsequent identification of the Facts with the -Idea. The expression appears to be simple and apt, when we say, for -instance, that the Facts of Geography are identified with the Idea -of globular Earth; the Facts of Planetary Astronomy with the Idea of -the Heliocentric system; and ultimately, with the Idea of Universal -Gravitation. - -8. We may further remark, that though by successive steps in science, -successive Facts are reduced to Ideas, this process can never be -complete. However the point may shift which separates the two poles, -the two poles will always remain. However, far the ideal element may -extend, there will always be something beyond it. However far the -phenomena may be idealized, there will always remain some which are -not idealized, and which are mere phenomena. This also is implied -by making our expressions refer to the fundamental antithesis: for -because the antithesis _is_ fundamental, its two elements will always -be present; the objective as well as the subjective. And thus, in the -contemplation of the universe, however much we understand, there must -always be something which we do not understand; however far we may -trace necessary truths, there must always be things which are to our -apprehension arbitrary: however far we may extend the sphere of our -internal world, in which we feel power and see light, it must always -be surrounded by our external world, in which we see no light, and -only feel resistance. Our subjective being is inclosed in an objective -shell, which, though it seems to yield to our efforts, continues entire -and impenetrable beyond our reach, and even enlarges in its extent -while it appears to give up to us a portion of its substance. - - -II. _Successive German Philosophies._ - -9. The doctrine of the Fundamental Antithesis of two elements of which -the union is involved in all knowledge, and of which the separation -is the task of all philosophy, affords us a special and distinct mode -of criticizing the philosophies which have succeeded each other in the -world; and we may apply it to the German Philosophies of which we have -spoken. - -The doctrine of the Fundamental Antithesis is briefly this: - -_That in every act of knowledge (1) there are two opposite elements -which we may call Ideas and Perceptions; but of which the opposition -appears in various other antitheses; as Thoughts and Things, Theories -and Facts, Necessary Truths and Experiential Truths; and the like: (2) -that our knowledge derives from the former of these elements, namely -our Ideas, its form and character as knowledge, our Ideas of space -and time being the necessary forms, for instance, of our geometrical -and arithmetical knowledge; (3) and in like manner, all our other -knowledge involving a development of the ideal conditions of knowledge -existing in our minds: (4) but that though ideas and perceptions are -thus separate elements in our philosophy, they cannot, in fact, be -distinguished and separated, but are different aspects of the same -thing; (5) that the only way in which we can approach to truth is by -gradually and successively, in one instance after another, advancing -from the perception to the idea; from the fact to the theory; from -the apprehension of truths as actual to the apprehension of them as -necessary. (6) This successive and various progress from fact to theory -constitutes the history of science; (7) and this progress, though -always leading us nearer to that central unity of which both the idea -and the fact are emanations, can never lead us to that point, nor to -any measurable proximity to it, or definite comprehension of its place -and nature._ - -10. Now the doctrine being thus stated, successive sentences of the -statement contain successive steps of German philosophy, as it has -appeared in the series of celebrated authors whom I have named. - -Ideas, and Perceptions or Sensations, being regarded as the two -elements of our knowledge, Locke, or at least the successors of -Locke, had rejected the former element, Ideas, and professed to -resolve all our knowledge into Sensation. After this philosophy had -prevailed for a time, Kant exposed, to the entire conviction of the -great body of German speculators, the untenable nature of this account -of our knowledge. He taught (one of the first sentences of the above -statement) that (2) _Our knowledge derives from our Ideas its form -and character as knowledge; our Ideas of space and time being, for -instance, the necessary forms of our geometrical and arithmetical -knowledge_. Fichte carried still further this view of our knowledge, -as derived from our Ideas, or from its nature as knowledge; and held -that (3) _all our knowledge is a development of the ideal conditions of -knowledge existing in our minds_ (one of our next following sentences). -But when the ideal element of our knowledge was thus exclusively -dwelt upon, it was soon seen that this ideal system no more gave a -complete explanation of the real nature of knowledge, than the old -sensational doctrine had done. Both elements, Ideas and Sensations, -must be taken into account. And this was attempted by Schelling, who, -in his earlier works, taught (as we have also stated above) that (4) -_Ideas and Facts are different aspects of the same thing_:--this thing, -the central basis of truth in which both elements are involved and -identified, being, in Schelling's language, the _Absolute_, while each -of the separate elements is subjected to _conditions_ arising from -their union. But this Absolute, being a point inaccessible to us, and -inconceivable by us, as _our_ philosophy teaches (as above), cannot -to any purpose be made the basis of our philosophy: and accordingly -this _Philosophy of the Absolute_ has not been more permanent than -its predecessors. Yet the philosophy of Hegel, which still has a wide -and powerful sway in Germany, is, in the main, a development of the -same principle as that of Schelling;--the identity of the idea and the -fact; and Hegel's _Identity-System_, is rather a more methodical and -technical exposition of Schelling's Philosophy of the Absolute than -a new system. But Hegel traces the manifestation of the identity of -the idea and fact in the _progress_ of human knowledge; and thus in -some measure approaches to our doctrine (above stated), that (5) _the -way in which we approach to truth is by gradually and successively, in -one instance after another_, that is, _historically, advancing from -the perception to the idea, from the fact to the theory_: while at the -same time Hegel has not carried out this view in any comprehensive or -complete manner, so as to show that (6) _this process constitutes the -history of science_: and as with Schelling, his system shows an entire -want of the conviction (above expressed as part of our doctrine), -(7) that _we can never, in our speculations reach or approach to the -central unity of which both idea and fact are emanations_. - -11. This view of the relation of the Sensational School, of the Schools -of Kant, Fichte, Schelling, and Hegel, and of the fundamental defects -of all, may be further illustrated. It will, of course, be understood -that our illustration is given only as a slight and imperfect sketch of -these philosophies; but their relation may perhaps become more apparent -by the very brevity with which it is stated; and the object of the -present chapter is not the detailed criticism of systems, but this very -relation of systems to each other. - -The actual and the ideal, the external and the internal elements -of knowledge, were called by the Germans the _objective_ and the -_subjective_ elements respectively. The forms of knowledge and -especially space and time, were pronounced by Kant to be essentially -_subjective_; and this view of the nature of knowledge, more fully -unfolded and extended to all knowledge, became the _subjective -ideality_ of Fichte. But the subjective and the objective are, as -we have said, in their ultimate and supreme form, one; and hence -we are told of the _subjective-objective_, a phrase which has also -been employed by Mr. Coleridge. Fichte had spoken of the subjective -element as the _Me_, (das Ich); and of the objective element as the -_Not-me_, (das Nicht-Ich); and has deduced the _Not-me_ from the _Me_. -Schelling, on the contrary, laboured with great subtlety to deduce -the _Me_ from the _Absolute_ which includes both. And this Absolute, -or Subjective-objective, is spoken of by Schelling as unfolding itself -into endless other antitheses. It was held that from the assumption of -such a principle might be deduced and explained the oppositions which, -in the contemplation of nature, present themselves at every step, as -leading points of general philosophy:--for example, the opposition -of matter as _passive_ and _active_, as _dead_ and _organized_, -as _unconscious_ or _conscious_; the opposition of _individual_ -and _species_, of _will_ and _moral rule_. And this antithetical -development was carried further by Hegel, who taught that the Absolute -Idea developes itself so as to assume qualities, limitations, and -seeming oppositions, and then completes the cycle of its development by -returning into unity. - -12. That there is, in the history of Science, much which easily lends -itself to such a formula, the views which I have endeavoured to -expound, show and exemplify in detail. But yet the attempts to carry -this view into detail by conjecture--by a sort of divination--with -little or no attention to the historical progress and actual -condition of knowledge, (and such are those which have been made by -the philosophers whom I have mentioned,) have led to arbitrary and -baseless views of almost every branch of knowledge. Such oppositions -and differences as are found to exist in nature, are assumed as the -representatives of the elements of necessary antitheses, in a manner -in which scientific truth and inductive reasoning are altogether -slighted. Thus, this peculiar and necessary antithetical character is -assumed to be displayed in attraction and repulsion, in centripetal and -centrifugal forces, in a supposed positive and negative electricity, -in a supposed positive and negative magnetism; in still more doubtful -positive and negative elements of light and heat; in the different -elements of the atmosphere, which are, quite groundlessly, assumed to -have a peculiar antithetical character: in animal and vegetable life: -in the two sexes; in gravity and light. These and many others, are -given by Schelling, as instances of the radical opposition of forces -and elements which necessarily pervades all nature. I conceive that the -heterogeneous and erroneous principles involved in these views of the -material world show us how unsafe and misleading is the philosophical -assumption on which they rest. And the Triads of Hegel, consisting of -Thesis, Antithesis, and Union, are still more at variance with all -sound science. Thus we are told that matter and motion are determined -as _inertia_, _impulsion_, _fall_; that Absolute Mechanics determines -itself as _centripetal force_, _centrifugal force_, _universal -gravitation_. Light, it is taught, is a secondary determination of -matter. Light is the most intimate element of nature, and might be -called _the Me_ of nature: it is limited by what we may call negative -light, which is darkness. - -13. In these rash and blind attempts to construct physical science -_à priori_, we may see how imperfect the Hegelian doctrines are as -a complete philosophy. In the views of moral and political subjects -the results of such a scheme are naturally less obviously absurd, and -may often be for a moment striking and attractive, as is usually the -case with attempts to reduce history to a formula. Thus we are told -that _the State_ appears under the following determinations:--first -as one, substantial, self-included: next, varied, individual, active, -disengaging itself from the substantial and motionless unity: next, -as two principles, altogether distinct, and placed front to front in -a marked and active opposition: then, arising out of the ruins of the -preceding, the idea appears afresh, one, identical, harmonious. And the -East, Greece, Rome, Germany, are declared to be the historical forms -of these successive determinations. Whatever amount of real historical -colour there may be for this representation, it will hardly, I think, -be accepted as evidence of a profound political philosophy; but on such -parts of the subject I shall not here dwell. - -14. I may observe that in the series of philosophical systems now -described, the two elements of the Fundamental Antithesis are -alternately dwelt upon in an exaggerated degree, and then confounded. -The Sensational School could see in human knowledge nothing but -facts: Kant and Fichte fixed their attention almost entirely upon -ideas: Schelling and Hegel assume the identity of the two, (a point -we never can reach,) as the origin of their philosophy. The external -world in Locke's school was all in all. In the speculations of -Kant this external world became a dim and unknown region. Things -were acknowledged to be _something_ in themselves, but _what_, the -philosopher could not tell. Besides the _phænomenon_ which we see, Kant -acknowledged a _noumenon_ which we think of; but this assumption, for -such it is, exercises no influence upon his philosophy. - -15. We may for the sake of illustration imagine to ourselves each -system of philosophy as a Drama in which _Things_ are the _Dramatis -Personæ_ and the _Idea_ which governs the system is the _Plot_ of the -drama. In Kant's Drama, Things in themselves are merely a kind of 'Mute -Personages,' κωφὰ πρόσωπα, which stand on the stage to be pointed at -and talked about, but which do not tell us anything, or enter into the -action of the piece. Fichte carries this further, and if we go on with -the same illustration, we may say that he makes the whole drama into -a kind of Monologue; in which the author tells the story, and merely -names the persons who appear. If we would still carry on the image, -we may say that Schelling, going upon the principle that the whole of -the drama is merely a progress to the Denouement, which denouement -contains the result of all the preceding scenes and events, starts -with the last scene of the piece; and bringing all the characters on -the stage in their final attitudes, would elicit the story from this. -While the true mode of proceeding is, to follow the drama Scene by -Scene, learning as much as we can of the Action and the Characters, -but knowing that we shall not be allowed to see the Denouement, and -that to do so is probably not the lot of our species on earth. So far -as any philosopher has thus followed the historical progress of the -grand spectacle offered to the eyes of speculative man, in which the -Phenomena of Nature are the Scenes, and the Theory of them the Plot, he -has taken the course by which knowledge really has made its advances. -But those who have partially done this, have often, like Hegel, assumed -that they had divined the whole course and end of the story, and have -thus criticised the scenes and the characters in a spirit quite at -variance with that by which any real insight into the import of the -representation can be obtained. - -If it be asked which position we can assign, in this dramatic -illustration, to those who hold that all our knowledge is derived from -facts only, and who reject the supposition of ideas; we may say that -they look on with a belief that the drama has _no_ plot, and that these -scenes are improvised without connexion or purpose. - -16. I will only offer one more illustration of the relative position -of these successive philosophies. Kant compares the change which he -introduced into philosophy to the change which Copernicus introduced -into astronomical theory. When Copernicus found that nothing could be -made of the phenomena of the heavens so long as everything was made -to turn round the spectator, he tried whether the matter might not be -better explained if he made the spectator turn, and left the stars -at rest. So Kant conceives that our experience is regulated by our -own faculties, as the phenomena of the heavens are regulated by our -own motions. But accepting and carrying out this illustration, we may -say that Kant, in explaining the phenomena of the heavens by means -of the motions of the earth, has almost forgotten that the planets -have their own proper motions, and has given us a system which hardly -explains anything besides broadest appearances, such as the annual and -daily motions of the sun; and that Fichte appears as if he wished to -deduce all the motions of the planets, as well as of the sun, from the -conditions of the spectator;--while Schelling goes to the origin of -the system, like Descartes, and is not content to show how the bodies -move, without also proving that from some assumed original condition, -all the movements and relations of the system must necessarily be what -they are. It may be that a theory which explains how the planets, -with their orbits and accompaniments, have come into being, may offer -itself to bold speculators, like those who have framed and produced -the nebular hypothesis. But I need not remind my readers either how -precarious such a hypothesis is; or, that if it be capable of being -considered probable, its proofs must gradually dawn upon us, step by -step, age after age: and that a system of doctrine which assumes such -a scheme as a certain and fundamental truth, and deduces the whole of -astronomy from it, must needs be arbitrary, and liable to the gravest -error at every step. Such a precarious and premature philosophy, at -best, is that of Schelling and Hegel; especially as applied to those -sciences in which, by the past progress of all sure knowledge, we are -taught what the real cause and progress of knowledge is: while at the -same time we may allow that all these forms of philosophy, since they -do recognize the condition and motion of the spectator, as a necessary -element in the explanation of the phenomena, are a large advance upon -the Ptolemaic scheme--the view of those who appeal to phenomena alone -as the source of our knowledge, and say that the sun, the moon, and -the planets move as we see them move, and that all further theory is -imaginary and fantastical. - - -FOOTNOTES: - -[Footnote 295: The substance of this and the next chapter was printed -as a communication to the Cambridge Phil. Soc. in 1840.] - -[Footnote 296: Or in the earlier editions, in the _Philosophy of the -Inductive Sciences_.] - - - - -CHAPTER XXV. - -THE FUNDAMENTAL ANTITHESIS AS IT EXISTS IN THE MORAL WORLD. - - -1. We have hitherto spoken of the Fundamental Antithesis as the ground -of our speculations concerning the material world, at least mainly. -We have indeed been led by the physical sciences, and especially by -Biology, to the borders of Psychology. We have had to consider not only -the mechanical effects of muscular contraction, but the sensations -which the nerves receive and convey:--the way in which sensations -become perceptions; the way in which perceptions determine actions. In -this manner we have been led to the subject of volition or will[297], -and this brings us to a new field of speculation, the moral nature of -man; and this moral nature is a matter not only of speculative but -of practical interest. On this subject I shall make only a few brief -remarks. - -2. Even in the most purely speculative view, the moral aspect of man's -nature differs from the aspect of the material universe, in this -respect, that in the moral world, external events are governed in -some measure by the human will. When we speculate concerning the laws -of material nature, we suppose that the phenomena of nature follow a -course and order which we may perhaps, in some measure, discover and -understand, but which we cannot change or control. But when we consider -man as an agent, we suppose him able to determine some at least of the -events of the external world; and thus, able to determine the actions -of other men, and to lay down laws for them. He cannot alter the -properties of fire and metals, stones and fluids, air and light; but he -can use fire and steel so as to compel other men's actions; stone-walls -and ocean-shores so as to control other men's motions; gold and gems -so as to have a hold on other men's desires; articulate sounds and -intelligible symbols so as to direct other men's thoughts and move -their will. There is an external world of Facts; and in this, the Facts -are such as he makes them by his Acts. - -3. But besides this, there is also, standing over against this external -world of Facts, an internal world of Ideas. The Moral Acts without are -the results of Moral Ideas within. Men have an Idea of Justice, for -instance, according to which they are led to external acts, as to use -force, to make a promise, to perform a contract, as individuals; or to -make war and peace, to enact laws and to execute them, as a nation. - -4. Some such internal moral Idea necessarily exists, along with -all properly human actions. Man feels not only pain and anger, but -indignation and the sentiment of wrong, which feelings imply a moral -idea of right and wrong. Again, what he thinks of as wrong, he tries to -prevent; what he deems right, he attempts to realize. The Idea gives -a character to the Act; the Act embodies the Idea. In the moral world -as in the natural world, the Antithesis is universal and inseparable. -It is an Antithesis of inseparable elements. In human action, there is -ever involved the Idea of what is right, and the external Act in which -this idea is in some measure embodied. - -5. But the moral Ideas, such as that of Justice, of Rightness, and -the like, are always embodied incompletely in the world of external -action. Although men's actions are to a great extent governed by the -Ideas of Justice, Rightness and the like; (for it must be recollected -that we include in their actions, laws, and the enforcement of laws;) -yet there is a large portion of human actions which is not governed by -such ideas: (actions which result from mere desire, and violations of -law). There is a perpetual Antithesis of Ideas and Facts, which is the -fundamental basis of moral as of natural philosophy. In the former as -in the latter subject, besides what is ideal, there is an Actual which -the ideal does not include. This Actual is the region in which the -results of mere desire, of caprice, of apparent accident, are found. It -is the region of history, as opposed to justice; it is the region of -what _is_, as distinct from what _ought_ to be. - -6. Now what I especially wish here to remark, is this;--that the -progress of man as a moral being consists in a constant extension of -the Idea into the region of Facts. This progress consists in making -human actions conform more and more to the moral Ideas of Justice, -Rightness, and the like; including in human actions, as we have said, -Laws, the enforcement of Laws, and other collective acts of bodies of -men. The History of Man _as_ Man consists in this extension of moral -Ideas into the region of Facts. It is not that the actual history of -what men do has always consisted in such an extension of moral Ideas; -for there has ever been, in the actual doings of men, a large portion -of facts which had no moral character; acts of desire, deeds of -violence, transgressions of acknowledged law, and the like. But such -events are not a part of the genuine progress of humanity. They do -not belong to the history of man as man, but to the history of man as -brute. On the other hand, there are events which belong to the history -of man as man, events which belong to the genuine progress of humanity; -such as the establishment of just laws; their enforcement; their -improvement by introducing into them a fuller measure of moral Ideas. -By such means there is a constant progress of man as a moral being. -By this _realization of moral Ideas_ there is a constant progress of -Humanity. - -7. I have made this reflection, because it appears to me to bring -into view an analogy between the Progress of Science and the Progress -of Man, or of Humanity, in the sense in which I have used the term. -In both these lines of Progress, Facts are more and more identified -with Ideas. In both, there is a fundamental Antithesis of Ideas -and Facts, and progress consists in a constant advance of the point -which separates the two elements of this Antithesis. In both, Facts -are constantly won over to the domain of Ideas. But still, there is -a difference in the two cases; for in the one case the Facts are -beyond our control. We cannot make them other than they are; and all -that we can do, if we can do that, is to shape our Ideas so that they -shall coincide with the Facts, and still have the manifest connexion -which belongs to them as Ideas. In the other case, the Facts are, to -a certain extent, in our power. They are what we make them, for they -are what we do. In this case, the Facts ought to come towards the -Ideas, rather than the Ideas towards the Facts. As we called the former -process the Idealization of Facts, we may call this the Realization of -Ideas; and the analogy which I have here wished to bring into view may -be expressed by saying, that the Progress of Physical Science consists -in a constant successive Idealization of Physical Facts; and the -Progress of man's Moral Being is a constant successive Realization of -Moral Ideas. - -8. Thus the necessary co-existence of an objective and a subjective -element belongs not only to human knowledge, as was before explained, -but also to human action. The objective and the subjective element are -inseparable in this case as in the other. We have always the Fact of -Positive Law, along with the Idea of Absolute Justice; the Facts of -Gain or Loss, along with the Idea of Rights. The Idea of Justice is -inseparable from historical facts, for justice gives to each his own, -and history determines what that is. We cannot even conceive justice -without society, or society without law, and thus in the moral and in -the natural world the fundamental antithesis is inseparable, even in -thought. The two elements must always subsist; for however far the -moral ideas be realized in the world, there will always remain much in -the world which is not conformable to moral ideas, even if it were only -through its necessary dependence on an unmoral and immoral past. As -in the physical world so in the moral, however much the ideal sphere -expands, it is surrounded by a region which is not conformable to the -idea, although in one case the expansion takes place by educing ideas -out of facts, in the other, by producing facts from ideas. - -I shall hereafter venture to pursue further this train of speculation, -but at present I shall make some remarks on writers who may be regarded -as the successors amongst ourselves of these German schools of -Philosophy. - - -FOOTNOTES: - -[Footnote 297: _Phil. of Biol._ c. v.] - - - - -CHAPTER XXVI. - -OF THE "PHILOSOPHY OF THE INFINITE." - - -In the last Chapter but one I stated that Schelling propounded a -Philosophy of the Absolute, the Absolute being the original basis -of truth in which the two opposite elements, Ideas and Facts, are -identified, and that Hegel also founded his philosophy on the Identity -of these two elements. These German philosophies appear to me, as I -have ventured to intimate, of small or no value in their bearing on -the history of actual science. I have in the history of the sciences -noted instances in which these writers seem to me to misconceive -altogether the nature and meaning of the facts of scientific history; -as where[298] Schelling condemns Newton's Opticks as a fabric of -fallacies: and where[299] Hegel says that the glory due to Kepler has -been unjustly transferred to Newton. As it appears to me important that -English philosophers should form a just estimate of Hegel's capacity of -judging and pronouncing on this subject, I will print in the Appendix a -special discussion of what he has said respecting Newton's discovery of -the law of gravitation. - -Recently attempts have been made to explain to English readers -these systems of German philosophy, and in these attempts there are -some points which may deserve our notice as to their bearing on the -philosophy of science. I find some difficulty in discussing these -attempts, for they deal much with phrases which appear to me to -offer no grasp to man's power of reason. What, for instance, is the -_Absolute_, which occupies a prominent place in these expositions? It -is, as I have stated, in Schelling, the central basis of truth in which -things and thoughts are united and identified. To attempt to reason -about such an "Absolute" appears to me to be an entire misapprehension -of the power of reason. Again; one of the most eminent of the -expositors has spoken of each system of this kind as a _Philosophy of -the Unconditioned_[300]. But what, we must ask, is the _Unconditioned_? -That which is subject to no conditions, is subject to no conditions -which distinguish it from any thing else, and so, cannot be a matter of -thought. But again; this _Absolute_ or _Unconditioned_ is (if I rightly -understand) said to be described also by various other names; _unity_, -_identity_, _substance_, _absolute cause_, the _infinite_, _pure -thought_, &c. As each of these terms expresses some condition on which -the name fixes our thoughts, I cannot understand why they should any of -them be called the _Unconditioned_; and as they express very different -thoughts, I cannot understand why they should be called by the same -name. From speculations starting from such a point, I can expect -nothing but confusion and perplexity; nor can I find that anything else -has come of them. They appear to me more barren, and more certain to be -barren, of any results which have any place in our real knowledge, than -the most barren speculations of the schoolmen of the middle ages: which -indeed they much resemble in all their features--their acuteness, their -learning, their ambitious aim, and their actual failure. - -2. But leaving the Absolute and the Unconditioned, as notions which -cannot be dealt with by our reason without being something entirely -different from their definitions, we may turn for a moment to another -notion which is combined with them by the expositors of whom I speak, -and which has some bearing upon our positive science, because it enters -into the reasonings of mathematics: I mean the notion of _Infinite_. -Some of those who hold that we can know nothing concerning the -Absolute and the Unconditioned, (which they pretend to prove, though -concerning such words I do not conceive that anything can be true or -false,) hold also that the Infinite is in the same condition;--that we -can know nothing concerning what is Infinite;--therefore, I presume, -nothing concerning infinite space, infinite time, infinite number, or -infinite degrees. - -To disprove this doctrine, it might be sufficient to point out that -there is a vast mass of mathematical science which includes the notion -of infinites, and leads to a great body of propositions concerning -Infinites. The whole of the infinitesimal calculus depends upon -conceiving finite magnitudes divided into an infinite number of parts: -these parts are infinitely small, and of these parts there are other -infinitesimal parts infinitely smaller still, and so on, as far as we -please to go. And even those methods which shun the term _infinite_, as -Newton's method of Ultimate Ratios, the method of Indivisibles, and the -method of Exhaustions of the ancient geometers, do really involve the -notion of infinite; for they imply a process continued without limit. - -3. But perhaps it will be more useful to point out the fallacies of -the pretended proofs that we can know nothing concerning Infinity and -infinite things. - -The argument offered is, that of infinity we have no notion but the -negation of a limit, and that from this negative notion no positive -result can be deduced. - -But to this I reply: It is not at all true that our notion of what is -infinite is merely that it is _that_ which has no limit. We must ask -further that _what_? that space? that time? that number?--And if that -space, that what kind of space? That line? that surface? that solid -space?--And if that line, that line bounded at one end, or not? If that -surface, that surface bounded on one, or on two, or on three sides? -or on none? However any of these questions are answered, we may still -have an infinite space. Till they are answered, we can assert nothing -about the space; not because we can assert nothing about infinites; but -because we are not told what _kind_ of infinite we are talking of. - -In reality the definition of an Infinite Quantity is not negative -merely, but contains a positive part as well. We assume a quantity -of a certain kind which may be augmented by carrying onward its -limits in one or more directions: this is a finite quantity of a -given kind. We _then_--when we have thus positively determined the -kind of the quantity--suppose the limit in one or more directions to -be annihilated, and thus we have an infinite quantity. But in this -infinite quantity there remain the positive properties from which we -began, as well as the negative property, the negation of a limit; and -the positive properties joined with the negative property may and do -supply grounds of reasoning respecting the infinite quantity. - -4. This is lore so elementary to mathematicians that it appears almost -puerile to dwell upon it; but this seems to have been overlooked, in -the proof that we can have no knowledge concerning infinites. In such -proof it is assumed as quite evident, that all infinites are equal. -Yet, as we have seen, infinites may differ infinitely among themselves, -both in quantity and in kind. A German writer is quoted[301] for an -"ingenious" proof of this kind. In his writings, the opponent is -supposed to urge that a line _BAC_ may be made infinite by carrying -the extremity _C_ infinitely to the right, and again infinite by -carrying the extremity _B_ infinitely to the left; and thus the line -infinitely extended both ways would be double of the line infinite on -one side only. The supposed reply to this is, that it cannot be so, -because one infinite is equal to another: and moreover that what is -bounded at one end _A_, cannot be infinite: both which assumptions are -without the smallest ground. That one infinite quantity may be double -of another, is just as clear and certain as that one finite quantity -may. For instance, if one leaf of the book which the reader has before -him were produced infinitely upwards it would be an infinite space, -though bounded at the bottom and at both sides. If the other leaf were -in like manner produced infinitely upwards it would in like manner be -infinite; and the two together, though each infinite, would be double -of either of them. - -5. As I have said, infinite quantities are conceived by conceiving -finite quantities increased by the transfer of a certain limit, and -then by negativing this limit altogether. And thus an infinite number -is conceived by assuming the series 1, 2, 3, 4, and so on, up to a -limit, and then removing this limit altogether. And this shows the -baselessness of another argument quoted from Werenfels. The opponent -asks, Are there in the infinite line an infinite number of feet? -Then in the double line there must be twice as many; and thus the -former infinite number did not contain all the (possible) unities; -(numerus infinitus non omnes habet unitates, sed præter eum concipi -possunt totidem unitates, quibus ille careat, eique possunt addi). -To which I reply, that the definition of an infinite number is not -that it contains all possible unities: but this--that the progress of -numeration being begun according to a certain law, goes on without -limit. And accordingly it is easy to conceive how one infinite number -may be larger than another infinite number, in any proportion. If, for -instance, we take, instead of the progression of the natural numbers 1, -2, 3, 4, &c. and the progression of the square numbers 1, 4, 9, 16, &c. -any term of the latter series will be greater than the corresponding -term of the other series in a ratio constantly increasing, and the -infinite term of the one, infinitely greater than the corresponding -infinite term of the other. - -6. In the same manner we form a conception of infinite time, by -supposing time to begin now, and to go on, after the nature of time, -without limit; or by going back in thought from the present to a past -time, and by continuing this retrogression without limit. And thus we -have time infinite _a parte ante_ and _a parte post_, as the phrase -used to run; and time infinite both ways includes both, and is the most -complete notion of eternity. - -7. Perhaps those who thus maintain that we cannot conceive anything -infinite, mean that we cannot form to ourselves a definite image of -anything infinite. And this of course is true. We cannot form to -ourselves an image of anything of which one of the characteristics is -that it is, in a certain way, unlimited. But this impossibility does -not prevent our reasoning about infinite quantities; combining as -elements of our reasoning, the absence of a limit with other positive -characters. - -8. One of the consequences which is drawn by the assertors of the -doctrine that we cannot know anything about Infinity, is that we cannot -obtain from science any knowledge concerning God: And I have been the -more desirous to show the absence of proof of this doctrine, because I -conceive that science _does_ give us some knowledge, though it be very -little, of the nature of God: as I shall endeavour to show hereafter. - -For instance, I conceive that when we say that God is an _eternal_ -Being, this phraseology is not empty and unmeaning. It has been used -by the wisest and most thoughtful men in all ages, and, as I conceive, -may be used with undiminished, or with increased propriety, after -all the light which science and philosophy have thrown upon such -declarations. The reader of Newton will recollect how emphatically he -uses this expression along with others of a cognate character[302]: -"God is eternal and infinite, ... that is, He endures from eternity -to eternity, and is present from infinity to infinity.... He is not -eternity and infinity, but eternal and infinite. He is not duration and -space, but He endures and is present. He endures always, and is present -everywhere, and by existing always and everywhere He constitutes -duration and space." We shall see shortly that the view to which we are -led may be very fitly expressed by this language. - -But I will first notice some other aspects of this philosophy. - - -FOOTNOTES: - -[Footnote 298: _Hist. Ind. Sc._ b. ix. c. iii.] - -[Footnote 299: _Ibid._ b. vii. c. ii.] - -[Footnote 300: Sir W. Hamilton's Note on the _Philosophy of the -Unconditioned_.] - -[Footnote 301: Werenfels in Mr. Mansel's _Bampton Lectures_, lect. ii. -Note 15.] - -[Footnote 302: _Scholium Generale_ at the end of the _Principia_.] - - - - -CHAPTER XXVII. - -SIR WILLIAM HAMILTON ON INERTIA AND WEIGHT. - - -In a preceding chapter I have spoken of Sir William Hamilton as the -expositor, to English readers, of modern German systems, and especially -of the so-called "Philosophy of the Unconditioned." But the same writer -is also noticeable as a continuator of the speculations of English and -Scottish philosophers concerning primary and secondary qualities; and -these speculations bear so far upon the philosophy of science that it -is proper to notice them here. - - -1. In our survey of the sciences, we have spoken of a class which we -have termed the Secondary Mechanical Sciences; these being the sciences -which explain certain sensible phenomena, as sound, light, and heat, by -means of a medium interposed between external bodies and our organs of -sense. In these cases, we ascribe to bodies certain qualities: we call -them resonant, bright, red or green, hot or cold. But in the sciences -which relate to these subjects, we explain these qualities by the -figure, size and motions of the parts of the medium which intervenes -between the object and the ear, eye, or other sensible organ. And those -former qualities, sound, warmth and colour, are called _secondary -qualities_ of the bodies; while the latter, figure, size and motion, -are called the _primary qualities_ of body. - - -2. This distinction, in its substance, is of great antiquity. The -atomic theory which was set up at an early period of Greek philosophy -was an attempt to account for the secondary qualities of bodies by -means of their primary qualities. And this is really the scientific -ground of the distinction. _Those_ are primary qualities or attributes -of body by means of which we, in a scientific view, explain and derive -their other qualities. But the explanation of the sensible qualities -of bodies by means of their operation through a medium has till now -been very defective, and is so still. We have to a certain extent -theories of Sound, Light and Heat, which reduce these qualities to -scales and standards, and in some measure account mechanically for -their differences and gradations. But we have as yet no similar theory -of Smells and Tastes. Still, we do not doubt that fragrance and flavour -are perceived by means of an aerial medium in which odours float, and -a fluid medium in which sapid matters are dissolved. And the special -odour and flavour which are thus perceived must depend upon the size, -figure, motion, number, &c. of the particles thus conveyed to the -organs of taste and smell: that is, _those_ secondary qualities, as -well as the others, must depend upon the primary qualities of the parts -of the medium. - - -3. In this way the distinction of primary and secondary qualities is -definite and precise. But when men attempt to draw the distinction -by guess, without any scientific principle, the separation of -the two classes is vague and various. I have, in the _History of -Scientific Ideas_[303], pointed out some of the variations which -are to be found on this subject in the writings of philosophers. -Sir William Hamilton[304] has given an account of many more which -he has compared and analysed with great acuteness. He has shown how -this distinction is treated, among others, by the ancient atomists, -Leucippus and Democritus, by Aristotle, Galen, Galileo, Descartes, -Boyle, Malebranche, Locke, Reid, Stewart, Royer-Collard. He then -proceeds to give his own view; which is, that we may most properly -divide the qualities of bodies into _three_ classes, which he calls -_Primary_, _Secundo-primary_, and _Secondary_. The former he enumerates -as 1, Extension; 2, Divisibility; 3, Size; 4, Density or Rarity; 5, -Figure; 6, Incompressibility absolute; 7, Mobility; 8, Situation. -The Secundo-primary are Gravity, Cohesion, Inertia, Repulsion. The -Secondary are those commonly so called, Colour, Sound, Flavour, -Savour, and Tactical Sensation; to which he says may be added the -muscular and cutaneous sensation which accompany the perception of the -Secundo-primary qualities. "Such, though less directly the result of -foreign causes, are Titillation, Sneezing, Horripilation, Shuddering, -the feeling of what is called Setting-the-teeth-on-edge, &c." - -The Secundo-primary qualities Sir William Hamilton traces in further -detail. He explains that with reference to Gravity, bodies are _heavy_ -or _light_. With reference to Cohesion, there are many coordinate -pairs, of which he enumerates these:--_hard_ and _soft_; _firm_ -and _fluid_,--the fluid being subdivided into _thick_ and _thin_; -_viscid_ and _friable_; _tough_ and _brittle_; _rigid_ and _flexible_; -_fissile_ and _infissile_; _ductile_ and _inductile_; _retractile_ -and _irretractile_; _rough_ and _smooth_; _slippery_ and _tenacious_. -With reference to Repulsion he gives these qualities:--_compressible_ -and _incompressible_; _elastic_ and _inelastic_. And with reference to -Inertia he mentions only _moveable_ and _immoveable_. - -I do not see what advantage is gained to philosophy by such an -enumeration of qualities as this, which, after all, does not pretend -to completeness; nor do I see anything either precise or fundamental -in such distinctions as that of elasticity, a mode of cohesion, and -elasticity, a mode of repulsion. But a question in which our philosophy -is really concerned is how far any of these qualities are _universal_ -qualities of matter. Sir W. Hamilton holds that they are none of them -necessary qualities of matter, and therefore of course not universal, -and argues this point at some length. With regard to one of his -Secundo-primary qualities, I will make some remarks. - - -4. _Inertia._--In discussing the Ideas which enter into the Mechanical -Sciences[305], I have stated that the Idea of Force and Resistance to -Force, that is, of _Force_ and _Matter_, are the necessary foundations -of those sciences. Force cannot act without matter to act on; Matter -cannot exist without Force to keep its parts together and to keep it in -its place. But Force acting upon matter may either be Force producing -rest, or Force producing motion. If we consider Force producing motion, -the motion produced, that is, the velocity produced, must depend upon -the quantity of matter moved. It cannot be that the same power, acting -in the same way, shall produce the same velocity by pushing a small -pebble and a large rock. If this were so, we could have no science on -such matters. It must needs be that the same force produces a smaller -velocity in the larger body; and this according to some measure of -its largeness. The measure of the degree in which the body thus -resists this communication of motion is _inertia_. And the inertia is -necessarily supposed to be proportional to the quantity of matter, -because it is by this inertia that this existence and quantity of the -matter is measured. If therefore any Science concerning Force and -Matter is to exist, matter must have inertia, and the inertia must be -proportional to the quantity of matter. - - -5. Sir W. Hamilton, in opposition to this, says, that we can conceive -a body occupying space, and yet without attraction or repulsion for -another body, and wholly indifferent to this or that position, in -space, to motion and to rest. He infers thence that inertia is not a -necessary quality of bodies. - -To this I reply, that even if we can conceive such bodies, (which in -fact man, living in a world of matter cannot conceive,) at any rate -we cannot conceive any _science_ about such bodies. If bodies were -indifferent to motion and rest, Forces could not be measured by their -effects; nor could be measured or known in any way. Such bodies might -float about like clouds, visible to the eye, but intangible, and -governed by no laws of motion. But if we have any science about bodies, -they must be tangible, and governed by laws of motion. Not, then, from -any observed properties of bodies, but from the possibility of any -science about bodies, does it follow that all bodies have inertia. - - -6. _Gravity._--Reasoning of the same kind may be employed about weight. -We can conceive, it is urged, matter without weight. But I reply, -we cannot conceive a _science_ which deals with matter that has no -weight:--a science, I mean, which deals with the quantity of matter of -bodies, as arising from the sum of their elements. For the quantity of -matter of bodies is and must be measured by those sensible properties -of matter which undergo quantitative addition, subtraction and -division, as the matter is added, subtracted, and divided. The quantity -of matter cannot be known in any other way. But this mode of measuring -the quantity of matter, in order to be true at all, must be universally -true. If it were only partially true--if some kinds of matter had -weight and others had not--the limits of the mode of measuring matter -by weight would be arbitrary: and therefore the whole procedure -would be arbitrary, and as a mode of obtaining philosophical truth, -altogether futile. But we suppose truth respecting the composition of -bodies to be attainable; therefore we must suppose the rule, which is -the necessary basis of such truth, to be itself true. - -Sir W. Hamilton has replied to these arguments, but, as I conceive, -without affecting the force of them. I will repeat here the answer -which I have already given[306], and will reprint in the Appendix the -Memoir by which his objections were occasioned. - -He says, (1), that our reasoning assumes that we must necessarily have -it in our power to ascertain the Quantity of Matter; whereas this may -be a problem out of the reach of human determination. - -To this I reply, that my reasoning _does_ assume that there is a -science, or sciences, which make assertions concerning the Quantity -of Matter: Mechanics and Chemistry are such sciences. My assertion -is, that to make such sciences possible, Quantity of Matter must -be proportional to Weight. If my opponent deny that Mechanics and -Chemistry can exist as science, he may invalidate my proof; but not -otherwise. - -(2) He says that there are two conceivable ways of estimating the -Quantity of Matter: by the Space occupied, and by the Weight or -Inertia; and that I assume the second measure gratuitously. - -To which I reply, that the most elementary steps in Mechanics and -in Chemistry contradict the notion that the Quantity of Matter is -proportionate to the Space. They proceed necessarily on a distinction -between Space and Matter:--between mere Extension and material -Substance. - -(3) He allows that we cannot make the Extension of a body the -measure of the Quantity of Matter, because, he says, we do not -know if "the compressing force" is such as to produce "the closest -compression." That is, he assumes a compressing force, assumes a -"closest compression," assumes a peculiar (and very improbable) atomic -hypothesis; and all this, to supply a reason why we are not to believe -the first simple principle of Mechanics and Chemistry. - -(4) He speaks of "a series of apparent fluids (as Light or its vehicle, -the Calorific, the Electro-galvanic, and Magnetic agents) which we can -neither denude of their character of substance, nor clothe with the -attribute of weight." - -To which my reply is, that precisely because I cannot "clothe" these -agents with the attribute of Weight, I _do_ "denude them of the -character of Substance." They are not substances, but agencies. These -Imponderable Agents are not properly called "Imponderable Fluids." This -I conceive that I have proved; and the proof is not shaken by denying -the conclusion without showing any defect in the reasoning. - -(5) Finally, my critic speaks about "a logical canon," and about "a -criterion of truth, subjectively necessary and objectively certain;" -which matters I shall not waste the reader's time by discussing. - - -FOOTNOTES: - -[Footnote 303: B. iv. c. i.] - -[Footnote 304: Reid's _Works_, Supplementary Dissertation D.] - -[Footnote 305: _Hist. Sc. Id._ b. iii.] - -[Footnote 306: _Hist. Sc. Id._ b. vi. c. iii.] - - - - -CHAPTER XXVIII. - -INFLUENCE OF GERMAN SYSTEMS OF PHILOSOPHY IN BRITAIN. - - -The philosophy of Kant, as I have already said, involved a definite -doctrine on the subject of the Fundamental Antithesis, and a correction -of some of the errors of Locke and his successors. It was not however -at first favourably received among British philosophers, and those who -accepted it were judged somewhat capriciously and captiously. I will -say a word on these points[307]. - -1. (_Stewart_)--Dugald Stewart, in his _Dissertation on the Progress -of the Moral Sciences_, repeatedly mentions Kant's speculations, and -always unfavourably. In Note I to Part I. of the Dissertation he says, -"In our own times, Kant and his followers seem to have thought that -they had thrown a strong light on the nature of _space_ and also of -_time_, when they introduced the word _form_ (_form of the intellect_) -as a common term applicable to both. Is not this to revert to the -scholastic folly of verbal generalization?" And in Part II. he gives a -long and laborious criticism of a portion of Kant's speculations; of -which the spirit may be collected from his describing them as resulting -in "the metaphysical _conundrum_, that the human mind (considered as -a _noumenon_ and not as a _phenomenon_) neither exists in space nor -time." And after mentioning Meiners and Herder along with Kant, he -adds, "I am ashamed to say that in Great Britain the only one of these -names which has been much talked of is Kant." And again in Note EE, he -translates some portion of the German philosopher, adding, that to the -expressions so employed he can attach no meaning. - -Stewart, in his criticism of Kant's doctrines, remarks that, in -asserting that the human mind possesses, in its own ideas, an element -of necessary and universal truth, not derived from experience, Kant had -been anticipated by Price, by Cudworth, and even by Plato; to whose -_Theætetus_ both Price and Cudworth refer, as containing views similar -to their own. And undoubtedly this doctrine of ideas, as indispensable -sources of necessary truths, was promulgated and supported by weighty -arguments in the _Theætetus_; and has ever since been held by many -philosophers, in opposition to the contrary doctrine, also extensively -held, that all truth is derived from experience. But, in pointing out -this circumstance as diminishing the importance of Kant's speculations, -Stewart did not sufficiently consider that doctrines, fundamentally the -same, may discharge a very different office at different periods of -the history of philosophy. Plato's Dialogues did not destroy, nor even -diminish, the value of Cudworth's "Immutable Morality." Notwithstanding -Cudworth's publications, Price's doctrines came out a little afterwards -with the air and with the effect of novelties. Cudworth's assertion of -ideas did not prevent the rise of Hume's skepticism; and it was Hume's -skepticism which gave occasion to Kant's new assertion of necessary -and universal truth, and to his examination into the grounds of the -possibility and reality of such truth. To maintain such doctrine -_after_ the appearance of intermediate speculations, and with reference -to them, was very different from maintaining it before; and this is the -merit which Kant's admirers claim for him. Nor can it be denied that -his writings produced an immense effect upon the mode of treating such -questions in Germany; and have had, even in this country, an influence -far beyond what Mr. Stewart would have deemed their due. - - -2. (_Mr. G. H. Lewes._)--But as injustice has thus been done to Kant by -confounding his case with that of his predecessors of like opinions, -so on the other hand, injustice has also been done, both to him and -those who have followed him in the assertion of ideas, by confounding -_their_ case with his. This injustice seems to me to be committed by a -writer on the History of Philosophy, who has given an account of the -successive schools of philosophy up to our own time;--has assigned -to Kant an important and prominent place in the recent history of -metaphysics;--but has still maintained that Kant's philosophy, and -indeed every philosophy, is and must be a failure. In order to prove -this thesis, the author naturally has to examine Kant's doctrines and -the reasons assigned for them, and to point out what he conceives to be -the fallacy of these arguments. This accordingly he professes to do; -but as soon as he has entered upon the argument, he substitutes, as -his opponent, for the philosopher of Königsberg, a writer of our own -time and country, who does not profess himself a Kantian, who has been -repeatedly accused, with whatever justice, of misrepresenting what he -has borrowed from Kant, and whose main views are, in the opinion of -the writer himself, very different from Kant's. Mr. Lewes[308], in the -chapter entitled "Examination of Kant's Fundamental Principles," after -a preliminary statement of the points he intends to consider, says "Now -to the question. As Kant confessedly was led to his own system by the -speculations of Hume," and so on; and forthwith he introduces the name -of _Dr. Whewell_ as the writer whose views he has to criticize, without -stating how he connects him with Kant, and goes on arguing against -_him_ for a dozen pages to the end of the Chapter. - -3. It is true, however, that I had adopted some of Kant's views, or at -least some of his arguments. The chapters[309] on the Ideas of Space -and Time in the _Philosophy of the Inductive Sciences_, were almost -literal translations of chapters in the _Kritik der Reinen Vernunft_. -Yet the author was charged by a reviewer at the time, with explaining -these doctrines "in a manner incompatible with the clear views of -Emanuel Kant." It appeared to be assumed by the English admirers of the -Kantian philosophy, that Kant's views were true and clear in Germany, -but became untenable when adopted in England. - - -4. (_Mr. Mansel_)--But the most important of my critics on this -ground is Mr. Mansel, who has revived the censure of my speculations -as not doing justice to the Kantian philosophy. "It is much to be -regretted," he says[310], "that Dr. Whewell, who has made good use of -Kantian principles in many parts of his _Philosophy of the Inductive -Sciences_," has not more accurately observed Kant's distinction between -the necessary laws under which all men think, and the contingent -laws under which certain men think of certain things. And further on -Mr. Mansel, after giving great praise to the general spirit of the -_Philosophy of the Inductive Sciences_, says, "It is to be regretted -that the accuracy of his theory has been in so many instances vitiated -by a stumble at the threshold of the Critical Philosophy." Mr. Mansel -is, indeed, by much the most zealous English Kantian whose writings I -have seen;--among those, I mean, who have brought original powers of -philosophical thought to bear upon such subjects; and have not been, as -some have been, enslaved by an admiration of German systems, just as -bigotted as the contempt of them which others feel. And as Mr. Mansel -has stated distinctly some of the points in which he conceives that I -have erred in deviating from the doctrines of Kant, I should wish to -make a few remarks on those points. - -5. Kant considers that Space and Time are conditions of perception, -and hence sources of necessary and universal truth. Dr. Whewell agrees -with Kant in placing in the mind certain sources of necessary truth; -he calls these Fundamental Ideas, and reckons, besides Space and Time, -others, as Cause, Likeness, Substance, and several more. Mr. Mill, -the most recent and able expounder of the opposite doctrine, derives -all truths from Observation, and denies that there is such a separate -source of truth as Ideas. Mr. Mansel does not agree either with Mr. -Mill or Dr. Whewell; he adheres to the original Kantian thesis, that -Space and Time are sources of necessary truths, but denies the office -to the other Fundamental Ideas of Dr. Whewell. In reading what has -been said by Mr. Mill, Mr. Mansel, and other critics, on the subject -of what I have called _Fundamental Ideas_, I am led to perceive that -I have expressed myself incautiously, with regard to the identity of -character between the first two of these Fundamental Ideas, namely, -Space and Time, and the others, as Force, Composition, and the like. -And I am desirous of explaining, to those who take an interest in these -speculations, how far I claim for the other Fundamental Ideas the same -character and attributes as for Space and Time. - -6. The special and characteristic property of all the Fundamental Ideas -is what I have already mentioned, that they are the mental sources of -necessary and universal scientific truths. I call them _Ideas_, as -being something not derived from sensation, but governing sensation, -and consequently giving form to our experience;--_Fundamental_, as -being the foundation of knowledge, or at least of Science. And the way -in which those Ideas become the foundations of Science is, that when -they are clearly and distinctly entertained in the mind, they give rise -to inevitable convictions or intuitions, which may be expressed as -_Axioms_; and these Axioms are the foundations of Sciences respective -of each Idea. The Idea of Space, when clearly possessed, gives rise -to geometrical Axioms, and is thus the foundation of the Science of -Geometry. The Idea of Mechanical Force, (a modification of the Idea of -Cause,) when clearly developed in the mind, gives birth to Axioms which -are the foundation of the Science of Mechanics. The Idea of Substance -gives rise to the Axiom which is universally accepted,--that we cannot, -by any process, (for instance, by chemical processes,) create or -destroy matter, but can only combine and separate elements;--and thus -gives rise to the Science of Chemistry. - - -7. Now it may be observed, that in giving this account of the -foundation of Science, I lay stress on the condition that the Ideas -must be _clearly and distinctly possessed_. The Idea of Space must be -quite clear in the mind, or else the Axioms of Geometry will not be -seen to be true: there will be no _intuition_ of their truth; and for -a mind in such a state, there can be no Science of Geometry. A man may -have a confused and perplexed, or a vacant and inert state of mind, in -which it is not clearly apparent to him, that two straight lines cannot -inclose a space. But this is not a frequent case. The Idea of Space is -much more commonly clear in the minds of men than the other Ideas on -which science depends, as Force, or Substance. It is much more common -to find minds in which these latter Ideas are not so clear and distinct -as to make the Axioms of Mechanics or of Chemistry self-evident. -Indeed the examples of a state of mind in which the Ideas of Force -or of Substance are so clear as to be made the basis of science, are -comparatively few. They are the examples of minds scientifically -cultivated, at least to some extent. Hence, though the Axioms of -Mechanics or of Chemistry may be, in their own nature, as evident as -those of Geometry, they are not evident to so many persons, nor at so -early a period of intellectual or scientific culture. And this being -the case, it is not surprising that some persons should doubt whether -these Axioms are evident at all;--should think that it is an error to -assert that there exist, in such sciences as Mechanics or Chemistry, -Fundamental Ideas, fit to be classed with Space, as being, like it, the -origin of Axioms. - -In speaking of all the Fundamental Ideas as being alike the source of -Axioms when clearly possessed, without dwelling sufficiently upon the -amount of mental discipline which is requisite to give the mind this -clear possession of most of them; and in not keeping before the reader -the different degrees of evidence which, in most minds, the Axioms -of different sciences naturally have, I have, as I have said, given -occasion to my readers to misunderstand me. I will point out one or two -passages which show that this misunderstanding has occurred, and will -try to remove it. - -8. The character of axiomatic truths seen by intuition is, that -they are not only seen to be true, but to be necessary;--that the -contrary of them is not only false, but inconceivable. But this -inconceivableness depends entirely upon the clearness of the Ideas -which the axioms involve. So long as those Ideas are vague and -indistinct, the contrary of an Axiom may be assented to, though it -cannot be distinctly conceived. It may be assented to, not because it -is possible, but because _we_ do not see clearly what _is_ possible. To -a person who is only beginning to think geometrically, there may appear -nothing absurd in the assertion, that two straight lines may inclose -a space. And in the same manner, to a person who is only beginning -to think of mechanical truths, it may not appear to be absurd, that -in mechanical processes, Reaction should be greater or less than -Action; and so, again, to a person who has not thought steadily -about Substance, it may not appear inconceivable, that by chemical -operations, we should generate new matter, or destroy matter which -already exists. - -Here then we have a difficulty:--the test of Axioms is that the -contrary of them is inconceivable; and yet persons, till they have in -some measure studied the subject, do not see this inconceivableness. -Hence our Axioms must be evident only to a small number of thinkers; -and seem not to deserve the name of self-evident or necessary truths. - -This difficulty has been strongly urged by Mr. Mill, as supporting -his view, that all knowledge of truth is derived from experience. And -in order that the opposite doctrine, which I have advocated, may not -labour under any disadvantages which really do not belong to it, I must -explain, that I do not by any means assert that those truths which -I regard as necessary, are all equally evident to common thinkers, -or evident to persons in all stages of intellectual development. I -may even say, that some of those truths which I regard as necessary, -and the necessity of which I believe the human mind to be capable of -seeing, by due preparation and thought, are still such, that this -amount of preparation and thought is rare and peculiar; and I will -willingly grant, that to attain to and preserve such a clearness and -subtlety of mind as this intuition requires, is a task of no ordinary -difficulty and labour. - -9. This doctrine,--that some truths may be seen by intuition, but yet -that the intuition of them may be a rare and difficult attainment,--I -have not, it would seem, conveyed with sufficient clearness to obviate -misapprehension. Mr. Mill has noticed a passage of my _Philosophy_ -on this subject, which he has understood in a sense different from -that which I intended. Speaking of the two Principles of Chemical -Science,--that combinations are definite in kind, and in quantity,--I -had tried to elevate myself to the point of view in which these -Principles are seen, not only to be true, but to be necessary. I was -aware that even the profoundest chemists had not ventured to do this; -yet it appeared to me that there were considerations which seemed to -show that any other rule would imply that the world was a world on -which the human mind could not employ itself in scientific speculation -at all. These considerations I ventured to put forwards, not as views -which could at present be generally accepted, but as views to which -chemical philosophy appeared to me to tend. Mr. Mill, not unnaturally, -I must admit, supposed me to mean that the two Principles of Chemistry -just stated, are self-evident, in the same way and in the same -degree as the Axioms of Geometry are so. I afterwards explained that -what I meant to do was, to throw out an opinion, that _if_ we could -conceive the composition of bodies _distinctly_, we might be able to -see that it is necessary that the modes of this composition should -be definite. This Mr. Mill does not object to[311]: but he calls it -a great attenuation of my former opinion; which he understood to be -that we, (that is, men in general,) already see, or may see, or ought -to see, this necessity. Such a general apprehension of the necessity -of definite chemical composition I certainly never reckoned upon; -and even in my own mind, the thought of such a necessity was rather -an anticipation of what the intuitions of philosophical chemists in -another generation would be, than an assertion of what they now are or -ought to be; much less did I expect that persons, neither chemists nor -philosophers, would already, or perhaps ever, see that a proposition, -so recently discovered to be true, is not only true, but necessary. - -10. Of the bearing of this view on the question at issue between Mr. -Mill and me, I may hereafter speak; but I will now notice other persons -who have misunderstood me in the same way. - -An able writer in the _Edinburgh Review_[312] has, in like manner, -said, "Dr. Whewell seems to us to have gone much too far in reducing -to necessary truths what assuredly the generality of mankind will not -feel to be so." It is a fact which I do not at all contest, that the -_generality of mankind_ will not feel the Axioms of Chemistry, or even -of Mechanics, to be necessary truths. But I had said, not that the -generality of mankind would feel this necessity, but (in a passage -just before quoted by the Reviewer) that the mind under certain -circumstances _attains a point of view_ from which it can pronounce -mechanical (and other) fundamental truths to be necessary in their -nature, though disclosed to us by experience and observation. - -Both the Edinburgh Reviewer and Mr. Mansel appear to hold a distinction -between the fundamental truths of Geometry, and those of the other -subjects which I have classed with them. The latter says, that -perhaps metaphysicians may hereafter establish the existence of other -subjective conditions of intuitions (or, as I should call them, -Fundamental Ideas,) besides Space and Time, but that in asserting -such to exist in the science of Mechanics, I certainly go too far: -and he gives as an instance my Essay,--"Demonstration that all matter -is heavy." I certainly did not expect that the Principles asserted -in that Essay would be assented to as readily or as generally as the -Axioms of Geometry; but I conceive that I have there proved that -Chemical Science, using the balance as one of its implements, cannot -admit "imponderable bodies" among its elements. This impossibility -will, I think, not only be found to exist in fact, but seen to exist -necessarily, by chemists, in proportion as they advance towards general -propositions of Chemical Science in which the so-called "imponderable -fluids" enter. But even if I be right in this opinion, to how few will -this necessity be made apparent, and how slowly will the intuition -spread! I am as well aware as my critics, that the necessity will -probably never be apparent to ordinary thinkers. - - -11. Though Mr. Mansel does not acknowledge any subjective conditions -of intuition besides Space and Time, he does recognize other _kinds -of necessity_, which I should equally refer to Fundamental Ideas; -because they are, no less than Space and Time, the foundations of -universal and necessary truths in science. Such are[313] the Principle -of Substance;--All Qualities exist in some subject: and the Principle -of Causality;-- Every Event has its Cause. To these Principles he -ascribes a "metaphysical necessity," the nature and grounds of which -he analyses with great acuteness. But what I have to observe is, that -whatever _differences_ may be pointed out between the _grounds_ of -the necessity, in this case of _metaphysical_ necessity, and in that -which Mr. Mansel calls _mathematical_ necessity which belongs to the -Conditions or Ideas of Space and of Time; still, it is not the less -true that the Ideas of Substance and of Cause, _do_ afford a foundation -for necessary truths, and that on these truths are built Sciences. That -every Change must have a Cause, with the corresponding Axioms,--that -the Cause is known by the Effect, and Measured by it,--is the basis -of the Science of Mechanics. That there is a Substance to which -qualities belong, with the corresponding Axiom,--that we cannot create -or destroy Substance, though we may alter Qualities by combining and -separating Substances,--is the basis of the Science of Chemistry. And -that this doctrine of the Indestructibility of Substance is a primary -axiomatic truth, is certain; both because it has been universally taken -for granted by men seeking for general truths; and because it is not -and cannot be proved by experience[314]. So that I have here, even -according to Mr. Mansel's own statement, other grounds besides Space -and Time, for necessary truths in Science. - -12. Besides mathematical and metaphysical necessity, Mr. Mansel -recognizes also a _logical necessity_. I will not pretend to say -that this kind of necessity is exactly represented by any of those -Fundamental Ideas which are the basis of Science; but yet I think it -will be found that this logical necessity mainly operates through -the attribution of Names to things; and that a large portion of its -cogency arises from these maxims,--that names must be so imposed that -General Propositions shall be possible,--and so that Reasoning shall be -possible. Now these maxims are really the basis of Natural History, -and are so stated in the _Philosophy of the Inductive Sciences_. The -former maxim is the principle of all Classification; and though we have -no syllogisms in Natural History, the apparatus of _genus_, _species_, -_differentia_, and the like, which was introduced in the analysis of -syllogistic reasoning, is really more constantly applied in Natural -History than in any other science. - -13. Besides the different kinds of necessity which Mr. Mansel thus -acknowledges, I do not see why he should not, on his own principles, -recognize others; as indeed he appears to me to do. He acknowledges, -I think, the distinction of Primary and Secondary qualities; and -this must involve him in the doctrine that Secondary Qualities are -necessarily perceived by means of a _Medium_. Again: he would, I -think, acknowledge that in organized bodies, the parts exist for a -_Purpose_; and Purpose is an Idea which cannot be inferred by reasoning -from facts, without being possessed and applied as an Idea. So that -there would, I conceive, exist, in his philosophy, all the grounds of -necessary truth which I have termed Fundamental Ideas; only that he -would further subdivide, classify, and analyse, the kinds and grounds -of this necessity. - -In this he would do well; and some of his distinctions and analyses -of this kind are, in my judgment, very instructive. But I do not see -what objection there can be to my putting together all these kinds of -necessity, when my purpose requires it; and, inasmuch as they all are -the bases of Science, I may call them by a general name; for instance, -Grounds of Scientific Necessity; and these are precisely what I mean by -_Fundamental Ideas_. - -That some steady thought, and even some progress in the construction -of Science, is needed in order to see the necessity of the Axioms thus -introduced, is true, and is repeatedly asserted and illustrated in the -History of the Sciences. The necessity of such Axioms is seen, but it -is not seen at first. It becomes clearer and clearer to each person, -and clear to one person after another, as the human mind dwells more -and more steadily on the several subjects of speculation. _There are -scientific truths which are seen by intuition, but this intuition -is progressive._ This is the remark which I wish to make in answer -to those of my critics who have objected that truths which I have -propounded as Axioms, are not evident to all. - - -14. That the Axioms of Science are not evident _to all_, is true -enough, and too true. Take the Axiom of Substance:--that we may change -the condition of a substance in various ways, but cannot destroy it. -This has been assumed as evident by philosophers in all ages; but if -we ask an ordinary person whether a body can be destroyed by fire, or -diminished, will he unhesitatingly reply, that it cannot? It requires -some thought to say[315], as the philosopher said, that the weight of -the smoke is to be found by subtracting the weight of the ashes from -that of the fuel; nay, even when this is said, it appears, at first, -rather an epigram than a scientific truth. Yet it is by thinking only, -not by an experiment, that, from a happy guess it becomes a scientific -truth. And the thought is the basis, not the result, of experimental -truths; for which reason I ascribe it to a Fundamental Idea. And so, -such truths are the genuine growth of the human mind; not innate, -as if they needed not to grow; still less, dead twigs plucked from -experience and stuck in from without; not universal, as if they grew -up everywhere; but not the less, under favourable circumstances, the -genuine growth of the scientific intellect. - -15. Not only do I hold that the Axioms, on which the truths of science -rest, grow from guesses into Axioms in various ways, and often -gradually, and at different periods in different minds, and partially, -even in the end; but I conceive that this may be shown by the history -of science, as having really happened, with regard to all the most -conspicuous of such principles. The scientific insight which enabled -discoverers to achieve their exploits, implied that they were among -the first to acquire an intuitive conviction of the Axioms of their -Science: the controversies which form so large a portion of the history -of science, arise from the struggles between the clear-sighted and -the dimsighted, between those who were forwards and those who were -backwards in the progress of ideas; and these controversies have very -often ended in diffusing generally a clearness of thought, on the -controverted subject, which at first, the few only, or perhaps not -even they, possessed. The History of Science consists of the History -of Ideas, as well as of the History of Experience and Observation. -The latter portion of the subject formed the principal matter of my -_History_ of the Inductive Sciences; the former occupied a large -portion of the _Philosophy_ of the Inductive Sciences[316]; which, I -may perhaps be allowed to explain, is, for the most part, a Historical -Work no less than the other; and was written in a great measure, at the -same time, and from the same survey of the works of scientific writers. - -16. I am aware that the explanation which I have given, may naturally -provoke the opponents of the doctrine of scientific necessity to -repeat their ordinary fundamental objections, in a form adapted to -the expressions which I have used. They may say, the fact that these -so-called Axioms thus become evident only during the progress of -experience, proves that they are derived from experience: they may, -in reply to our image, say, that truths are stuck into the mind by -experience, as seeds are stuck into the ground; and that to maintain -that they can grow under any other conditions, is to hold the -doctrine of spontaneous generation, which is equally untenable in the -intellectual and in the physical world. I shall not however here resume -the general discussion; but shall only say briefly in reply, that -Axioms,--for instance, this Axiom, that _material substances cannot be -created or annihilated by any process which we can apply_,--though it -becomes evident in the progress of experience, cannot be derived from -experience; for it is a proposition which never has nor can be proved -by experience; but which, nevertheless, has been always assumed by men, -seeking for general truths, as necessarily true, and as controlling -and correcting all possible experience. And with regard to the image -of vegetable development, I may say, that as such development implies -both inherent forms in the living seed, and nutritive powers in earth -and air; so the development of our scientific ideas implies both a -formative power, and materials acted on; and that, though the analogy -must be very defective, we conceive that we best follow it by placing -the formative power in the living mind, and in the external world the -materials acted on: while the doctrine that all truth is derived from -experience only, appears to reject altogether one of these elements, or -to assert the two to be one. - - -FOOTNOTES: - -[Footnote 307: The remarks contained in this chapter have for the most -part been already printed and circulated in a _Letter to the Author of -Prolegomena Logica_, 1852.] - -[Footnote 308: _Biographical History of Philosophy_, 1846. In a more -recent edition the author of this work has modified his expressions, -but still employs himself in arguing against Dr. Whewell, in order to -overthrow Kant. So far as his arguments affect my philosophy, they are, -as I conceive, answered in the various expositions which I have given -of that philosophy.] - -[Footnote 309: B. ii. The Philosophy of the Pure Sciences. Chap. -ii. Of the Idea of Space. Chap. iii. Of some peculiarities of the -Idea of Space. Chap. vii. Of the Idea of Time. Chap. viii. Of some -peculiarities of the Idea of Time.] - -[Footnote 310: _Prolegomena Logica_, by H. L. Mansel, M.A. 1851.] - -[Footnote 311: _Logic_, i. p. 273, 3rd edit.] - -[Footnote 312: No. 193, p. 29.] - -[Footnote 313: _Prol. Log._ p. 123.] - -[Footnote 314: See _Phil. Ind. Sc._ b. vi. c. iii.] - -[Footnote 315: Kant.] - -[Footnote 316: Republished as _The History of Scientific Ideas_.] - - - - -CHAPTER XXIX. - -NECESSARY TRUTH IS PROGRESSIVE. - - -OBJECTIONS CONSIDERED. - -The doctrine that necessary truth is progressive is a doctrine very -important in its bearing upon the nature of the human mind; and, as -I conceive, in its theological bearing also. But it is a doctrine to -which objections are likely to be made from various quarters, and I -will consider some of these objections. - -1. Necessary truths, it will be said, cannot increase in number. New -ones cannot be added to the old ones. For necessary truths are those of -which the necessity is plain and evident to all mankind--to the common -sense of man; such as the axioms of geometry. But that which is evident -to all mankind must be evident from the first: that which is plain to -the common sense of man cannot require scientific discovery: that which -is necessarily true cannot require accumulated proof. - -To this I reply, that necessary truths require for their apprehension -a certain growth and development of the human mind. Though it is seen -that they are necessarily true, this is seen only by those who think -steadily and clearly, and to think steadily and clearly on any kind -of subject, requires time and attention;--requires mental culture. -This may be seen even in the case of the axioms of geometry. These -axioms are self-evident: but to _whom_ are they self-evident? Not to -uncultured savages, or young children; or persons of loose vague habits -of thought. To see the truth and necessity of geometrical axioms, we -need geometrical culture. - -Therefore that any axioms are not evident without patient thought and -continued study of the subject, does not disprove their necessity. -Principles may be axiomatic and necessary, although they require time, -and the progress of thought and of knowledge, to bring them to light. -And axioms may be thus gradually brought to light by the progress of -knowledge. - -Nor is it difficult to give examples of such axioms, other than -geometrical. There is an axiom which has obtained currency among -thoughtful men from the time that man began to speculate about himself -and the universe:--_E nihilo nil fit_: Nothing can be made of nothing. -No material substance can be produced or destroyed by natural causes, -though its form and consistence may be changed indefinitely. Is not -this an axiom? a necessary truth? Yet it is not evident to all men -at first, and without mental culture. At first and before habits of -steady and consistent thought are formed, men think familiarly of the -creation and destruction of matter. Only when the mind has received -some philosophical culture does it see the truth and necessity of the -axiom of substance, and _then_ it does see it. - -And the axioms on which the science of mechanics rests, that the cause -is measured by the effects, that reaction is equal and opposite to -action, and the like,--are not these evident to a mind cultivated by -steady thought on such subjects? and do they not require such culture -of the mind in order to see them? Are they not obscure or uncertain -to those who are not so cultured, that is to common thinkers: to the -general bulk of mankind? Thus then it requires the discipline of the -science of mechanics to enable the mind to see the axioms of that -science. - -And does not this go further, as science and the careful study of -the grounds of science go further? To a person well disciplined in -mechanical reasoning it has become, not a conclusion, but a principle, -that in mechanical action what is gained in power is lost in time: -or that in any change, the force gained is equal to the force lost, -so that new force cannot be generated, any more than new matter, by -natural changes. Is this an axiom? a necessary fundamental truth? It -appears so to at least one great thinker and discoverer now alive -among us. If it do not appear so to us, or not in the same sense, -may not this be because we have not yet reached his point of view? -May not the conviction which is now his alone become hereafter the -conviction of the philosophical world? And whatever the case may be -in this instance, have there not been examples of this progress? Did -not Galileo and the disciples of Galileo reduce several mechanical -principles to the character of necessary truths, after they had by -experiment and reasoning discovered them to be actually true? And -have we not in these cases so many proofs that necessary truth is -progressive, along with the progress of knowledge? - -2. But, it will be said, the necessary character claimed for such -truths is an illusion. The propositions so brought into view are really -established by observation: by the study of external facts: and it is -only the effect of habit and familiarity which makes men of science, -when they well know them to be true, think them to be necessarily true. -They are really the results of experience, as their history shows; and -therefore cannot be necessary and _à priori_ truths. - -To which I reply: Such principles as I have mentioned,--that material -substance cannot be produced or destroyed--that the cause is measured -by the effect--that reaction is equal and opposite to action: are not -the results of experience, nor can be. No experience can prove them; -they are necessarily assumed as the interpretation of experience. -They were not proved in the course of scientific investigations, but -brought to light as such investigations showed their necessity. They -are not the results, but the conditions of experimental sciences. -If the Axiom of Substance were not true, and were not assumed, we -could not have such a science as Chemistry, that is, we could have -no knowledge at all respecting the changes of form of substances. -If the Axioms of Mechanics were not true and were not assumed, we -could have no science of Mechanics, that is, no knowledge of the laws -of force acting on matter. It is not any special _results_ of the -science in such cases; but the _existence_, the _possibility_, of -any science, which establishes the necessity of these axioms. They -are not the consequences of knowledge, acquired from without, but -the internal condition of our being able to know. And when we are to -_know_ concerning any new subject contained in the universe, it is not -inconceivable nor strange that there should be new conditions of our -knowledge. - -It is not inconceivable or strange, therefore, that as new sciences -are formed, new axioms, the foundations of such sciences, should come -into view. As the light of clear and definite knowledge is kindled in -successive chambers of the universe, it may disclose, not only the -aspect of those new apartments, but also the form and structure of the -lamp which man is thus allowed to carry from point to point, and to -transmit from hand to hand. And though the space illumined to man's -vision may always be small in comparison with the immeasurable abyss of -darkness by which it is surrounded, and though the light may be dim and -feeble, as well as partial; this need not make us doubt that, so far as -we can by the aid of this lamp, we see truly: so far as we discern the -necessary laws of the universe, the laws are true, and their truth is -rooted in that in which the being of the universe is rooted. - -And, to dwell for a moment longer on this image, we may also -conceive that all that this lamp--the intellect of man cultivated by -science,--does, by the light which it gives, is this--that it dispels a -darkness which is dark for man alone, and discloses to him some things -in some measure as all things lie in clear and perfect light before the -eye of God. To the Divine Mind all the laws of the universe are plain -and clear in all their multiplicity, extent and depth. The human mind -is capable of seeing some of these laws, though only a few; to some -extent, though but a little way; to some depth, though never to the -bottom. But the Human Mind, can, in the course of ages and generations, -by the long exercise of thought, successfully employed in augmenting -knowledge, improve its powers of vision; and may thus come to see more -laws than at first, to trace their extent more largely, to understand -them more thoroughly; and thus the inward intellectual light of man may -become broader and broader from age to age, though ever narrow when -compared with completeness. - -3. Is it strange to any one that inward light, as well as outward -knowledge, should thus increase in the course of man's earthly career? -that as knowledge extends, the foundations of knowledge should expand? -that as man goes on discovering new truths, he should also discover -something concerning the conditions of truth? Is it wonderful that -as science is progressive the philosophy of science also should be -progressive? that as we know more of everything else, we should also -come to know more of our powers of knowing? - -This does not seem to have been supposed by philosophers in general; -or rather, they have assumed that they could come to know more about -the powers of knowing by thinking about them, even without taking -into account the light thrown upon the nature of knowledge by the -progress of knowledge. From Plato downwards, through Aristotle, -through the Schoolmen, to Descartes, to Locke, to Kant, Schelling and -Hegel, philosophers have been perpetually endeavouring to explore -the nature, the foundations, the consequences of our knowledge. But -since Plato, scarcely one of them has ever proceeded as if new light -were thrown upon knowledge by new knowledge. They have, many or all -of them, attempted to establish fundamental truths, some of them new -fundamental truths, about the human mind and the nature and conditions -of its knowledge. These attempts show that they do not deny or doubt -that there may be such new fundamental truths. Such new fundamental -truths respecting the human mind and respecting knowledge must be, in -many cases at least, (as it will be seen that they _are_, on examining -the systems proposed by the philosophers just mentioned,) seen by -their own light to be true. They are _new axioms_ in philosophy. These -philosophers therefore, or their disciples, cannot consistently blame -us for holding the possibility of new axioms being introduced into -philosophy from age to age, as there arise philosophers more and more -clear-sighted. - -4. But though _they_ have no ground for rejecting _our_ new axioms -merely because they are new, _we_ may have good ground for doubting -the value of _their_ new axioms, that is, of the foundations of their -systems; because they are new truths about knowledge gathered by -merely exploring the old fields of knowledge. We found our hopes of -obtaining a larger view of the constitution of the human mind than the -early philosophers had, on this:--that we obtain our view by studying -the operation of the human mind _since their time_; its progress -in acquiring a large stock of uncontested truths and in obtaining -a wide and real knowledge of the universe. Here are new materials -which the ancients had not; and which may therefore justify the hope -that we may build our philosophy higher than the ancients did. But -modern philosophers who use only the same materials as the ancient -philosophers used, have not the same grounds for hope which we have. If -they borrow all their examples and illustrations of man's knowledge of -the universe, from the condition of the universe as existing in Space -and Time, that is, from the geometrical condition of the universe, they -may fail to obtain the light which might be obtained if they considered -that the universe is also subject to conditions of _Substance_, of -_Cause_ and _Effect_, of _Force_ and _Matter_: is filled with _Kinds_ -of things, in whose structure we assume _Design_ and _Ends_; and so on; -and if they reflected that these conditions or _Ideas_ are not mere -vague notions, but the bases of sciences which all thoughtful persons -allow to be certain and real. - -It is then, as I have said, from taking advantage of the progressive -character which physical science, in the history of man, has been -found to possess, that I hope to learn more of the nature and -prospects of the human mind and soul, than those can learn who still -take their stand on the old limited ground of man's knowledge. -The knowledge of Geometry by the Greeks was the starting-point of -their sound philosophy. It showed that something might be certainly -known, and it showed, in some degree, how it was known. It thus -refuted the skepticism which was destroying philosophy, and offered -specimens of solid truth for the philosopher to analyse. But the -Greeks tried to go beyond geometry in their knowledge of the universe. -They tried to construct a science of Astronomy--of Harmonics--of -Optics--of Mechanics. In the two former subjects, they succeeded to -a very considerable extent. The question then arose, What was the -philosophical import of these new sciences? What light did they throw -on the nature of the universe, on the nature of knowledge, on the -nature of the human mind? These questions Plato attempted to answer. He -said that the lesson of these new sciences is this:--that the universe -is framed upon the _Divine Ideas_; that man can to a certain extent -obtain sight of these Ideas; and that when he does this, he _knows_ -concerning the universe. And again, he also put the matter otherwise: -there is an _Intelligible World_, of which the Visible and Sensible -world is only a dim image. _Science_ consists in understanding the -Intelligible World, which man is to a certain extent able to do, by the -nature of his understanding. This was Plato's philosophy, founded upon -the progress which human knowledge had made up to his time. Since his -time, knowledge, that is science, has made a large additional progress. -What is the philosophical lesson to be derived from this progress, -and from the new provinces thus added to human knowledge? This is a -question which I have tried to answer. I am not aware that any one -since Plato has taken this line of speculation;--I mean, has tried -to spell out the lesson of philosophy which is taught us, not by one -specimen, or a few only, of the knowledge respecting the universe which -man has acquired; but by including in his survey all the provinces of -human knowledge, and the whole history of each. At any rate, whatever -any one else may have done in this way, it seems to me that new -inferences remain to be drawn, of the nature of those which Plato drew: -and those I here attempt to deduce and to illustrate. - - - - -CHAPTER XXX. - -THE THEOLOGICAL BEARING OF THE PHILOSOPHY OF DISCOVERY. - - -That necessary truth is progressive;--that science is the idealization -of facts, and that this process goes on from age to age, and advances -with the advance of scientific discovery;--these are doctrines which -I have endeavoured to establish and to elucidate. If these doctrines -are true, they are so important that I may be excused should I return -to them again and again, and trace their consequences in various -directions. Especially I would examine the bearing of these doctrines -upon our religious philosophy. I have hitherto abstained in a great -measure from discussing religious doctrines; but such a reserve carried -too far must deprive our philosophy of all completeness. No philosophy -of science can be complete which is not also a philosophy of the -universe; and no philosophy of the universe can satisfy thoughtful -men, which does not include a reference to the power by which the -universe came to be what it is. Supposing, then, such a reference to be -admitted, let us see what aspect our doctrines give to it. - - -1. (_How can there be necessary truths concerning the actual -universe?_)--In looking at the bearing of our doctrine on the -philosophy of the universe, we are met by a difficulty, which is -indeed, only a former difficulty under a new aspect. When we are come -to the conclusion that science consists of facts idealized, we are led -to ask, How this can be? _How can_ facts be idealized? How can that -which is a fact of external observation become a result of internal -thought? How can that which was known _à posteriori_ become known _à -priori_? How can the world of things be identified with the world -of thoughts? How can we discover a necessary connexion among mere -phenomena? - -Or to put the matter otherwise: How is it that the deductions of the -intellect are verified in the world of sense? How is it that the truths -of science obtained _à priori_ are exemplified in the general rules of -facts observed _à posteriori_? How is it that facts, in science, always -do correspond to our ideas? - -I have propounded this paradox in various forms, because I wish it -to be seen that it is, at first sight, a real, not merely a verbal -contradiction, or at least a difficulty. If we can discover the -solution of this difficulty in any one form, probably we can transpose -the answer so as to suit the other forms of the question. - -2. Suppose the case to be as I have stated it; that in some sciences at -least, laws which were at first facts of observation come to be seen as -necessary truths; and let us see to what this amounts in the several -sciences. - -It amounts to this: the truths of Geometry, such as we discern them by -the exercise of our own thoughts, are always verified in the world of -observation. The laws of space, derived from our Ideas, are universally -true in the external world. - -In the same way, as to number: the laws or truths respecting number, -which are deduced from our Idea of Number, are universally true in the -external world. - -In the same way, as to the science which deals with matter and force: -the truths of which I have spoken as derived from Ideas:--that -action is equal to reaction; and that causes are measured by their -effects;--are universally verified in all the laws of phenomena of the -external world, which are disclosed by the science of Mechanics. - -In the same way with regard to the composition and resolution of bodies -into their elements; the truths derived from our Idea of Matter:--that -no composition or resolution can increase or diminish the quantity -of matter in the world, and that the properties of compounds are -determined by their composition;--are truths derived from Ideas of -quantity of matter, and of composition and resolution; but these truths -are universally verified when we come to the facts of Chemistry. - -In the same way it is a truth flowing from the Ideas of the Kinds of -things, (as the possible subject of general propositions expressed in -language,) that the kinds of things must be definite; and this law is -verified whenever we express general propositions in general terms: for -instance, when we distinguish species in Mineralogy. - -3. This last example may appear to most readers doubtful. I have -purposely pursued the enumeration till I came to a doubtful example, -because it is, and I conceive always will be, impossible to extend this -general view to _all_ the Sciences. On the contrary, this doctrine -applies at present to only a very few of the sciences, even in the eyes -of those who hold the existence of ideal truths. The doctrine extends -at present to a few only of the sciences, even if it extend to one -or two besides those which have been mentioned--Geometry, Mechanics, -Chemistry, Mineralogy: and though it may hereafter appear that Ideal -Truths are possible and attainable for a few other sciences, yet the -laws disclosed by sciences which cannot be reduced to ideal elements -will, I conceive, always very far outnumber those which can be so -reduced. The great body of our scientific knowledge will always be -knowledge obtained by mere observation, not knowledge obtained by the -use of theories alone. - -4. The survey of the history and philosophy of the Sciences which we -have attempted in previous works enables us to offer a sort of estimate -of the relative portions of science which have and which have not -thus been idealized. For the Aphorisms[317] which we have collected -from that survey, contain Axioms which may be regarded as the Ideal -portions of the various sciences; and the inspection of that series of -aphorisms will show us to how such a portion of science, anything of -this axiomatic or ideal character can he applied. These Axioms are the -Axioms of Geometry (Aphorism XXVI); of Arithmetic (XXXVI); of Causation -(XLVII); of a medium for the sensation of secondary qualities (LVIII), -and their measure (LXIX); of Polarity (LXXII); of Chemical Affinity -(LXXVI); of Substance (LXXVII); of Atoms (LXXIX). - -Have we any axioms in the sciences which succeed these in our survey, -as Botany, Zoology, Biology, Palæontology? - -There is the Axiom of Symmetry (LXXX); of Kind, (already in some -measure spoken of, (LXXXIII)); of Final Cause (CV); of First Cause -(CXVI). - - -5. (_Small extent of necessary truth._)--It is easily seen how small -a portion of each of these latter sciences is included in these -axioms: while, with regard to the sciences first mentioned, the Axioms -include, in a manner, the whole of the science. The science is only -the consequence of the Axioms. The whole science of Mechanics is only -the development of the Axioms concerning action and reaction, and -concerning cause and its measures, which I have mentioned as a part of -our Ideal knowledge. - -In fact, beginning from Geometry and Arithmetic, and going through -the sciences of Mechanics, of Secondary Qualities, and of Chemistry, -onwards to the sciences which deal with Organized Beings, we find that -our ideal truths occupy a smaller and smaller share of the sciences -in succession, and that the vast variety of facts and phenomena -which nature offers to us, is less and less subject to any rules or -principles which we can perceive to be necessary. - -But still, that there are principles,--necessary principles, which -prevail universally even in these higher parts of the natural -sciences,--appears on a careful consideration of the axioms which I -have mentioned:--that in symmetrical natural bodies the similar parts -are similarly affected;--that every event must have a cause;--that -there must be a First Cause, and the like. - -6. It being established, then, that in the progress of science, -facts are idealized--that _à posteriori_ truths become _à priori_ -truths;--that the world of things is identified with the world of -thoughts to a certain extent;--to an extent which grows larger as we -see into the world of things more clearly; the question recurs which I -have already asked: How can this be? - -How can it be that the world without us is thus in some respects -identical with the world within us?--that is our question. - - -7. (_How did things come to be as they are?_)--It would seem that we -may make a step in the solution of this question, if we can answer this -other: How did the world without us and the world within us come to be -what they are? - -To this question, two very different answers are returned by those who -do and those who do not believe in a Supreme Mind or Intelligence, as -the cause and foundation of the world. - -Those who do not believe that the world has for its cause and -foundation a Supreme Intelligence, or who do not connect their -philosophy with this belief, would reply to our inquiry, that the -reason why man's thoughts and ideas agree with the world is, that they -are borrowed from the world; and that the persuasion that these Ideas -and truths derived from them have any origin except the world without -us, is an illusion. - -On this view I shall not now dwell; for I wish to trace out the -consequences of the opposite view, that there exists a Supreme Mind, -which is the cause and foundation of the universe. Those who hold this, -and who also hold that the human mind can become possessed of necessary -truths, if they are asked how it is that these necessary truths are -universally verified in the material world, will reply, that it is -so because the Supreme Creative-Mind has made it so to be:--that the -truths which exist or can be generated in man's mind agree with the -laws of the universe, because He who has made and sustains man and the -universe has caused them to agree:--that our Ideas correspond to the -Facts of the world, and the Facts to our Ideas, because our Ideas are -given us by the same power which made the world, and given so that -these can and must agree with the world so made. - - -8. (_View of the Theist_).--This, in its general form, would be the -answer of the _theist_, (so we may call him who believes in a Supreme -Intelligent Cause of the world and of man,) to the questions which we -have propounded--the perplexity or paradox which we have tried to bring -into view. But we must endeavour to trace this view--this answer--more -into detail. - -If a Supreme Intelligence be the cause of the world and of the Laws -which prevail among its phenomena, these Laws must exist as Acts of -that Intelligence--as Laws caused by the thoughts of the Supreme -Mind--as Ideas in the Mind of God. And then the question would be, How -we are to conceive these thoughts, these Ideas, to be at the same time -Divine and human:--to be at the same time Ideas in the Divine Mind, and -necessary truths in the human mind; and this is the question which I -would now inquire into. - - -9. (_Is this Platonism?_)--To the terms in which the inquiry is now -propounded it may be objected that I am taking for granted the Platonic -doctrine, that the world is constituted according to the Ideas of the -Divine Mind. It may be said that this doctrine is connected with gross -extravagancies of speculation and fiction, and has long been obsolete -among sound philosophers. - -To which I reply, that if such doctrines have been pushed into -extravagancies, with _them_ I have nothing to do, nor have I any -disposition or wish to revive them. But I do not conceive the doctrine, -to the extent to which I have stated it, to be at all obsolete:--that -the Cause and Foundation of the Universe is a Divine Mind: and from -that doctrine it necessarily follows, that the laws of the Universe are -in the Ideas of the Divine Mind. - -I would then, as I have said, examine the consequences of this -doctrine, in reference to the question of which I have spoken. And -in order to do this, it may help us, if we consider separately the -bearing of this doctrine upon separate portions of our knowledge of -the universe;--separately its bearing upon the laws which form the -subject-matter of different sciences:--if we take particular human -Ideas, and consider what the Divine Ideas must be with regard to each -of them. - -10. (_Idea of Space._)--Let us take, in the first place, the Idea -of Space. Concerning this Idea we possess necessary truths; namely, -the Axioms of Geometry; and, as necessarily resulting from them, the -whole body of Geometry. And our former inquiry, as narrowed within the -limits of this Idea, will be, How is it that the truths of Geometry--_à -priori_ truths--are universally verified in the observed phenomena of -the universe? And the theist's answer which we have given will now -assume this form:--This is so because the Supreme Mind has constituted -and constitutes the universe according to the Idea of Space. The -universe conforms to the Idea of Space, and the Idea of Space exists -in the human mind;--is necessarily evoked and awakened in the human -mind existing in the universe. And since the Idea of Space, which is -a constituent of the universe, is also a constituent of the human -mind, the consequences of this Idea in the universe and in the human -mind necessarily coincide; that is, the _spacial_ Laws of the universe -necessarily coincide with the _spacial_ Science which man elaborates -out of his mind. - -11. To this it may be objected, that we suppose the Idea of Space in -the Divine Mind (according to which Idea, among others, the universe is -constituted,) to be identical with the Idea of Space in the human mind; -and this, it may be urged, is too limited and material a notion of the -Divine Mind to be accepted by a reverent philosophy. - -I reply, that I suppose the Divine Idea of Space and the human Idea -of Space to coincide, _only so far_ as the human Idea goes; and -that the Divine Idea may easily have so much more luminousness and -comprehensiveness as Divine Ideas may be supposed to have compared with -human. Further, that this Idea of Space, the first of the Ideas on -which human science is founded, is the most luminous and comprehensive -of such Ideas; and there are innumerable other Ideas, the foundations -of sciences more or less complete, which are extremely obscure and -limited in the human mind, but which must be conceived to be perfectly -clear and unlimitedly comprehensive in the Divine Mind. And thus, the -distance between the human and the Divine Mind, even as to the views -which constitute the most complete of the human sciences, is as great -in our view as in any other. - -12. That the Idea of Space in the human mind, though sufficiently clear -and comprehensive to be the source of necessary truths, is far too -obscure and limited to be regarded as identical with the Divine Idea, -will be plain to us, if we call to mind the perplexities which the -human mind falls into when it speculates concerning space infinite. -An Intelligence in which all these perplexities should vanish by the -light of the Idea itself, would be infinitely elevated in clearness and -comprehensiveness of intellectual vision above human intelligence, even -though its Idea of Space should coincide with the human Idea as far as -the human Idea goes. - -I do not shrink from saying, therefore, that the Idea of Space which -is a constituent of the human mind existing in the universe is, as far -as it goes, identical with the Idea of Space which is a constituent of -the universe. And this I give as the answer to the question, How it is -that the necessary truths of Geometry universally coincide with the -relations of the phenomena of the universe? And this doctrine, it is -to be remembered, carries us to the further doctrine, that the Idea of -Space in the human mind is, so far as it goes, coincident with the Idea -of Space in the Divine Mind. - - -13. (_Idea of Time._)--What I have said of the Idea of Space, may -be repeated, for the most part, with regard to the Idea of Time; -except that the Idea of Time, as such, does not give rise to a large -collection of necessary truths, such as the propositions of Geometry. -Some philosophers regard Number as a modification or derivative of -the Idea of Time. If we accept this view, we have, in the Science of -Arithmetic, a body of necessary truths which flow from the Idea of -Time. But this doctrine, whichever way held, does not bear much on -the question with which we are now concerned. That which we do hold -is, that the Idea of Time in the human mind is, so far as it goes, -coincident with the Idea of Time in the Divine Mind: and that this -is the reason why the events of the universe, as contemplated by us, -conform to necessary laws of succession: while at the same time we must -suppose that all the perplexities in the Idea of Time which embarrass -the human mind--the perplexities, for instance, which arise from -contemplating a past and a future eternity, are, in the Divine Mind, -extinguished in the Light of the Idea itself. - -Space and Time have, and have generally been regarded as having, -peculiar prerogatives in our speculations concerning the constitution -of the universe. We see and perceive all things as subject to the laws -of Space and Time; or rather (for the term _Law_ does not here satisfy -us), as being and happening _in_ space and _in_ time: and probably most -persons will have no repugnance to the doctrine that the Divine Mind, -as well as the human, so regards them, and has so constituted them and -us that they _must_ be so regarded. Space and Time are human Ideas -which include all objects and events, and are the foundation of all -human Science. And we can conceive that Space and Time are also Divine -Ideas which the Divine Mind causes to include all objects and events, -and makes to be the foundation of all existence. So far as these Ideas -go, our doctrine is not difficult or new. - - -14. (_Ideas of Force and Matter._)--But what are we to say of the -Ideas which come next in the survey of the sciences, Force and Matter? -These are human Ideas--the foundations of several sciences--of the -mechanical sciences in particular. But are they the foundations of -necessary truths? Have we necessary truths respecting Force and Matter? -We have endeavoured to prove that we have:--that certain fundamental -propositions in the Science of Mechanics, although, historically -speaking, they were discovered by observation and experience, are yet, -philosophically speaking, necessary propositions. And being such, the -facts of the universe must needs conform to these propositions; and -the reason why they do so, we hold, in this as in the former case, -to be, that these Ideas, Force and Matter, are Ideas in the Divine -Mind:--Ideas according to which the universe is, by the Divine Cause, -constituted and established. - -15. That Force and Matter are Ideas existing in the Divine Mind, and -coincident with the Idea of Force and Matter in the human mind, as -far as these go, is a doctrine which is important in our view of the -universe in relation to its Cause and Foundation. - -These are very comprehensive and fundamental Ideas, and there are -certain universal relations among external things which rest upon these -Ideas. The two, Force and Matter, are, in a certain way, the necessary -antithesis and opposite condition each of the other. Force (that is -Mechanical Force, Pressure or Impulse) cannot act without matter to -act upon. Matter (that is Body) cannot exist without Force by which -it is kept in its place, by which its parts are held together, and by -which it excludes every other body from the place which it occupies. We -cannot conceive Force without Matter, or Matter without Force; the two -are, as Action and Reaction, necessarily co-ordinate and coexistent. -In every part of the universe they must be so. In every part of the -universe, if there be material objects, there must be Force; if there -be Force, there must be material objects. - -Our apprehension of this universal necessity arises from our having the -Ideas of Force and Matter which are human Ideas. The actuality of this -universal antithesis arises from the Ideas of Force and Matter being -Ideas in the Divine Mind;--Ideas realized as a part of the fundamental -constitution of the universe. - -That Force and Matter are thus among the Ideas in the Divine Mind, -and that, with them, the Ideas of Force and Matter in the human mind, -regarded in their most general form, agree so far as they go, is -another step in the doctrine which I am trying to unfold. That the -Ideas of Force and Matter in the Divine Mind are such as to banish by -their own light, innumerable contradictions and perplexities which -darken these Ideas in the human mind, is to be supposed: and thus the -Divine Mind is infinitely luminous and comprehensive compared with the -human mind. - - -16. (_Creation of Matter._)--It may perhaps be urged, as an objection -to this doctrine, that it asserts Matter to be a necessary constituent -of the universe, and thus involves the assertion of the eternity of -Matter. But in reality the doctrine asserts Matter to be eternal, only -in the way in which time and space are eternal. Whether we hold that -there was a creation before which time and space did not exist,--with -the poet who says - - Ere Time and Space _were_ Time and Space were _not_,-- - -is not essential to our present inquiry. Certainly we cannot conceive -such a state, and therefore cannot reason about it. We have no occasion -here to speak of Creation, nor have spoken of it. What I have said -is, that Space and Time, Force and Matter are universal elements, -principles, constituents, of the universe as it is--and necessary -Ideas of the human mind existing in that universe. If there ever -was a Creation before which Matter did not exist, it was a Creation -before which Force did not exist. And in the universe as it is, the -two are necessarily co-existent in the human thought because they are -co-existent in the Divine Thought which makes the world. - -We apply then to Force and Matter the doctrine--the Platonic doctrine, -if any one please so to call it,--that the world is constituted -according to the Ideas of the Divine Mind, and that the human mind -apprehends the inward and most fundamental relations of the universe by -sharing in some measure of those same Ideas. - - -17. (_Platonic Ideas._)--But do we go on with Plato to extend this -doctrine of Ideas to all the objects and all the aspects of objects -which constitute the material universe? Do we say with Plato that there -is not only an Idea of a Triangle by conformity to which a figure is a -triangle, but an Idea of Gold, by conformity to which a thing is gold, -and Idea of a Table, by conformity to which a thing is a table? - -We say none of these things. We say nothing which at all approaches to -them. We do not say that there is an Idea of a Triangle, the archetype -of all triangles; we only say that man has an Idea of Space, which is -an Idea of a fundamental reality; and that therefore from this Idea -flow real and universal truths--about triangles and other figures. -Still less do we say that we have an archetypal Idea of Gold, or of a -Metal in general, or of any of the kinds of objects which exist in the -world. Here we part company with Plato altogether. - -But have we any Ideas at all with regard to objects which we thus speak -of as separable into Kinds? We can have knowledge,--even exact and -general knowledge, that is, science--with regard to such things--with -regard to plants and metals--gold and iron. Do we possess in our minds, -with regard to those objects, any Ideas, any universal principles, such -as we possess with regard to geometrical figures or mechanical actions? -And if so, are those human Ideas verified in the universe, as the Ideas -hitherto considered are? and do they thus afford us further examples -of Ideas in the human mind which are also Ideas in the Divine Mind, -manifested in the constitution of the universe? - - -18. (_Idea of Kinds._)--We answer _Yes_ to these questions, on this -ground:--the objects that exist in the world, plants and metals, gold -and iron, for example, in order that they may be objects with regard -to which we can have any knowledge, must be objects of distinct and -definite thought. Plant must differ from metal, gold from iron, in -order that we may know anything at all about any of these objects. -The differences by which such objects differ need not necessarily -be expressed by _definitions_, as the difference of a triangle and -a square are expressed; but there must manifestly _be_ fixed and -definite differences, in order that we may have any knowledge about -them. These Kinds of things must be so far distinct and definite, as -to be objects of distinct and definite thought. The _Kinds_ of natural -objects must differ, and we must think of things as of different Kinds, -in order that we may know anything about natural objects. Living in a -world in which we exercise our Intellect upon the natural objects which -surround us, we must regard them as distinct from each other in Kind. -We must have an Idea of Kinds of natural objects. - -19. The Idea of a Kind involves this principle: That where the Kind -differs the Properties may differ, but so far as the Kind is the same -the Properties contemplated in framing the notion of each Kind are the -same. Gold cannot have the distinctive properties of Iron without being -Iron. - -In the case of human knowledge, each Kind is marked by a _word_--a -_name_; and the doctrine that the notion of the Kind must be so applied -that this same Kind of object shall have the same properties, has -been otherwise expressed by saying that Names must be so applied that -general propositions may be possible. We must so apply the name of Gold -that we may be able to say, gold has a specific gravity of a certain -amount and is ductile in a certain degree. - -20. But this condition of the names of Kinds,--that they must be -such that general propositions about these Kinds of objects shall be -possible;--is it a necessary result of the Idea of Kind? And if so, can -the Idea of Kind, thus implying the use of language, and a condition -depending on the use of language, be an Idea in the Divine as well as -in the human mind? Can it be, in this respect, like the Ideas which we -have already considered, Space and Time, Force and Matter? - -We cannot suppose that the Ideas which exist in the Divine Mind imply, -in the Supreme Intelligence, the need of language, like human language. -But there is no incongruity in supposing that they imply that which -we take as the _condition_ of such language as we speak of, namely, -distinct thought. There is nothing incongruous in supposing that the -Supreme Intelligence regards the objects which exist in the universe as -distinct in Kind: and that the Idea of Kind in the human mind agrees -with the Idea of Kind in the Divine Mind, as far as it goes. And as -we have seen, the Idea of Properties is correlative and coexistent -with the Idea of Kind, so that the one changing, the other changes -also. There is nothing incongruous in supposing that the Divine Mind -manifests in the universe of which it is the Cause and Foundation, -these two, its co-ordinate Ideas: and that the human mind sees that -these two Ideas are co-ordinate and coexistent, in virtue of its -participating in these Ideas of the Divine Mind. The universe is full -of things which man perceives do and must differ correspondingly in -kind and in properties; and this is so, because the Ideas of various -Kinds and various Properties are part of the scheme of the universe in -the Divine Mind. - -21. That the Ideas of Kinds and Properties as coordinate and -interdependent, though common, to a certain extent, to the human and -the Divine Mind, are immeasurably more luminous, penetrating and -comprehensive in the Divine than in the human mind, is abundantly -evident. In fact, though man assents to such axioms as these,--that -the Properties of Things depend upon their Kinds, and that the Kinds -of Things are determined by their Properties,--yet the nature of -connexion of Kinds and Properties is a matter in which man's mind is -all but wholly dark, and on which the Divine Mind must be perfectly -clear. For in how few cases--if indeed in any one--can we know what -is the essence of any Kind;--what is the real nature of the connexion -between the character of the Kind and its Properties! Yet on this point -we must suppose that the Divine Intellect, which is the foundation of -the world, is perfectly clear. Every Kind of thing, every genus and -species of object, appears to Him in its essential character, and its -properties follow as necessary consequences. He sees the essences of -things through all time and through all space; while we, slowly and -painfully, by observation and experiment, which we cannot idealize or -can idealize only in the most fragmentary manner, make out a few of the -properties of each Kind of thing. Our Science here is but a drop in the -ocean of that truth, which is known to the Divine Mind but kept back -from us; but still, that we can know and do know anything, arises from -our taking hold of that principle, human as well as Divine, that there -are differences of Kinds of things, and corresponding differences of -their properties. - - -22. (_Idea of Substance._)--I shall not attempt to enumerate all -the Ideas which, being thus a part of the foundation of Science in -the human mind and of Existence in the universe, are shown to be at -the same time Ideas in the Divine and in the human mind. But there -is one other of which the necessary and universal application is so -uncontested, that it may well serve further to exemplify our doctrine. -In all reasonings concerning the composition and resolution of the -elements of bodies, it is assumed that the quantity of matter cannot be -increased or diminished by anything which we can do to them. We have an -Idea of _Substance_, as something which may have its qualities altered -by our operations upon it, but cannot have its quantity changed. -And this Idea of Substance is universally verified in the facts of -observation and experiment. Indeed it cannot fail to be so; for it -regulates and determines the way in which we interpret the facts of -observation and experiment. It authorized the philosopher who was asked -the weight of a column of smoke to reply, "Subtract the weight of the -ashes from that of the fuel, and you have the weight of the smoke:" -for in virtue of that idea we assume that, in combustion, or in any -other operation, all the substance which is subjected to the operation -must exist in the result in some form or other. Now why may we -reasonably make this assumption, and thus, as it were, prescribe laws -to the universe? Our reply is, Because Substance is one of the Ideas -according to which the universe is constituted. The material things -which make up the universe are substance according to this Idea. They -are substance according to this Idea in the Divine Mind, and they are -substance according to this Idea in the human mind, because the human -mind has this Idea, to a certain extent, in common with the Divine -Mind. In this, as in the other cases, the Idea must be immeasurably -more clear and comprehensive in the Divine Mind than in the human. -The human Idea of substance is full of difficulty and perplexity: as -for instance; how a substance can assume successively a solid, fluid -and airy form; how two substances can be combined so as entirely to -penetrate one another and have new qualities: and the like. All these -perplexities and difficulties we must suppose to vanish in the Divine -Idea of Substance. But still there remains in the human, as in the -Divine Idea, the source and root of the universal truth, that though -substances may be combined or separated or changed in form in the -processes of nature or of art, no portion of substance can come into -being or cease to be. - - -23. (_Idea of Final Cause._)--There is yet one other Idea which I shall -mention, though it is one about which difficulties have been raised, -since the consideration of such difficulties may be instructive: -the Idea of a purpose, or as it is often termed, a _Final Cause_, -in organized bodies. It has been held, and rightly[318], that the -assumption of a Final Cause of each part of animals and plants is as -inevitable as the assumption of an efficient cause of every event. -The maxim, that in organized bodies nothing is _in vain_, is as -necessarily true as the maxim that nothing happens _by chance_. I have -elsewhere[319] shown fully that this Idea is not deduced from any -special facts, but is assumed as a law governing all facts in organic -nature, directing the researches and interpreting the observations -of physiologists. I have also remarked that it is not at variance -with that other law, that plants and that animals are constructed -upon general plans, of which plans, it may be, we do not see the -necessity, though we see how wide is their generality. This Idea of a -purpose,--of a Final Cause,--then, thus supplied by our minds, is found -to be applicable throughout the organic world. It is in virtue of this -Idea that we conceive animals and plants as subject to _disease_; for -disease takes place when the parts do not fully answer their _purpose_; -when they do not do what they _ought_ to do. How is it then that we -thus find an Idea which is _supplied_ by our own minds, but which is -_exemplified_ in every part of the organic world? Here perhaps the -answer will be readily allowed. It is because this Idea is an Idea of -the Divine Mind. There _is_ a Final Cause in the constitution of these -parts of the universe, and therefore we can interpret them by means of -the Idea of Final Cause. We can _see_ a purpose, because there _is_ -a purpose. Is it too presumptuous to suppose that we can thus enter -into the Ends and Purposes of the Divine Mind? We willingly grant and -declare that it would be presumptuous to suppose that we can enter into -them to any but a very small degree. They doubtless go immeasurably -beyond our mode of understanding or conceiving them. But to a certain -extent we _can_ go. We can go so far as to see that they _are_ Ends and -Purposes. It is _not_ a vain presumption in us to suppose that we know -that the eye was made for seeing and the ear for hearing. In this the -most pious of men see nothing impious: the most cautious philosophers -see nothing rash. And that we can see thus far into the designs of -the Divine Mind, arises, we hold, from this:--that we have an Idea of -Design and of Purpose which, so far as it is merely _that_, is true; -and so far, is Design and Purpose in the same sense in the one case and -in the other. - -I am very far from having exhausted the list of Fundamental Ideas which -the human mind possesses and which have been made the foundations of -Sciences. Of all such Ideas, I might go on to remark, that they are of -universal validity and application in the region of external Facts. In -all the cases I might go on to inquire, How is it that man's Ideas, -developed in his internal world, are found to coincide universally -with the laws of the external world? By what necessity, on what ground -does this happen? And in all cases I should have had to reply, that -this happens, and must happen, because these Ideas of the human mind -are also Ideas of the Divine Mind according to which the universe is -constituted. Man has these thoughts, and sees them verified in the -universe, because God had these thoughts and exemplifies them in the -universe. - - -24. (_Human immeasurably inferior to Divine_).--But of all these Ideas, -I should also have to remark, that the way in which man possesses them -is immeasurably obscure and limited in comparison with the way in -which God must be supposed to possess them. These human Ideas, though -clear and real as far as they go, in every case run into obscurity and -perplexity, from which the Ideas of the Divine Mind must be supposed to -be free. In every case, man, by following the train of thought involved -in each Idea, runs into confusion and seeming contradictions. It may -be that by thinking more and more, and by more and more studying the -universe, he may remove some of this confusion and solve some of these -contradictions. But when he has done in this way all that he can, an -immeasurable region of confusion and contradiction will still remain; -nor can he ever hope to advance very far, in dispelling the darkness -which hangs over the greater part of the universe. His knowledge, his -science, his Ideas, extend only so far as he can keep his footing -in the shallow waters which lie on the shore of the vast ocean of -unfathomable truth. - -25. But further, we have not, even so, exhausted our estimate of the -immeasurable distance between the human mind and the Divine Mind:--very -far from it: we have only spoken of the smallest portion of the region -of truth,--that about which we have Sciences and Scientific Ideas. -In that region alone do we claim for man the possession of Ideas the -clearness of which has in it something divine. But how narrow is the -province of Science compared with the whole domain of human thought! We -may enumerate the sciences of which we have been speaking, and which -involve such Ideas as I have mentioned. How many are they? Geometry, -Arithmetic, Chemistry, Classification, Physiology. To these we might -have added a few others; as the sciences which deal with Light, Heat, -Polarities; Geology and the other Palætiological Sciences; and there -our enumeration at present must stop. For we can hardly as yet claim to -have Sciences, in the rigorous sense in which we use the term, about -the Vital Powers of man, his Mental Powers, his historical attributes, -as Language, Society, Arts, Law, and the like. On these subjects few -philosophers will pretend to exhibit to us Ideas of universal validity, -prevailing through all the range of observation. Yet all these things -proceed according to Ideas in the Divine Mind by which the universe, -and by which man, is constituted. In such provinces of knowledge, -at least, we have no difficulty in seeing or allowing how blind man -is with regard to their fundamental and constituent principles; how -weak his reason; how limited his view. If on some of the plainest -portions of possible knowledge, man have Ideas which may be regarded -as coincident to a certain extent with those by which the universe is -really constituted; still on by far the largest portion of the things -which most concern him, he has no knowledge but that which he derives -from experience, and which he cannot put in so general a form as to -have any pretensions to rest it upon a foundation of connate Ideas. - - -26. (_Science advances towards the Divine Ideas._)--But there is yet -one remark tending somewhat in the opposite direction, which I must -make, as a part of the view which I wish to present. Science, in the -rigorous sense of the term, involves, we have said, Ideas which to a -certain extent agree with the Ideas of the Divine Mind. But science in -that sense is progressive; new sciences are formed and old sciences -extended. Hence it follows that the Ideas which man has, and which -agree with the Ideas of the Divine Mind, may receive additions to their -number from time to time. This may seem a bold assertion; yet this is -what, with due restriction, we conceive to be true. Such Ideas as we -have spoken of receive additions, in respect of their manifestation -and development. The Ideas, the germ of them at least, were in the -human mind before; but by the progress of scientific thought they are -unfolded into clearness and distinctness. That this takes place with -regard to scientific Ideas, the history of science abundantly shows. -The Ideas of Space and Time indeed, were clear and distinct from the -first, and accordingly the Sciences of Geometry and Arithmetic have -existed from the earliest times of man's intellectual history. But the -Ideas upon which the Science of Mechanics depends, having been obscure -in the ancient world, are become clear in modern times. The Ideas of -Composition and Resolution have only in recent centuries become so -clear as to be the basis of a definite science. The Idea of Substance -indeed was always assumed, though vaguely applied by the ancients; and -the Idea of a Design or End in vital structures is at least as old as -Socrates. But the Idea of Polarities was never put forth in a distinct -form till quite recently; and the Idea of Successive Causation, as -applied in Geology and in the other Palætiological Sciences, was never -scientifically applied till modern times: and without attempting to -prove the point by enumeration, it will hardly be doubted that many -Scientific Ideas are clear and distinct among modern men of science -which were not so in the ancient days. - -Now all such scientific Ideas are, as I have been urging, points on -which the human mind is a reflex of the Divine Mind. And therefore in -the progress of science, we obtain, not indeed new points where the -human mind reflects the Divine, but new points where this reflection is -clear and luminous. We do not assert that the progress of science can -bring _into existence_ new elements of truth in the human mind, but it -may bring them _into view_. It cannot add to the characters of Divine -origin in the human mind, but it may add to or unfold the _proofs_ of -such an origin. And this is what we conceive it does. And though we -do not conceive that the Ideas which science thus brings into view -are the most important of man's thoughts in other respects, yet they -may, and we conceive do, supply a proof of the Divine nature of the -human mind, which proof is of peculiar cogency. What other proofs may -be collected from other trains of human thought, we shall hereafter -consider. - - -27. (_Recapitulation._)--This, then, is the argument to which we -have been led by the survey of the sciences in which we have been -engaged:--That the human mind can and does put forth, out of its -natural stores, duly unfolded, certain Ideas as the bases of scientific -truths: These Ideas are universally and constantly verified in the -universe: And the reason of this is, that they agree with the Ideas -of the Divine Mind according to which the universe is constituted and -sustained: The human mind has thus in it an element of resemblance to -the Divine Mind: To a certain extent it looks upon the universe as -the Divine Mind does; and therefore it is that it can see a portion -of the truth: And not only can the human mind thus see a portion of -the truth, as the Divine Mind sees it: but this portion, though at -present immeasurably small, and certain to be always immeasurably small -compared with the whole extent of truth which with greater intellectual -powers, he might discern, nevertheless may increase from age to age. - -This is then, I conceive, one of the results of the progress of -scientific discovery--the Theological Result of the Philosophy of -Discovery, as it may, I think, not unfitly be called:--That by every -step in such discovery by which external facts assume the aspect of -necessary consequences of our Ideas, we obtain a fresh proof of the -Divine nature of the human mind: And though these steps, however far -we may go in this path, can carry us only a very little way in the -knowledge of the universe, yet that such knowledge, so far as we do -obtain it, is Divine in its kind, and shows that the human mind has -something Divine in its nature. - -The progress by which external facts assume the aspect of necessary -consequences of our Ideas, we have termed the idealization of facts; -and in this sense we have said, that the progress of science consists -in the Idealization of Facts. But there is another way in which the -operation of man's mind may be considered--an opposite view of the -identification of Ideas with Facts; which we must consider, in order to -complete our view of the bearing of the progress of human thought upon -the nature of man. - - -FOOTNOTES: - -[Footnote 317: Given in the _Novum Organon Renovatum_.] - -[Footnote 318: _Nov. Org. Ren._ Aph. cv.] - -[Footnote 319: _Hist. Sc. Id._ b. ix. c. vi.] - - - - -CHAPTER XXXI. - -MAN'S KNOWLEDGE OF GOD. - - -1. Man's powers and means of knowledge are so limited and imperfect -that he can know _little_ concerning God. It is well that men in their -theological speculations should recollect that it is so, and should -pursue all such speculations in a modest and humble spirit. - -But this humility and modesty defeat their own ends, when they lead us -to think that we can know _nothing_ concerning God: for to be modest -and humble in dealing with this subject, implies that we know _this_, -at least, that God is a proper object of modest and humble thought. - -2. Some philosophers have been led, however, by an examination of man's -faculties and of the nature of being, to the conclusion that man can -know _nothing_ concerning God. But we may very reasonably doubt the -truth of this conclusion. We may ask, How can we _know_ that we _can_ -know nothing? If we can know nothing, we cannot even know that. - -It is much more reasonable to begin with things that we really do know, -and to examine how far such knowledge can carry us, respecting God, as -well as anything else. This is the course which we have been following, -and its results are very far from being trifling or unimportant. - -In thus beginning from what we know, we start from two points, on each -of which we have, we conceive, some real and sure knowledge:--namely, -mathematical and physical knowledge of the universe without us; and a -knowledge of our own moral and personal nature within us. - - -3. (_From Nature we learn something of God._)--In pursuing the first -line of thought, we are led to reason thus. The universe is governed -by certain Ideas: for instance, everything which exists and happens in -the universe, exists and happens IN _Space_ and _Time_. Why is this? -It is, we conceive, because God has constituted and constitutes the -universe so that it may be so; that is, because the Ideas of Space and -of Time are Ideas according to which God has established and upholds -the universe. - -But we may proceed further in this way, as we have already said. -The universe not only exists in space and time, but it has in it -substances--material substances: or taking it collectively, Material -_Substance_. Can we know anything concerning this substance? Yes: -something we can know; for we know that material substance cannot be -brought into being or annihilated by any natural process. We have then -an Idea of Substance which is a Law of the universe. How is this?--We -reply, that it is because our Idea of Substance is an Idea on which God -has established and upholds the universe. - -Can we proceed further still? Can we discern any other Ideas according -to which the universe is constituted? Yes: as we have already remarked, -we can discern several, though as we go on from one to another -they become gradually fainter in their light, less cogent in their -necessity. We can see that Force as well as Material Substance is -an Idea on which the universe is constituted, and that _Force_ and -_Matter_ are a necessary and universal antithesis: we can see that -the Things which occupy the universe must be of definite _Kinds_, in -order that an intelligent mind may occupy itself about them, and thus -that the Idea of Kind is a constitutive Idea of the universe. We can -see that some kinds of things have life, and our Idea of Life is, -that every part of a living thing is a means to an End; and thus we -recognize _End_, or Final Cause, as an Idea which prevails throughout -the universe, and we recognize this Idea as an Idea according to which -God constitutes and upholds the universe. - -Since we know so much concerning the universe, and since every Law of -the universe which is a necessary form of thought about the universe -must exist in the _Divine_ Mind, in order that it may find a place in -_our_ minds, how can we say that we can know nothing concerning the -Divine Mind? - - -4. (_Though but Little._)--But on the other hand, we easily see how -little our knowledge is, compared with what we do not know. Even the -parts of our knowledge which are the clearest are full of perplexities; -and of the Laws of the universe, including living as well as lifeless -things, how small a portion do we know at all! - -Even the parts of our knowledge which are the clearest, I say, are -full of perplexities. Infinite Space and an infinite Past, an infinite -Future,--how helplessly our reason struggles with these aspects of -our Ideas! And with regard to _Substance_, how did ingenerable and -indestructible substance come into being? And with regard to _Matter_, -how can passive Matter be endued with living force? And with regard to -_Kinds_, how immeasurably beyond our power of knowing are their numbers -and their outward differences: still more their internal differences -and central essence! And with regard to the _Design_ which we see in -the organs of living things, though we can confidently say we see it, -how obscurely is it shown, and how much is our view of it disturbed by -other Laws and Analogies! And the Life of things, the end to which such -Design tends, how full of impenetrable mysteries is it! or rather how -entirely a mass of mystery into which our powers of knowledge strive in -vain to penetrate! - -There is therefore no danger that by following this train of thought -we should elevate our view of man too high, or bring down God in our -thoughts to the likeness of man. Even if we were to suppose the Idea -of the Divine Mind to be of the same kind as the Ideas of the human -mind, the very few Ideas of this kind, which man possesses, compared -with the whole range of the universe, and the scanty length to which -he can follow each, make his knowledge so small and imperfect, that -he has abundant reason to be modest and humble in his contemplations -concerning the Intelligence that knows all and constitutes all. He can, -as I have already said, wade but a few steps into the margin of the -boundless and unfathomable ocean of truth. - -5. But the Ideas of the Divine Mind must necessarily be different in -kind, as well as in number and extent, from the Ideas of the human -mind, on this very account, that they are complete and perfect. The -Mind which can conceive all the parts and laws of the universe in all -their mutual bearings, fundamental reasons, and remote consequences, -must be different in kind, as well as in extent, from the mind which -can only trace a few of these parts, and see these laws in a few of -their aspects, and cannot sound the whole depth of any of them. The -Divine Mind differs from the human, in the way in which we must needs -suppose what is Divine to differ from what is human. - -6. It has sometimes been said that the Divine Mind differs from the -human as the Infinite from the finite. And this has been given as a -reason why we cannot know anything concerning God; for we cannot, -it is said, know _anything_ concerning the Infinite. Our conception -of the Infinite being merely negative, (the negation of a limit,) -makes all knowledge about it impossible. But this is not truly said. -Our conception of the Infinite is _not_ merely negative. As I have -elsewhere remarked, our conception of the Infinite is positive in this -way:--that in order to form this conception, we begin to follow a given -Idea in a given direction; and then, having thus begun, we suppose that -the progress of thought goes on in that direction without limit. To -arrive at our Idea of infinite space, for example, we must determine -what kind of space we mean,--line, area or solid; and from what origin -we begin: and infinite space has different attributes as we take -different beginnings in this way. - -And so with regard to the kinds of infinity (for there are many) which -belong to the Divine Mind. _We_ have a few Ideas which represent the -Laws of the universe:--as Space, Time, Substance, Force, Matter, Kind, -End; of such Ideas the Divine Mind may have an infinite number. These -Ideas in the human mind are limited in depth and clearness: in the -Divine Mind they must be infinitely clearer than the clearest human -Intuition; infinitely more profound than the profoundest human thought. -And in this way, and, as we shall see, in other ways also, the Divine -Mind infinitely transcends the human mind when most fully instructed -and unfolded. - -In this way and in other ways also, I say. For we have hitherto spoken -of the human mind only as contemplating the external world;--as -discerning, to a certain small extent, the laws of the universe. We -have spoken of the world of things without: we must now speak of the -world within us;--of the world of our thoughts, our being, our moral -and personal being. - - -7. (_From ourselves we learn something concerning God._)--We must -speak of this: for this is, as I have said, another starting point and -another line in which we may proceed from what we know, and see how far -our knowledge carries us, and how far it teaches us anything concerning -God. - -Looking at ourselves, we perceive that we have to act, as well as -to contemplate: we are practical as well as speculative beings. And -tracing the nature and conditions of our actions, in the depths of our -thought we find that there is in the aspect of actions a supreme and -inevitable distinction of right and wrong. We cannot help judging of -our actions as right and wrong. We acknowledge that there must be such -a judgment appropriate to them. We have these Ideas of _right_ and -_wrong_ as attributes of actions; and thus we are _moral_ beings. - -8. And again: the actions are _our_ actions. _We_ act in this way or -that. And _we_ are not mere _things_, which move and change as they -are acted on, but which do not themselves act, as man acts. I am not a -Thing but a _Person_; and the men with whom I act, who act with me--act -in various ways towards me, well or ill--are also persons. Man is a -personal being. - -The Ideas of right and wrong--the _moral_ Ideas of man--are then a part -of the scheme of the universe to which man belongs. Could they be this, -if they were not also a part of the nature of that Divine Mind which -constitutes the universe?--It would seem not: the Moral Law of the -universe must be a Law of the Divine Mind, in order that it may be a -Law felt and discerned by man. - - -9. (_Objection answered._)--But, it may be objected, the Moral Law -of the universe is a Law in a different sense from the Laws of the -universe of which we spoke before--the mathematical and physical laws -of the universe. Those were laws according to which things _are_, and -events _occur_: but Moral Laws are Laws according to which men _ought_ -to act, and according to which actions _ought_ to be. There is a -difference, so that we cannot reason from the human to the Divine Mind -in the same manner in this case as in the other. - -True: we cannot reason _in the same manner_. But we can reason still -more confidently. For the Law directing what _ought to be_ is the -_Supreme Law_, and the mind which constitutes the Supreme Law is the -_Supreme Mind_, that is, the Divine Mind. - -10. That the Moral Law is not verified among men in fact, is not a -ground for doubting that it is a Law of the Divine Mind; but it is a -ground for inquiring what consequences the Divine Mind has annexed to -the violation of the Law; and in what manner the supremacy of the Law -will be established in the total course of the history of the universe, -including, it may be, the history of other worlds than that in which we -now live. - -Considering how dimly and imperfectly we see what consequences the -Divine Governor has annexed to the violation of the Moral Law, He who -sees all these consequences and has provided for the establishment of -His Law in the whole history of the human race, must be supposed to be -infinitely elevated above man in wisdom;--more even in virtue of this -aspect of His nature, than in virtue of that which is derived from the -contemplation of the universe. - -11. Man is a person; and his personality is his _highest_ attribute, -or at least, that which makes all his highest attributes possible. -And the highest attribute which belongs to the finite minds which -exist in the universe must exist also in the Infinite Mind which -constitutes the universe as it is. The Divine Mind must reside in a -_Divine Person_. And as man, by his personality, acts in obedience to -or in transgression of a moral law, so God, by His Personality, acts in -establishing the Law and in securing its supremacy in the whole history -of the world. - - -12. (_Creation._)--Acknowledging a Divine Mind which is the foundation -and support of the world as it is, constituting and upholding its laws, -it may be asked, Does this view point to a beginning of the world? -Was there a time when the Divine Mind called into being the world, -before non-existent? Was there a Creation of the world? - -I do not think that an answer to this question, given either way, -affects the argument which I have been urging. The Laws of the -Universe discoverable by the human mind, are the Laws of the Divine -Mind, whether or not there was a time when these Laws first came into -operation, or first produced the world which we see. The argument -respecting the nature of the Divine Mind is the same, whether or not we -suppose a Creation. - -But, in point of fact, every part of our knowledge of the Universe does -seem to point to a beginning. Every part of the world has been, so far -as we can see, formed by natural causes out of something different -from what it now is. The Earth, with its lands and seas, teeming with -innumerable forms of living things, has been produced from an earth -formed of other lands and seas, occupied with quite different forms of -life: and if we go far enough back, from an earth in which there was -no life. The stars which we call _fixed_ move and change; the nebulæ -in their shape show that they too are moving and changing. The Earth -was, some at least hold, produced by the condensation of a nebula. -The history of man, as well as of others of its inhabitants, points -to a beginning. Languages, Arts, Governments, Histories, all seem to -have begun from a starting-point, however remote. Indeed not only a -beginning, but a beginning at no remote period, appears to be indicated -by most of the sciences which carry us backwards in the world's history. - -But we must allow, on the other hand, that though all such lines of -research point _towards_ a beginning, none of them can be followed _up -to_ a beginning. All the lines converge, but all melt away before they -reach the point of convergence. As I have elsewhere said[320], in no -science has man been able to arrive at a beginning which is homogeneous -with the known course of events, though we can often go very far -back, and limit the hypotheses respecting the origin. We have, in the -impossibility of thus coming to any conclusion by natural reason on the -subject of creation, another evidence of the infinitely limited nature -of the human mind, when compared with the Creative or Constitutive -Divine Mind. - - -13. (_End of the World._)--But if our natural reason, aided by all -that science can teach, can tell us nothing respecting the origin -and beginning of this world, still less can reason tell us anything -with regard to the _End_ of this world. On this subject, the natural -sciences are even more barren of instruction than on the subject of -Creation. Yet we may say that as the Constitution of the Universe, and -its conformity to a Collection of eternal and immutable Ideas as its -elements, are not inconsistent with the supposition of a Beginning of -the present course of the world, so neither are they inconsistent with -the supposition of an End. Indeed it would not be at all impossible -that physical inquiries should present the prospect of an End, even -more clearly than they afford the retrospect of a Beginning. If, for -instance, it should be found that the planets move in a resisting -medium which constantly retards their velocity, and must finally -make them fall in upon the central sun, there would be an end of the -earth as to its present state. We cannot therefore, on the grounds of -Science, deny either a Beginning or an End of the present world. - - -14. But here another order of considerations comes into play, namely, -those derived from moral and theological views of the world. On these -we must, in conclusion, say a few words. - -It is very plain that these considerations may lead us to believe in -a view of the Beginning, Middle, and End of the history of the world, -very different from anything which the mere physical and natural -sciences can disclose to us. And these expressions to which I have -been led, the _Beginning_, the _Middle_, and the _End_ of the world's -history according to theological views, are full of suggestions of the -highest interest. But the interest which belongs to these suggestions -is of a solemn and peculiar kind; and the considerations to which -such suggestions point are better, I think, kept apart from such -speculations as those with which I have been concerned in the present -volume. - - -FOOTNOTES: - -[Footnote 320: _Hist. Ind. Sc._ b. xviii. c. vi. sect. 5] - - - - -CHAPTER XXXII. - -ANALOGIES OF PHYSICAL AND RELIGIOUS PHILOSOPHY. - - -1. Any assertion of analogy between physical and religious philosophy -will very properly be looked upon with great jealousy as likely to -be forced and delusive; and it is only in its most general aspects -that a sound philosophy on the two subjects can offer any points of -resemblance. But in some of its general conditions the discovery of -truth in the one field of knowledge and in the other may offer certain -analogies, as well as differences, which it may be instructive to -notice; and to some such aspects of our philosophy I shall venture to -refer. - -For the physical sciences--the sciences of observation and -speculation--the progress of our exact and scientific knowledge, as -I have repeatedly said, consists in reducing the objects and events -of the universe to a conformity with Ideas which we have in our own -minds:--the Ideas, for instance, of Space, Force, Substance, and the -like. In this sense, the intellectual progress of men consists in the -Idealization of Facts. - -2. In moral subjects, on the other hand, where man has not merely to -observe and speculate, but also to act;--where he does not passively -leave the facts and events of the world such as they are, but tries -actively to alter them and to improve the existing state of things, -his progress consists in doing this. He makes a moral advance when he -succeeds in doing what he thus attempts:--when he really improves the -state of things with which he has to do by removing evil and producing -good:--when he makes the state of things, namely, the relations between -him and other persons, his acts and their acts, conform more and -more to Ideas which he has in his own mind:--namely, to the Ideas of -Justice, Benevolence, and the like. His moral progress thus consists in -the realization of Ideas. - -And thus we are led to the Aphorism, as we may call it, that _Man's -Intellectual Progress consists in the Idealization of Facts, and his -Moral Progress consists in the Realization of Ideas_. - - -3. But further, though that progress of science which consists in -the idealization of facts may be carried through several stages, and -indeed, in the history of science, has been carried through many -stages, yet it is, and always must be, a progress exceedingly imperfect -and incomplete, when compared with the completeness to which its nature -points. Only a few sciences have made much progress; none are complete; -most have advanced only a step or two. In none have we reduced all the -Facts to Ideas. In all or almost all the unreduced Facts are far more -numerous and extensive than those which have been reduced. The general -mass of the facts of the universe are mere facts, unsubdued to the rule -of science. The Facts are not Idealized. The intellectual progress -is miserably scanty and imperfect, and would be so, even if it were -carried much further than it is carried. How can we hope that it will -ever approach to completeness? - -4. And in like manner, the _moral_ progress of man is still more -miserably scanty and incomplete. In how small a degree has he in this -sense realized his Ideas! In how small a degree has he carried into -real effect, and embodied in the relations of society, in his own acts -and in those of others with whom he is concerned, the Ideas of Justice -and Benevolence and the like! How far from a complete realization of -such moral Ideas are the acts of the best men, and the relations of -the best forms of society! How far from perfection in these respects -is man! and how certain it is that he will always be very far from -perfection! Far below even such perfection as he can conceive, he will -always be in his acts and feelings. The moral progress of man, of each -man, and of each society, is, as I have said, miserably scanty and -incomplete; and when regarded as the realization of his moral Ideas, -its scantiness and incompleteness become still more manifest than -before. - -Hence we are led to another Aphorism:--_that man's progress in the -realization of Moral Ideas, and his progress in the Scientific -idealization of Facts, are, and always will be, exceedingly scanty and -incomplete_. - - -5. But there is another aspect of Ideas, both physical and moral, -in which this scantiness and incompleteness vanish. In the Divine -Mind, all the physical Ideas are entertained with complete fulness -and luminousness; and it is because they are so entertained in the -Divine Mind, and it is because the universe is constituted and framed -upon them, that we find them verified in every part of the universe, -whenever we make our observation of facts and deduce their laws. - -In like manner the Moral Ideas exist in the Divine Mind in complete -fulness and luminousness; and we are naturally led to believe and -expect that they must be exemplified in the moral universe, as -completely and universally as the physical laws are exemplified in the -physical universe. Is this so? or under what conditions can we conceive -this to be? - -6. In answering this question, we must consider how far the moral, -still more even than the physical Ideas of the Divine Mind, are -elevated above our human Ideas; but yet not so far as to have no -resemblance to our corresponding human Ideas; for if this were so, we -could not reason about them at all. - -In speaking of man's moral Ideas, Benevolence, Justice, and the like, -we speak of them as belonging to man's _Soul_, rather than to his -_Mind_, which we have commonly spoken of as the seat of his physical -Ideas. A distinction is thus often made between the intellectual and -the moral faculties of man; but on this distinction we here lay no -stress. We may speak of man's _Mind_ and _Soul_, meaning that part of -his being in which are all his Ideas, intellectual and moral. - -And now let us consider the question which has just been asked:--how we -can conceive the Divine Benevolence and Justice to be completely and -universally realized in the moral world, as the Ideas of Space, Time, -&c. are in the physical world? - - -7. Our Ideas of Benevolence, Justice, and of other Virtues, may be -elevated above their original narrowness, and purified from their -original coarseness, by moral culture; as our Ideas of Force and -Matter, of Substance and Elements, and the like, may be made clear -and convincing by philosophical and scientific culture. This appears, -in some degree, in the history of moral terms, as the progress of -clearness and efficacy in the Idea of the material sciences appears in -the history of the terms belonging to such sciences. Thus among the -Romans, while they confined their kindly affections within their own -class, a stranger was universally an enemy; _peregrinus_ was synonymous -with _hostis_. But at a later period, they regarded all _men_ as having -a claim on their kindness; and he who felt and acted on this claim was -called _humane_. This meaning of the word _humanity_ shows the progress -(in their Ideas at least) of the virtue which the word _humanity_ -designates. - -8. And as man can thus rise to a point of view where he sees that man -is to be loved as man, so the humane and loving man inevitably assumes -that God loves all men; and thus assumes that there is, or may be, a -love of man in man's heart, which represents and resembles in kind, -however remote in degree, the love of God to man. - -But as in man's love of man there are very widely different stages, -rising from the narrow love of a savage to his family or his tribe, -to the widest and warmest feelings of the most enlightened and loving -universal philanthropist;--so must we suppose that there are stages -immeasurably wider by which God's love of man is more comprehensive and -more tender than any love of man for man. The religious philosopher -will fully assent to the expressions of this conviction delivered by -pious men in all ages. "The eternal God is thy refuge, and beneath -thee are the everlasting arms." "When my father and my mother forsake -me the Lord taketh me up," is the expression of Divine Love, consistent -with philosophy as well as with revelation. But as the Divine Love is -more comprehensive and enduring than any human love, so is it in an -immeasurably greater degree, more enlightened. It is not a love that -seeks merely the pleasure and gratification of its object; _that_ -even an enlightened human love does not do. It seeks the good of its -objects; and such a good as is the greatest good, to an Intelligence -which can embrace all cases, causes, and contingencies. To our limited -understanding, evil seems often to be inflicted, and the good of a -part seems inconsistent with the good of another part. Our attempts to -conceive a Supreme and complete Good provided for all the creatures -which exist in the universe, baffle and perplex us, even more than our -attempts to conceive infinite space, infinite time, and an infinite -chain of causation. But as the most careful attention which we can -give to the Ideas of Space, Time, and Causation convinces us that -these Ideas are perfectly clear and complete in the Divine Mind, and -that _our_ perplexity and confusion on these subjects arise only from -the vast distance between the Divine Mind and our human mind, so is -it reasonable to suppose the same to be the source of the confusion -which we experience when we attempt to determine what most conduces to -the good of our fellow-creatures; and when, urged by love to them, we -endeavour to promote this good. We can do little of what Infinite Love -would do, yet are we not thereby dispensed from seeking in some degree -to imitate the working of Divine Love. We can see but little of what -Infinite Intelligence sees, and this should be one source of confidence -and comfort, when we stumble upon perplexities produced by the seeming -mixture of good and evil in the world. - -9. But when we ask the questions which have already been stated: -Whether this Infinite Divine Love is realized in the world, and if -so, How: I conceive that we are irresistibly impelled to reply to the -former question, that it is: and we then turn to the latter. We are -led to assume that there is in God an Infinite Love of man, a creature -in a certain degree of a Divine nature. We must, as a consequence of -this, assume that the Love of God to man, necessarily is, in the end, -and on the whole, completely and fully realized in the history of the -world. But what is the complete history of the world! Is it that which -consists in the lives of men such as we see them between their birth -and their death? If the minds or souls of men are alive after the death -of the body, that future life, as well as this present life, belongs to -the history of the world;--to that providential history, of which the -totality, as we have said, must be governed by Infinite Divine Love. -And in addition to all other reasons for believing that the minds and -souls of men do thus survive their present life, is this:--that we thus -can conceive, what otherwise it is difficult or impossible to conceive, -the operation of Infinite Love in the whole of the history of mankind. -If there be a Future State in which men's souls are still under the -authority and direction of the Divine Governor of the world, all that -is here wanting to complete the scheme of a perfect government of -Intelligent Love may thus be applied: all seeming and partial evil may -be absorbed and extinguished in an ultimate and universal good. - - -10. The Idea of Justice as belonging to God suggests to us some of the -same kind of reflexions as those which we have made respecting the -Divine Love. We believe God to be just: otherwise, as has been said, -He would not be God. And as we thus, from the nature of our minds and -souls, believe God to be just, we must, in this belief, understand -Justice according to the Idea which we have of Justice; that is, in -some measure, according to the Idea of Justice, as exemplified in -human actions and feelings. It would be absurd to combine the two -propositions, that we necessarily believe that God is just, and that by -_just_, we mean something entirely different from the common meaning of -the word. - -But though the Divine Idea of Justice must necessarily, in some -measure, coincide with our Idea of Justice, we must believe in this, -as in other cases, that the Divine Idea is immeasurably more profound, -comprehensive, and clear, than the human Idea. Even the human Idea of -Justice is susceptible of many and large progressive steps, in the way -of clearness, consistency, and comprehensiveness. In the moral history -of man this Idea advances from the hard rigour of inflexible written -Law to the equitable estimation of the real circumstances of each case; -it advances also from the narrow Law of a single community to a larger -Law, which includes and solves the conflicts of all such Laws. Further, -the administration of human Law is always imperfect, often erroneous, -in consequence of man's imperfect knowledge of the facts of each case, -and still more, from his ignorance of the designs and feelings of the -actors. If the Judge could see into the heart of the person accused, -and could himself rise higher and higher in judicial wisdom, he might -exemplify the Idea of Justice in a far higher degree than has ever yet -been done. - -11. But all such advance in the improvement of human Justice must -still be supposed to stop immeasurably short of the Divine Justice, -which must include a perfect knowledge of all men's actions, and all -men's hearts and thoughts; and a universal application of the wisest -and most comprehensive Laws. And the difference of the Divine and of -the human Idea of Justice may, like the differences of other Divine -and human Ideas, include the solution of all the perplexities in which -we find ourselves involved when we would trace the Idea to all its -consequences. The Divine Idea is immeasurably elevated above the human -Idea; in the Divine Idea all inconsistency, defect, and incompleteness -vanish, and Justice includes in its administration every man, without -any admixture of injustice. This is what we must conceive of the Divine -administration, since God is perfectly just. - -12. But here, as before, we have another conclusion suggested to us. We -are, by the considerations just now spoken of, led to believe that, in -the Divine administration of the world is an administration of perfect -Justice;--that is, such is the Divine Administration in the end and on -the whole, taking into account the whole of the providential history of -the world. But the course of the world, taking into account only what -happens to man in this present life, is not, we may venture to say, a -complete and entire administration of justice. It often happens that -injustice is successful and triumphant, even in the end, so far as the -end is seen here. It happens that wrong is done, and is not remedied -or punished. It happens that blameless and virtuous men are subjected -to pain, grief, violence, and oppression, and are not protected, -extricated, or avenged. In the affairs of this world, the prevalence of -injustice and wrong-doing is so apparent, as to be a common subject of -complaint: and though the complaint may be exaggerated, and though a -calm and comprehensive view may often discern compensating and remedial -influences which are not visible at first sight, still we cannot regard -the lot of happiness or misery which falls to each man in this world -and this life as apportioned according to a scheme of perfect and -universal justice, such as in our thoughts we cannot but require the -Divine administration to be. - -13. Here then we are again led to the same conviction by regarding the -Divine administration of the world as the realization of the Divine -Justice, to which we were before led by regarding it as the realization -of the Divine Love. Since the Idea is not fully or completely realized -in man's life in this present world, this present world cannot be the -whole of the Divine Administration. To complete the realization of the -Idea of Justice, as an element of the Divine Administration, there -must be a life of man after his life in this present world. If man's -mind and soul, the part of him which is susceptible of happiness and -misery, survive this present life, and be still subject to the Divine -Administration, the Idea of Divine Justice may still be completely -realized, notwithstanding all that here looks like injustice or -defective justice; and it belongs to the Idea of Justice to remedy -and compensate, not to prevent wrong. And thus by this supposition -of a Future State of man's existence, we are enabled to conceive -that, in the whole of the Divine Government of the universe, all -seeming injustice and wrong may be finally corrected and rectified, -in an ultimate and universal establishment of a reign of perfect -Righteousness. - - -14. Admitting the view thus presented, we may again discern a -remarkable analogy between what we have called our _physical_ Ideas -(those of Space, Time, Cause, Substance, and the like), and our _moral_ -Ideas, (those of Benevolence, Justice, &c.). In both classes we must -suppose that our human Ideas represent, though very incompletely and at -an immeasurable distance, the Divine Ideas. Even our physical Ideas, -when pursued to their consequences, are involved in a perplexity -and confusion from which the Divine Ideas are free. Our Ideas of -Benevolence and Justice are still more full of imperfections and -inconsistency, when we would frame them into a complete scheme, and -yet from such imperfections and inconsistency we must suppose that -the Divine Benevolence and Justice are exempt. Our physical Ideas we -find in every case exactly exemplified and realized in the universe, -and we account for this by considering that they are the Divine Ideas, -on which the universe is constituted. Our moral Ideas, the Ideas of -Benevolence and Justice in particular, must also be realized in the -universe, as a scheme of Divine Government. But they are not realized -in the world as constituted of man living this present life. The Divine -Scheme of the world, therefore, extends beyond this present life of -man. If we could include in our survey the future life as well as the -present life of man, and the future course of the Divine Government, we -should have a scheme of the Moral Government of the universe, in which -the Ideas of Perfect Benevolence and Perfect Justice are as completely -and universally exemplified and realized, as the Ideas of Space, Time, -Cause, Substance, and the like, are in the physical universe. - - -15. There is one other remark bearing upon this analogy, which seems -to deserve our attention. As I have said in the last chapter, the -scheme of the world, as governed by our physical Ideas, seems to point -to a Beginning of the world, or at least of the present course of the -world: and if we suppose a Beginning, our thoughts naturally turn to -an End. But if our physical Ideas point to a Beginning and suggest an -End, do our Ideas of Divine Benevolence and Justice in any way lend -themselves to this suggestion?--Perhaps we might venture to say that in -some degree they do, even to the eye of a mere philosophical reason. -Perhaps our reason alone might suggest that there is a progression in -the human race, in various moral attributes--in art, in civilization, -and even in humanity and in justice, which implies a beginning. And -that at any rate there is nothing inconsistent with our Idea of the -Divine Government in the supposition that the history of this world has -a Beginning, a Middle and an End. - -16. If therefore there should be conveyed to us by some channel -especially appropriated to the communication and development of moral -and religious Ideas, the knowledge that the world, as a scheme of -Divine Government, has _a Beginning_, _a Middle_, and _an End_, of -a Kind, or at least, invested with circumstances quite different -from any which our physical Ideas can disclose to us, there would -be, in such a belief, nothing at all inconsistent with the analogies -which our philosophy--the philosophy of our Ideas illustrated by the -whole progress of science--has impressed upon us. On the grounds of -this philosophy, we need find no difficulty in believing that as the -visible universe exhibits the operation of the Divine Ideas of Space, -Time, Cause, Substance, and the like, and discloses to us traces of -a Beginning of the present mode of operation, so the moral universe -exhibits to us the operation of the Divine Benevolence and Justice; and -that these Divine attributes wrought in a special and peculiar manner -in the Beginning; interposed in a peculiar and special manner in the -Middle; and will again act in a peculiar and special manner in the End -of the world. And thus the conditions of the physical universe, and the -Government of the Moral world, are both, though in different ways, a -part of the work which God is carrying on from the Beginning of things -to the End--_opus quod Deus operator a principio usque ad finem_. - - -17. We are led by such analogies as I have been adducing to believe -that the whole course of events in which the minds and souls of men -survive the present life, and are hereafter subjected to the Divine -government in such a way as to complete all that is here deficient in -the world's history, is a scheme of perfect Benevolence and Justice. -Now, can we discern in man's mind or soul itself any indication of a -destiny like this? Are there in us any powers and faculties which seem -as if they were destined to immortality? If there be, we have in such -faculties a strong confirmation of that belief in the future life of -man which has already been suggested to us as necessary to render the -Divine government conceivable. - - -18. According to our philosophy there are powers and faculties which -do thus seem fitted to endure, and not fitted to terminate and be -extinguished. The Ideas which we have in our minds--the physical -Ideas, as we have called them, according to which the universe is -constituted,--agree, as far as they go, with the Ideas of the Divine -Mind, seen in the constitution of the universe. But these Divine -Ideas are eternal and imperishable: we therefore naturally conclude -that the human mind which includes such elements, is also eternal and -imperishable. Since the mind can take hold of eternal truths, it must -be itself eternal. Since it is, to a certain extent, the image of God -in its faculties, it cannot ever cease to be the image of God. When it -has arrived at a stage in which it sees several aspects of the universe -in the same form in which they present themselves to the Divine Mind, -we cannot suppose that the Author of the human mind will allow it and -all its intellectual light to be extinguished. - -19. And our conviction that this extinction of the human mind cannot -take place becomes stronger still, when we consider that the mind, -however imperfect and scanty its discernment of truth may be, is -still capable of a vast, and even of an unlimited progress in the -pursuit and apprehension of truth. The mind is capable of accepting -and appropriating, through the action of its own Ideas, every step in -science which has ever been made--every step which shall hereafter -be made. Can we suppose that this vast and boundless capacity exists -for a few years only, is unfolded only into a few of its simplest -consequences, and is then consigned to annihilation? Can we suppose -that the wonderful powers which carry man on, generation by generation, -from the contemplation of one great and striking truth to another, are -buried with each generation? May we not rather suppose that that mind, -which is capable of indefinite progression, is allowed to exist in an -infinite duration, during which such progression may take place? - -20. I propose this argument as a ground of hope and satisfactory -reflexion to those who love to dwell on the natural arguments for the -Immortality of the Soul. I do not attempt to follow it into detail. -I know too well how little such a cause can gain by obstinate and -complicated argumentation, to attempt to urge the argument in that -manner: and probably different persons, among those who accept the -argument as valid, would give different answers to many questions of -detail, which naturally arise out of the acceptance of this argument. -I will not here attempt to solve, or even to propound these questions. -My main purpose in offering these views and this argument at all, is -to give some satisfaction to those who would think it a sad and blank -result of this long survey of the nature and progress of science in -which we have been so long engaged (through this series of works), that -it should in no way lead to a recognition of the Author of that world -about which our Science is, and to the high and consolatory hopes which -lift man beyond this world. No survey of the universe can be at all -satisfactory to thoughtful men, which has not a theological bearing; -nor can any view of man's powers and means of knowing be congenial to -such men, which does not recognize an infinite destination for the mind -which has an infinite capacity; an eternal being of the Faculty which -can take a steady hold of eternal being. - - -21. And as we may derive such a conviction from our physical Ideas, so -too may we no less from our moral Ideas. Our minds apprehend Space and -Time and Force and the like, as Ideas which are not dependent on the -body; and hence we believe that our minds shall not perish with our -bodies. And in the same manner our souls conceive pure Benevolence and -perfect Justice, which go beyond the conditions of this mortal life; -and hence we believe that our souls have to do with a life beyond this -mortal life. - -It is more difficult to speak of man's indefinite moral progression -even than of his indefinite intellectual progression. Yet in every -path of moral speculation we have such a progression suggested to us. -We may begin, for instance, with the ordinary feelings and affections -of our daily nature:--Love, Hate, Scorn. But when we would elevate the -Soul in our imagination, we ascend above these ordinary affections, and -take the repulsive and hostile ones as fitted only to balance their own -influences. And thus the poet, speaking of a morally poetical nature, -describes it: - - The Poet in a golden clime was born, - With golden stars above. - He felt the hate _of_ hate, the scorn _of_ scorn, - The love _of_ love. - -But the loftier moralist can rise higher than this, and can, and will, -reject altogether Hate and Scorn from his view of man's better nature. -His description would rather be-- - - The good man in a loving clime was born, - With loving stars above. - He felt sorrow for hate, pity for scorn, - And love of love. - -He would, in his conception of such a character, ascribe to it all -the virtues which result from the control and extinction of these -repulsive and hostile affections:--the virtues of magnanimity, -forgivingness, unselfishness, self-devotion, tenderness, sweetness. And -these we can conceive in a higher and higher degree, in proportion as -our own hearts become tender, forgiving, pure and unselfish. And though -in every human stage of such a moral proficiency, we must suppose -that there is still some struggle with the remaining vestiges of our -unkind, unjust, angry and selfish affections, we can see no limit to -the extent to which this struggle may be successful; no limit to the -degree in which these traces of the evil of our nature may be worn -out by an enduring practice and habit of our better nature. And when -we contemplate a human character which has, through a long course of -years, and through many trials and conflicts, made a large progress in -this career of melioration, and is still capable, if time be given, -of further progress towards moral perfection, is it not reasonable to -suppose that He who formed man capable of such progress, and who, as we -must needs believe, looks with approval on such progress where made, -will not allow the progress to stop when it has gone on to the end of -man's short earthly life? Is it not rather reasonable to suppose that -the pure and elevated and all-embracing affection, extinguishing all -vices and including all virtues, to which the good man thus tends, -shall continue to prevail in him as a permanent and ever-during -condition, in a life after this? - -But can man raise himself to such a stage of moral progress, by his own -efforts? Such a progress is an approximation towards the perfection of -moral Ideas, and therefore an approximation towards the image of God, -in whom that perfection resides: is it not then reasonable to suppose -that man needs a Divine Influence to enable him to reach this kind of -moral completeness? And is it not also reasonable to suppose that, -as he needs such aid, in order that the Idea of his moral progress -may be realized, so he will receive such aid from the Divine Power -which realizes the Idea of Divine Love in the world; and to do so, -must realize it in those human souls which are most fitted for such a -purpose? - -But these questions remind me how difficult, and indeed, how impossible -it is to follow such trains of reflexion by the light of philosophy -alone. To answer such questions, we need, not Religious Philosophy -only, but Religion: and as I do not here venture beyond the domain of -philosophy, I must, however abruptly, conclude. - - -THE END. - - - - -APPENDIX. - - -APPENDIX A. - -OF THE PLATONIC THEORY OF IDEAS. - -(_Cam. Phil. Soc._ Nov. 10, 1856.) - - -Though Plato has, in recent times, had many readers and admirers -among our English scholars, there has been an air of unreality and -inconsistency about the commendation which most of these professed -adherents have given to his doctrines. This appears to be no captious -criticism, for instance, when those who speak of him as immeasurably -superior in argument to his opponents, do not venture to produce -his arguments in a definite form as able to bear the tug of modern -controversy;--when they use his own Greek phrases as essential to the -exposition of his doctrines, and speak as if these phrases could not be -adequately rendered in English;--and when they assent to those among -the systems of philosophy of modern times which are the most clearly -opposed to the system of Plato. It seems not unreasonable to require, -on the contrary, that if Plato is to supply a philosophy for us, it -must be a philosophy which can be expressed in our own language;--that -his system, if we hold it to be well founded, shall compel us to deny -the opposite systems, modern as well as ancient;--and that, so far as -we hold Plato's doctrines to be satisfactorily established, we should -be able to produce the arguments for them, and to refute the arguments -against them. These seem reasonable requirements of the adherents of -_any_ philosophy, and therefore, of Plato's. - -I regard it as a fortunate circumstance, that we have recently had -presented to us an exposition of Plato's philosophy which does conform -to those reasonable conditions; and we may discuss this exposition with -the less reserve, since its accomplished author, though belonging to -this generation, is no longer alive. I refer to the _Lectures_ on the -History of Ancient Philosophy, by the late Professor Butler of Dublin. -In these Lectures, we find an account of the Platonic Philosophy which -shows that the writer had considered it as, what it is, an attempt -to solve large problems, which in all ages force themselves upon the -notice of thoughtful men. In Lectures VIII. and X., of the Second -Series, especially, we have a statement of the Platonic Theory of -Ideas, which may be made a convenient starting point for such remarks -as I wish at present to make. I will transcribe this account; omitting, -as I do so, the expressions which Professor Butler uses, in order to -present the theory, not as a dogmatical assertion, but as a view, at -least not extravagant. For this purpose, he says, of the successive -portions of the theory, that one is "not too absurd to be maintained;" -that another is "not very extravagant either;" that a third is "surely -allowable;" that a fourth presents "no incredible account" of the -subject; that a fifth is "no preposterous notion in substance, and no -unwarrantable form of phrase." Divested of these modest formulæ, his -account is as follows: [Vol. II. p. 117.] - -"Man's soul is made to contain not merely a consistent scheme of its -own notions, but a direct apprehension of _real and eternal laws beyond -it_. These real and eternal laws are things _intelligible_, and not -things sensible. - -"These laws impressed upon creation by its Creator, and apprehended -by man, are something distinct equally from the Creator and from man, -and the whole mass of them may fairly be termed the World of Things -Intelligible. - -"Further, there are qualities in the supreme and ultimate Cause of all, -which are manifested in His creation, and not merely manifested, but, -in a manner--after being brought out of his super-essential nature into -the stage of being [which is] below him, but next to him--are then by -the causative act of creation deposited in things, differencing them -one from the other, so that the things partake of them (μετέχουσι), -communicate with them (κοινωνοῦσι). - -"The intelligence of man, excited to reflection by the impressions -of these objects thus (though themselves transitory) participant of -a divine quality, may rise to higher conceptions of the perfections -thus faintly exhibited; and inasmuch as these perfections are -unquestionably _real_ existences, and _known_ to be such in the very -act of contemplation,--this may be regarded as a direct intellectual -apperception of them,--a Union of the Reason with the Ideas in that -sphere of being which is common to both. - -"Finally, the Reason, in proportion as it learns to contemplate the -Perfect and Eternal, _desires_ the enjoyment of such contemplations in -a more consummate degree, and cannot be fully satisfied, except in the -actual fruition of the Perfect itself. - -"These suppositions, taken together, constitute the Theory of Ideas." - -In remarking upon the theory thus presented, I shall abstain from any -discussion of the theological part of it, as a subject which would -probably be considered as unsuited to the meetings of this Society, -even in its most purely philosophical form. But I conceive that it will -not be inconvenient, if it be not wearisome, to discuss the Theory of -Ideas as an attempt to explain the existence of real knowledge; which -Prof. Butler very rightly considers as the necessary aim of this and -cognate systems of philosophy[321]. - -I conceive, then, that one of the primary objects of Plato's Theory -of Ideas is, to explain the existence of real knowledge, that is, of -demonstrated knowledge, such as the propositions of geometry offer -to us. In this view, the Theory of Ideas is one attempt to solve a -problem, much discussed in our times, What is the ground of geometrical -truth? I do not mean that this is the whole object of the Theory, or -the highest of its claims. As I have said, I omit its theological -bearings; and I am aware that there are passages in the Platonic -Dialogues, in which the Ideas which enter into the apprehension and -demonstration of geometrical truths are spoken of as subordinate to -Ideas which have a theological aspect. But I have no doubt that one -of the main motives to the construction of the Theory of Ideas was, -the desire of solving the Problem, "How is it possible that man should -apprehend necessary and eternal truths?" That the truths are necessary, -makes them eternal, for they do not depend on time; and that they are -eternal, gives them at once a theological bearing. - -That Plato, in attempting to explain the nature and possibility of -real knowledge, had in his mind geometrical truths, as examples of -such knowledge is, I think, evident from the general purport of his -discourses on such subjects. The advance of Greek geometry into a -conspicuous position, at the time when the Heraclitean sect were -proving that nothing could be proved and nothing could be known, -naturally suggested mathematical truth as the refutation of the -skepticism of mere sensation. On the one side it was said, we can -know nothing except by our sensations; and that which we observe with -our senses is constantly changing; or at any rate, may change at any -moment. On the other hand it was said, we _do_ know geometrical truths, -and as truly as we know them, that they cannot change. Plato was quite -alive to the lesson, and to the importance of this kind of truths. -In the _Meno_ and in the _Phædo_ he refers to them, as illustrating -the nature of the human mind: in the _Republic_ and the _Timæus_ he -again speaks of truths which far transcend anything which the senses -can teach, or even adequately exemplify. The senses, he argues in the -_Theætetus_, cannot give us the knowledge which we have; the source -of it must therefore be in the mind itself; in the _Ideas_ which -it possesses. The impressions of sense are constantly varying, and -incapable of giving any certainty: but the Ideas on which real truth -depends are constant and invariable, and the certainty which arises -from these is firm and indestructible. Ideas are the permanent, perfect -objects, with which the mind deals when it contemplates necessary and -eternal truths. They belong to a region superior to the material world, -the world of sense. They are the objects which make up the furniture of -the Intelligible World; with which the Reason deals, as the Senses deal -each with its appropriate Sensation. - -But, it will naturally be asked, what is the Relation of Ideas to the -Objects of Sense? Some connexion, or relation, it is plain, there -must be. The objects of sense can suggest, and can illustrate real -truths. Though these truths of geometry cannot be proved, cannot even -be exactly exemplified, by drawing diagrams, yet diagrams are of use -in helping ordinary minds to see the proof; and to all minds, may -represent and illustrate it. And though our conclusions with regard to -objects of sense may be insecure and imperfect, they have some show of -truth, and therefore some resemblance to truth. What does this arise -from? How is it explained, if there is no truth except concerning Ideas? - -To this the Platonist replied, that the phenomena which present -themselves to the senses partake, in a certain manner, of Ideas, and -thus include so much of the nature of Ideas, that they include also -an element of Truth. The geometrical diagram of Triangles and Squares -which is drawn in the sand of the floor of the Gymnasium, partakes of -the nature of the true Ideal Triangles and Squares, so that it presents -an imitation and suggestion of the truths which are true of them. The -real triangles and squares are in the mind: they are, as we have said, -objects, not in the Visible, but in the Intelligible World. But the -Visible Triangles and Squares make us call to mind the Intelligible; -and thus the objects of sense suggest, and, in a way, exemplify the -eternal truths. - -This I conceive to be the simplest and directest ground of two primary -parts of the Theory of Ideas;--The Eternal Ideas constituting an -Intelligible World; and the Participation in these Ideas ascribed to -the objects of the world of sense. And it is plain that so far, the -Theory meets what, I conceive, was its primary purpose; it answers the -questions, How can we have certain knowledge, though we cannot get it -from Sense? and, How can we have knowledge, at least apparent, though -imperfect, about the world of sense? - -But is this the ground on which Plato himself rests the truth of his -Theory of Ideas? As I have said, I have no doubt that these were the -questions which suggested the Theory; and it is perpetually applied -in such a manner as to show that it was held by Plato in this sense. -But his applications of the Theory refer very often to another part -of it;--to the Ideas, not of Triangles and Squares, of space and its -affections; but to the Ideas of Relations--as the Relations of Like and -Unlike, Greater and Less; or to things quite different from the things -of which geometry treats, for instance, to Tables and Chairs, and other -matters, with regard to which no demonstration is possible, and no -general truth (still less necessary an eternal truth) capable of being -asserted. - -I conceive that the Theory of Ideas, thus asserted and thus supported, -stands upon very much weaker ground than it does, when it is -asserted concerning the objects of thought about which necessary and -demonstrable truths are attainable. And in order to devise arguments -against _this_ part of the Theory, and to trace the contradictions to -which it leads, we have no occasion to task our own ingenuity. We find -it done to our hands, not only in Aristotle, the open opponent of the -Theory of Ideas, but in works which stand among the Platonic Dialogues -themselves. And I wish especially to point out some of the arguments -against the Ideal Theory, which are given in one of the most noted of -the Platonic Dialogues, the _Parmenides_. - -The _Parmenides_ contains a narrative of a Dialogue held between -Parmenides and Zeno, the Eleatic Philosophers, on the one side, and -Socrates, along with several other persons, on the other. It may be -regarded as divided into two main portions; the first, in which the -Theory of Ideas is attacked by Parmenides, and defended by Socrates; -the second, in which Parmenides discusses, at length, the Eleatic -doctrine that _All things are One_. It is the former part, the -discussion of the Theory of Ideas, to which I especially wish to direct -attention at present: and in the first place, to that extension of -the Theory of Ideas, to things of which no general truth is possible; -such as I have mentioned, tables and chairs. Plato often speaks of -a Table, by way of example, as a thing of which there must be an -Idea, not taken from any special Table or assemblage of Tables; but -an Ideal Table, such that all Tables are Tables by participating in -the nature of this Idea. Now the question is, whether there is any -force, or indeed any sense, in this assumption; and this question is -discussed in the _Parmenides_. Socrates is there represented as very -confident in the existence of Ideas of the highest and largest kind, -the Just, the Fair, the Good, and the like. Parmenides asks him how -far he follows his theory. Is there, he asks, an Idea of Man, which is -distinct from us men? an Idea of Fire? of Water? "In truth," replies -Socrates, "I have often hesitated, Parmenides, about these, whether -we are to allow such Ideas." When Plato had proceeded to teach that -there is an Idea of a Table, of course he could not reject such Ideas -as Man, and Fire, and Water. Parmenides, proceeding in the same line, -pushes him further still. "Do you doubt," says he, "whether there -are Ideas of things apparently worthless and vile? Is there an Idea -of a Hair? of Mud? of Filth?" Socrates has not the courage to accept -such an extension of the theory. He says, "By no means. These are not -Ideas. These are nothing more than just what we see them. I have often -been perplexed what to think on this subject. But after standing to -this a while, I have fled the thought, for fear of falling into an -unfathomable abyss of absurdities." On this, Parmenides rebukes him for -his want of consistency. "Ah Socrates," he says, "you are yet young; -and philosophy has not yet taken possession of you as I think she will -one day do--when you will have learned to find nothing despicable in -any of these things. But now your youth inclines you to regard the -opinions of men." It is indeed plain, that if we are to assume an Idea -of a Chair or a Table, we can find no boundary line which will exclude -Ideas of everything for which we have a name, however worthless or -offensive. And this is an argument against the assumption of _such_ -Ideas, which will convince most persons of the groundlessness of the -assumption:--the more so, as _for_ the assumption of such Ideas, it -does not appear that Plato offers any argument whatever; nor does -this assumption solve any problem, or remove any difficulty[322]. -Parmenides, then, had reason to say that consistency required Socrates, -if he assumed any such Ideas, to assume all. And I conceive his reply -to be to this effect; and to be thus a _reductio ad absurdum_ of the -Theory of Ideas in this sense. According to the opinions of those -who see in the _Parmenides_ an exposition of Platonic doctrines, I -believe that Parmenides is conceived in this passage, to suggest to -Socrates what is necessary for the completion of the Theory of Ideas. -But upon either supposition, I wish especially to draw the attention -of my readers to the position of superiority in the Dialogue in which -Parmenides is here placed with regard to Socrates. - -Parmenides then proceeds to propound to Socrates difficulties with -regard to the Ideal Theory, in another of its aspects;--namely, when it -assumes Ideas of Relations of things; and here also, I wish especially -to have it considered how far the answers of Socrates to these -objections are really satisfactory and conclusive. - -"Tell me," says he (§ 10, Bekker), "You conceive that there are certain -Ideas, and that things partaking of these Ideas, are called by the -corresponding names;--an Idea of _Likeness_, things partaking of -which are called _Like_;--of _Greatness_, whence they are _Great_: of -_Beauty_, whence they are _Beautiful_?" Socrates assents, naturally: -this being the simple and universal statement of the Theory, in this -case. But then comes one of the real difficulties of the Theory. Since -the special things participate of the General Idea, has each got -the whole of the Idea, which is, of course, One; or has each a part -of the Idea? "For," says Parmenides, "can there be any other way of -participation than these two?" Socrates replies by a similitude: "The -Idea, though One, may be wholly in each object, as the Day, one and the -same, is wholly in each place." The physical illustration, Parmenides -damages by making it more physical still. "You are ingenious, -Socrates," he says, (§ 11) "in making the same thing be in many places -at the same time. If you had a number of persons wrapped up in a sail -or web, would you say that each of them had the whole of it? Is not the -case similar?" Socrates cannot deny that it is. "But in this case, each -person has only a part of the whole; and thus your Ideas are partible." -To this, Socrates is represented as assenting in the briefest possible -phrase; and thus, here again, as I conceive, Parmenides retains his -superiority over Socrates in the Dialogue. - -There are many other arguments urged against the Ideal Theory by -Parmenides. The next is a consequence of this partibility of Ideas, -thus supposed to be proved, and is ingenious enough. It is this: - -"If the Idea of Greatness be distributed among things that are Great, -so that each has a part of it, each separate thing will be Great in -virtue of a part of Greatness which is less than Greatness itself. Is -not this absurd?" Socrates submissively allows that it is. - -And the same argument is applied in the case of the Idea of Equality. - -"If each of several things have a part of the Idea of Equality, it -will be Equal to something, in virtue of something which is less than -Equality." - -And in the same way with regard to the Idea of Smallness. - -"If each thing be small by having a part of the Idea of Smallness, -Smallness itself will be greater than the small thing, since that is a -part of itself." - -These ingenious results of the partibility of Ideas remind us of the -ingenuity shown in the Greek geometry, especially the Fifth Book of -Euclid. They are represented as not resisted by Socrates (§ 12): "In -what way, Socrates, can things participate in Ideas, if they cannot -do so either integrally or partibly?" "By my troth," says Socrates, -"it does not seem easy to tell." Parmenides, who completely takes the -conduct of the Dialogue, then turns to another part of the subject and -propounds other arguments. "What do you say to this?" he asks. - -"There is an Ideal Greatness, and there are many things, separate from -it, and Great by virtue of it. But now if you look at Greatness and the -Great things together, since they are all Great, they must be Great in -virtue of some higher Idea of Greatness which includes both. And thus -you have a Second Idea of Greatness; and in like manner you will have a -third, and so on indefinitely." - -This also, as an argument against the separate existence of Ideas, -Socrates is represented as unable to answer. He replies interrogatively: - -"Why, Parmenides, is not each of these Ideas a Thought, which, by its -nature, cannot exist in anything except in the Mind? In that case your -consequences would not follow." - -This is an answer which changes the course of the reasoning: but still, -not much to the advantage of the Ideal Theory. Parmenides is still -ready with very perplexing arguments. (§ 13.) - -"The Ideas, then," he says, "are Thoughts. They must be Thoughts of -something. They are Thoughts of something, then, which exists in all -the special things; some one thing which the Thought perceives in all -the special things; and this one Thought thus involved in all, is the -_Idea_. But then, if the special things, as you say, participate in the -Idea, they participate in the Thought; and thus, all objects are made -up of Thoughts, and all things think; or else, there are thoughts in -things which do not think." - -This argument drives Socrates from the position that Ideas are -Thoughts, and he moves to another, that they are Paradigms, Exemplars -of the qualities of things, to which the things themselves are like, -and their being thus like, is their participating in the Idea. But here -too, he has no better success. Parmenides argues thus: - -"If the Object be like the Idea, the Idea must be like the Object. -And since the Object and the Idea are like, they must, according to -your doctrine, participate in the Idea of Likeness. And thus you have -one Idea participating in another Idea, and so on in infinitum." -Socrates is obliged to allow that this demolishes the notion of objects -partaking in their Ideas by likeness: and that he must seek some other -way. "You see then, O Socrates," says Parmenides, "what difficulties -follow, if any one asserts the independent existence of Ideas!" -Socrates allows that this is true. "And yet," says Parmenides, "you -do not half perceive the difficulties which follow from this doctrine -of Ideas." Socrates expresses a wish to know to what Parmenides -refers; and the aged sage replies by explaining that if Ideas exist -independently of us, we can never know anything about them: and that -even the Gods could not know anything about man. This argument, though -somewhat obscure, is evidently stated with perfect earnestness, and -Socrates is represented as giving his assent to it. "And yet," says -Parmenides (end of § 18), "if any one gives up entirely the doctrine of -Ideas, how is any reasoning possible?" - -All the way through this discussion, Parmenides appears as vastly -superior to Socrates; as seeing completely the tendency of every line -of reasoning, while Socrates is driven blindly from one position to -another; and as kindly and graciously advising a young man respecting -the proper aims of his philosophical career; as well as clearly -pointing out the consequences of his assumptions. Nothing can be -more complete than the higher position assigned to Parmenides in the -Dialogue. - -This has not been overlooked by the Editors and Commentators of Plato. -To take for example one of the latest; in Steinhart's Introduction to -Hieronymus Müller's translation of _Parmenides_ (Leipzig, 1852), p. -261, he says: "It strikes us, at first, as strange, that Plato here -seems to come forward as the assailant of his own doctrine of Ideas. -For the difficulties which he makes Parmenides propound against that -doctrine are by no means sophistical or superficial, but substantial -and to the point. Moreover there is among all these objections, which -are partly derived from the Megarics, scarce one which does not appear -again in the penetrating and comprehensive argumentations of Aristotle -against the Platonic Doctrine of Ideas." - -Of course, both this writer and other commentators on Plato offer -something as a solution of this difficulty. But though these -explanations are subtle and ingenious, they appear to leave no -satisfactory or permanent impression on the mind. I must avow that, to -me, they appear insufficient and empty; and I cannot help believing -that the solution is of a more simple and direct kind. It may seem bold -to maintain an opinion different from that of so many eminent scholars; -but I think that the solution which I offer, will derive confirmation -from a consideration of the whole Dialogue; and therefore I shall -venture to propound it in a distinct and positive form. It is this: - -I conceive that the _Parmenides_ is not a Platonic Dialogue at all; -but Antiplatonic, or more properly, _Eleatic_: written, not by Plato, -in order to explain and prove his Theory of Ideas, but by some one, -probably an admirer of Parmenides and Zeno, in order to show how strong -were his master's arguments against the Platonists and how weak their -objections to the Eleatic doctrine. - -I conceive that this view throws an especial light on every part of the -Dialogue, as a brief survey of it will show. Parmenides and Zeno come -to Athens to the Panathenaic festival: Parmenides already an old man, -with a silver head, dignified and benevolent in his appearance, looking -five and sixty years old: Zeno about forty, tall and handsome. They are -the guests of Pythodorus, outside the Wall, in the Ceramicus; and there -they are visited by Socrates then young, and others who wish to hear -the written discourses of Zeno. These discourses are explanations of -the philosophy of Parmenides, which he had delivered in verse. - -Socrates is represented as showing, from the first, a disposition to -criticize Zeno's dissertation very closely; and without any prelude or -preparation, he applies the Doctrine of Ideas to refute the Eleatic -Doctrine that All Things are One. (§ 3.) When he had heard to the -end, he begged to have the first Proposition of the First Book read -again. And then, "How is it, O Zeno, that you say, That if the Things -which exist are Many, and not One, they must be at the same time like -and unlike? Is this your argument? Or do I misunderstand you?" "No," -says Zeno, "you understand quite rightly." Socrates then turns to -Parmenides, and says, somewhat rudely, as it seems, "Zeno is a great -friend of yours, Parmenides: he shows his friendship not only in -other ways, but also in what he writes. For he says the same things -which you say, though he pretends that he does not. You say, in your -poems, that All Things are One, and give striking proofs: he says that -existences are not many, and he gives many and good proofs. You seem -to soar above us, but you do not really differ." Zeno takes this sally -good-humouredly, and tells him that he pursues the scent with the -keenness of a Laconian hound. "But," says he (§ 6), "there really is -less of ostentation in my writing than you think. My Essay was merely -written as a defence of Parmenides long ago, when I was young; and is -not a piece of display composed now that I am older. And it was stolen -from me by some one; so that I had no choice about publishing it." - -Here we have, as I conceive, Socrates already represented as placed -in a disadvantageous position, by his abruptness, rude allusions, and -readiness to put bad interpretations on what is done. For this, Zeno's -gentle pleasantry is a rebuke. Socrates, however, forthwith rushes into -the argument; arguing, as I have said, for his own Theory. - -"Tell me," he says, "do you not think there is an Idea of Likeness, and -an Idea of Unlikeness? And that everything partakes of these Ideas? The -things which partake of Unlikeness are unlike. If all things partake of -both Ideas, they are both like and unlike; and where is the wonder? (§ -7.) If you could show that Likeness itself was Unlikeness, it would be -a prodigy; but if things which partake of these opposites, have both -the opposite qualities, it appears to me, Zeno, to involve no absurdity. - -"So if Oneness itself were to be shown to be Maniness" (I hope I may -use this word, rather than _multiplicity_) "I should be surprised; but -if any one say that _I_ am at the same time one and many, where is the -wonder? For I partake of maniness: my right side is different from my -left side, my upper from my under parts. But I also partake of Oneness, -for I am here One of us seven. So that both are true. And so if any one -say that stocks and stones, and the like, are both one and many,--not -saying that Oneness is Maniness, nor Maniness Oneness, he says nothing -wonderful: he says what all will allow. (§ 8.) If then, as I said -before, any one should take separately the Ideas or Essence of Things, -as Likeness and Unlikeness, Maniness and Oneness, Rest and Motion, and -the like, and then should show that these can mix and separate again, -I should be wonderfully surprised, O Zeno: for I reckon that I have -tolerably well made myself master of these subjects[323]. I should -be much more surprised if any one could show me this contradiction -involved in the Ideas themselves; in the object of the Reason, as well -as in Visible objects." - -It may be remarked that Socrates delivers all this argumentation with -the repetitions which it involves, and the vehemence of its manner, -without waiting for a reply to any of his interrogations; instead -of making every step the result of a concession of his opponent, as -is the case in the Dialogues where he is represented as triumphant. -Every reader of Plato will recollect also that in those Dialogues, -the triumph of temper on the part of Socrates is represented as -still more remarkable than the triumph of argument. No vehemence or -rudeness on the part of his adversaries prevents his calmly following -his reasoning; and he parries coarseness by compliment. Now in this -Dialogue, it is remarkable that this kind of triumph is given to the -adversaries of Socrates. "When Socrates had thus delivered himself," -says Pythodorus, the narrator of the conversation, "we thought that -Parmenides and Zeno would both be angry. But it was not so. They -bestowed entire attention upon him, and often looked at each other, -and smiled, as in admiration of Socrates. And when he had ended, -Parmenides said: 'O Socrates, what an admirable person you are, for the -earnestness with which you reason! Tell me then, Do you then believe -the doctrine to which you have been referring;--that there are certain -Ideas, existing independent of Things; and that there are, separate -from the Ideas, Things which partake of them? And do you think that -there is an Idea of Likeness besides the likeness which we have; and a -Oneness and a Maniness, and the like? And an Idea of the Right, and the -Good, and the Fair, and of other such qualities?'" Socrates says that -he does hold this; Parmenides then asks him, how far he carries this -doctrine of Ideas, and propounds to him the difficulties which I have -already stated; and when Socrates is unable to answer him, lets him off -in the kind but patronizing way which I have already described. - -To me, comparing this with the intellectual and moral attitude of -Socrates in the most dramatic of the other Platonic Dialogues, it is -inconceivable, that this representation of Socrates should be Plato's. -It is just what Zeno would have written, if he had wished to bestow -upon his master Parmenides the calm dignity and irresistible argument -which Plato assigns to Socrates. And this character is kept up to the -end of the Dialogue. When Socrates (§ 19) has acknowledged that he is -at loss which way to turn for his philosophy, Parmenides undertakes, -though with kind words, to explain to him by what fundamental error in -the course of his speculative habits he has been misled. He says; "You -try to make a complete Theory of Ideas, before you have gone through -a proper intellectual discipline. The impulse which urges you to such -speculations is admirable--is divine. But you must exercise yourself in -reasoning which many think trifling, while you are yet young; if you -do not, the truth will elude your grasp." Socrates asks submissively -what is the course of such discipline: Parmenides replies, "The course -pointed out by Zeno, as you have heard." And then, gives him some -instructions in what manner he is to test any proposed Theory. Socrates -is frightened at the laboriousness and obscurity of the process. He -says, "You tell me, Parmenides, of an overwhelming course of study; and -I do not well comprehend it. Give me an example of such an examination -of a Theory." "It is too great a labour," says he, "for one so old -as I am." "Well then, you, Zeno," says Socrates, "will you not give -us such an example?" Zeno answers, smiling, that they had better get -it from Parmenides himself; and joins in the petition of Socrates to -him, that he will instruct them. All the company unite in the request. -Parmenides compares himself to an aged racehorse, brought to the course -after long disuse, and trembling at the risk; but finally consents. -And as an example of a Theory to be examined, takes his own Doctrine, -that All Things are One, carrying on the Dialogue thenceforth, not -with Socrates, but with Aristoteles (not the Stagirite, but afterwards -one of the Thirty), whom he chooses as a younger and more manageable -respondent. - -The discussion of this Doctrine is of a very subtle kind, and it would -be difficult to make it intelligible to a modern reader. Nor is it -necessary for my purpose to attempt to do so. It is plain that the -discussion is intended seriously, as an example of true philosophy; and -each step of the process is represented as irresistible. The Respondent -has nothing to say but _Yes_; or _No_; _How so_? _Certainly_; _It does -appear_; _It does not appear_. The discussion is carried to a much -greater length than all the rest of the Dialogue; and the result of -the reasoning is summed up by Parmenides thus: "If One exist, it is -Nothing. Whether One exist or do not exist, both It and Other Things -both with regard to Themselves and to Each other, All and Everyway are -and are not, appear and appear not." And this also is fully assented -to; and so the Dialogue ends. - -I shall not pretend to explain the Doctrines there examined that One -exists, or One does not exist, nor to trace their consequences. But -these were Formulæ, as familiar in the Eleatic school, as Ideas in the -Platonic; and were undoubtedly regarded by the Megaric contemporaries -of Plato as quite worthy of being discussed, after the Theory of Ideas -had been overthrown. This, accordingly, appears to be the purport of -the Dialogue; and it is pursued, as we see, without any bitterness -toward Socrates or his disciples; but with a persuasion that they were -poor philosophers, conceited talkers, and weak disputants. - -The external circumstances of the Dialogue tend, I conceive, to confirm -this opinion, that it is not Plato's. The Dialogue begins, as the -_Republic_ begins, with the mention of a Cephalus, and two brothers, -Glaucon and Adimantus. But this Cephalus is not the old man of the -Piræus, of whom we have so charming a picture in the opening of the -_Republic_. He is from Clazomenæ, and tells us that his fellow-citizens -are great lovers of philosophy; a trait of their character which does -not appear elsewhere. Even the brothers Glaucon and Adimantus are not -the two brothers of Plato who conduct the Dialogue in the later books -of the _Republic_: so at least Ast argues, who holds the genuineness of -the Dialogue. This Glaucon and Adimantus are most wantonly introduced; -for the sole office they have, is to say that they have a half-brother -Antiphon, by a second marriage of their mother. No such half-brother of -Plato, and no such marriage of his mother, are noticed in other remains -of antiquity. Antiphon is represented as having been the friend of -Pythodorus, who was the host of Parmenides and Zeno, as we have seen. -And Antiphon, having often heard from Pythodorus the account of the -conversation of his guests with Socrates, retained it in his memory, or -in his tablets, so as to be able to give the full report of it which we -have in the Dialogue _Parmenides_[324]. To me, all this looks like a -clumsy imitation of the Introductions to the Platonic Dialogues. - -I say nothing of the chronological difficulties which arise -from bringing Parmenides and Socrates together, though they are -considerable; for they have been explained more or less satisfactorily; -and certainly in the _Theætetus_, Socrates is represented as saying -that he when very young had seen Parmenides who was very old[325]. -Athenæus, however[326], reckons this among Plato's fictions. -Schleiermacher gives up the identification and relation of the persons -mentioned in the Introduction as an unmanageable story. - -I may add that I believe Cicero, who refers to so many of Plato's -Dialogues, nowhere refers to the _Parmenides_. Athenæus does refer to -it; and in doing so blames Plato for his coarse imputations on Zeno -and Parmenides. According to our view, these are hostile attempts to -ascribe rudeness to Socrates or to Plato. Stallbaum acknowledges that -Aristotle nowhere refers to this Dialogue. - -FOOTNOTES: - -[Footnote 321: P. 116. "No amount of human knowledge can be adequate -which does not solve the phenomena of these absolute certainties."] - -[Footnote 322: Prof. Butler, Lect. ix. Second Series, p. 136, appears -to think that Plato had sufficient grounds (of a theological kind) for -the assumption of such Ideas; but I see no trace of them.] - -[Footnote 323: I am aware that this translation is different from the -common translation. It appears to me to be consistent with the habit -of the Greek language. It slightly leans in favour of my view; but I -do not conceive that the argument would be perceptibly weaker, if the -common interpretation were adopted.] - -[Footnote 324: In the _First Alcibiades_, Pythodorus is mentioned as -having paid 100 minæ to Zeno for his instructions (119 A).] - -[Footnote 325: P. 183 e.] - -[Footnote 326: _Deip._ xi. c. 15, p. 105.] - - -APPENDIX B. - -ON PLATO'S SURVEY OF THE SCIENCES. - -(_Cam. Phil. Soc._ APRIL 23, 1855.) - - -A survey by Plato of the state of the Sciences, as existing in his -time, may be regarded as hardly less interesting than Francis Bacon's -Review of the condition of the Sciences of _his_ time, contained in the -_Advancement of Learning_. Such a survey we have, in the seventh book -of Plato's _Republic_; and it will be instructive to examine what the -Sciences then were, and what Plato aspired to have them become; aiding -ourselves by the light afforded by the subsequent history of Science. - -In the first place, it is interesting to note, in the two writers, -Plato and Bacon, the same deep conviction that the large and profound -philosophy which they recommended, had not, in their judgment, been -pursued in an adequate and worthy manner, by those who had pursued it -at all. The reader of Bacon will recollect the passage in the _Novum -Organon_ (Lib. I. Aphorism 80) where he speaks with indignation of -the way in which philosophy had been degraded and perverted, by being -applied as a mere instrument of utility or of early education: "So that -the great mother of the Sciences is thrust down with indignity to the -offices of a handmaid;--is made to minister to the labours of medicine -or mathematics; or again, to give the first preparatory tinge to the -immature minds of youth[327]." - -In the like spirit, Plato says (_Rep._ VI. § 11, Bekker's ed.): - -"Observe how boldly and fearlessly I set about my explanation of my -assertion that philosophers ought to rule the world. For I begin by -saying, that the State must begin to treat the study of philosophy in a -way opposite to that now practised. Now, those who meddle at all with -this study are put upon it when they are children, between the lessons -which they receive in the farm-yard and in the shop[328]; and as soon -as they have been introduced to the hardest part of the subject, are -taken off from it, even those who get the most of philosophy. By the -hardest part, I mean, the discussion of principles--Dialectic[329]. -And in their succeeding years, if they are willing to listen to a -few lectures of those who make philosophy their business, they think -they have done great things, as if it were something foreign to the -business of life. And as they advance towards old age, with a very -few exceptions, philosophy in them is extinguished: extinguished far -more completely than the Heraclitean sun, for theirs is not lighted -up again, as that is every morning:" alluding to the opinion which -was propounded, by way of carrying the doctrine of the _unfixity_ of -sensible objects to an extreme; that the Sun is extinguished every -night and lighted again in the morning. In opposition to this practice, -Plato holds that philosophy should be the especial employment of men's -minds when their bodily strength fails. - -What Plato means by _Dialectic_, which he, in the next Book, calls the -highest part of philosophy, and which is, I think, what he here means -by the hardest part of philosophy, I may hereafter consider: but at -present I wish to pass in review the Sciences which he speaks of, as -leading the way to that highest study. These Sciences are Arithmetic, -Plane Geometry, Solid Geometry, Astronomy and Harmonics. - -The view in which Plato here regards the Sciences is, as the -instruments of that culture of the philosophical spirit which is -to make the philosopher the fit and natural ruler of the perfect -State--the Platonic Polity. It is held that to answer this purpose, the -mind must be instructed in something more stable than the knowledge -supplied by the senses;--a knowledge of objects which are constantly -changing, and which therefore can be no real permanent Knowledge, but -only Opinion. The real and permanent Knowledge which we thus require is -to be found in certain sciences, which deal with _truths necessary and -universal_, as we should now describe them: and which therefore are, -in Plato's language, a knowledge of that which really _is_[330]. - -This is the object of the Sciences of which Plato speaks. And hence, -when he introduces Arithmetic, as the first of the Sciences which are -to be employed in this mental discipline, he adds (VII. § 8) that -it must be not mere common Arithmetic, but a science which leads to -speculative truths[331], seen by Intuition[332]; not an Arithmetic -which is studied for the sake of buying and selling, as among tradesmen -and shopkeepers, but for the sake of pure and real Science[333]. - -I shall not dwell upon the details with which he illustrates this view, -but proceed to the other Sciences which he mentions. - -Geometry is then spoken of, as obviously the next Science in order; -and it is asserted that it really does answer the required condition -of drawing the mind from visible, mutable phenomena to a permanent -reality. Geometers indeed speak of their visible diagrams, as if their -problems were certain practical processes; to erect a perpendicular; to -construct a square: and the like. But this language, though necessary, -is really absurd. The figures are mere aids to their reasonings. -Their knowledge is really a knowledge not of visible objects, but of -permanent realities: and thus, Geometry is one of the helps by which -the mind may be drawn to Truth; by which the philosophical spirit may -be formed, which looks upwards instead of downwards. - -Astronomy is suggested as the Science next in order, but Socrates, the -leader of the dialogue, remarks that there is an intermediate Science -first to be considered. Geometry treats of plane figures; Astronomy -treats of solids in motion, that is, of spheres in motion; for the -astronomy of Plato's time was mainly the doctrine of the sphere. But -before treating of solids in motion, we must have a science which -treats of solids simply. After taking space of two dimensions, we must -take space of three dimensions, length, breadth and depth, as in cubes -and the like[334]. But such a Science, it is remarked, has not yet -been discovered. Plato "notes as deficient" this branch of knowledge; -to use the expression employed by Bacon on the like occasions in his -Review. Plato goes on to say, that the cultivators of such a science -have not received due encouragement; and that though scorned and -starved by the public, and not recommended by any obvious utility, it -has still made great progress, in virtue of its own attractiveness. - -In fact, researches in Solid Geometry had been pursued with great zeal -by Plato and his friends, and with remarkable success. The five Regular -Solids, the Tetrahedron or Pyramid, Cube, Octahedron, Dodecahedron -and Icosahedron, had been discovered; and the curious theorem, that -of Regular Solids there can be just so many, these and no others, -was known. The doctrine of these Solids was already applied in a -way, fanciful and arbitrary, no doubt, but ingenious and lively, to -the theory of the Universe. In the _Timæus_, the elements have these -forms assigned to them respectively. Earth has the Cube: Fire has the -Pyramid: Water has the Octahedron: Air has the Icosahedron: and the -Dodecahedron is the plan of the Universe itself. This application of -the doctrine of the Regular Solids shows that the knowledge of those -figures was already established; and that Plato had a right to speak -of Solid Geometry as a real and interesting Science. And that this -subject was so recondite and profound,--that these five Regular Solids -had so little application in the geometry which has a bearing on man's -ordinary thoughts and actions,--made it all the more natural for Plato -to suppose that these solids had a bearing on the constitution of the -Universe; and we shall find that such a belief in later times found a -ready acceptance in the minds of mathematicians who followed in the -Platonic line of speculation. - -Plato next proceeds to consider Astronomy; and here we have an amusing -touch of philosophical drama. Glaucon, the hearer and pupil in the -Dialogue, is desirous of showing that he has profited by what his -instructor had said about the real uses of Science. He says Astronomy -is a very good branch of education. It is such a very useful science -for seamen and husbandmen and the like. Socrates says, with a smile, -as we may suppose: "You are very amusing with your zeal for utility. -I suppose you are afraid of being condemned by the good people of -Athens for diffusing Useless Knowledge." A little afterwards Glaucon -tries to do better, but still with no great success. He says, "You -blamed me for praising Astronomy awkwardly: but now I will follow your -lead. Astronomy is one of the sciences which you require, because it -makes men's minds look upwards, and study things above. Any one can -see that." "Well," says Socrates, "perhaps any one can see it except -me--I cannot see it." Glaucon is surprised, but Socrates goes on: "Your -notice of 'the study of things above' is certainly a very magnificent -one. You seem to think that if a man bends his head back and looks at -the ceiling he 'looks upwards' with his mind as well as his eyes. You -may be right and I may be wrong: but I have no notion of any science -which makes the _mind_ look upwards, except a science which is about -the permanent and the invisible. It makes no difference, as to that -matter, whether a man gapes and looks up or shuts his mouth and looks -down. If a man merely look up and stare at sensible objects, his mind -does not look upwards, even if he were to pursue his studies swimming -on his back in the sea." - -The Astronomy, then, which merely looks at phenomena does not satisfy -Plato. He wants something more. What is it? as Glaucon very naturally -asks. - -Plato then describes Astronomy as a real science (§ 11). "The -variegated adornments which appear in the sky, the visible luminaries, -we must judge to be the most beautiful and the most perfect things of -their kind: but since they are mere visible figures, we must suppose -them to be far inferior to the true objects; namely, those spheres -which, with their real proportions of quickness and slowness, their -real number, their real figures, revolve and carry luminaries in their -revolutions. These objects are to be apprehended by reason and mental -conception, not by vision." And he then goes on to say that the varied -figures which the skies present to the eye are to be used as _diagrams_ -to assist the study of that higher truth; just as if any one were to -study geometry by means of beautiful diagrams constructed by Dædalus or -any other consummate artist. - -Here then, Plato points to a kind of astronomical science which goes -beyond the mere arrangement of phenomena: an astronomy which, it -would seem, did not exist at the time when he wrote. It is natural -to inquire, whether we can determine more precisely what kind of -astronomical science he meant, and whether such science has been -brought into existence since his time. - -He gives us some further features of the philosophical astronomy which -he requires. "As you do not expect to find in the most exquisite -geometrical diagrams the true evidence of quantities being equal, or -double, or in any other relation: so the true astronomer will not think -that the proportion of the day to the month, or the month to the year, -and the like, are real and immutable things. He will seek a deeper -truth than these. We must treat Astronomy, like Geometry, as a series -of problems suggested by visible things. We must apply the intelligent -portion of our mind to the subject." - -Here we really come in view of a class of problems which astronomical -speculators at certain periods have proposed to themselves. What is the -real ground of the proportion of the day to the month, and of the month -to the year, I do not know that any writer of great name has tried to -determine: but to ask the reason of these proportions, namely, that of -the revolution of the earth on its axis, of the moon in its orbit, and -of the earth in its orbit, are questions just of the same kind as to -ask the reason of the proportion of the revolutions of the planets in -their orbits, and of the proportion of the orbits themselves. Now who -has attempted to assign such reasons? - -Of course we shall answer, Kepler: not so much in the Laws of the -Planetary motions which bear his name, as in the Law which at an -earlier period he thought he had discovered, determining the proportion -of the distances of the several Planets from the Sun. And, curiously -enough, this solution of a problem which we may conceive Plato to have -had in his mind, Kepler gave by means of the Five Regular Solids which -Plato had brought into notice, and had employed in his theory of the -Universe given in the _Timæus_. - -Kepler's speculations on the subject just mentioned were given to the -world in the _Mysterium Cosmographicum_ published in 1596. In his -Preface, he says "In the beginning of the year 1595 I brooded with -the whole energy of my mind on the subject of the Copernican system. -There were three things in particular of which I pertinaciously sought -the causes; why they are not other than they are: the number, the -size, and the motion of the orbits." We see how strongly he had his -mind impressed with the same thought which Plato had so confidently -uttered: that there must be some reason for those proportions in the -scheme of the Universe which appear casual and vague. He was confident -at this period that he had solved two of the three questions which -haunted him;--that he could account for the number and the size of the -planetary orbits. His account was given in this way.--"The orbit of -the Earth is a circle; round the sphere to which this circle belongs -describe a dodecahedron; the sphere including this will give the orbit -of Mars. Round Mars inscribe a tetrahedron; the circle including this -will be the orbit of Jupiter. Describe a cube round Jupiter's orbit; -the circle including this will be the orbit of Saturn. Now inscribe in -the Earth's orbit an icosahedron: the circle inscribed in it will be -the orbit of Venus. Inscribe an octahedron in the orbit of Venus; the -circle inscribed in it will be Mercury's orbit. This is the reason of -the number of the planets;" and also of the magnitudes of their orbits. - -These proportions were only approximations; and the Rule thus asserted -has been shown to be unfounded, by the discovery of new Planets. This -Law of Kepler has been repudiated by succeeding Astronomers. So far, -then, the Astronomy which Plato requires as a part of true philosophy -has not been brought into being. But are we thence to conclude -that the demand for such a kind of Astronomy was a mere Platonic -imagination?--was a mistake which more recent and sounder views have -corrected? We can hardly venture to say that. For the questions which -Kepler thus asked, and which he answered by the assertion of this -erroneous Law, are questions of exactly the same kind as those which -he asked and answered by means of the true Laws which still fasten his -name upon one of the epochs of astronomical history. If he was wrong -in assigning reasons for the number and size of the planetary orbits, -he was right in assigning a reason for the proportion of the motions. -This he did in the _Harmonice Mundi_, published in 1619: where he -established that the squares of the periodic times of the different -Planets are as the cubes of their mean distances from the central Sun. -Of this discovery he speaks with a natural exultation, which succeeding -astronomers have thought well founded. He says: "What I prophesied -two and twenty years ago as soon as I had discovered the five solids -among the heavenly bodies; what I firmly believed before I had seen -the _Harmonics_ of Ptolemy; what I promised my friends in the title of -this book (_On the perfect Harmony of the celestial motions_), which -I named before I was sure of my discovery; what sixteen years ago I -regarded as a thing to be sought; that for which I joined Tycho Brahe, -for which I settled in Prague, for which I devoted the best part of my -life to astronomical contemplations; at length I have brought to light, -and have recognized its truth beyond my most sanguine expectations." -(_Harm. Mundi_, Lib. V.) - -Thus the Platonic notion, of an Astronomy which deals with doctrines -of a more exact and determinate kind than the obvious relations of -phænomena, may be found to tend either to error or to truth. Such -aspirations point equally to the five regular solids which Kepler -imagined as determining the planetary orbits, and to the Laws of -Kepler in which Newton detected the effect of universal gravitation. -The realities which Plato looked for, as something incomparably more -real than the visible luminaries, are found, when we find geometrical -figures, epicycles and eccentrics, laws of motion and laws of force, -which explain the appearances. His Realities are Theories which account -for the Phenomena, Ideas which connect the Facts. - -But, is Plato right in holding that such Realities as these are _more -real_ than the Phenomena, and constitute an Astronomy of a higher kind -than that of mere Appearances? To this we shall, of course, reply -that Theories and Facts have each their reality, but that these are -realities of different kinds. Kepler's Laws are as real as day and -night; the force of gravity tending to the Sun is as real as the Sun; -but not more so. True Theories and Facts are equally real, for true -Theories _are_ Facts, and Facts are familiar Theories. Astronomy is, as -Plato says, a series of Problems suggested by visible Things; and the -Thoughts in our own minds which bring the solutions of these Problems, -have a reality in the Things which suggest them. - -But if we try, as Plato does, to separate and oppose to each other the -Astronomy of Appearances and the Astronomy of Theories, we attempt that -which is impossible. There are no Phenomena which do not exhibit some -Law; no Law can be conceived without Phenomena. The heavens offer a -series of Problems; but however many of these Problems we solve, there -remain still innumerable of them unsolved; and these unsolved Problems -have solutions, and are not different in kind from those of which the -extant solution is most complete. - -Nor can we justly distinguish, with Plato, Astronomy into transient -appearances and permanent truths. The theories of Astronomy are -permanent, and are manifested in a series of changes: but the change is -perpetual just _because_ the theory is permanent. The perpetual change -_is_ the permanent theory. The perpetual changes in the positions -and movements of the planets, for instance, manifest the permanent -machinery: the machinery of cycles and epicycles, as Plato would -have said, and as Copernicus would have agreed; while Kepler, with a -profound admiration for both, would have asserted that the motions -might be represented by ellipses, more exactly, if not more truly. The -cycles and epicycles, or the ellipses, are as real as space and time, -_in_ which the motions take place. But we cannot justly say that space -and time and motion are more real than the bodies which move in space -and time, or than the appearances which these bodies present. - -Thus Plato, with his tendency to exalt Ideas above Facts,--to find a -Reality which is more real than Phenomena,--to take hold of a permanent -Truth which is more true than truths of observation,--attempts what -is impossible. He tries to separate the poles of the Fundamental -Antithesis, which, however antithetical, are inseparable. - -At the same time, we must recollect that this tendency to find a -Reality which is something beyond appearance, a permanence which is -involved in the changes, is the genuine spring of scientific discovery. -Such a tendency has been the cause of all the astronomical science -which we possess. It appeared in Plato himself, in Hipparchus, in -Ptolemy, in Copernicus, and most eminently in Kepler; and in him -perhaps in a manner more accordant with Plato's aspirations when he -found the five Regular Solids in the Universe, than when he found there -the Conic Sections which determine the form of the planetary orbits. -The pursuit of this tendency has been the source of the mighty and -successful labours of succeeding astronomers: and the anticipations of -Plato on this head were more true than he himself could have conceived. - -When the above view of the nature of true astronomy has been proposed, -Glaucon says: - -"That would be a task much more laborious than the astronomy now -cultivated." Socrates replies: "I believe so: and such tasks must be -undertaken, if our researches are to be good for anything." - -After Astronomy, there comes under review another Science, which is -treated in the same manner. It is presented as one of the Sciences -which deal with real abstract truth; and which are therefore suited to -that development of the philosophic insight into the highest truth, -which is here Plato's main object. This Science is _Harmonics_, the -doctrine of the mathematical relations of musical sounds. Perhaps -it may be more difficult to explain to a general audience, Plato's -views on this than on the previous subjects: for though Harmonics is -still acknowledged as a Science including the mathematical truths to -which Plato here refers, these truths are less generally known than -those of geometry or astronomy. Pythagoras is reported to have been -the discoverer of the cardinal proposition in this Mathematics of -Music:--namely, that the musical notes which the ear recognizes as -having that definite and harmonious relation which we call an _octave_, -a _fifth_, a _fourth_, a _third_, have also, in some way or other, the -numerical relation of 2 to 1, 3 to 2, 4 to 3, 5 to 4. I say "some way -or other," because the statements of ancient writers on this subject -are physically inexact, but are right in the essential point, that -those simple numerical ratios are characteristic of the most marked -harmonic relations. The numerical ratios really represent the rate of -vibration of the air when those harmonics are produced. This perhaps -Plato did not know: but he knew or assumed that those numerical ratios -were cardinal truths in harmony: and he conceived that the exactness -of the ratios rested on grounds deeper and more intellectual than any -testimony which the ear could give. This is the main point in his mode -of applying the subject, which will be best understood by translating -(with some abridgement) what he says. Socrates proceeds: - -(§ 11 near the end.) "Motion appears in many aspects. It would take a -very wise man to enumerate them all: but there are two obvious kinds. -One which appears in astronomy, (the revolutions of the heavenly -bodies,) and another which is the echo of that[335]. As the eyes are -made for Astronomy, so are the ears made for the motion which produces -Harmony[336]: and thus we have two sister sciences, as the Pythagoreans -teach, and we assent. - -(§ 12.) "To avoid unnecessary labour, let us first learn what _they_ -can tell us, and see whether anything is to be added to it; retaining -our own view on such subjects: namely this:--that those whose education -we are to superintend--real philosophers--are never to learn any -imperfect truths:--anything which does not tend to that point (exact -and permanent truth) to which all our knowledge ought to tend, as we -said concerning astronomy. Now those who cultivate music take a very -different course from this. You may see them taking immense pains in -measuring musical notes and intervals by the ear, as the astronomers -measure the heavenly motions by the eye. - -"Yes, says Glaucon, they apply their ears close to the instrument, as -if they could catch the note by getting near to it, and talk of some -kind of recurrences[337]. Some say they can distinguish an interval, -and that this is the smallest possible interval, by which others are to -be measured; while others say that the two notes are identical: both -parties alike judging by the ear, not by the intellect. - -"You mean, says Socrates, those fine musicians who torture their -notes, and screw their pegs, and pinch their strings, and speak of the -resulting sounds in grand terms of art. We will leave them, and address -our inquiries to our other teachers, the Pythagoreans." - -The expressions about the small interval in Glaucon's speech appear to -me to refer to a curious question, which we know was discussed among -the Greek mathematicians. If we take a keyed instrument, and ascend -from a key note by two _octaves_ and a _third_, (say from _A__{1} to -_C__{3}) we arrive at the _same nominal note_, as if we ascend four -times by a _fifth_ (_A__{1} to _E__{1}, _E__{1} to _B__{2}, _B__{2} -to _F__{2}, _F__{2} to _C__{3}). Hence one party might call this the -_same_ note. But if the Octaves, Fifths, and Third be perfectly true -intervals, the notes arrived at in the two ways will not be really -the same. (In the one case, the note is ½ × ½ × ⅘; in the other -⅔ × ⅔ × ⅔ × ⅔; which are ⅕ and 16/81, or in the ratio of -81 to 80). This small interval by which the two notes really differ, -the Greeks called a _Comma_, and it was the smallest musical interval -which they recognized. Plato disdains to see anything important in this -controversy; though the controversy itself is really a curious proof -of his doctrine, that there is a mathematical truth in Harmony, higher -than instrumental exactness can reach. He goes on to say: - - "The musical teachers are defective in the same way as the - astronomical. They do indeed seek numbers in the harmonic notes, which - the ear perceives: but they do not ascend from them to the Problem, - What are harmonic numbers and what are not, and what is the reason of - each[338]?" "That", says Glaucon, "would be a sublime inquiry." - -Have we in Harmonics, as in Astronomy, anything in the succeeding -History of the Science which illustrates the tendency of Plato's -thoughts, and the value of such a tendency? - -It is plain that the tendency was of the same nature as that which -induced Kepler to call his work on Astronomy _Harmonice Mundi_; and -which led to many of the speculations of that work, in which harmonical -are mixed with geometrical doctrines. And if we are disposed to judge -severely of such speculations, as too fanciful for sound philosophy, we -may recollect that Newton himself seems to have been willing to find an -analogy between harmonic numbers and the different coloured spaces in -the spectrum. - -But I will say frankly, that I do not believe there really exists any -harmonical relation in either of these cases. Nor can the problem -proposed by Plato be considered as having been solved since his -time, any further than the recurrence of vibrations, when their -ratios are so simple, may be easily conceived as affecting the ear -in a peculiar manner. The imperfection of musical scales, which the -_comma_ indicates, has not been removed; but we may say that, in the -case of this problem, as in the other ultimate Platonic problems, -the duplication of the cube and the quadrature of the circle, the -impossibility of a solution has been already established. The problem -of a perfect musical scale is impossible, because no power of 2 can -be equal to a power of 3; and if we further take the multiplier 5, of -course it also cannot bring about an exact equality. This impossibility -of a perfect scale being recognized, the practical problem is what is -the system of _temperament_ which will make the scale best suited for -musical purposes; and this problem has been very fully discussed by -modern writers. - - -FOOTNOTES: - -[Footnote 327: Accedit et illud quod naturalis philosophia in iis ipsis -viris, qui ei incubuerunt, vacantem et integrum hominem, præsertim -his recentioribus temporibus, vix nacta sit; nisi forte quis monachi -alicujus in cellula, aut nobilis in villula lucubrantis, exemplum -adduxerit; sed facta est demum naturalis philosophia instar transitus -cujusdam et pontisternii ad alia. Atque magna ista scientiarum mater -ad officia ancillæ detrusa est; quæ medicinæ aut mathematicis operibus -ministrat, et rursus quæ adolescentium immatura ingenia lavat et imbuat -velut tinctura quadam prima, ut aliam postea felicius et commodius -excipiant.] - -[Footnote 328: μεταξὺ οἰκονομίας καὶ χρεματισμοῦ, between house-keeping -and money-getting.] - -[Footnote 329: τὸ περὶ τοὺς λόγους.] - -[Footnote 330: The Sciences are to draw the mind from that which grows -and perishes to that which really is: μάθημα ψυχῆς ὁλκὸν ἀπὸ τοῦ -γιγνομένου ἐπι τὸ ὅν.] - -[Footnote 331: ἐπὶ θέαν τῆς τῶν ἀριθμῶν φύσεως.] - -[Footnote 332: τῇ νοηήσει αὐτῇ.] - -[Footnote 333: He adds "and for the sake of war;" this point I have -passed by. Plato does not really ascribe much weight to this use of -Science, as we see in what he says of Geometry and Astronomy.] - -[Footnote 334: ἀρθῶς ἕχει ἑξῆς μετὰ δευτέραν αὕξην τρίτην λαμβάνειν, -ἕστι δέ που τοῦτο περὶ τὴν τῶν κύβων αύξην καὶ τὸ βάθους μέτεχον.] - -[Footnote 335: ἀντίστροφον αὐτοῦ.] - -[Footnote 336: πρὸς ἐναρμόνιον φορὰν ὦτα παγῆναι.] - -[Footnote 337: πυκνώματα ἄ ττα.] - -[Footnote 338: τίνες ξύμφωνοι ἀριθμοὶ, &c.] - - -APPENDIX BB. - -ON PLATO'S NOTION OF DIALECTIC. - -(_Cam. Phil. Soc._ MAY 7, 1855.) - - -The survey of the sciences, arithmetic, plane geometry, solid geometry, -astronomy and harmonics--which is contained in the seventh Book of -the Republic (§ 6-12), and which has been discussed in the preceding -paper, represents them as instruments in an education, of which the -end is something much higher--as steps in a progression which is to go -further. "Do you not know," says Socrates (§ 12), "that all this is -merely a prelude to the strain which we have to learn?" And what that -strain is, he forthwith proceeds to indicate. "That these sciences -do not suffice, you must be aware: for--those who are masters of -such sciences--do they seem to you to be good in dialectic? δεινοὶ -διαλεκτικοὶ εἷναι;" - -"In truth, says Glaucon, they are not, with very few exceptions, so far -as I have fallen in with them." - -"And yet, said I, if persons cannot give and receive a reason, they -cannot attain that knowledge which, as we have said, men ought to have." - -Here it is evident that "to give and to receive a reason," is a -phrase employed as coinciding, in a general way at least, with being -"good in dialectic;" and accordingly, this is soon after asserted in -another form, the verb being now used instead of the adjective. "It is -dialectic discussion τὸ διαλέγεσθαι, which executes the strain which we -have been preparing." It is further said that it is a progress to clear -intellectual light, which corresponds to the progress of bodily vision -in proceeding from the darkened cave described in the beginning of the -Book to the light of day. This progress, it is added, of course you -call _Dialectic_ διαλεκτικήν. - -Plato further says, that other sciences cannot properly be called -sciences. They begin from certain assumptions, and give us only the -consequences which follow from reasoning on such assumptions. But these -assumptions they cannot prove. To do so is not in the province of -each science. It belongs to a higher science: to the science of Real -Existences. You call the man Dialectical, who requires a reason of the -essence of each thing[339]. - -And as Dialectic gives an account of other real existences, so does -it of that most important reality, the true guide of Life and of -Philosophy, the Real Good. He who cannot follow this through all the -windings of the battle of Life, knows nothing to any purpose. And -thus Dialectic is the pinnacle, the top stone of the edifice of the -sciences[340]. - -Dialectic is here defined or described by Plato according to the -_subject_ with which it treats, and the _object_ with which it is to -be pursued: but in other parts of the Platonic Dialogues, Dialectic -appears rather to imply a certain _method_ of investigation;--to -describe the _form_ rather than the _matter_ of discussion; and it will -perhaps be worth while to compare these different accounts of Dialectic. - -(_Phædrus._) One of the cardinal passages on this Point is in the -Phædrus, and may be briefly quoted. Phædrus, in the Dialogue which -bears his name, appears at first as an admirer of Lysias, a celebrated -writer of orations, the contemporary of Plato. In order to expose this -writer's style of composition as frigid and shallow, a specimen of it -is given, and Socrates not only criticises this, but delivers, as rival -compositions, two discourses on the same subject. Of these discourses, -given as the inspiration of the moment, the first is animated and -vigorous; the second goes still further, and clothes its meaning in a -gorgeous dress of poetical and mythical images. Phædrus acknowledges -that his favourite is outshone; and Socrates then proceeds to point -out that the real superiority of his own discourse consists in its -having a dialectical structure, beneath its outward aspect of imagery -and enthusiasm. He says: (§ 109, Bekker. It is to be remembered that -the subject of all the discourses was _Love_, under certain supposed -conditions.) - -"The rest of the performance may be taken as play: but there were, in -what was thus thrown out by a random impulse, two features, of which, -if any one could reduce the effect to an art, it would be a very -agreeable and useful task. - -"What are they? Phædrus asks. - -"In the first place, Socrates replies, the taking a connected view of -the scattered elements of a subject, so as to bring them into one -Idea; and thus to give a definition of the subject, so as to make it -clear what we are speaking of; as was then done in regard to _Love_. -A definition was given of it, what it is: whether the definition was -good or bad, at any rate there was a definition. And hence, in what -followed, we were able to say what was clear and consistent with itself. - -"And what, Phædrus asks, was the other feature? - -"The dividing the subject into kinds or elements, according to the -nature of the thing itself:--not breaking its natural members, like a -bad carver who cannot hit the joint. So the two discourses which we -have delivered, took the irrational part of the mind, as their common -subject; and as the body has two different sides, the right and the -left, with the same names for its parts; so the two discourses took -the irrational portion of man; and the one took the left-hand portion, -and divided this again, and again subdivided it, till, among the -subdivisions, it found a left-handed kind of Love, of which nothing -but ill was to be said. While the discourse that followed out the -right-hand side of phrenzy, (the irrational portion of man's nature,) -was led to something which bore the name of _Love_ like the other, -but which is divine, and was praised as the source of the greatest -blessing." - -"Now I," Socrates goes on to say, "am a great admirer of these -processes of division and comprehension, by which I endeavour to speak -and to think correctly. And if I can find any one who is able to see -clearly what is by nature reducible to one and manifested in many -elements, I follow his footsteps as a divine guide. Those who can do -this, I call--whether rightly or not, God knows--but I have hitherto -been in the habit of calling them _dialectical_ men." - -It is of no consequence to our present purpose whether either of the -discourses of Socrates in the Phædrus, or the two together, as is here -assumed, do contain a just division and subdivision of that part of the -human soul which is distinguishable from Reason, and do thus exhibit, -in its true relations, the affection of Love. It is evident that -division and subdivision of this kind is here presented as, in Plato's -opinion, a most valuable method; and those who could successfully -practise this method are those whom he admires as dialectical men. This -is here his _Dialectic_. - -(_Sophistes._) We are naturally led to ask whether this method of -dividing a subject as the best way of examining it, be in any other -part of the Platonic Dialogues more fully explained than it is in the -Phædrus; or whether any rules are given for this kind of Dialectic. - -To this we may reply, that in the Dialogue entitled _The Sophist_, a -method of dividing a subject, in order to examine it, is explained -and exemplified with extraordinary copiousness and ingenuity. The -object proposed in that Dialogue is, to define what a Sophist is; -and with that view, the principal speaker, (who is represented as an -Eleatic stranger,) begins by first exemplifying what is his method of -framing a definition, and by applying it to define an _Angler_. The -course followed, though it now reads like a burlesque of philosophical -methods, appears to have been at that time a _bona fide_ attempt to be -philosophical and methodical. It proceeds thus: - -"We have to inquire concerning _Angling_. Is it an Art? It is. Now -what kind of art? All art is an art of making or an art of getting: -(_Poietic_ or _Ktetic_.) It is Ktetic. Now the art of getting, is -the art of getting by exchange or by capture: (_Metabletic_ or -_Chirotic_.) Getting by capture is by contest or by chase: (_Agonistic_ -or _Thereutic_.) Getting by chase is a chase of lifeless or of living -things: (the first has no name, the second is _Zootheric_.) The chase -of living things is the chase of land animals or of water animals: -(_Pezotheric_ or _Enygrotheric_.) Chase of water animals is of birds -or of fish: (_Ornithothereutic_ and _Halieutic_.) Chase of fish is by -inclosing or by striking them: (_Hercotheric_ or _Plectic_.) We strike -them by day with pointed instruments, or by night, using torches: -(hence the division _Ankistreutic_ and _Pyreutic_.) Of Ankistreutic, -one kind consists in spearing the fish downwards from above, the other -in twitching them upwards from below: (these two arts are _Triodontic_ -and _Aspalieutic_.) And thus we have, what we sought, the notion and -the description of angling: namely that it is a Ktetic, Chirotic, -Thereutic, Zootheric, Enygrotheric, Halieutic, Plectic, Ankistreutic, -Aspalieutic Art." - -Several other examples are given of this ingenious mode of definition, -but they are all introduced with reference to the definition of the -Sophist. And it will further illustrate this method to show how, -according to it, the Sophist is related to the Angler. - -The Sophistical Art is an art of getting, by capture, living things, -namely men. It is thus a Ktetic, Chirotic, Thereutic art, and so far -agrees with that of the Angler. But here the two arts diverge, since -that of the Sophist is Pezotheric, that of the Angler Enygrotheric. -To determine the Sophist still more exactly, observe that the chase -of land animals is either of tame animals (including man) or of -wild animals: (_Hemerotheric_ and _Agriotheric_.) The chase of tame -animals is either by violence, (as kidnapping, tyranny, and war in -general,) or by persuasion, (as by the arts of speech;) that is, it -is _Biaiotheric_ or _Pithanurgic_. The art of persuasion is a private -or a public proceeding: (_Idiothereutic_ or _Demosiothereutic_.) -The art of private persuasion is accompanied with the giving of -presents, (as lovers do,) or with the receiving of pay: (thus it is -_Dorophoric_ or _Mistharneutic_.) To receive pay as the result of -persuasion, is the course, either of those who merely earn their bread -by supplying pleasure, namely flatterers, whose art is _Hedyntic_; -or of those who profess for pay to teach virtue. And who are they? -Plainly the Sophists. And thus _Sophistic_ is that kind of Ktetic, -Chirotic, Thereutic, Zootheric, Pezotheric, Hemerotheric, Pithanurgic, -Idiothereutic, Mistharneutic art, which professes to teach virtue, and -takes money on that account. - -The same process is pursued along several other lines of inquiry: and -at the end of each of them the Sophist is detected, involved in a -number of somewhat obnoxious characteristics. This process of division -it will be observed, is at every step bifurcate, or as it is called, -_dichotomous_. Applied as it is in these examples, it is rather the -vehicle of satire than of philosophy. Yet, I have no doubt that this -bifurcate method was admired by some of the philosophers of Plato's -time, as a clever and effective philosophical invention. We may the -more readily believe this, inasmuch as one of the most acute persons -of our own time, who has come nearer than any other to the ancient -heads of sects in the submission with which his followers have accepted -his doctrines, has taken up this Dichotomous Method, and praised it -as the only philosophical mode of dividing a subject. I refer to Mr. -Jeremy Bentham's _Chrestomathia_ (published originally in 1816), in -which this exhaustive bifurcate method, as he calls it, was applied -to classify sciences and arts, with a view to a scheme of education. -How exactly the method, as recommended by him, agrees with the method -illustrated in the _Sophist_, an examination of any of his examples -will show. Thus to take Mineralogy as an example: according to Bentham, -Ontology is Cœnoscopic or Idioscopic: the Idioscopic is Somatoscopic -or Pneumatoscopic; the Somatoscopic is Pososcopic or Poioscopic: -Poioscopic is Physiurgoscopic or Anthropurgoscopic: Physiurgoscopic is -Uranoscopic or Epigeoscopic: Epigeoscopic is Abioscopic or Embioscopic. -And thus Mineralogy is the Science Idioscopic, Somatoscopic, -Poioscopic, Physiurgoscopic, Epigeoscopic, Abioscopic: inasmuch as -it is the science which regards bodies, with reference to their -qualities,--bodies, namely, the works of nature, terrestrial, lifeless. - -I conceive that this bifurcate method is not really philosophical or -valuable: but that is not our business here. What we have to consider -is whether this is what Plato meant by the term _Dialectic_. - -The general description of Dialectic in the _Sophistes_ agrees very -closely with that quoted from the _Phædrus_, that it is the separation -of a subject according to its natural divisions. - -Thus, see in the Sophist the passage § 83: "To divide a subject -according to the kinds of things, so as neither to make the same -kind different nor different kinds identical, is the office of the -Dialectical Science." And this is illustrated by observing that it is -the office of the science of Grammar to determine what letters may be -combined and what may not; it is the office of the science of Music to -determine what sounds differing as acute and grave, may be combined, -and what may not: and in like manner it is the office of the science of -Dialectic to determine what _kinds_ may be combined in one subject and -what may not. And the proof is still further explained. - -In many of the Platonic Dialogues, the Dialectic which Socrates is thus -represented as approving, appears to include the form of Dialogue, -as well as the subdivision of the subject into its various branches. -Socrates is presented as attaching so much importance to this form, -that in the Protagoras (§ 65) he rises to depart, because his opponent -will not conform to this practice. And generally in Plato, Dialectic is -opposed to Rhetoric, as a string of short questions and answers to a -continuous dissertation. - -Xenophon also seems to imply (_Mem._ IV. 5, 11) that Socrates included -in his notion of Dialectic the form of Dialogue as well as the division -of the subject. - -But that the method of close Dialogue was not called _Dialectic_ by -the author of the _Sophist_, we have good evidence in the work itself. -Among other notions which are analysed by the bifurcate division here -exhibited, is that of getting by contest (_Agonistic_, previously given -as a division of _Ktetic_). Now getting by contest may be by peaceful -trial of superiority, or by fight: (_Hamilletic_ or _Machelic_). The -fight may be of body against body, or of words against words: these -may be called _Biastic_ and _Amphisbetic_. The fight of words about -right and wrong, may be by long discourses opposed to each other, as -in judicial cases; or by short questions and answers: the former may -be called _Dicanic_, the latter _Antilogic_. Of these colloquies, -about right and wrong, some are natural and spontaneous, others -artificial and studied: the former need no special name; the latter are -commonly called _Eristic_. Of Eristic colloquies, some are a source -of expense to those who hold them, some of gain: that is, they are -_Chrematophthoric_ or _Chrematistic_: the former, the occupation of -those who talk for pleasure's and for company's sake, is _Adoleschic_, -wasteful garrulity; the latter, that of those who talk for the sake -of gain, is _Sophistic_. And thus Sophistic is an art Eristic, which -is part of Antilogic, which is part of Amphisbetic, which is part of -Agonistic, which is part of Chirotic, which is a part of Ktetic. (§ 23.) - -We may notice here an indication that satire rather than exact reason -directs these analyses; in that Sophistic, which was before a part of -the _thereutic_ branch of _chirotic_ and _ktetic_, is here a part of -the other branch, _agonistic_. - -But the remark which I especially wish to make here is, that the art of -discussing points of right and wrong by short questions and answers, -being here brought into view, is not called _Dialectic_, which we -might have expected; but _Antilogic_. It would seem therefore that the -Author of the Sophist did not understand by _Dialectic_ such a process -as Socrates describes in Xenophon; (_Mem._ IV. 5, 11, 12;) where he -says it was called _Dialectic_, because it was followed by persons -_dividing things into their kinds in conversation_: (κοινῇ βουλεύεσθαι -διαλέγοντας:)or such as the Socrates of Plato insisted upon in the -Protagoras and the Gorgias. Of the two elements which the Dialectical -Process of Socrates implied, Division of the subject and Dialogue, the -author of the _Sophistes_ does not claim the name of _Dialectic_ for -either, and seems to reject it for the second. - -But without insisting upon the name, are we to suppose that the -Dichotomous Method of the _Sophistes_ Dialogue, (I may add of the -_Politicus_, for the method is the same in this Dialogue also,) is the -method of division of a subject according to its natural members, of -which Plato speaks in the _Phædrus_? - -If the _Sophistes_ be the work of Plato, the answer is difficult either -way. If this method be Plato's _Dialectic_, how came he to omit to say -so there? how came he even to seem to deny it? But on the other hand, -if this dichotomous division be a different process from the division -called _Dialectic_ in the Phædrus, had Plato two methods of division of -a subject? and yet has he never spoken of them as two, or marked their -distinction? - -This difficulty would be removed if we were to adopt the opinion, to -which others, on other grounds, have been led, that the Sophistes, -though of Plato's time, is not Plato's work. The grounds of this -opinion are,--that the doctrines of the Sophistes are not Platonic: -(the doctrine of Ideas is strongly impugned and weakly defended:) -Socrates is not the principal speaker, but an Eleatic stranger: and -there is, in the Dialogue, none of the dramatic character which we -generally have in Plato. The Dialogue seems to be the work of some -Eleatic opponent of Plato, rather than his. - -(_Rep._ B. VII.) But we can have no doubt that the _Phædrus_ contains -Plato's real view of the nature of Dialectic, as to its form; let us -see how this agrees with the view of Dialectic, as to its matter and -object, given in the seventh Book of the _Republic_. - -According to Plato, Real Existences are the objects of the exact -sciences (as number and figure, of Arithmetic and Geometry). The things -which are the objects of sense transitory phenomena, which have no -reality, because no permanence. Dialectic deals with Realities in a -more general manner. This doctrine is everywhere inculcated by Plato, -and particularly in this part of the _Republic_. He does not tell us -how we are to obtain a view of the higher realities, which are the -objects of Dialectic: only he here assumes that it will result from -the education which he enjoins. He says (§ 13) that the Dialectic -Process (ἡ διαλεκτικὴ μέθοδος) alone leads to true science: it makes -no assumptions, but goes to First Principles, that its doctrines may -be firmly grounded: and thus it purges the eye of the soul, which was -immersed in barbaric mud, and turns it upward; using for this purpose -the aid of the sciences which have been mentioned. But when Glaucon -inquires about the details of this Dialectic, Socrates says he will not -then answer the inquiry. We may venture to say, that it does not appear -that he had any answer ready. - -Let us consider for a moment what is said about a philosophy rendering -a reason for the First Principles of each Science, which the Science -itself cannot do. That there is room for such a branch of philosophy -in some sciences, we easily see. Geometry, for instance, proceeds -from Axioms, Definitions and Postulates; but by the very nature of -these terms, does not prove these First Principles. These--the Axioms, -Definitions and Postulates,--are, I conceive, what Plato here calls the -_Hypotheses_ upon which Geometry proceeds, and for which it is not the -business of Geometry to render a reason. According to him, it is the -business of "Dialectic" to give a just account of these "Hypotheses." -What then is _Dialectic?_ - -(_Aristotle._) It is, I think, well worthy of remark, that Aristotle, -giving an account in many respects different from that of Plato, of -the nature of Dialectic, is still led in the same manner to consider -Dialectic as the branch of philosophy which renders a reason for First -Principles. In the _Topics_, we have a distinction drawn between -reasoning demonstrative, and reasoning dialectical: and the distinction -is this:--(_Top_. I. 1) that demonstration is by syllogisms from true -first principles, or from true deductions from such principles; and -that the Dialectical Syllogism is that which syllogizes from probable -propositions (ἠξ ἠνδόξων). And he adds that probable propositions are -those which are accepted by all, or by the greatest part, or by the -wise. In the next chapter, he speaks of the uses of Dialectic, which, -he says, are three, mental discipline, debates, and philosophical -science. And he adds (_Top_. I. 2, 6) that it is also useful with -reference to the First Principles in each Science: for from the -appropriate Principles of each science we cannot deduce anything -concerning First Principles, since these principles are the beginning -of reasoning. But from the probable principles in each province of -science we must reason concerning First Principles: and this is either -the peculiar office of Dialectic, or the office most appropriate to it; -for it is a process of investigation, and must lead to the Principles -of all methods. - -That a demonstrative science, as such, does not explain the origin -of its own First Principles, is undoubtedly true. Geometry does not -undertake to give a reason for the Axioms, Definitions, and Postulates. -This has been attempted, both in ancient and in modern times, by the -Metaphysicians. But the Metaphysics employed on such subjects has not -commonly been called Dialectic. The term has certainly been usually -employed rather as describing a Method, than as determining the subject -of investigation. Of the Faculty which apprehends First Principles, -both according to Plato and to Aristotle, I will hereafter say a few -words. - -The object of the dichotomous process pursued in the Sophistes, and -its result in each case, is a Definition. Definition also was one of -the main features of the inquiries pursued by Socrates, Induction -being the other; and indeed in many cases Induction was a series of -steps which ended in Definition. And Aristotle also taught a peculiar -method, the object and result of which was the construction of -Definitions:--namely his _Categories_. This method is one of division, -but very different from the divisions of the Sophistes. His method -begins by dividing the whole subject of possible inquiry into ten heads -or _Categories_--Substance, Quantity, Quality, Relation, Place, Time, -Position, Habit, Action, Passion. These again are subdivided: thus -Quality is Habit or Disposition, Power, Affection, Form. And we have -an example of the application of this method to the construction of a -Definition in the Ethics; where he determines Virtue to be a Habit with -certain additional limitations. - -Thus the Induction of Socrates, the Dichotomy of the Eleatics, the -Categories of Aristotle, may all be considered as methods by which we -proceed to the construction of Definitions. If, by any method, Plato -could proceed to the construction of a Definition, or rather of an -Idea, of the Absolute Realities on which First Principles depend, -such a method would correspond with the notion of Dialectic in the -_Republic_. And if it was a method of division like the Eleatic or -Aristotelic, it would correspond with the notion of Dialectic in the -_Phædrus_. - -That Plato's notion, however, cannot have been exactly either of these -is, I think, plain. The colloquial method of stimulating and testing -the progress of the student in Dialectic is implied, in the sequel -of this discussion of the effect of scientific study. And the method -of Dialogue, as the instrument of instruction, being thus supposed, -the continuation of the account in the _Republic_, implies that Plato -expected persons to be made dialectical by the study of the exact -sciences in a comprehensive spirit. After insisting on Geometry and -other sciences, he says (_Rep._ VII. § 16): "The synoptical man is -dialectical; and he who is not the one, is not the other." - -But, we may ask, does a knowledge of sciences lead naturally to a -knowledge of Ideas, as absolute realities from which First Principles -flow? And supposing this to be true, as the Platonic Philosophy -supposes, is the Idea of the Good, as the source of moral truths, to -be thus attained to? That it is, is the teaching of Plato, here and -elsewhere; but have the speculations of subsequent philosophers in the -same direction given any confirmation of this lofty assumption? - -In reply to this inquiry, I should venture to say, that this assumption -appears to be a remnant of the Socratic doctrine from which Plato -began his speculations, that Virtue is a kind of knowledge; and that -all attempts to verify the assumption have failed. What Plato added to -the Socratic notion was, that the inquiry after The Good, the Supreme -Good, was to be aided by the analogy or suggestions of those sciences -which deal with necessary and eternal truths; the supreme good being -of the nature of those necessary and eternal truths. This notion is a -striking one, as a suggestion, but it has always failed, I think, in -the attempts to work it out. Those who in modern times, as Cudworth -and Samuel Clarke, have supposed an analogy between the necessary -truths of Geometry and the truths of Morality, though they have used -the like expressions concerning the one and the other class of truths, -have failed to convey clear doctrines and steady convictions to their -readers; and have now, I believe, few or no followers. - -The result of our investigation appears to be, that though Plato added -much to the matter by means of which the mind was to be improved and -disciplined in its research after Principles and Definitions, he did -not establish any form of Method according to which the inquiry -must be conducted, and by which it might be aided. The most definite -notion of Dialectic still remained the same with the original informal -view which Socrates had taken of it, as Xenophon tells us, (_Mem._ -IV. 5, 11) when he says: "He said that Dialectic (τὸ διαλέγεσθαι) -was so called because it is an inquiry pursued by persons who take -counsel together, separating the subjects considered according to -their kinds (διαλέγοντας). He held accordingly that men should try -to be well prepared for such a process, and should pursue it with -diligence: by this means, he thought, they would become good men, -fitted for responsible offices of command, and truly dialectical" -(διαλέκτικωτάτους). And this is, I conceive, the answer to Mr. Grote's -interrogatory exclamation (Vol. VIII. p. 577): "Surely the Etymology -here given by Xenophon or Socrates of the word (διαλέγεσθαι) cannot -be considered as satisfactory." The two notions, of investigatory -Dialogue, and Distribution of notions according to their kinds, which -are thus asserted to be connected in etymology, were, among the -followers of Socrates, connected in fact; the dialectic dialogue was -supposed to involve of course the dialectic division of the subject. - - -FOOTNOTES: - -[Footnote 339: Η καὶ διαλεκτικὸν καλεῖς τὸν λόγον ἐκάστου λαμβάνοντα -τῆς οὐσίας; (§ 14).] - -[Footnote 340: ὥσπερ θριγγὸς τοῖς μαθήμασιν ἡ διαλεκτικὴ ἦμιν ἐπάνω -κεῖσθαι. (§ 14).] - - -APPENDIX C. - -OF THE INTELLECTUAL POWERS ACCORDING TO PLATO. - -(_Cam. Phil. Soc._ NOV. 10, 1856.) - - -In the Seventh Book of Plato's _Republic_, we have certain sciences -described as the instruments of a philosophical and intellectual -education; and we have a certain other intellectual employment spoken -of, namely, Dialectic, as the means of carrying the mind beyond these -sciences, and of enabling it to see the sources of those truths which -the sciences assume as their first principles. These points have been -discussed in the two preceding papers. But this scheme of the highest -kind of philosophical education proceeds upon a certain view of the -nature and degrees of knowledge, and of the powers by which we know; -which view had been presented in a great measure in the Sixth Book; -this view I shall now attempt to illustrate. - -To analyse the knowing powers of man is a task so difficult, that we -need not be surprised if there is much obscurity in this portion of -Plato's writings. But as a reason for examining what he has said, we -must recollect that if there be in it anything on this subject which -was true then, it is true still; and also, that if we know any truth on -that subject now, we shall find something corresponding to that truth -in the best speculations of sagacious ancient writers, like Plato. -It may therefore be worth while to discuss the Platonic doctrines on -this matter, and to inquire how they are to be expressed in modern -phraseology. - -Plato's doctrine will perhaps be most clearly understood, if we begin -by considering the _diagram_ by which he illustrates the different -degrees of knowledge[341]. He sets out from the distinction of -_visible_ and _intelligible_ things. There are visible objects, -squares and triangles, for instance; but these are not the squares -and triangles about which the Geometer reasons. The exactness of -his reasoning does not depend on the exactness of his diagrams. He -reasons from certain mental squares and triangles, as he conceives and -understands them. "Thus there are visible and there are intelligible -things. There is a visible and an intelligible world[342]: and there -are two different regions about which our knowledge is concerned. -Now take a line divided into two unequal segments to represent these -two regions: and again, divide each segment in the same ratio. The -parts of each segment are to represent differences of clearness and -distinctness, and in the visible world these parts are _things_ and -_images_. By _images_ I mean shadows, and reflections in water, and in -polished bodies; and by _things_, I mean that of which these images -are the resemblances; as animals, plants, things made by man. This -difference corresponds to the difference of _Knowledge_ and mere -_Opinion_; and the _Opinable_ is to the _Knowable_ as the Image to the -Reality." - -This analogy is assented to by Glaucon; and thus there is assumed a -ground for a further construction of the diagram. - -"Now," he says, "we have to divide the segment which represents -Intelligible Things in the same way in which we have divided that which -represents Visible Things. The one part must represent the knowledge -which the mind gets by dealing as it were with images, and by reasoning -downwards _from_ Principles; the other that which it has by dealing -with the Ideas themselves, and going _to_ First Principles. - -"The one part depends upon assumptions or hypotheses[343], the other is -unhypothetical or absolute truth. - -"One kind of Intelligible Things, then, is Conceptions; for instance, -geometrical conceptions of figures, by means of which we reason -downwards, assuming certain First Principles. - -"Now the other kind of Intelligible Things is this:--that which the -Reason includes in virtue of its power of reasoning, when it regards -the assumptions of the Sciences as, what they are, assumptions only; -and uses them as occasions and starting points, that from these it may -ascend to the _absolute_, (ἀνυπόθετον, unhypothetical,) which does -not depend upon assumption, but is the origin of scientific truth. -The Reason takes hold of this first principle of truth; and availing -itself of all the connections and relations of this principle, it -proceeds to the conclusion; using no sensible image in doing this, but -contemplating the Ideas alone; and with these Ideas the process begins, -goes on, and terminates." - -This account of the matter will probably seem to require at least -further explanation; and that accordingly is acknowledged in the -Dialogue itself. Glaucon says: - -"I apprehend your meaning in a certain degree, but not very clearly, -for the matter is somewhat abstruse. You wish to prove that the -knowledge which, by the Reason, we acquire, of Real Existence and -Intelligible Things, is of a higher degree of certainty than the -knowledge which belongs to what are commonly called Sciences. Such -sciences, you say, have certain assumptions for their bases; and these -assumptions are, by the students of such sciences, apprehended, not -by Sense (that is, the Bodily Senses), but by a Mental Operation,--by -Conception. But inasmuch as such students ascend no higher than the -assumptions, and do not go to the First Principles of Truth, they do -not seem to you to have true knowledge--intuitive insight--_Nous_--on -the subject of their reasonings, though the subjects are intelligible, -along with their principle. And you call this habit and practice of the -Geometers and others by the name _Conception_, not _Intuition_[344]; -taking Conception to be something between Opinion on the one side, and -Intuitive Insight on the other." - -"You have explained it well, said I. And now consider the four sections -(of the line) of which we have spoken, as corresponding to four -affections in the mind. Intuition, the highest; Conception, the next; -the third, Belief; and the fourth, Conjecture (from likenesses); and -arrange them in order, so that they may have more or less of certainty, -as their objects have more or less of truth[345]. - -"I understand, said he. I agree to what you say, and I arrange them as -you direct." - -And so the Sixth Book ends: and the Seventh Book opens with the -celebrated image of the Cave, in which men are confined, and see all -external objects only by the shadows which they cast on the walls of -their prison. And this imperfect knowledge of things is to the true -vision of them, which is attained by those who ascend to the light of -day, as the ordinary knowledge of men is to the knowledge attainable by -those whose minds are purged and illuminated by a true philosophy. - -Confining ourselves at present to the part of Plato's speculations -which we have mentioned, namely, the degrees of knowledge, and the -division of our knowing faculties, we may understand, and may in a -great degree accept, Plato's scheme. We have already (in the preceding -papers) seen that, by the knowledge of real things, he means, in the -first place, the knowledge of universal and necessary truths, such -as Geometry and the other exact sciences deal with. These _we_ call -sciences of Demonstration; and we are in the habit of contrasting the -knowledge which constitutes such sciences with the knowledge obtained -by the Senses, by Experience or mere Observation. This distinction of -Demonstrative and Empirical knowledge is a cardinal point in Plato's -scheme also; the former alone being allowed to deserve the name of -_Knowledge_, and the latter being only _Opinion_. The Objects with -which Demonstration deals may be termed _Conceptions_, and the objects -with which Observation or Sense has to do, however much speculation may -reduce them to mere Sensations, are commonly described as _Things_. Of -these Things, there may be Shadows or Images, as Plato says; and as we -may obtain a certain kind of knowledge, namely Opinion or Belief, by -seeing the Things themselves, we may obtain an inferior kind of Opinion -or Belief by seeing their Images, which kind of opinion we may for the -moment call _Conjecture_. Whether then we regard the distinctions of -knowledge itself or of the objects of it, we have three terms before us. - - If we consider the kinds of knowledge, they are - Demonstration: Belief: Conjecture. - If the objects of this knowledge, they are - Conceptions: Things: Images. - -But in each of these Series, the first term is evidently wanting: for -Demonstration supposes Principles to reason from. Conceptions suppose -some basis in the mind which gives them their evidence. What then is -the first term in each of these two Series? - -The Principles of Demonstration must be seen by _Intuition_. - -Conceptions derive their properties from certain powers or attributes -of the mind which we may term _Ideas_. - -Therefore the two series are - - Intuition: Demonstration: Belief: Conjecture. - Ideas: Conceptions: Things: Images. - -Plato further teaches that the two former terms in each Series belong -to the Intelligible, the two latter to the Visible World: and he -supposes that the ratio of these two primary segments of the line is -the same as the ratio in which each segment is divided[346]. - -In using the term _Ideas_ to describe the mental sources from which -Conceptions derive their validity in demonstration, I am employing a -phraseology which I have already introduced in the _Philosophy of the -Inductive Sciences_. But independently altogether of this, I do not -see what other term could be employed to denote the mental objects, -attributes, or powers, whatever they be, from which Conceptions derive -their evidence, as Demonstrative Truths derive their evidence from -Intuitive Truths. - -That the Scheme just presented is Plato's doctrine on this subject, -I do not conceive there can be any doubt. There is a little want of -precision in his phraseology, arising from his mixing together the two -series. In fact, his final series - - _Noësis_: _Dianoia_: _Pistis_: _Eikasia_; - -is made by putting in the second place, instead of _Demonstration_, -which is the _process_ pursued, or _Science_, which is the _knowledge_ -obtained, _Conception_, which is the _object_ with which the mind -deals. Such deviations from exact symmetry and correlation in speaking -of the faculties of the mind, are almost unavoidable in every language. -And there is yet another source of such inaccuracies of language; for -we have to speak, not only of the process of acquiring knowledge, and -of the objects with which the mind deals, but of the Faculties of the -mind which are thus employed. Thus _Intuition_ is the Process; _Ideas_ -are the Object, in the first term of our series. The Faculty also we -may call _Intuition_; but the Greek offers a distinction. _Noësis_ is -the _Process_ of Intuition; but the _Faculty_ is _Nous_. If we wish to -preserve this distinction in English, what must we call the Faculty? -I conceive we must call it _the Intuitive Reason_, a term well known -to our older philosophical writers[347]. Again: taking the second -term of the series, _Demonstration_ is the process, _Science_, the -result; and _Conceptions_ are the objects with which the mind deals. -But what is the _Faculty_ thus employed? What is the Faculty employed -in Demonstration? The same philosophical writers of whom I spoke would -have answered at once, _the Discursive Reason_; and I do not know -that, even now, we can suggest any better term. The Faculty employed -in acquiring the two lower kinds of knowledge, the Faculty which deals -with Things and their Images is, of course, _Sense_, or _Sensation_. - -The assertion of a Faculty of the mind by which it apprehends Truth, -which Faculty is higher than the Discursive Reason, as the Truth -apprehended by it is higher than mere Demonstrative Truth, agrees (as -it will at once occur to several of my readers) with the doctrine -taught and insisted upon by the late Samuel Taylor Coleridge. And so -far as he was the means of inculcating this doctrine, which, as we -see, is the doctrine of Plato, and I might add, of Aristotle, and of -many other philosophers, let him have due honour. But in his desire -to impress the doctrine upon men's minds, he combined it with several -other tenets, which will not bear examination. He held that the two -Faculties by which these two kinds of truth are apprehended, and which, -as I have said, our philosophical writers call _the Intuitive Reason_ -and _the Discursive Reason_, may be called, and ought to be called, -respectively, _The Reason_ and _The Understanding_; and that the second -of these is of the nature of the _Instinct_ of animals, so as to be -something intermediate between Reason and Instinct. These opinions, -I may venture to say, are altogether erroneous. The Intuitive Reason -and the Discursive Reason are not, by any English writers, called the -Reason and the Understanding; and accordingly, Coleridge has had to -alter all the passages, namely, those taken from Leighton, Harrington, -and Bacon, from which his exposition proceeds. The Understanding is so -far from being especially the Discursive or Reasoning Faculty, that -it is, in universal usage, and by our best writers, _opposed_ to the -Discursive or Reasoning Faculty. Thus this is expressly declared by Sir -John Davis in his poem _On the Immortality of the Soul_. He says, of -the soul, - - When she _rates_ things, and moves from ground to ground, - The name of _Reason_ (_Ratio_) she acquires from this: - But when by reason she truth hath found, - And standeth fixt, she _Understanding_ is. - -Instead of the Reason being fixed, and the Understanding discursive, -as Mr. Coleridge says, the Reason is distinctively discursive; that -is, it obtains conclusions by running from one point to another. This -is what is meant by _Discursus_; or, taking the full term, _Discursus -Rationis_, _Discourse of Reason_. Understanding is fixed, that is, it -dwells upon one view of a subject, and not upon the steps by which that -view is obtained. The verb _to reason_, implies the substantive, _the -Reason_, though it is not coextensive with it: for as I have said, -there is the Intuitive Reason as well as the Discursive Reason. But it -is by the Faculty of Reason that we are capable of reasoning; though -undoubtedly the practice or the pretence of reasoning may be carried so -far as to seem at variance with reason in the more familiar sense of -the term; as is the case also in French. Moliere's Crisale says (in the -_Femmes Savantes_), - - Raisonner est l'emploi de toute ma maison, - Et le raisonnement en bannit la Raison. - -If Mr. Coleridge's assertion were true, that the Understanding is the -discursive and the Reason the fixed faculty, we should be justified in -saying that _The Understanding is the faculty by which we reason, and -the Reason is the faculty by which we understand_. But this is not so. - -Nor is the Understanding of the nature of Instinct, nor does it -approach nearer than the Reason to the nature of Instinct, but the -contrary. The Instincts of animals bear a very obscure resemblance -to any of man's speculative Faculties; but so far as there is any -such resemblance, Instinct is an obscure image of Reason, not of -Understanding. Animals are said to act as if they reasoned, rather than -as if they understood. The verb _understand_ is especially applied to -man as distinguished from animals. Mr. Coleridge tells a tale from -Huber, of certain bees which, to prevent a piece of honey from falling, -balanced it by their weight, while they built a pillar to support it. -They did this by Instinct, not _understanding_ what they did; men, -doing the same, would have _understood_ what they were doing. Our -Translation of the Scriptures, in making it the special distinction of -man and animals, that _he has Understanding_ and they have not, speaks -quite consistently with good philosophy and good English. - -Mr. Coleridge's object in his speculations is nearly the same as -Plato's; namely, to declare that there is a truth of a higher kind than -can be obtained by mere reasoning; and also to claim, as portions of -this higher truth, certain fundamental doctrines of Morality. Among -these, Mr. Coleridge places the Authority of Conscience, and Plato, the -Supreme Good. Mr. Coleridge also holds, as Plato held, that the Reason -of man, in its highest and most comprehensive form, is a portion of a -Supreme and Universal Reason; and leads to Truth, not in virtue of its -special attributes in each person, but by its own nature. - -Many of the opinions which are combined with these doctrines, both -in Plato and in Coleridge, are such as we should, I think, find it -impossible to accept, upon a careful philosophical examination of them; -but on these I shall not here dwell. - -I will only further observe, that if any one were to doubt whether the -term Νοῦς is rightly rendered _Intuitive Reason_, we may find proof -of the propriety of such a rendering in the remarkable discussion -concerning the Intellectual Virtues, which we have in the Sixth Book -of the Nicomachean Ethics. It can hardly be questioned that Aristotle -had in his mind, in writing that passage, the doctrines of Plato, as -expounded in the passage just examined, and similar passages. Aristotle -there says that there are five Intellectual Virtues, or Faculties -by which the Mind aims at Truth in asserting or denying:--namely, -_Art_, _Science_, _Prudence_, _Wisdom_, _Nous_. In this enumeration, -passing over Art, Prudence, and Wisdom, as virtues which are mainly -concerned from practical life, we have, in the region of speculative -Truth, a distinction propounded between _Science_ and _Nous_: and this -distinction is further explained (c. 6) by the remarks that Science -reasons with Principles; and that these Principles cannot be given -_by_ Science, because Science reasons _from_ them; nor by Art, nor -Prudence, for these are conversant with matters contingent, not with -matters demonstrable; nor can the First Principles of the Reasonings -of Science be given by Wisdom, for Wisdom herself has often to reason -from Principles. Therefore the First Principles of Demonstrative -Reasoning must be given by a peculiar Faculty, _Nous_. As we have -said, _Intuitive Reason_ is the most appropriate English term for this -Faculty. - -The view thus given of that higher kind of Knowledge which Plato and -Aristotle place above ordinary Science, as being the Knowledge of and -Faculty of learning First Principles, will enable us to explain some -expressions which might otherwise be misunderstood. Socrates, in the -concluding part of this Sixth Book of the _Republic_, says, that this -kind of knowledge is "that of which the Reason (λόγος) takes hold, -_in virtue of its power of reasoning_[348]." Here we are plainly not -to understand that we arrive at First Principles _by reasoning_: for -the very opposite is true, and is here taught;--namely, that First -Principles are not what we reason _to_, but what we reason _from_. -The meaning of this passage plainly is, that First Principles are -those of which the Reason takes hold _in virtue of its power of -reasoning_;--they are the conditions which must exist in order to make -any reasoning possible:--they are the propositions which the Reason -must involve implicitly, in order that we may reason explicitly;--they -are the intuitive roots of the dialectical power. - -In accordance with the views now explained, Plato's Diagram may be -thus further expanded. The term ιδέα is not used in this part of the -_Republic_; but, as is well known, occurs in its peculiar Platonic -sense in the Tenth Book. - - +---------+------------------------------------+-----------------------+ - | | Intelligible World. νοήτον. | Visible World. ὁρατον.| - +---------+-----------------+------------------+-----------------------+ - |_Object_ | Ideas | Conceptions | Things | Images | - | | ἰδέαι | διάνοια | ζῶα κ.τ.λ.| εἰκἰνες | - +---------+-----------------+------------------+-----------------------+ - |_Process_| Intuition | Demonstration | Belief | Conjecture| - | | νἰησις | ἐπιστήμη | πίστις | είκασία | - +---------+-----------------+------------------+-----------------------+ - |_Faculty_|Intuitive Reason | Discursive Reason| Sensation | - | | νοῦς | λόγος | αἴσθησις | - +---------+-----------------+------------------+-----------------------+ - - -FOOTNOTES: - -[Footnote 341: _Pol_. vi. § 19.] - -[Footnote 342: He adds, "This _oraton_, this visible world, I will not -say has any connexion with _ouranon_, heaven, that I may not be accused -of playing upon words."] - -[Footnote 343: It is plain that Plato, by _Hypotheses_, in this place, -means the usual foundations of Arithmetic and Geometry; namely, -Definitions and Postulates. He says that "the arithmeticians and -geometers take as hypotheses (hυποθεμενοι) odd and even, and the -three kinds of angles (right, acute, and obtuse); and figures, (as -a triangle, a square,) and the like." I say his "hypotheses" are -the Definitions and Postulates, not the Axioms: for the Axioms of -Arithmetic and Geometry belong to the Higher Faculty, which ascends -to First Principles. But this Faculty operates rather in using these -axioms than in enunciating them. It knows them implicitly rather than -expresses them explicitly.] - -[Footnote 344: διάνοιαν άλλ' οὐ νοῦν.] - -[Footnote 345: The Diagram, as here described, would be this: - - +---------------------------+---------------------------+ - | _Intelligible World._ | _Visible World._ | - |-------------+-------------+-------------+-------------+ - | Intuition. | Conception. | Things. | Images. | - +-------------+-------------+-------------+-------------+ - -Plato supposes the whole, and each of the two parts, to be divided in -the same ratio, in order that the _analogy_ of the division in each -case may be represented.] - -[Footnote 346: The four segments might be as 4: 2: 2: 1; or as 9: 6: 6: -4; or generally, as _a_: _ar_: _ar_: _ar_^2.] - -[Footnote 347: - - Hence the mind Reason receives - Intuitive or Discursive. - - MILTON.] - -[Footnote 348: τῇ τοῦ διαλέγεσθαι δυνόμει.] - - -APPENDIX D. - -CRITICISM OF ARISTOTLE'S ACCOUNT OF INDUCTION. - -(_Cam. Phil. Soc._ FEB. 11, 1850.) - - -The Cambridge Philosophical Society has willingly admitted among -its proceedings not only contributions to science, but also to the -philosophy of science; and it is to be presumed that this willingness -will not be less if the speculations concerning the philosophy of -science which are offered to the Society involve a reference to ancient -authors. Induction, the process by which general truths are collected -from particular examples, is one main point in such philosophy: and the -comparison of the views of Induction entertained by ancient and modern -writers has already attracted much notice. I do not intend now to go -into this subject at any length; but there is a cardinal passage on the -subject in Aristotle's _Analytics_, (_Analyt. Prior._ II. 25) which I -wish to explain and discuss. I will first translate it, making such -emendations as are requisite to render it intelligible and consistent, -of which I shall afterwards give an account. - -I will number the sentences of this chapter of Aristotle in order that -I may afterwards be able to refer to them readily. - -§ 1. "We must now proceed to observe that we have to examine not only -syllogisms according to the aforesaid _figures_,--syllogisms logical -and demonstrative,--but also rhetorical syllogisms,--and, speaking -generally, any kind of proof by which belief is influenced, following -any method. - -§ 2. "All belief arises either from Syllogism or from Induction: [we -must now therefore treat of Induction.] - -§ 3. "Induction, and the Inductive Syllogism, is when by means of one -extreme term we infer the other extreme term to be true of the middle -term. - -§ 4. "Thus if _A_, _C_, be the extremes, and _B_ the mean, we have to -show, by means of _C_, that _A_ is true of _B_. - -§ 5. "Thus let _A_ be _long-lived_; _B_, _that which has no -gall-bladder;_ and _C_, particular long-lived animals, as _elephant_, -_horse_, _mule_. - -§ 6. "Then every _C_ is _A_, for all the animals above named are -long-lived. - -§ 7. "Also every _C_ is _B_, for all those animals are destitute of -gall-bladder. - -§ 8. "If then _B_ and _C_ are convertible, and the mean (_B_) does not -extend further than extreme (_C_), it necessarily follows that every -_B_ is _A_. - -§ 9. "For it was shown before, that, if any two things be true of the -same, and if either of them be convertible with the extreme, the other -of the things predicated is true of the convertible (extreme). - -§ 10. "But we must conceive that _C_ consists of a collection of all -the particular cases; for Induction is applied to all the cases. - -§ 11. "But such a syllogism is an inference of a first truth and -immediate proposition. - -§ 12. "For when there is a mean term, there is a demonstrative -syllogism through the mean; but when there is not a mean, there is -proof by Induction. - -§ 13. "And in a certain way, Induction is contrary to Syllogism; for -Syllogism proves, by the middle term, that the extreme is true of the -third thing: but Induction proves, by means of the third thing, that -the extreme is true of the mean. - -§ 14. "And Syllogism concluding by means of a middle term is prior -by nature and more usual to us; but the proof by Induction, is more -luminous." - -I think that the chapter, thus interpreted, is quite coherent and -intelligible; although at first there seems to be some confusion, from -the author sometimes saying that Induction is a kind of Syllogism, and -at other times that it is not. The amount of the doctrine is this. - -When we collect a general proposition by Induction from particular -cases, as for instance, that all animals destitute of gall-bladder -(_acholous_), are long-lived, (if this proposition were true, of which -hereafter,) we may express the process in the form of a Syllogism, if -we will agree to make a collection of particular cases our middle term, -and assume that the proposition in which the second extreme term occurs -is convertible. Thus the known propositions are - - Elephant, horse, mule, &c., are long-lived. - Elephant, horse, mule, &c., are _acholous_. - -But if we suppose that the latter proposition is convertible, we shall -have these propositions: - - Elephant, horse, mule, &c., are long-lived. - All acholous animals are elephant, horse, mule, &c., - -from whence we infer, quite rigorously as to _form_, - - All acholous animals are long-lived. - -This mode of putting the Inductive inference shows both the strong and -the weak point of the illustration of Induction by means of Syllogism. -The strong point is this, that we make the inference perfect as to -form, by including an indefinite collection of particular cases, -elephant, horse, mule, &c., in a single term, _C_. The Syllogism then is - - All _C_ are long-lived. - All acholous animals are _C_. - Therefore all acholous animals are long-lived. - -The weak point of this illustration is, that, at least in some -instances, when the number of actual cases is necessarily indefinite, -the representation of them as a single thing involves an unauthorized -step. In order to give the reasoning which really passes in the mind, -we must say - - Elephant, horse, &c., are long-lived. - All acholous animals are _as_ elephant, horse, &c., - Therefore all acholous animals are long-lived. - -This "_as_" must be introduced in order that the "all _C_" of the first -proposition may be justified by the "_C_" of the second. - -This step is, I say, necessarily unauthorized, where the number of -particular cases is indefinite; as in the instance before us, the -species of acholous animals. We do not know how many such species -there are, yet we wish to be able to assert that _all_ acholous -animals are long-lived. In the proof of such a proposition, put in a -syllogistic form, there must necessarily be a logical defect; and the -above discussion shows that this defect is the substitution of the -proposition, "All acholous animals are _as_ elephant, &c.," for the -converse of the experimentally proved proposition, "elephant, &c., are -acholous." - -In instances in which the number of particular cases is limited, the -necessary existence of a logical flaw in the syllogistic translation -of the process is not so evident. But in truth, such a flaw exists in -all cases of Induction _proper_: (for Induction by _mere enumeration_ -can hardly be called _Induction_). I will, however, consider for a -moment the instance of a celebrated proposition which has often been -taken as an example of Induction, and in which the number of particular -cases is, or at least is at present supposed to be, limited. Kepler's -laws, for instance the law that the planets describe ellipses, may -be regarded as examples of Induction. The law was inferred, we will -suppose, from an examination of the orbits of Mars, Earth, Venus. And -the syllogistic illustration which Aristotle gives, will, with the -necessary addition to it, stand thus, - - Mars, Earth, Venus describe ellipses. - Mars, Earth, Venus are planets. - -Assuming the convertibility of this last proposition, _and its -universality_, (which is the necessary addition in order to make -Aristotle's syllogism valid) we say - - All the planets are as Mars, Earth, Venus. - -Whence it follows that all the planets describe ellipses. - -If, instead of this assumed universality, the astronomer had made a -real enumeration, and had established the fact of each particular, he -would be able to say - - Saturn, Jupiter, Mars, Earth, Venus, Mercury, describe ellipses. - - Saturn, Jupiter, Mars, Earth, Venus, Mercury are all the planets. - -And he would obviously be entitled to convert the second proposition, -and then to conclude that - - All the planets describe ellipses. - -But then, if this were given as an illustration of Induction by means -of syllogism, we should have to remark, in the first place, that the -conclusion that "all the planets describe ellipses," adds nothing to -the major proposition, that "S., J., M., E., V., m., do so." It is -merely the same proposition expressed in other words, so long as S., -J., M., E., V., m., are supposed to be all the planets. And in the -next place we have to make a remark which is more important; that the -minor, in such an example, must generally be either a very precarious -truth, or, as appears in this case, a transitory error. For that the -planets known at any time are _all_ the planets, must always be a -doubtful assertion, liable to be overthrown to-night by an astronomical -observation. And the assertion, as received in Kepler's time, has been -overthrown. For Saturn, Jupiter, Mars, Earth, Venus, Mercury, are -not all the planets. Not only have several new ones been discovered -at intervals, as Uranus, Ceres, Juno, Pallas, Vesta, but we have new -ones discovered every day; and any conclusion depending upon this -premiss that _A_, _B_, _C_, _D_, _E_, _F_, _G_, _H_, to _Z_ are all the -planets, is likely to be falsified in a few years by the discovery of -_A´_, _B´_, _C´_, &c. If, therefore, this were the syllogistic analysis -of Induction, Kepler's discovery rested upon a false proposition; -and even if the analysis were now made conformable to our present -knowledge, that induction, analysed as above, would still involve a -proposition which to-morrow may show to be false. But yet no one, I -suppose, doubts that Kepler's discovery was really a discovery--the -establishment of a scientific truth on solid grounds; or, that it is -a scientific truth for us, notwithstanding that we are constantly -discovering new planets. Therefore the syllogistic analysis of it now -discussed (namely, that which introduces simple enumeration as a step) -is not the right analysis, and does not represent the grounds of the -Inductive Truth, that all the planets describe ellipses. - -It may be said that all the planets discovered since Kepler's time -conform to his law, and thus confirm his discovery. This we grant: -but they only _confirm_ the discovery, they do not make it; they are -not its groundwork. It was a discovery before these new cases were -known; it was an inductive truth without them. Still, an objector might -urge, if any one of these new planets had contradicted the law, it -would have overturned the discovery. But this is too boldly said. A -discovery which is so precise, so complex (in the phenomena which it -explains), so supported by innumerable observations extending through -space and time, is not so easily overturned. If we find that Uranus, -or that Encke's comet, deviates from Kepler's and Newton's laws, we -do not infer that these laws must be false; we say that there must -be some disturbing cause in these cases. We seek, and we find these -disturbing causes: in the case of Uranus, a new planet; in the case -of Encke's comet, a resisting medium. Even in this case therefore, -though the number of particulars is limited, the Induction was not -made by a simple enumeration of all the particulars. It was made from -a few cases, and when the law was discerned to be true in these, it -was extended to all; the conversion and assumed universality of the -proposition that "these are planets," giving us the proposition which -we need for the syllogistic exhibition of Induction, "all the planets -are as these." - -I venture to say further, that it is plain, that Aristotle did not -regard Induction as the result of simple enumeration. This is plain, -in the first place, from his example. Any proposition with regard to -a special class of animals, cannot be proved by simple enumeration: -for the number of particular cases, that is, of animal species in -the class, is indefinite at any period of zoological discovery, and -must be regarded as infinite. In the next place, Aristotle says (§ -10 of the above extract), "We must conceive that _C_ consists of a -collection of all the particular cases; for induction is applied to -all the cases." We must _conceive_ (νοεῖν) that _C_ in the major, -consists of all the cases, in order that the conclusion may be true -of all the cases; but we cannot _observe_ all the cases. But the -evident proof that Aristotle does not contemplate in this chapter an -Induction by simple enumeration, is the contrast in which he places -Induction and Syllogism. For Induction by simple enumeration stands -in no contrast to Syllogism. The Syllogism of such Induction is quite -logical and conclusive. But Induction from a comparatively small -number of particular cases to a general law, does stand in opposition -to Syllogism. It gives us a truth,--a truth which, as Aristotle -says (§ 14), is more luminous than a truth proved syllogistically, -though Syllogism may be _more natural and usual_. It gives us (§ 11) -immediate propositions, obtained directly from observation, and not -by a chain of reasoning: "first truths," the principles from which -syllogistic reasonings may be deduced. The Syllogism proves by means of -a middle term (§ 13) that the extreme is true of a third thing: thus, -(_acholous_ being the middle term): - - Acholous animals are long-lived: - All elephants are acholous animals: - Therefore all elephants are long-lived. - -But Induction proves by means of a third thing (namely, particular -cases) that the extreme is true of the mean; thus (_acholous_, still -being the middle term) - - Elephants are long-lived: - Elephants are acholous animals: - Therefore acholous animals are long-lived. - -It may be objected, such reasoning as this is quite inconclusive: -and the answer is, that this is precisely what we, and as I believe, -Aristotle, are here pointing out. Induction _is_ inconclusive _as -reasoning_. It is not reasoning: it is another way of getting at -truth. As we have seen, no reasoning can prove such an inductive -truth as this, that all planets describe ellipses. It is _known_ from -observation, but it is not _demonstrated_. Nevertheless, no one doubts -its universal truth, (except, as aforesaid, when disturbing causes -intervene). And thence, Induction is, as Aristotle says, opposed to -syllogistic reasoning, and yet is a means of discovering truth: not -only so, but a means of discovering primary truths, immediately derived -from observation. - -I have elsewhere taught that all Induction involves a _Conception_ of -the mind applied to facts. It may be asked whether this applies in -such a case as that given by Aristotle. And I reply, that Aristotle's -instance is a very instructive example of what I mean. The Conception -which is applied to the facts in order to make the induction possible -is the want of the gall-bladder;--and Aristotle supplies us with a -special term for this conception; _acholous_[349]. But, it may be -said, that the animals observed, the elephant, horse, mule, &c., are -acholous, is a mere fact of observation, not a Conception. I reply -that it is a _Selected_ Fact, a fact selected and compared in several -cases, which is what we mean by a _Conception_. That there is needed -for such selection and comparison a certain activity of the mind, is -evident; but this also may become more clear by dwelling a little -further on the subject. Suppose that Aristotle, having a desire to know -what class of animals are long-lived, had dissected for that purpose -many animals; elephants, horses, cows, sheep, goats, deer and the like. -How many resemblances, how many differences, must he have observed -in their anatomy! He was very likely long in fixing upon any one -resemblance which was common to all the long-lived. Probably he tried -several other characters, before he tried the presence and absence -of the gall-bladder:--perhaps, trying such characters, he found them -succeed for a few cases, and then fail in others, so that he had to -reject them as useless for his purpose. All the while, the absence of -the gall-bladder in the long-lived animals was a fact: but it was of -no use to him, because he had not selected it and drawn it forth from -the mass of other facts. He was looking for a mean term to connect his -first extreme, _long-lived_, with his second, the special cases. He -sought this middle term in the entrails of the many animals which he -used as extremes: it _was_ there, but he could not find it. The fact -existed, but it was of no use for the purpose of Induction, because -it did not become a special Conception in his mind. He considered the -animals in various points of view, it may be, as ruminant, as horned, -as hoofed, and the contrary; but not as _acholous_ and the contrary. -When he looked at animals in that point of view,--when he took up that -character as the ground of distinction, he forthwith imagined that he -found a separation of long-lived and short-lived animals. When that -Fact became a Conception, he obtained an inductive truth, or, at any -rate, an inductive proposition. - -He obtained an inductive proposition by applying the Conception -_acholous_ to his observation of animals. This Conception divided -them into two classes; and these classes were, he fancied, long-lived -and short-lived respectively. That it was the Conception, and not -the Fact which enabled him to obtain his inductive proposition, is -further plain from this, that the supposed Fact is not a fact. Acholous -animals are not longer-lived than others. The presence or absence of -the gall-bladder is no character of longevity. It is true, that in one -familiar class of animals, the herbivorous kind, there is a sort of -first seeming of the truth of Aristotle's asserted rule: for the horse -and mule which have not the gall-bladder are longer-lived than the -cow, sheep, and goat, which have it. But if we pursue the investigation -further, the rule soon fails. The deer-tribe that want the gall-bladder -are not longer-lived than the other ruminating animals which have it. -And as a conspicuous evidence of the falsity of the rule, man and the -elephant are perhaps, for their size, the longest-lived animals, and -of these, man has, and the elephant has not, the organ in question. -The inductive proposition, then, is false; but what we have mainly -to consider is, where the fallacy enters, according to Aristotle's -analysis of Induction into Syllogism. For the two premisses are still -true; that elephants, &c., are long-lived; and that elephants, &c., -are acholous. And it is plain that the fallacy comes in with that -conversion and generalization of the latter proposition, which we have -noted as necessary to Aristotle's illustration of Induction. When we -say "All acholous animals are as elephants, &c.," that is, as those -in their biological conditions, we say what is not true. Aristotle's -condition (§ 8) is not complied with, that the middle term shall not -extend beyond the extreme. For the character _acholous_ does extend -beyond the elephant and the animals biologically resembling it; it -extends to deer, &c., which are not like elephants and horses, in the -point in question. And thus, we see that the assumed conversion and -generalization of the minor proposition, is the seat of the fallacy of -false Inductions, as it is the seat of the peculiar logical character -of true Inductions. - -As true Inductive Propositions cannot be logically demonstrated by -syllogistic rules, so they cannot be discovered by any rule. There -is no formula for the discovery of inductive truth. It is caught by -a peculiar sagacity, or power of divination, for which no precepts -can be given. But from what has been said, we see that this sagacity -shows itself in the discovery of propositions which are both _true_, -and _convertible_ in the sense above explained. Both these steps may -be difficult. The former is often very laborious: and when the labour -has been expended, and a true proposition obtained, it may turn out -useless, because the proposition is not convertible. It was a matter -of great labour to Kepler to prove (from calculation of observations) -that Mars moves elliptically. Before he proved this, he had tried -to prove many similar propositions:--that Mars moved according to -the "bisection of the eccentricity,"--according to the "vicarious -hypothesis,"--according to the "physical hypothesis,"--and the like; -but none of these was found to be exactly true. The proposition that -Mars moves elliptically was proved to be true. But still, there was -the question, Is it convertible? Do all the planets move as Mars -moves? This was proved, (suppose,) to be true, for the Earth and -Venus. But still the question remains, Do all the planets move as -Mars, Earth, Venus, do? The inductive generalizing impulse boldly -answers, Yes, to this question; though the rules of Syllogism do not -authorize the answer, and though there remain untried cases. The -inductive Philosopher tries the cases as fast as they occur, in order -to confirm his previous conviction; but if he had to wait for belief -and conviction till he had tried every case, he never could have belief -or conviction of such a proposition at all. He is prepared to modify or -add to his inductive truth according as new cases and new observations -instruct him; but he does not fear that new cases or new observations -will overturn an inductive proposition established by exact comparison -of many complex and various phenomena. - -Aristotle's example offers somewhat similar reflections. He had to -establish a proposition concerning long-lived animals, which should -be true, and should be susceptible of generalized conversion. To -prove that the elephant, horse and mule are destitute of gall-bladder -required, at least, the labour of anatomizing those animals in the -seat of that organ. But this labour was not enough; for he would find -those animals to agree in many other things besides in being acholous. -He must have selected that character somewhat at a venture. And the -guess was wrong, as a little more labour would have shown him; if -for instance he had dissected deer: for they are acholous, and yet -short-lived. A trial of this kind would have shown him that the extreme -term, _acholous_, did extend beyond the mean, namely, animals such -as elephant, horse, mule; and therefore, that the conversion was not -allowable, and that the Induction was untenable. In truth, there is no -relation between bile and longevity[350], and this example given by -Aristotle of generalization from induction is an unfortunate one. - - * * * * * - -In discussing this passage of Aristotle, I have made two alterations in -the text, one of which is necessary on account of the fact; the other -on account of the sense. In the received text, the particular examples -of long-lived animals given are _man_, horse, and mule (ἐφ' ᾧ δὲ Γ, τὸ -καθέκαστον μακρόβιον, οἷον ἄνθρωπος, καὶ ἵππος, καὶ ἡμίονος). And it is -afterwards said that all these are _acholous_: (ἀλλὰ καὶ τὸ Β, τὸ μὴ -ἔχον χολὴν, παντὶ ὑπάρχει τῷ Γ). But man _has_ a gall-bladder: and the -fact was well known in Aristotle's time, for instance, to Hippocrates; -so that it is not likely that Aristotle would have made the mistake -which the text contains. But at any rate, it is a mistake; if not of -the transcriber, of Aristotle; and it is impossible to reason about the -passage, without correcting the mistake. The substitution of ἔλεφας -for ἄνθρωπος makes the reasoning coherent; but of course, any other -acholous long-lived animal would do so equally well. - -The other emendation which I have made is in § 6. In the received text -§ 6 and 7 stand thus: - - 6. Then every _C_ is _A_, for _every acholous animal is long-lived_ - - (τῷ δὴ Γ ὅλω ὑπάρχει τὸ Α, πᾶν γὰρ τὸ ἄχολον μακρόβιον). - - 7. Also every _C_ is _B_, for all _C_ is destitute of bile. - -Whence it may be inferred, says Aristotle, under certain conditions, -that every _B_ is _A_ (τὸ Α τῷ Β ὑπάρχειν) that is, that _every -acholous animal is long-lived_. But this conclusion is, according -to the common reading, identical with the major premiss; so that -the passage is manifestly corrupt. I correct it by substituting for -ἄχολον, Γ; and thus reading πᾶν γὰρ τὸ Γ μακρόβιον "for every _C_ is -long-lived:" just as in the parallel sentence, 7, we have ἀλλὰ καὶ τὸ -Β, τὸ μὴ ἔχον χολην, παντὶ ὑπάρχει τῷ Γ. In this way the reasoning -becomes quite clear. The corrupt substitution of ἄχολον for Γ may have -been made in various ways; which I need not suggest. As my business is -with the sense of the passage, and as it makes no sense without the -change, and very good sense with it, I cannot hesitate to make the -emendation. And these emendations being made, Aristotle's view of the -nature and force of Induction becomes, I think, perfectly clear and -very instructive. - - * * * * * - -ADDITIONAL NOTE. - -I take the liberty of adding to this Memoir the following remarks, for -which I am indebted to Mr. Edleston, Fellow of Trinity College. - -Several of the earlier editions of Aristotle have γ instead of ἄχολον -in the passage referred to in the above paper: ex. gr. - -(1) The edition printed at Basle, 1539 (after Erasmus): "τὸ γ." - -(2) Basil (Erasmus) 1550. "τὸ γ." - -(3) Burana's Latin version, Venet. 1552, has "omne enim _C_ longævum." - -(4) Sylburg, Francf. 1587 "τὸ γ" is printed in brackets thus: "[τὸ γ] -τὸ ἄχολον." - -(5) So also in Casaubon's edition, 1590. - -(6) Casaub. 1605 "τὸ γ," (though the Latin version has "vacans bile;") -not "[τὸ γ] τὸ ἄχολον," as the edition of 1590. - -(7) In the edition printed Aurel. Allobr. 1607, "[τὸ γ] τὸ ἄχολον," as -in (4) and (5). - -(8) Du Val's editions, Paris, 1619, 1629, 1654 "τὸ γ," though in -Pacius's translation in the adjacent column we find "vacans bile." - -(9) In the critical notes to Waitz's edition of the _Organon_ (Lips. -1844) it is stated that "post ἄχολον del. γ. _n_," implying apparently, -that in the MS. marked _n_, the letter γ, which had been originally -written after ἄχολον, had been erased. - - * * * * * - -The following passages throw light upon the question whether ἄνθρωπος -ought or ought not to be retained in the passage discussed in the -Memoir. - -(A) Aristot. _De Animalibus Histor._ II. 15, 9 (Bekk.), τῶν μὲν -ζωοτόκων καὶ τετραπόδων ἔλαφος οὐκ ἔχει [χολήν] οὐδὲ πρόξ, ἕτι δὲ -ἵππος, ὀρεύς, ὄνος, φώκη καὶ τῶν ὑῶν ἔνιοι.... Ἔχει δὲ καὶ ὁ ἐλέφας τὸ -ῆπαρ ἄχολον μέν, κ.τ.λ. - -(B) Conf. Ib. I. 17, 10, 11. (In the beginning of Chap. 16, he says -that the external μορια of man are γνώριμα, "τὰ δ' ἐντὸς τοὐναντίον. -Ἄγνωστα γάρ ἐστι μάλιστα τὰ τῶν ἀνθρώπων, ὡστε δεῖ πρὸς τὰ τῶν ἄλλων μόρια -ζώων ἀνάγοντας σκοπεῖν," ...) - -(C) Id _De Part. Animal._ IV. 2, 2. τὰ μὲν γὰρ ὅλως οὐκ ἕχει χολήν, -οἷον ἱππος και ὀρεύς καὶ ονος καὶ ἔλαφος καὶ πρόξ..... Ἐν δὲ τοῖς -γένεσι τοῖς αὐτοῖς τὰ μὲν ἔχειν φαίνεται, τὰ δ' οὐκ ἔχειν, οἷον ἐν -τῷ τῶν μυῶν. Τούτων δ' ἐστὶ καὶ ὁ ἄνθρωπος· ἔνιοι μὲν γὰρ φαίνονται -ἔχοντες χολὴν ἐπὶ του ἥπατος, ἔνιοι δ' οὐκ ἔχοντες. Διο καὶ γίνεται -ἀμφισβήτησις περὶ ὁλου τοῦ γένους· οἱ γὰρ ἐντυχόντες ὁποτερωσοῦν ἔχουσι -περὶ πάντων ὑπολαμβάνουσιν ὡς ἁπάντων ἐχόντων..... - -(D) Ib. § 11. Διὸ καὶ χαριέστατα λέγουσι τῶν ῶρχαίων ὁι φάσκοντες -αἴτιον εῖναι τοῦ πλείω ζῆν χρόνον το μὴ ἔχειν χολήν, βλέψαντες ἐπὶ τὰ -μωνυχα και τὰς ελαφους· ταῦτα γὰρ ἄχολά τε καὶ ζῇ πολὺν χρόνον. Ἔτι -δὲ καὶ τὰ μὴ ἑωραμένα ὑπ' ἐκείνων ὁτι οὐκ ἔχει χολήν, οἷον δελφις καὶ -κάμηλος, καὶ ταῦτα τυγχάνει μακρόβια ὄντα. Εὔλογον γάρ, κ.τ.λ. - -(E) The elephant and man are mentioned together as long-lived animals -(_De Long. et Brev. Vitæ_, IV. 2, and _De Generat. Animal._ IV. 10, 2.) - - * * * * * - -The following is the import of these passages: - -(_A_) "Of viviparous quadrupeds, the deer, roe, horse, mule, ass, seal, -and some of the swine have not the gall-bladder.... - -The elephant also has the liver without gall-bladder, &c." - -(_B_) "The external parts of man are well known: the internal parts are -far from being so. The parts of man are in a great measure unknown; so -that we must judge concerning them by reference to the analogy of other -animals...." - -(_C_) "Some animals are altogether destitute of gall-bladder, as the -horse, the mule, the ass, the deer, the roe.... But in some kinds it -appears that some have it, and some have it not, as the mice kind. And -among these is man; for some men appear to have a gall-bladder on the -liver, and some not to have one. And thus there is a doubt as to the -species in general; for those who have happened to examine examples of -either kind, hold that all the cases are of that kind." - -(_D_) Those of the ancients speak most plausibly, who say that the -absence of the gall-bladder is the cause of long life; looking at -animals with uncloven hoof, and deer: for these are destitute of -gall-bladder, and live a long time. And further, those animals in which -the ancients had not the opportunity of ascertaining that they have not -the gall-bladder, as the dolphin, and the camel, are also long-lived -animals." - -It appears, from these passages, that Aristotle was aware that some -persons had asserted man to have a gall-bladder, but that he also -conceived this not to be universally true. He may have inclined to -the opinion, that the opposite case was the more usual, and may have -written ἄνθρωπος in the passage which I have been discussing. Another -mistake of his is the reckoning deer among long-lived animals. - -It appears probable, from the context of the passages (_C_) and (_D_), -that the conjecture of a connexion between absence of the gall-bladder -and length of life was suggested by some such notion as this:--that -the gall, from its bitterness, is the cause of irritation, mental and -bodily, and that irritation is adverse to longevity. The opinion is -ascribed to "the ancients," not claimed by Aristotle as his own. - - -FOOTNOTES: - -[Footnote 350: Mr. Owen, to whom I am indebted for the physiological -part of this criticism, tells me, "All mammalia have bile, the -carnivora in greater proportion than the herbivora: the gall-bladder -is a comparatively unimportant accessory to the biliary apparatus; -adjusting it to certain modifications of stomach and intestine: there -is no relation between natural longevity and bile. Neither has the -presence or absence of the gall-bladder any connexion with age. Man and -the elephant are perhaps for their size the longest lived animals, and -the latest at coming to maturity: one has the gall-bladder, and the -other not."] - - -APPENDIX E. - -ON THE FUNDAMENTAL ANTITHESIS OF PHILOSOPHY. - -(_Cam. Phil. Soc._ FEB. 5, 1844.) - - -1. All persons who have attended in any degree to the views generally -current of the nature of reasoning are familiar with the distinction -of _necessary_ truths and _truths of experience_; and few such -persons, or at least few students of mathematics, require to have this -distinction explained or enforced. All geometricians are satisfied that -the geometrical truths with which they are conversant are necessarily -true: they not only are true, but they must be true. The meaning of the -terms being understood, and the proof being gone through, the truth -of the proposition must be assented to. That parallelograms upon the -same base and between the same parallels are equal;--that angles in the -same segment are equal;--these are propositions which we learn to be -true by demonstrations deduced from definitions and axioms; and which, -when we have thus learnt them, we see could not be otherwise. On the -other hand, there are other truths which we learn from experience; -as for instance, that the stars revolve round the pole in one day; -and that the moon goes through her phases from full to full again in -thirty days. These truths we see to be true; but we know them only -by experience. Men never could have discovered them without looking -at the stars and the moon; and having so learnt them, still no one -will pretend to say that they are necessarily true. For aught we can -see, things might have been otherwise; and if we had been placed in -another part of the solar system, then, according to the opinions of -astronomers, experience would have presented them otherwise. - -2. I take the astronomical truths of experience to contrast with the -geometrical necessary truths, as being both of a familiar definite -sort; we may easily find other examples of both kinds of truth. The -truths which regard numbers are necessary truths. It is a necessary -truth, that 27 and 38 are equal to 65; that half the sum of two -numbers added to half their difference is equal to the greater -number. On the other hand, that sugar will dissolve in water; that -plants cannot live without light; and in short, the whole body of our -knowledge in chemistry, physiology, and the other inductive sciences, -consists of truths of experience. If there be any science which offer -to us truths of an ambiguous kind, with regard to which we may for a -moment doubt whether they are necessary or experiential, we will defer -the consideration of them till we have marked the distinction of the -two kinds more clearly. - -3. One mode in which we may express the difference of necessary truths -and truths of experience, is, that necessary truths are those _of -which we cannot distinctly conceive the contrary_. We can very readily -conceive the contrary of experiential truths. We can conceive the stars -moving about the pole or across the sky in any kind of curves with any -velocities; we can conceive the moon always appearing during the whole -month as a luminous disk, as she might do if her light were inherent -and not borrowed. But we cannot conceive one of the parallelograms on -the same base and between the same parallels larger than the other; -for we find that, if we attempt to do this, when we separate the -parallelograms into parts, we have to conceive one triangle larger -than another, both having all their parts equal; which we cannot -conceive at all, if we conceive the triangles distinctly. We make this -impossibility more clear by conceiving the triangles to be placed so -that two sides of the one coincide with two sides of the other; and it -is then seen, that in order to conceive the triangles unequal, we must -conceive the two bases which have the same extremities both ways, to -be different lines, though both straight lines. This it is impossible -to conceive: we assent to the impossibility as an axiom, when it is -expressed by saying, that two straight lines cannot inclose a space; -and thus we cannot distinctly conceive the contrary of the proposition -just mentioned respecting parallelograms. - -4. But it is necessary, in applying this distinction, to bear in mind -the terms of it;--that we cannot _distinctly_ conceive the contrary -of a necessary truth. For in a certain loose, indistinct way, persons -conceive the contrary of necessary geometrical truths, when they -erroneously conceive false propositions to be true. Thus, Hobbes -erroneously held that he had discovered a means of geometrically -doubling the cube, as it is called, that is, finding two mean -proportionals between two given lines; a problem which cannot be solved -by plane geometry. Hobbes not only proposed a construction for this -purpose, but obstinately maintained that it was right, when it had -been proved to be wrong. But then, the discussion showed how indistinct -the geometrical conceptions of Hobbes were; for when his critics had -proved that one of the lines in his diagram would not meet the other -in the point which his reasoning supposed, but in another point near -to it; he maintained, in reply, that one of these points was large -enough to include the other, so that they might be considered as the -same point. Such a mode of conceiving the opposite of a geometrical -truth, forms no exception to the assertion, that this opposite cannot -be distinctly conceived. - -5. In like manner, the indistinct conceptions of children and of rude -savages do not invalidate the distinction of necessary and experiential -truths. Children and savages make mistakes even with regard to numbers; -and might easily happen to assert that 27 and 38 are equal to 63 or -64. But such mistakes cannot make such arithmetical truths cease to be -necessary truths. When any person conceives these numbers and their -addition distinctly, by resolving them into parts, or in any other way, -he sees that their sum is necessarily 65. If, on the ground of the -possibility of children and savages conceiving something different, it -be held that this is not a necessary truth, it must be held on the same -ground, that it is not a necessary truth that 7 and 4 are equal to 11; -for children and savages might be found so unfamiliar with numbers as -not to reject the assertion that 7 and 4 are 10, or even that 4 and 3 -are 6, or 8. But I suppose that no persons would on such grounds hold -that these arithmetical truths are truths known only by experience. - -6. Necessary truths are established, as has already been said, by -demonstration, proceeding from definitions and axioms, according to -exact and rigorous inferences of reason. Truths of experience are -collected from what we see, also according to inferences of reason, -but proceeding in a less exact and rigorous mode of proof. The former -depend upon the relations of the ideas which we have in our minds: -the latter depend upon the appearances or phenomena, which present -themselves to our senses. Necessary truths are formed from our -thoughts, the elements of the world within us; experiential truths are -collected from things, the elements of the world without us. The truths -of experience, as they appear to us in the external world, we call -Facts; and when we are able to find among our ideas a train which will -conform themselves to the apparent facts, we call this a Theory. - -7. This distinction and opposition, thus expressed in various forms; -as Necessary and Experiential Truth, Ideas and Senses, Thoughts and -Things, Theory and Fact, may be termed the _Fundamental Antithesis -of Philosophy_; for almost all the discussions of philosophers have -been employed in asserting or denying, explaining or obscuring this -antithesis. It may be expressed in many other ways; but is not -difficult, under all these different forms, to recognize the same -opposition: and the same remarks apply to it under its various forms, -with corresponding modifications. Thus, as we have already seen, the -antithesis agrees with that of Reasoning and Observation: again, it -is identical with the opposition of Reflection and Sensation: again, -sensation deals with Objects; facts involve Objects, and generally all -things without us are Objects:--Objects of sensation, of observation. -On the other hand, we ourselves who thus observe objects, and in whom -sensation is, may be called the Subjects of sensation and observation. -And this distinction of Subject and Object is one of the most general -ways of expressing the fundamental antithesis, although not yet perhaps -quite familiar in English. I shall not scruple however to speak of -the Subjective and Objective element of this antithesis, where the -expressions are convenient. - -8. All these forms of antithesis, and the familiar references to them -which men make in all discussions, show the fundamental and necessary -character of the antithesis. We can have no knowledge without the -union, no philosophy without the separation, of the two elements. We -can have no knowledge, except we have both impressions on our senses -from the world without, and thoughts from our minds within:--except we -attend to things, and to our ideas;--except we are passive to receive -impressions, and active to compare, combine, and mould them. But on -the other hand, philosophy seeks to distinguish the impressions of our -senses from the thoughts of our minds;--to point out the difference of -ideas and things;--to separate the active from the passive faculties -of our being. The two elements, sensations and ideas, are both -requisite to the existence of our knowledge, as both matter and form -are requisite to the existence of a body. But philosophy considers the -matter and the form separately. The properties of the form are the -subject of geometry, the properties of the matter are the subject of -chemistry or mechanics. - -9. But though philosophy considers these elements of knowledge -separately, they cannot really be separated, any more than can matter -and form. "We cannot exhibit matter without form, or form without -matter; and just as little can we exhibit sensations without ideas, or -ideas without sensations;--the passive or the active faculties of the -mind detached from each other. - -In every act of my knowledge, there must be concerned the things -whereof I know, and thoughts of me who know: I must both passively -receive or have received impressions, and I must actively combine -them and reason on them. No apprehension of things is purely ideal: -no experience of external things is purely sensational. If they -be conceived as _things_, the mind must have been awakened to the -conviction of things by sensation: if they be _conceived_ as things, -the expressions of the senses must have been bound together by -conceptions. If we _think_ of any _thing_, we must recognize the -existence both of thoughts and of things. _The fundamental antithesis -of philosophy is an antithesis of inseparable elements._ - -10. Not only cannot these elements be separately exhibited, but they -cannot be separately conceived and described. The description of them -must always imply their relation; and the names by which they are -denoted will consequently always bear a relative significance. And thus -_the terms which denote the fundamental antithesis of philosophy cannot -be applied absolutely and exclusively in any case_. We may illustrate -this by a consideration of some of the common modes of expressing the -antithesis of which we speak. The terms Theory and Fact are often -emphatically used as opposed to each other: and they are rightly so -used. But yet it is impossible to say absolutely in any case, This is -a Fact and not a Theory; this is a Theory and not a Fact, meaning by -Theory, true Theory. Is it a fact or a theory that the stars appear -to revolve round the pole? Is it a fact or a theory that the earth is -a globe revolving round its axis? Is it a fact or a theory that the -earth revolves round the sun? Is it a fact or a theory that the sun -attracts the earth? Is it a fact or a theory that a loadstone attracts -a needle? In all these cases, some persons would answer one way and -some persons another. A person who has never watched the stars, and has -only seen them from time to time, considers their circular motion round -the pole as a theory, just as he considers the motion of the sun in the -ecliptic as a theory, or the apparent motion of the inferior planets -round the sun in the zodiac. A person who has compared the measures of -different parts of the earth, and who knows that these measures cannot -be conceived distinctly without supposing the earth a globe, considers -its globular form a fact, just as much as the square form of his -chamber. A person to whom the grounds of believing the earth to revolve -round its axis and round the sun, are as familiar as the grounds for -believing the movements of the mail-coaches in this country, conceives -the former events to be facts, just as steadily as the latter. And a -person who, believing the fact of the earth's annual motion, refers it -distinctly to its mechanical course, conceives the sun's attraction as -a fact, just as he conceives as a fact the action of the wind which -turns the sails of a mill. We see then, that in these cases we cannot -apply absolutely and exclusively either of the terms, Fact or Theory. -Theory and Fact are the elements which correspond to our Ideas and our -Senses. The Facts are facts so far as the Ideas have been combined with -the sensations and absorbed in them: the Theories are Theories so far -as the Ideas are kept distinct from the sensations, and so far as it is -considered as still a question whether they can be made to agree with -them. A true Theory is a fact, a Fact is a familiar theory. - -In like manner, if we take the terms Reasoning and Observation; at -first sight they appear to be very distinct. Our observation of the -world without us, our reasonings in our own minds, appear to be clearly -separated and opposed. But yet we shall find that we cannot apply -these terms absolutely and exclusively. I see a book lying a few feet -from me: is this a matter of observation? At first, perhaps, we might -be inclined to say that it clearly is so. But yet, all of us, who -have paid any attention to the process of vision, and to the mode in -which we are enabled to judge of the distance of objects, and to judge -them to be distant objects at all, know that this judgment involves -inferences drawn from various sensations;--from the impressions on -our two eyes;--from our muscular sensations; and the like. These -inferences are of the nature of reasoning, as much as when we judge of -the distance of an object on the other side of a river by looking at -it from different points, and stepping the distance between them. Or -again: we observe the setting sun illuminate a gilded weathercock; but -this is as much a matter of reasoning as when we observe the phases of -the moon, and infer that she is illuminated by the sun. All observation -involves inferences, and inference is reasoning. - -11. Even the simplest terms by which the antithesis is expressed cannot -be applied: ideas and sensations, thoughts and things, subject and -object, cannot in any case be applied absolutely and exclusively. Our -sensations require ideas to bind them together, namely, ideas of space, -time, number, and the like. If not so bound together, sensations do not -give us any apprehension of things or objects. All things, all objects, -must exist in space and in time--must be one or many. Now space, time, -number, are not sensations or things. They are something different -from, and opposed to sensations and things. We have termed them ideas. -It may be said they are _relations_ of things, or of sensations. But -granting this form of expression, still a _relation_ is not a thing -or a sensation; and therefore we must still have another and opposite -element, along with our sensations. And yet, though we have thus these -two elements in every act of perception, we cannot designate any -portion of the act as absolutely and exclusively belonging to one of -the elements. Perception involves sensation, along with ideas of time, -space, and the like; or, if any one prefers the expression, involves -sensations along with the apprehension of relations. Perception is -sensation, along with such ideas as make sensation into an apprehension -of things or objects. - -12. And as perception of objects implies ideas, as observation implies -reasoning; so, on the other hand, ideas cannot exist where sensation -has not been: reasoning cannot go on when there has not been previous -observation. This is evident from the necessary order of development -of the human faculties. Sensation necessarily exists from the first -moments of our existence, and is constantly at work. Observation -begins before we can suppose the existence of any reasoning which is -not involved in observation. Hence, at whatever period we consider -our ideas, we must consider them as having been already engaged in -connecting our sensations, and as modified by this employment. By being -so employed, our ideas are unfolded and defined, and such development -and definition cannot be separated from the ideas themselves. We -cannot conceive space without boundaries or forms; now forms involve -sensations. We cannot conceive time without events which mark the -course of time; but events involve sensations. We cannot conceive -number without conceiving things which are numbered; and things imply -sensations. And the forms, things, events, which are thus implied in -our ideas, having been the objects of sensation constantly in every -part of our life, have modified, unfolded and fixed our ideas, to -an extent which we cannot estimate, but which we must suppose to be -essential to the processes which at present go on in our minds. We -cannot say that objects create ideas; for to perceive objects we must -already have ideas. But we may say, that objects and the constant -perception of objects have so far modified our ideas, that we cannot, -even in thought, separate our ideas from the perception of objects. - -We cannot say of any ideas, as of the idea of space, or time, or -number, that they are absolutely and exclusively ideas. We cannot -conceive what space, or time, or number would be in our minds, if we -had never perceived any thing or things in space or time. We cannot -conceive ourselves in such a condition as never to have perceived any -thing or things in space or time. But, on the other hand, just as -little can we conceive ourselves becoming acquainted with space and -time or numbers as objects of sensation. We cannot reason without -having the operations of our minds affected by previous sensations; but -we cannot conceive reasoning to be merely a series of sensations. In -order to be used in reasoning, sensation must become observation; and, -as we have seen, observation already involves reasoning. In order to -be connected by our ideas, sensations must be things or objects, and -things or objects already include ideas. And thus, as we have said, -none of the terms by which the fundamental antithesis is expressed can -be absolutely and exclusively applied. - -13. I now proceed to make one or two remarks suggested by the views -which have thus been presented. And first I remark, that since, as -we have just seen, none of the terms which express the fundamental -antithesis can be applied absolutely and exclusively, the absolute -application of the antithesis in any particular case can never be a -conclusive or immoveable principle. This remark is the more necessary -to be borne in mind, as the terms of this antithesis are often used -in a vehement and peremptory manner. Thus we are often told that such -a thing is a _Fact_ and not a Theory, with all the emphasis which, in -speaking or writing, tone or italics or capitals can give. "We see from -what has been said, that when this is urged, before we can estimate the -truth, or the value of the assertion, we must ask to whom is it a fact? -what habits of thought, what previous information, what ideas does -it imply, to conceive the fact as a fact? Does not the apprehension -of the fact imply assumptions which may with equal justice be called -theory, and which are perhaps false theory? in which case, the fact is -no fact. Did not the ancients assert it as a fact, that the earth stood -still, and the stars moved? and can any fact have stronger apparent -evidence to justify persons in asserting it emphatically than this -had? These remarks are by no means urged in order to show that no fact -can be certainly known to be true; but only to show that no fact can -be certainly shown to be a fact merely by calling it a fact, however -emphatically. There is by no means any ground of general skepticism -with regard to truth involved in the doctrine of the necessary -combination of two elements in all our knowledge. On the contrary, -ideas are requisite to the essence, and things to the reality of our -knowledge in every case. The proportions of geometry and arithmetic are -examples of knowledge respecting our ideas of space and number, with -regard to which there is no room for doubt. The doctrines of astronomy -are examples of truths not less certain respecting the external world. - -14. I remark further, that since in every act of knowledge, observation -or perception, both the elements of the fundamental antithesis are -involved, and involved in a manner inseparable even in our conceptions, -it must always be possible to derive one of these elements from the -other, if we are satisfied to accept, as proof of such derivation, -that one always co-exists with and implies the other. Thus an -opponent may say, that our ideas of space, time, and number, are -derived from our sensations or perceptions, because we never were -in a condition in which we had the ideas of space and time, and had -not sensations or perceptions. But then, we may reply to this, that -we no sooner perceive objects than we perceive them as existing in -space and time, and therefore the ideas of space and time are not -derived from the perceptions. In the same manner, an opponent may -say, that all knowledge which is involved in our reasonings is the -result of experience; for instance, our knowledge of geometry. For -every geometrical principle is presented to us by experience as true; -beginning with the simplest, from which all others are derived by -processes of exact reasoning. But to this we reply, that experience -cannot be the origin of such knowledge; for though experience shows -that such principles are true, it cannot show that they _must be_ true, -which we also know. We never have seen, as a matter of observation, -two straight lines inclosing a space; but we venture to say further, -without the smallest hesitation, that we never shall see it; and if any -one were to tell us that, according to his experience, such a form was -often seen, we should only suppose that he did not know what he was -talking of. No number of acts of experience can add to the certainty -of our knowledge in this respect; which shows that our knowledge is -not made up of acts of experience. We cannot test such knowledge by -experience; for if we were to try to do so, we must first know that the -lines with which we make the trial _are_ straight; and we have no test -of straightness better than this, that two such lines cannot inclose a -space. Since then, experience can neither destroy, add to, nor test our -axiomatic knowledge, such knowledge cannot be derived from experience. -Since no one act of experience can affect our knowledge, no numbers of -acts of experience can make it. - -15. To this a reply has been offered, that it is a characteristic -property of geometric forms that the ideas of them exactly resemble the -sensations; so that these ideas are as fit subjects of experimentation -as the realities themselves; and that by such experimentation we learn -the truth of the axioms of geometry. I might very reasonably ask those -who use this language to explain how a particular class of ideas can -be said to resemble sensations; how, if they do, we can know it to be -so; how we can prove this resemblance to belong to geometrical ideas -and sensations; and how it comes to be an especial characteristic of -those. But I will put the argument in another way. Experiment can only -show what is, not what must be. If experimentation on ideas shows what -must be, it is different from what is commonly called experience. - -I may add, that not only the mere use of our senses cannot show that -the axioms of geometry _must be_ true, but that, without the light -of our ideas, it cannot even show that they _are_ true. If we had a -segment of a circle a mile long and an inch wide, we should have two -lines inclosing a space; but we could not, by seeing or touching any -part of either of them, discover that it was a bent line. - -16. That mathematical truths are not derived from experience is perhaps -still more evident, if greater evidence be possible, in the case of -numbers. We assert that 7 and 8 are 15. We find it so, if we try with -counters, or in any other way. But we do not, on that account, say that -the knowledge is derived from experience. We refer to our conceptions -of seven, of eight, and of addition, and as soon as we possess these -conceptions distinctly, we see that the sum must be fifteen. We cannot -be said to make a trial, for we should not believe the apparent result -of the trial if it were different. If any one were to say that the -multiplication table is a table of the results of experience, we should -know that he could not be able to go along with us in our researches -into the foundations of human knowledge; nor, indeed, to pursue with -success any speculations on the subject. - -17. Attempts have also been made to explain the origin of axiomatic -truths by referring them to the association of ideas. But this is -one of the cases in which the word _association_ has been applied so -widely and loosely, that no sense can be attached to it. Those who -have written with any degree of distinctness on the subject, have -truly taught, that the habitual association of the ideas leads us to -believe a connexion of the things: but they have never told us that -this association gave us the power of forming the ideas. Association -may determine belief, but it cannot determine the possibility of our -conceptions. The African king did not believe that water could become -solid, because he had never seen it in that state. But that accident -did not make it impossible to conceive it so, any more than it is -impossible for us to conceive frozen quicksilver, or melted diamond, -or liquefied air; which we may never have seen, but have no difficulty -in conceiving. If there were a tropical philosopher really incapable -of conceiving water solidified, he must have been brought into that -mental condition by abstruse speculations on the necessary relations of -solidity and fluidity, not by the association of ideas. - -18. To return to the results of the nature of the Fundamental -Antithesis. As by assuming universal and indissoluble connexion of -ideas with perceptions, of knowledge with experience, as an evidence -of derivation, we may assert the former to be derived from the latter, -so might we, on the same ground, assert the latter to be derived from -the former. We see all forms in space; and we might hence assert all -forms to be mere modifications of our idea of space. We see all events -happen in time; and we might hence assert all events to be merely -limitations and boundary-marks of our idea of time. We conceive all -collections of things as two or three, or some other number: it might -hence be asserted that we have an original idea of number, which is -reflected in external things. In this case, as in the other, we are met -at once by the impossibility of this being a complete account of our -knowledge. Our ideas of space, of time, of number, however distinctly -reflected to us with limitations and modifications, must be reflected, -limited and modified by something different from themselves. We must -have visible or tangible forms to limit space, perceived events to mark -time, distinguishable objects to exemplify number. But still, in forms, -and events, and objects, we have a knowledge which they themselves -cannot give us. For we know, without attending to them, that whatever -they are, they will conform and must conform to the truths of geometry -and arithmetic. There is an ideal portion in all our knowledge of the -external world; and if we were resolved to reduce all our knowledge -to one of its two antithetical elements, we might say that all our -knowledge consists in the relation of our ideas. Wherever there is -necessary truth, there must be something more than sensation can -supply: and the necessary truths of geometry and arithmetic show us -that our knowledge of objects in space and time depends upon necessary -relations of ideas, whatever other element it may involve. - -19. This remark may be carried much further than the domain of geometry -and arithmetic. Our knowledge of matter may at first sight appear -to be altogether derived from the senses. Yet we cannot derive from -the senses our knowledge of a truth which we accept as universally -certain;--namely, that we cannot by any process add to or diminish -the quantity of matter in the world. This truth neither is nor can be -derived from experience; for the experiments which we make to verify -it pre-suppose its truth. When the philosopher was asked what was -the weight of smoke, he bade the inquirer subtract the weight of -the ashes from the weight of the fuel. Every one who thinks clearly -of the changes which take place in matter, assents to the justice of -this reply: and this, not because any one had found by trial that such -was the weight of the smoke produced in combustion, but because the -weight lost was assumed to have gone into some other form of matter, -not to have been destroyed. When men began to use the balance in -chemical analysis, they did not prove by trial, but took for granted, -as self-evident, that the weight of the whole must be found in the -aggregate weight of the elements. Thus it is involved in the idea of -matter that its amount continues unchanged in all changes which take -place in its consistence. This is a necessary truth: and thus our -knowledge of matter, as collected from chemical experiments, is also -a modification of our idea of matter as the material of the world -incapable of addition or diminution. - -20. A similar remark may be made with regard to the mechanical -properties of matter. Our knowledge of these is reduced, in our -reasonings, to principles which we call the laws of motion. These laws -of motion, as I have endeavoured to show[351], depend upon the idea -of Cause, and involve necessary truths, which are necessarily implied -in the idea of cause;--namely, that every change of motion must have -a cause--that the effect is measured by the cause;--that reaction -is equal and opposite to action. These principles are not derived -from experience. No one, I suppose, would derive from experience the -principle, that every event must have a cause. Every attempt to see -the traces of cause in the world assumes this principle. I do not say -that these principles are anterior to experience; for I have already, -I hope, shown, that neither of the two elements of our knowledge is, -or can be, anterior to the other. But the two elements are co-ordinate -in the development of the human mind; and the ideal element may be -said to be the origin of our knowledge with the more propriety of the -two, inasmuch as our knowledge is the relation of ideas. The other -element of knowledge, in which sensation is concerned, and which -embodies, limits, and defines the necessary truths which express the -relations of our ideas, may be properly termed experience; and I have, -in the discussion just quoted, endeavoured to show how the principles -concerning mechanical causation, which I have just stated, are, by -observation and experiment, limited and defined, so that they become -the laws of motion. And thus we see that such knowledge is derived -from ideas, in a sense quite as general and rigorous, to say the least, -as that in which it is derived from experience. - -21. I will take another example of this; although it is one less -familiar, and the consideration of it perhaps a little more difficult -and obscure. The objects which we find in the world, for instance, -minerals and plants, are of different kinds; and according to their -kinds, they are called by various names, by means of which we know -what we mean when we speak of them. The discrimination of these kinds -of objects, according to their different forms and other properties, -is the business of chemistry and botany. And this business of -discrimination, and of consequent classification, has been carried on -from the first periods of the development of the human mind, by an -industrious and comprehensive series of observations and experiments; -the only way in which any portion of the task could have been effected. -But as the foundation of all this labour, and as a necessary assumption -during every part of its progress, there has been in men's minds -the principle, that objects are so distinguishable by resemblances -and differences, that they may be named, and known by their names. -This principle is involved in the idea of a Name; and without it no -progress could have been made. The principle may be briefly stated -thus:--Intelligible Names of kinds are possible. If we suppose this -not to be so, language can no longer exist, nor could the business -of human life go on. If instead of having certain definite kinds of -minerals, gold, iron, copper and the like, of which the external forms -and characters are constantly connected with the same properties and -qualities, there were no connexion between the appearance and the -properties of the object;--if what seemed externally iron might turn -out to resemble lead in its hardness; and what seemed to be gold during -many trials, might at the next trial be found to be like copper; not -only all the uses of these minerals would fail, but they would not be -distinguishable kinds of things, and the names would be unmeaning. And -if this entire uncertainty as to kind and properties prevailed for all -objects, the world would no longer be a world to which language was -applicable. To man, thus unable to distinguish objects into kinds, and -call them by names, all knowledge would be impossible, and all definite -apprehension of external objects would fade away into an inconceivable -confusion. In the very apprehension of objects as intelligibly sorted, -there is involved a principle which springs within us, contemporaneous, -in its efficacy, with our first intelligent perception of the kinds -of things of which the world consists. We assume, as a necessary -basis of our knowledge, that things are of definite kinds; and the aim -of chemistry, botany, and other sciences is to find marks of these -kinds; and along with these, to learn their definitely-distinguished -properties. Even here, therefore, where so large a portion of our -knowledge comes from experience and observation, we cannot proceed -without a necessary truth derived from our ideas, as our fundamental -principle of knowledge. - -22. What the marks are, which distinguish the constant differences of -kinds of things (definite marks, selected from among many unessential -appearances), and what their definite properties are, when they -are so distinguished, are parts of our knowledge to be learnt from -observation, by various processes; for instance, among others, by -chemical analysis. We find the differences of bodies, as shown by such -analysis, to be of this nature:--that there are various elementary -bodies, which, combining in different definite proportions, form kinds -of bodies definitely different. But, in arriving at this conclusion, -we introduce a new idea, that of Elementary Composition, which is not -extracted from the phenomena, but supplied by the mind, and introduced -in order to make the phenomena intelligible. That this notion of -elementary composition is not supplied by the chemical phenomena of -combustion, mixture, &c. as merely an observed fact, we see from this; -that men had in ancient times performed many experiments in which -elementary composition was concerned, and had not seen the fact. It -never was truly seen till modern times; and when seen, it gave a new -aspect to the whole body of known facts. This idea of elementary -composition, then, is supplied by the mind, in order to make the -facts of chemical analysis and synthesis intelligible _as_ analysis -and synthesis. And this idea being so supplied, there enters into our -knowledge along with it a corresponding necessary principle;--That the -elementary composition of a body determines its kind and properties. -This is, I say, a principle assumed, as a consequence of the idea of -composition, not a result of experience; for when bodies have been -divided into their kinds, we take for granted that the analysis of a -single specimen may serve to determine the analysis of all bodies of -the same kind: and without this assumption, chemical knowledge with -regard to the kinds of bodies would not be possible. It has been said -that we take only one experiment to determine the composition of any -particular kind of body, because we have a thousand experiments to -determine that bodies of the same kind have the same composition. But -this is not so. Our belief in the principle that bodies of the same -kind have the same composition is not established by experiments, -but is assumed as a necessary consequence of the ideas of Kind and of -Composition. If, in our experiments, we found that bodies supposed -to be of the same kind had not the same composition, we should not -at all doubt of the principle just stated, but conclude at once that -the bodies were _not_ of the same kind;--that the marks by which the -kinds are distinguished had been wrongly stated. This is what has very -frequently happened in the course of the investigations of chemists and -mineralogists. And thus we have it, not as an experiential fact, but -as a necessary principle of chemical philosophy, that the Elementary -Composition of a body determines its Kind and Properties. - -23. How bodies differ in their elementary composition, experiment must -teach us, as we have already said, that experiment has taught us. But -as we have also said, whatever be the nature of this difference, kinds -must be definite, in order that language may be possible: and hence, -whatever be the terms in which we are taught by experiment to express -the elementary composition of bodies, the result must be conformable -to this principle, That the differences of elementary composition -are definite. The law to which we are led by experiment is, that the -elements of bodies continue in definite proportions according to -weight. Experiments add other laws; as for instance, that of multiple -proportions in different kinds of bodies composed of the same elements; -but of these we do not here speak. - -24. We are thus led to see that in our knowledge of mechanics, -chemistry, and the like, there are involved certain necessary -principles, derived from our ideas, and not from experience. But to -this it may be objected, that the parts of our knowledge in which these -principles are involved has, in historical fact, all been acquired by -experience. The laws of motion, the doctrine of definite proportions, -and the like, have all become known by experiment and observation; and -so far from being seen as necessary truths, have been discovered by -long-continued labours and trials, and through innumerable vicissitudes -of confusion, error, and imperfect truth. This is perfectly true: but -does not at all disprove what has been said. Perception of external -objects and experience, experiment and observation are needed, -not only, as we have said, to supply the objective element of all -knowledge--to embody, limit, define, and modify our ideas; but this -intercourse with objects is also requisite to unfold and fix our ideas -themselves. As we have already said, ideas and facts can never be -separated. Our ideas cannot be exercised and developed in any other -form than in their combination with facts, and therefore the trials, -corrections, controversies, by which the matter of our knowledge is -collected, is also the only way in which the form of it can be rightly -fashioned. Experience is requisite to the clearness and distinctness of -our ideas, not because they are derived from experience, but because -they can only be exercised upon experience. And this consideration -sufficiently explains how it is that experiment and observation have -been the means, and the only means, by which men have been led to a -knowledge of the laws of nature. In reality, however, the necessary -principles which flow from our ideas, and which are the basis of such -knowledge, have not only been inevitably assumed in the course of such -investigations, but have been often expressly promulgated in words -by clear-minded philosophers, long before their true interpretation -was assigned by experiment. This has happened with regard to such -principles as those above mentioned; That every event must have a -cause; That reaction is equal and opposite to action; That the quantity -of matter in the world cannot be increased or diminished: and there -would be no difficulty in finding similar enunciations of the other -principles above mentioned;--That the kinds of things have definite -differences, and that these differences depend upon their elementary -composition. In general, however, it may be allowed, that the necessary -principles which are involved in those laws of nature of which we have -a knowledge become then only clearly known, when the laws of nature are -discovered which thus involve the necessary ideal element. - -25. But since this is allowed, it may be further asked, how we are to -distinguish between the necessary principle which is derived from our -ideas, and the law of nature which is learnt by experience. And to this -we reply, that the necessary principle may be known by the condition -which we have already mentioned as belonging to such principles: ... -that it is impossible distinctly to conceive the contrary. We cannot -conceive an event without a cause, except we abandon all distinct idea -of cause; we cannot distinctly conceive two straight lines inclosing -space; and if we seem to conceive this, it is only because we conceive -indistinctly. We cannot conceive 5 and 3 making 7 or 9; if a person -were to say that he could conceive this, we should know that he was a -person of immature or rude or bewildered ideas, whose conceptions had -no distinctness. And thus we may take it as the mark of a necessary -truth, that we cannot conceive the contrary distinctly. - -26. If it be asked what is the test of distinct conception (since it -is upon the distinctness of conception that the matter depends), we -may consider what answer we should give to this question if it were -asked with regard to the truths of geometry. If we doubted whether -anyone had these distinct conceptions which enable him to see the -necessary nature of geometrical truth, we should inquire if he could -understand the axioms as axioms, and could follow, as demonstrative, -the reasonings which are founded upon them. If this were so, we should -be ready to pronounce that he had distinct ideas of space, in the sense -now supposed. And the same answer may be given in any other case. That -reasoner has distinct conceptions of mechanical causes who can see -the axioms of mechanics as axioms, and can follow the demonstrations -derived from them as demonstrations. If it be said that the science, -as presented to him, may be erroneously constructed; that the axioms -may not be axioms, and therefore the demonstrations may be futile, we -still reply, that the same might be said with regard to geometry: and -yet that the possibility of this does not lead us to doubt either of -the truth or of the necessary nature of the propositions contained -in Euclid's Elements. We may add further, that although, no doubt, -the authors of elementary books maybe persons of confused minds, who -present as axioms what are not axiomatic truths; yet that in general, -what is presented as an axiom by a thoughtful man, though it may -include some false interpretation or application of our ideas, will -also generally include some principle which really is necessarily true, -and which would still be involved in the axiom, if it were corrected -so as to be true instead of false. And thus we still say, that if in -any department of science a man can conceive distinctly at all, there -are principles the contrary of which he cannot distinctly conceive, and -which are therefore necessary truths. - -27. But on this it may be asked, whether truth can thus depend upon -the particular state of mind of the person who contemplates it; and -whether that can be a necessary truth which is not so to all men. And -to this we again reply, by referring to geometry and arithmetic. It -is plain that truths may be necessary truths which are not so to all -men, when we include men of confused and perplexed intellects; for to -such men it is not a necessary truth that two straight lines cannot -inclose a space, or that 14 and 17 are 31. It need not be wondered -at, therefore, if to such men it does not appear a necessary truth -that reaction is equal and opposite to action, or that the quantity of -matter in the world cannot be increased or diminished. And this view of -knowledge and truth does not make it depend upon the state of mind of -the student, any more than geometrical knowledge and geometrical truth, -by the confession of all, depend upon that state. We know that a man -cannot have any knowledge of geometry without so much of attention to -the matter of the science, and so much of care in the management of -his own thoughts, as is requisite to keep his ideas distinct and clear. -But we do not, on that account, think of maintaining that geometrical -truth depends merely upon the state of the student's mind. We conceive -that he knows it because it is true, not that it is true because he -knows it. We are not surprised that attention and care and repeated -thought should be requisite to the clear apprehension of truth. For -such care and such repetition are requisite to the distinctness and -clearness of our ideas: and yet the relations of these ideas, and -their consequences, are not produced by the efforts of attention or -repetition which we exert. They are in themselves something which -we may discover, but cannot make or change. The idea of space, for -instance, which is the basis of geometry, cannot give rise to any -doubtful propositions. What is inconsistent with the idea of space -cannot be truly obtained from our ideas by any efforts of thought or -curiosity; if we blunder into any conclusion inconsistent with the idea -of space, our knowledge, so far as this goes, is no knowledge: any more -than our observation of the external world would be knowledge, if, from -haste or inattention, or imperfection of sense, we were to mistake the -object which we see before us. - -28. But further: not only has truth this reality, which makes it -independent of our mistakes, that it must be what is really consistent -with our ideas; but also, a further reality, to which the term -is more obviously applicable, arising from the principle already -explained, that ideas and perceptions are inseparable. For since, -when we contemplate our ideas, they have been frequently embodied and -exemplified in objects, and thus have been fixed and modified; and -since this compound aspect is that under which we constantly have -them before us, and free from which they cannot be exhibited; our -attempts to make our ideas clear and distinct will constantly lead us -to contemplate them as they are manifested in those external forms -in which they are involved. Thus in studying geometrical truth, we -shall be led to contemplate it as exhibited in visible and tangible -figures;--not as if these could be sources of truth, but as enabling -us more readily to compare the aspects which our ideas, applied to the -world of objects, may assume. And thus we have an additional indication -of the reality of geometrical truth, in the necessary possibility of -its being capable of being exhibited in a visible or tangible form. And -yet even this test by no means supersedes the necessity of distinct -ideas, in order to a knowledge of geometrical truth. For in the case -of the duplication of the cube by Hobbes, mentioned above, the diagram -which he drew made two points appear to coincide, which did not -really, and by the nature of our idea of space, coincide; and thus -confirmed him in his error. - -_Thus the inseparable nature of the Fundamental Antithesis of Ideas and -Things gives reality to our knowledge, and makes objective reality a -corrective of our subjective imperfections in the pursuit of knowledge. -But this objective exhibition of knowledge can by no means supersede a -complete development of the subjective condition, namely, distinctness -of ideas. And that there is a subjective condition, by no means makes -knowledge altogether subjective, and thus deprives it of reality; -because, as we have said, the subjective and the objective elements are -inseparably bound together in the fundamental antithesis._ - -29. It would be easy to apply these remarks to other cases, for -instance, to the case of the principle we have just mentioned, that -the differences of elementary composition of different kinds of bodies -must be definite. We have stated that this principle is necessarily -true;--that the contrary proposition cannot be distinctly conceived. -But by whom? Evidently, according to the preceding reasoning, by a -person who distinctly conceives Kinds, as marked by intelligible -names, and Composition, as determining the kinds of bodies. Persons -new to chemical and classificatory science may not possess these ideas -distinctly; or rather, cannot possess them distinctly; and therefore -cannot apprehend the impossibility of conceiving the opposite of -the above principle; just as the schoolboy cannot apprehend the -impossibility of the numbers in his multiplication table being other -than they are. But this inaptitude to conceive, in either case, does -not alter the necessary character of the truth: although, in one case, -the truth is obvious to all except schoolboys and the like, and the -other is probably not clear to any except those who have attentively -studied the philosophy of elementary compositions. At the same time, -this difference of apprehension of the truth in different persons does -not make the truth doubtful or dependent upon personal qualifications; -for in proportion as persons attain to distinct ideas, they will see -the truth; and cannot, with such ideas, see anything as truth which -is not truth. When the relations of elements in a compound become as -familiar to a person as the relations of factors in a multiplication -table, he will then see what are the necessary axioms of chemistry, as -he now sees the necessary axioms of arithmetic. - -30. There is also one other remark which I will here make. In the -progress of science, both the elements of our knowledge are constantly -expanded and augmented. By the exercise of observation and experiment, -we have a perpetual accumulation of facts, the materials of knowledge, -the objective element. By thought and discussion, we have a perpetual -development of man's ideas going on: theories are framed, the materials -of knowledge are shaped into form; the subjective element is evolved; -and by the necessary coincidence of the objective and subjective -elements, the matter and the form, the theory and the facts, each of -these processes furthers and corrects the other: each element moulds -and unfolds the other. Now it follows, from this constant development -of the ideal portion of our knowledge, that we shall constantly be -brought in view of new Necessary Principles, the expression of the -conditions belonging to the Ideas which enter into our expanding -knowledge. These principles, at first dimly seen and hesitatingly -asserted, at last become clearly and plainly self-evident. Such is the -case with the principles which are the basis of the laws of motion. -Such may soon be the case with the principles which are the basis -of the philosophy of chemistry. Such may hereafter be the case with -the principles which are to be the basis of the philosophy of the -connected and related polarities of chemistry, electricity, galvanism, -magnetism. That knowledge is possible in these cases, we know; that -our knowledge may be reduced to principles, gradually more simple, -we also know; that we have reached the last stage of simplicity of -our principles, few cultivators of the subject will be disposed to -maintain; and that the additional steps which lead towards very simple -and general principles will also lead to principles which recommend -themselves by a kind of axiomatic character, those who judge from the -analogy of the past history of science will hardly doubt. That the -principles thus axiomatic in their form, do also express some relation -of our ideas, of which experiment and observation have given a true -and real interpretation, is the doctrine which I have here attempted -to establish and illustrate in the most clear and undoubted of the -existing sciences; and the evidence of this doctrine in those cases -seems to be unexceptionable, and to leave no room to doubt that such is -the universal type of the progress of science. Such a doctrine, as we -have now seen, is closely connected with the views here presented of -the nature of the Fundamental Antithesis of Philosophy, which I have -endeavoured to illustrate. - - -FOOTNOTES: - -[Footnote 351: _Hist. Sc. Ind._ b. iii.] - - -APPENDIX F. - -REMARKS ON A REVIEW OF THE PHILOSOPHY OF THE INDUCTIVE SCIENCES. - - - _Trinity Lodge, April 11th, 1844._ - - MY DEAR HERSCHEL, - -Being about to send you a copy of a paper on a philosophical question -just printed in the Transactions of our Cambridge Society, I am tempted -to add, as a private communication, a few Remarks on another aspect of -the same question. These Remarks I think I may properly address to you. -They will refer to an Article in the _Quarterly Review_ for June, 1841, -respecting my _History_ and _Philosophy_ of the Inductive Sciences; and -without assigning any other reason, I may say that the interest I know -you to take in speculations on such subjects makes me confident that -you will give a reasonable attention to what I may have to say on the -subject of that Article. With the Reviewal itself, I am so far from -having any quarrel, that when it appeared I received it as affording -all that I hoped from Public Criticism. The degree and the kind of -admiration bestowed upon my works by a writer so familiar with science, -so comprehensive in his views, and so equitable in his decisions, as -the Reviewer manifestly was, I accepted as giving my work a stamp of -acknowledged value which few other hands could have bestowed. - -You may perhaps recollect, however, that the Reviewer dissented -altogether from some of the general views which I had maintained, -and especially from a general view which is also, in the main, that -presented in the accompanying Memoir, namely, that, besides Facts, -Ideas are an indispensable source of our knowledge; that Ideas are -the ground of necessary truth; that the Idea of Space, in particular, -is the ground of the necessary truths of geometry. This question, -and especially as limited to the last form, will be the subject of -my Remarks in the first place; and I wish to consider the Reviewer's -objections with the respect which their subtlety and depth of thought -well deserve. - -The Reviewer makes objections to the account which I have given of -the source whence geometrical truth derives its characters of being -necessary and universal; but he is not one of those metaphysicians -who deny those characters to the truths of geometry. He allows in the -most ample manner that the truths of geometry _are_ necessary. The -question between us therefore is from what this character is derived. -The Reviewer prefers, indeed, to have it considered that the question -is not concerning the necessity, but, as he says, the universality of -these truths; or rather, the nature and grounds of our conviction of -their universality. He might have said, with equal justice, the nature -and grounds of our conviction of their necessity. For his objection to -the term _necessity_ in this case--"that all the propositions about -realities are necessarily true, since every reality must be consistent -with itself," (p. 206)--does not apply to our conviction of necessity, -since we may not be able to see what are the properties of real things; -and therefore may have no conviction of their necessity. It may be a -necessary property of salt to be soluble, but we see no such necessity; -and therefore the assertion of such a property is not one of the -necessary truths with which we are here concerned. But to turn back to -the necessary or universal truths of geometry, and the ground of those -attributes: The main difference between the Author and the Reviewer is -brought into view, when the Reviewer discusses the general argument -which I had used, in order to show that truths which we see to be -necessary and universal cannot be derived from experience. The argument -is this,-- - -"Experience must always consist of a limited number of observations; -and however numerous these may be, they can show nothing with regard -to the infinite number of cases in which the experiment has not been -made.... Truths can only be known to be general, not universal, if -they depend upon experience alone. Experience cannot bestow that -universality which she herself cannot have; nor that necessity of which -she has no comprehension." (_Phil._ _i._ pp. 60, 61.) - -Here is that which must be considered as the cardinal argument on this -subject. It is therefore important to attend to the answer which the -Reviewer makes to it. He says,-- - -"We conceive that a full answer to this argument is afforded by the -nature of the inductive propensity,--by the irresistible impulse of -the mind to generalize _ad infinitum_, when nothing in the nature of -limitation or opposition offers itself to the imagination; and by our -involuntary application of the law of continuity to fill up, by the -same ideal substance of truth, every interval which uncontradicted -experience may have left blank in our inductive conclusion." (p. 207.) - -Now here we have two rival explanations of the same thing,--the -conviction of the universality of geometrical truths. The one -explanation is, that this universality is imposed upon such truths by -their involving a certain element, derived from the universal mode of -activity of the mind when apprehending such truths, which element I -have termed an Idea. The other explanation is, that this universality -arises from the _inductive propensity_--from the _irresistible impulse -to generalize ad infinitum_--from the _involuntary application of the -law of continuity_--from the _filling up all intervals with the same -ideal substance of truth_. - -With regard to these two explanations, I may observe, that so far as -they are thus stated they do not necessarily differ. They both agree -in expressing this; that the ground of the universality of geometrical -truths is a certain law of the mind's activity, which determines its -procedure when it is concerned in apprehending the external world. -One explanation says, that we impress upon the external world the -relations of our ideas, and thus believe more than we see,--the -other says, that we have an irresistible impulse to introduce into -our conviction a relation between what we do observe and what we do -not, namely, to generalize _ad infinitum_ from what we do see. One -explanation says, that we perceive all external objects as included -in absolute ideal space,--the other, that we fill up the intervals of -the objects which we perceive with the same ideal substance of truth. -Both sets of expressions may perhaps be admissible; and if admitted, -may be understood as expressing the same opinions, or opinions which -have much in common. The Author's expressions have the advantage, which -ought to belong to them, as the expressions employed in a systematic -work, of being fixed expressions, technical phrases, intentionally -selected, uniformly and steadily employed whenever the occasion recurs. -The Reviewer's expressions are more lively and figurative, and such -as well become an occasional composition; but hardly such as could -be systematically applied to the subject in a regular treatise. We -could not, as a standard and technical phrase, talk of filling up -the intervals of observation with the same ideal substance of truth; -and the inevitable impulse to generalize would hardly sufficiently -express that we generalize according to a certain idea, namely, the -idea of space. Perhaps that which is suggested to us as the common -import of the two sets of expressions may be conveyed by some other -phrase, in a manner free from the objections which lie against both the -Author's and the Critic's terms. Perhaps the mental idea governing -our experience, and the irresistible impulse to generalize our -observation, may both be superseded by our speaking of a law of the -mind's _activity_, which is really implied in both. There operates, in -observing the external world, a law of the mind's activity, by which it -connects its observations; and this law of the mind's activity may be -spoken of either as the idea of space, or as the irresistible impulse -to generalize the relations of space which it observes. And this -expression--_the laws of the mind's activity_--thus opposed to that -merely passive function by which the mind receives the impressions of -sense, may be applied to other ideas as well as to the idea of space, -and to the impulse to generalize in other truths as well as those of -geometry. - -So far, it would seem, that the Author and the Critic may be brought -into much nearer agreement than at first seemed likely, with regard -to the grounds of the necessity and universality in our knowledge. -But even if we adopt this conciliatory suggestion, and speak of the -necessity and universality of certain truths as arising from the laws -of the mind's activity, we cannot, without producing great confusion, -allow ourselves to say, as the Critic says, that these truths are thus -derived from _experience_, or from _observation_. It will, I say, be -found fatal to all philosophical precision of thought and language, -to say that the fundamental truths of geometry, the axioms, with the -conviction of their necessary truth, are derived from experience. Let -us take any axiomatic truth of geometry, and ask ourselves if this is -not so. - -It is, for example, an axiom in geometry that if a straight line cut -one of two parallel straight lines, it must cut the other also. Is this -truth derived or derivable from observation of actual parallel lines, -and a line cutting them, exhibited to our senses? Let those who say -that we do acquire this truth by observation, imagine to themselves -the mode in which the observation must be made. We have before us two -parallel straight lines, and we see that a straight line which cuts -the one cuts the other also. We see this again in another case, it -may be the angles and the distances being different, and in a third, -and in a fourth; and so on; and generalizing, we are irresistibly -led to believe the assertion to be universally true. But can any one -really imagine this to be the mode in which we arrive at this truth? -"We see," says this explanation, "two parallel straight lines, cut by -a third." But how do we know that the observed lines are parallel? -If we apply any test of parallelism, we must assume some property of -parallels, and thus involve some axiom on the subject, which we have no -more right to assume than the one now under consideration. We should -thus destroy our explanation as an account of the mode of arriving -at independent geometrical axioms. But probably those who would give -such an explanation would not do this. They would not suppose that in -observing this property of parallels we try by measurement whether the -lines are parallel. They would say, I conceive, that we suppose lines -to be parallel, and that then we see that the straight line which cuts -the one must cut the other. That when we make this supposition, we are -persuaded of the truth of the conclusion, is certain. But what I have -to remark is, that this being so, the conclusion is the result, not of -observation, but of the hypothesis. The geometrical truth here spoken -of, after this admission, no longer flows from experience, but from -supposition. It is not that we _ascertain_ the lines to be parallel, -and then _find_ that they have this property: but we _suppose_ the -lines to be parallel, and _therefore_ they have this property. This is -not a truth of experience. - -This, it may be said, is so evident that it cannot have been overlooked -by a very acute reasoner, such as you describe your Critic to be. -What, it may be asked, is the answer which he gives to so palpable an -objection as this? How does he understand his assertion that we learn -the truth of geometrical axioms from experience (p. 208), so as to make -it tenable on his own principles? What account does he give of the -origin of such axioms which makes them in any sense to be derived from -experience? - -In justice to the Reviewer's fairness (which is unimpeachable -throughout his argumentation) it must be stated that he does give an -account in which he professes to show how this is done. And the main -step of his explanation consists in introducing the conception of -_direction_, and _unity of direction_. He says (p. 208), "The _unity of -direction_, or that we cannot march from a given point by more than one -path _direct to the same object_, is a matter of practical experience, -long before it can by possibility become matter of abstract thought." -We might ask here, as in the former case, how this can be a matter of -experience, except we have some independent test of directness? and we -might demand to know what this test is. Or do we not rather, here as -in the other case, _suppose_ the directness of the path; and is not -the singleness of the direct path a consequence, not of its observed -form, but of its hypothetical directness; and thus by no means a -result of experience? But we may put our remark upon this deduction -of the geometrical axiom in another form. We generalize, it is said, -the observations which we have made ever since we were born. But this -term "generalize" is far too vague to pass for an explanation, without -being itself explained. We are impelled to believe that to be true in -general which we see to be true in particular. But how do we see any -truth? How do we pick out any proposition with respect to a diagram -which we see before us? We see in particular, and state in general, -some truth respecting straight lines, or parallel lines, or concerning -direction. But where do we find the conception of straightness, or -parallelism, or direction? These conceptions are not upon the surface -of things. The child does not, from his birth, see straightness -and parallelism so as to know that he sees them. How then does his -experience bear upon a proposition in which these conceptions are -involved? It is said that it is a matter of experience long before it -is a matter of abstract thought. But how can there be any experience -by which we learn these properties of a straight line, till our -thoughts are at least so abstract as to conceive what straightness is? -If it be said that this conception grows with our experience, and is -gradually unfolded with our unfolding materials of knowledge, so as -to give import and significance to them: I need make no objection to -such a statement, except this--that this power of unfolding out of the -mind conceptions which give meaning to our experience, is something -in addition to the mere employment of our senses upon the external -world. It is what I have called the ideal part of our knowledge. It -implies, not only an impulse to generalize from experience, but also -an impulse to form conceptions by which generalization is possible. It -requires, not only that nothing should oppose the tendency, but that -the direction in which the tendency is to operate should be determined -by the laws of the mind's activity; by an internal, not by an external -agency. - -One main ground on which the Reviewer is disposed to quarrel with and -reject several of the expressions used in the _Philosophy_;--such as -that space is an idea, a form of our perception, and the like,--is -this; that such expressions appear to deprive the external world of its -reality; to make it, or at least most of its properties, a creation of -the observing mind. He quotes the following argument which is urged in -the _Philosophy_, in order to prove that space is not a notion obtained -from experience: "Experience gives us information concerning things -without us, but our apprehending them as without us takes for granted -their existence in space. Experience acquaints us with the form, -position, magnitude, &c. of particular objects, but that they _have_ -form, position, magnitude, pre-supposes that they are in space." From -this statement he altogether dissents. No, says he, "the reason why we -apprehend things as without us is that they _are_ without us. We take -for granted that they exist in space, because they _do_ so exist, and -because such their existence is a matter of direct perception, which -can neither be explained in words nor contravened in imagination: -because, in short, space is a _reality_, and not a mere matter of -convention or imagination." - -Now, if by calling space an idea, we suggest any doubt of its reality -and of the reality of the external world, we certainly run the risk -of misleading our readers; for the external world is real if anything -be real: the bodies which exist in space are things, if things are -anywhere to be found. That bodies do exist in space, and that _that_ is -the reason why we apprehend them as existing in space, I readily grant. -But I conceive that the term Idea ought not to suggest any such doubt -of the reality of the knowledge in which it is involved. Ideas are -always, in our knowledge, conjoined with facts. Our real knowledge is -knowledge, because it involves ideas, real, because it involves facts. -We apprehend things as existing in space because they do so exist: and -our idea of space enables us so to observe them, and so to conceive -them. - -But we want, further, a reason why, apprehending them as they are, we -also apprehend, that in certain relations they could not be otherwise -(that two straight linear objects could not inclose a space, for -instance). This circumstance is no way accounted for by saying that we -apprehend them as they are; and is, I presume to say, inexplicable, -except by supposing that it arises from some property of the observing -mind:--an Idea, as I have termed it,--an irresistible Impulse to -generalize, as the Reviewer expresses it. Or, as I have suggested, we -may adopt a third phrase, a Law of the mind's activity: and in order -that no question may remain, whether we ascribe reality to the objects -and relations which we observe, we may describe it as "a Law of the -mind's activity in apprehending what is." And thus the real existence -of the object, and the ideal element which our apprehension of it -introduces, would both be clearly asserted. - -I am ready to use expressions which recognize the reality of space -and other external things more emphatically than those expressions -which I have employed in the _Philosophy_, if expressions can be -found which, while they do this, enable us to explain the possibility -of knowledge, and to analyze the structure of truth. It is, indeed, -extremely difficult to find, in speaking of this subject, expressions -which are satisfactory. The reality of the objects which we perceive -is a profound, apparently an insoluble problem[352]. We cannot but -suppose that existence is something different from our knowledge of -existence:--that which exists, does not exist merely in our knowing -that it does:--truth is truth whether we know it or not. Yet how can we -conceive truth, otherwise than as something known? How can we conceive -things as existing, without conceiving them as objects of perception? -Ideas and Things are constantly opposed, yet necessarily co-existent. -How they are thus opposite and yet identical, is the ultimate problem -of all philosophy. The successive phases of philosophy have consisted -in separating and again uniting these two opposite elements; in -dwelling sometimes upon the one and sometimes upon the other, as the -principal or original or only element; and then in discovering that -such an account of the state of the case was insufficient. Knowledge -requires ideas. Reality requires things. Ideas and things co-exist. -Truth _is_, and is known. But the complete explanation of these points -appears to be beyond our reach. At least it is not necessary for the -purposes of our philosophy. The separation of ideas and sensations -in order to discover the conditions of knowledge is our main task. -How ideas and sensations are united so as to form things, does not so -immediately concern us. - -I have stated that we may, without giving up any material portion -of the Philosophy of Science to which I have been led, express the -conclusions in other phraseology; and that instead of saying that all -our knowledge involves certain Fundamental Ideas, the sources from -which all universal truth is derived, we may say that there are certain -Laws of Mental Activity according to which alone all the real relations -of things are apprehended. If this alteration in the phraseology will -make the doctrines more generally intelligible or acceptable, there is -no reason why it should not be adopted. But I may remark, that a main -purpose of the _Philosophy_ was not merely to prove that there _are_ -such Fundamental Ideas or Laws of mental activity, but to enumerate -those of them which are involved in the existing sciences; and to state -the fundamental truths to which the fundamental ideas lead. This was -the task which was attempted; and if this have been executed with any -tolerable success, it may perhaps be received as a contribution to the -philosophy of science, of which the value is not small, in whatever -terms it be expressed. And this enumeration of fundamental ideas, and -of truths derived from them, must have something to correspond to it, -in any other mode of expressing that view of the nature of knowledge -which we are led to adopt. If instead of _Fundamental Ideas_, we speak -of Impulses of generalization, or of _Laws of mental activity_, we -must still distinguish such Impulses, or such Laws, according to the -distinctions of ideas to which the survey of science led us. We shall -thus have a series of groups of Laws, or of classes of generalizing -Impulses, corresponding to the series of Fundamental Ideas already -given. If we employ the language of the Reviewer, we shall have one -generalizing Impulse which suggests relations of Space; another which -directs us to properties of Numbers; another which deals with Time; -another with Cause: another which groups objects according to Likeness; -another which suggests a purpose as a necessary relation among -them; to which may be added, even while we confine ourselves to the -physical sciences, several others, as may be seen in the _Philosophy_. -Now when the fundamental conditions and elements of truth are thus -arranged into groups, it is not a matter of so much consequence to -decide whether each group shall be said to be bound together by an -idea or by an impulse of generalization; as it is to see that, if -this happen in virtue of ideas, here are so many distinct ideas which -enter into the structure of science, and give universality to its -matter; and again, if this happen in virtue of an irresistible impulse -of generalization in each case, we have so many different kinds of -impulses of generalization. The main purpose in the _Philosophy_ was to -analyze scientific truth into its conditions and elements; and I did -not content myself with saying that those elements are Sensations and -Ideas; the Ideas being that element which makes universal knowledge -conceivable and possible. I went further: I enumerated the Ideas -which thus enter into science. I showed that in the sciences which -I passed in review, the most acute and profound inquirers had taken -for granted that certain truths in each science are of universal and -necessary validity, and I endeavoured to select the idea in which this -universality and necessity resided, and to separate it from all other -ideas involved in other sciences. If therefore it be thought better -to say that those principles in each science upon which, as upon the -axioms in geometry, the universality and necessity of scientific truth -depends, are arrived at, not by ideas, but by an irresistible impulse -of generalization, those who employ such phraseology, if they make a -classification of such impulses corresponding to my classification of -ideas, will still adopt the greater part of my philosophy, altering -only the phraseology. Or if, as I suggested, instead of "Fundamental -Ideas," we use the phrase "Laws of Mental Activity," then our primary -intellectual Code--the Constitution of our minds, as it may be -termed--will consist of a Body of Laws of which the Titles correspond -with the Fundamental Ideas of the _Philosophy_. - -My object was, from the writings of the most sagacious and profound -philosophers who have laboured on each science, to extract such a -code, such a constitution. If I have in any degree succeeded in this, -the result must have a reality and a value independently of all forms -of expression. Still I do not think that any language can ever serve -for such legislation, in which the two elements of truth are not -distinguished. Even if we adopt the phraseology which I have just -employed, we shall have to recollect that Law and Fact must be kept -distinct, and that the Constitution has its Principles as well as its -History. - -But I will not longer detain you by seeking other modes of expressing -the Fundamental Antithesis to which the accompanying Memoir refers. -The Remarks which I here send you were written three years ago, on the -appearance of the Review which I have quoted. If I succeed in obtaining -for them a few minutes' attention from you and a few other friends, I -shall be glad that they have been preserved. - - I am, my dear Herschel, - always truly yours, - W. WHEWELL. - -P.S. I have abstained from sending you a large portion of my Remarks -as originally written. I had gone on to show that, in my _Philosophy_, -I had not only enumerated and analyzed a great number of different -Fundamental Ideas which belong to the different existing sciences, -but that I had also shown in what manner these ideas enter into their -respective sciences; namely, by the statement or use of Axioms, which -involve the ideas, and which form the basis of each science when -systematically exhibited. A number of these Axioms belonging to most -of the physical sciences, are stated in the _Philosophy_. I might have -added also that I have attempted to classify the historical steps -by which such Axioms are brought into view and applied. But it is -not necessary to dwell upon these points, in order to illustrate the -difference and the agreement between the Reviewer and me. - - _Sir John F. W. Herschel, Bart. &c._ - - -APPENDIX G. - -ON THE TRANSFORMATION OF HYPOTHESES IN THE HISTORY OF SCIENCE. - -(_Cam. Phil. Soc._ MAY 19, 1851.) - - -1. The history of science suggests the reflection that it is very -difficult for the same person at the same time to do justice to two -conflicting theories. Take for example the Cartesian hypothesis of -vortices and the Newtonian doctrine of universal gravitation. The -adherents of the earlier opinion resisted the evidence of the Newtonian -theory with a degree of obstinacy and captiousness which now appears -to us quite marvellous: while on the other hand, since the complete -triumph of the Newtonians, _they_ have been unwilling to allow any -merit at all to the doctrine of vortices. It cannot but seem strange, -to a calm observer of such changes, that in a matter which depends -upon mathematical proofs, the whole body of the mathematical world -should pass over, as in this and similar cases they seem to have done, -from an opinion confidently held, to its opposite. No doubt this must -be, in part, ascribed to the lasting effects of education and early -prejudice. The old opinion passes away with the old generation: the new -theory grows to its full vigour when its congenital disciples grow to -be masters. John Bernoulli continues a Cartesian to the last; Daniel, -his son, is a Newtonian from the first. Newton's doctrines are adopted -at once in England, for they are the solution of a problem at which his -contemporaries have been labouring for years. They find no adherents -in France, where Descartes is supposed to have already explained -the constitution of the world; and Fontenelle, the secretary of the -Academy of Sciences at Paris, dies a Cartesian seventy years after -the publication of Newton's _Principia_. This is, no doubt, a part -of the explanation of the pertinacity with which opinions are held, -both before and after a scientific revolution: but this is not the -whole, nor perhaps the most instructive aspect of the subject. There -is another feature in the change, which explains, in some degree, how -it is possible that, in subjects, mainly at least mathematical, and -therefore claiming demonstrative evidence, mathematicians should hold -different and even opposite opinions. And the object of the present -paper is to point out this feature in the successions of theories, and -to illustrate it by some prominent examples drawn from the history of -science. - -2. The feature to which I refer is this; that when a prevalent -theory is found to be untenable, and consequently, is succeeded by a -different, or even by an opposite one, the change is not made suddenly, -or completed at once, at least in the minds of the most tenacious -adherents of the earlier doctrine; but is effected by a transformation, -or series of transformations, of the earlier hypothesis, by means of -which it is gradually brought nearer and nearer to the second; and -thus, the defenders of the ancient doctrine are able to go on as if -still asserting their first opinions, and to continue to press their -points of advantage, if they have any, against the new theory. They -borrow, or imitate, and in some way accommodate to their original -hypothesis, the new explanations which the new theory gives, of the -observed facts; and thus they maintain a sort of verbal consistency; -till the original hypothesis becomes inextricably confused, or breaks -down under the weight of the auxiliary hypotheses thus fastened upon -it, in order to make it consistent with the facts. - -This often-occurring course of events might be illustrated from the -history of the astronomical theory of epicycles and eccentrics, as -is well known. But my present purpose is to give one or two brief -illustrations of a somewhat similar tendency from other parts of -scientific history; and in the first place, from that part which has -already been referred to, the battle of the Cartesian and Newtonian -systems. - -3. The part of the Cartesian system of vortices which is most -familiarly known to general readers is the explanation of the motions -of the planets by supposing them carried round the sun by a kind -of whirlpool of fluid matter in which they are immersed: and the -explanation of the motions of the satellites round their primaries by -similar subordinate whirlpools, turning round the primary, and carried, -along with it, by the primary vortex. But it should be borne in mind -that a part of the Cartesian hypothesis which was considered quite as -important as the cosmical explanation, was the explanation which it -was held to afford of terrestrial gravity. Terrestrial gravity was -asserted to arise from the motion of the vortex of subtle matter which -revolved round the earth's axis and filled the surrounding space. It -was maintained that by the rotation of such a vortex, the particles -of the subtle matter would exert a centrifugal force, and by virtue of -that force, tend to recede from the center: and it was held that all -bodies which were near the earth, and therefore immersed in the vortex, -would be pressed towards the center by the effort of the subtle matter -to recede from the center[353]. - -These two assumed effects of the Cartesian vortices--to carry bodies -in their stream, as straws are carried round by a whirlpool, and to -press bodies to the center by the centrifugal effort of the whirling -matter--must be considered separately, because they were modified -separately, as the progress of discussion drove the Cartesians from -point to point. The former effect indeed, the _dragging_ force -of the vortex, as we may call it, would not bear working out on -mechanical principles at all; for as soon as the law of motion was -acknowledged (which Descartes himself was one of the loudest in -proclaiming), that a body in motion keeps all the motion which it has, -and receives in addition all that is impressed upon it; as soon, in -short, as philosophers rejected the notion of an inertness in matter -which constantly retards its movements,--it was plain that a planet -perpetually dragged onwards in its orbit by a fluid moving quicker than -itself, must be perpetually accelerated; and therefore could not follow -those constantly-recurring cycles of quicker and slower motion which -the planets exhibit to us. - -The Cartesian mathematicians, then, left untouched the calculation of -the progressive motion of the planets; and, clinging to the assumption -that a vortex would produce a tendency of bodies to the center, made -various successive efforts to construct their vortices in such a manner -that the centripetal forces produced by them should coincide with those -which the phenomena required, and therefore of course, in the end, with -those which the Newtonian theory asserted. - -In truth, the Cartesian vortex was a bad piece of machinery for -producing a central force: from the first, objections were made to the -sufficiency of its mechanism, and most of these objections were very -unsatisfactorily answered, even granting the additional machinery which -its defenders demanded. One formidable objection was soon started, -and continued to the last to be the torment of the Cartesians. If -terrestrial gravity, it was urged, arise from the centrifugal force of -a vortex which revolves about the earth's axis, terrestrial gravity -ought to act in planes perpendicular to the earth's axis, instead -of tending to the earth's center. This objection was taken by James -Bernoulli[354], and by Huyghens[355] not long after the publication of -Descartes's _Principia_. Huyghens (who adopted the theory of vortices -with modifications of his own) supposes that there are particles of the -fluid matter which move about the earth in every possible direction, -within the spherical space which includes terrestrial objects; and -that the greater part of these motions being in spherical surfaces -concentric with the earth, produces a tendency towards the earth's -center. - -This was a procedure tolerably arbitrary, but it was the best which -could be done. Saurin, a little later[356], gave nearly the same -solution of this difficulty. The solution, identifying a vortex of some -kind with a central force, made the hypothesis of vortices applicable -wherever central forces existed; but then, in return, it deprived the -image of a vortex of all that clearness and simplicity which had been -its first great recommendation. - -But still there remained difficulties not less formidable. According -to this explanation of gravity, since the tendency of bodies to the -earth's center arose from the superior centrifugal force of the -whirling matter which pushed them inward as water pushes a light body -upward, bodies ought to tend more strongly to the center in proportion -as they are less dense. The rarest bodies should be the heaviest; -contrary to what we find. - -Descartes's original solution of this difficulty has a certain degree -of ingenuity. According to him (_Princip._ IV. 23) a terrestrial body -consists of particles of the _third element_, and the more it has -of such particles, the more it excludes the parts of the _celestial -matter_, from the revolution of which matter gravity arises; and -therefore the denser is the terrestrial body, and the heavier it will -be. - -But though this might satisfy him, it could not satisfy the -mathematicians who followed him, and tried to reduce his system to -calculation on mechanical principles. For how could they do this, -if the celestial matter, by the operation of which the phenomena -of force and motion were produced, was so entirely different from -ordinary matter, which alone had supplied men with experimental -illustrations of mechanical principles? In order that the celestial -matter, by its whirling, might produce the gravity of heavy bodies, -it was mechanically necessary that it must be very dense; and _dense_ -in the ordinary sense of the term; for it was by regarding density in -the ordinary sense of the term that the mechanical necessity had been -established. - -The Cartesians tried to escape this result (Huyghens, _Pesanteur_, p. -161, and John Bernoulli, _Nouvelles Pensées_, Art. 31) by saying that -there were two meanings of _density_ and _rarity_; that some fluids -might be rare by having their particles far asunder, others, by having -their particles very small though in contact. But it is difficult to -think that they could, as persons well acquainted with mechanical -principles, satisfy themselves with this distinction; for they could -hardly fail to see that the mechanical effect of any portion of fluid -depends upon the total mass moved, not on the size of its particles. - -Attempts made to exemplify the vortices experimentally only showed more -clearly the force of this difficulty. Huyghens had found that certain -bodies immersed in a whirling fluid tended to the center of the vortex. -But when Saulmon[357] a little later made similar experiments, he had -the mortification of finding that the heaviest bodies had the greatest -tendency to recede from the axis of the vortex. "The result is," as -the Secretary of the Academy (Fontenelle) says, "exactly the opposite -of what we could have wished, for the [Cartesian] system of gravity: -but we are not to despair; sometimes in such researches disappointment -leads to ultimate success." - -But, passing by this difficulty, and assuming that in some way or -other a centripetal force arises from the centrifugal force of the -vortex, the Cartesian mathematicians were naturally led to calculate -the circumstances of the vortex on mechanical principles; especially -Huyghens, who had successfully studied the subject of centrifugal -force. Accordingly, in his little treatise on the _Cause of -Gravitation_ (p. 143), he calculates the velocity of the fluid matter -of the vortex, and finds that, at a point in the equator, it is 17 -times the velocity of the earth's rotation. - -It may naturally be asked, how it comes to pass that a stream of fluid, -dense enough to produce the gravity of bodies by its centrifugal force, -moving with a velocity 17 times that of the earth (and therefore -moving round the earth in 85 minutes), does not sweep all terrestrial -objects before it. But to this Huyghens had already replied (p. 137), -that there are particles of the fluid moving _in all directions_, and -therefore that they neutralize each other's action, so far as lateral -motion is concerned. - -And thus, as early as this treatise of Huyghens, that is, in three -years from the publication of Newton's _Principia_, a vortex is made -to mean nothing more than some machinery or other for producing a -central force. And this is so much the case, that Huyghens commends -(p. 165), as confirming his own calculation of the velocity of his -vortex, Newton's proof that at the Moon's orbit the centripetal force -is equal to the centrifugal; and that thus, this force is less than the -centripetal force at the earth's surface in the inverse proportion of -the squares of the distances. - -John Bernoulli, in the same manner, but with far less clearness -and less candour, has treated the hypothesis of vortices as being -principally a hypothetical cause of central force. He had repeated -occasions given him of propounding his inventions for propping up the -Cartesian doctrine, by the subjects proposed for prizes by the Paris -Academy of Sciences; in which competition Cartesian speculations were -favourably received. Thus the subject of the Prize Essays for 1730 -was, the explanation of the Elliptical Form of the planetary orbits -and of the Motion of their Aphelia, and the prize was assigned to -John Bernoulli, who gave the explanation on Cartesian principles. He -explains the elliptical figure, not as Descartes himself had done, -by supposing the vortex which carries the planet round the sun to be -itself squeezed into an elliptical form by the pressure of contiguous -vortices; but he supposes the planet, while it is carried round by the -vortex, to have a limited oscillatory motion to and from the center, -produced by its being originally, not at the distance at which it would -float in equilibrium in the vortex, but above or below that point. On -this supposition, the planet would oscillate to and from the center, -Bernoulli says, like the mercury when deranged in a barometer: and -it is evident that such an oscillation, combined with a motion round -the center, might produce an oval curve, either with a fixed or with -a moveable aphelion. All this however merely amounts to a possibility -that the oval _may_ be an ellipse, not to a proof that it will be so; -nor does Bernoulli advance further. - -It was necessary that the vortices should be adjusted in such a manner -as to account for Kepler's laws; and this was to be done by making -the velocity of each stratum of the vortex depend in a suitable -manner on its radius. The Abbé de Molières attempted this on the -supposition of elliptical vortices, but could not reconcile Kepler's -first two laws, of equal elliptical areas in equal times, with his -third law, that the squares of the periodic times are as the cubes -of the mean distances[358]. Bernoulli, with his circular vortices, -could accommodate the velocities at different distances so that they -should explain Kepler's laws. He pretended to prove that Newton's -investigations respecting vortices (in the ninth Section of the Second -Book of the _Principia_) were mechanically erroneous; and in truth, -it must be allowed that, besides several arbitrary assumptions, there -are some errors of reasoning in them. But for the most part, the more -enlightened Cartesians were content to accept Newton's account of the -motions and forces of the solar system as part of their scheme; and to -say only that the hypothesis of vortices explained the origin of the -Newtonian forces; and that thus theirs was a philosophy of a higher -kind. Thus it is asserted (_Mém. Acad._ 1734), that M. de Molières -retains the beautiful theory of Newton entire, only he renders it -in a sort less Newtonian, by disentangling it from attraction, and -transferring it from a vacuum into a plenum. This plenum, though -not its native region, frees it from the need of attraction, which -is all the better for it. These points were the main charms of the -Cartesian doctrine in the eyes of its followers;--the getting rid of -attractions, which were represented as a revival of the Aristotelian -"occult qualities," "substantial forms," or whatever else was the -most disparaging way of describing the bad philosophy of the dark -ages[359];--and the providing some material intermedium, by means of -which a body may affect another at a distance; and thus avoid the -reproach urged against the Newtonians, that they made a body act where -it was not. And we are the less called upon to deny that this last -feature in the Newtonian theory was a difficulty, inasmuch as Newton -himself was never unwilling to allow that gravity might be merely an -effect produced by some ulterior cause. - -With such admissions on the two sides, it is plain that the Newtonian -and Cartesian systems would coincide, if the hypothesis of vortices -could be modified in such a way as to produce the force of gravitation. -All attempts to do this, however, failed: and even John Bernoulli, -the most obstinate of the mathematical champions of the vortices, -was obliged to give them up. In his Prize Essay for 1734, (on the -Inclinations of the Planetary Orbits[360],) he says (Art. VIII.), "The -gravitation of the Planets towards the center of the Sun and the weight -of bodies towards the center of the earth has not, for its cause, -either the attraction of M. Newton, or the centrifugal force of the -matter of the vortex according to M. Descartes;" and he then goes on to -assert that these forces are produced by a perpetual torrent of matter -tending to the center on all sides, and carrying all bodies with it. -Such a hypothesis is very difficult to refute. It has been taken up in -more modern times by Le Sage[361], with some modifications; and may be -made to account for the principal facts of the universal gravitation -of matter. The great difficulty in the way of such a hypothesis is, -the overwhelming thought of the whole universe filled with torrents -of an invisible but material and tangible substance, rushing in every -direction in infinitely prolonged straight lines and with immense -velocity. Whence can such matter come, and whither can it go? Where -can be its perpetual and infinitely distant fountain, and where the -ocean into which it pours itself when its infinite course is ended? -A revolving whirlpool is easily conceived and easily supplied; but -the central torrent of Bernoulli, the infinite streams of particles -of Le Sage, are an explanation far more inconceivable than the thing -explained. - -But however the hypothesis of vortices, or some hypothesis substituted -for it, was adjusted to explain the facts of attraction to a -center, this was really nearly all that was meant by a vortex or a -"tourbillon," when the system was applied. Thus in the case of the last -act of homage to the Cartesian theory which the French Academy rendered -in the distribution of its prizes, the designation of a Cartesian -Essay in 1741 (along with three Newtonian ones) as worthy of a prize -for an explanation of the Tides; the difference of high and low water -was not explained, as Descartes has explained it, by the pressure, on -the ocean, of the terrestrial vortex, forced into a strait where it -passes under the Moon; but the waters were supposed to rise towards the -Moon, the terrestrial vortex being disturbed and broken by the Moon, -and therefore less effective in forcing them down. And in giving an -account of a Tourmaline from Ceylon (Acad. Sc. 1717), when it has been -ascertained that it attracts and repels substances, the writer adds, as -a matter of course, "It would seem that it has a vortex." As another -example, the elasticity of a body was ascribed to vortices between its -particles: and in general, as I have said, a vortex implied what we now -imply by speaking of a central force. - -4. In the same manner vortices were ascribed to the Magnet, in order -to account for its attractions and repulsions. But we may note a -circumstance which gave a special turn to the hypothesis of vortices as -applied to this subject, and which may serve as a further illustration -of the manner in which a transition may be made from one to the other -of two rival hypotheses. - -If iron filings be brought near a magnet, in such a manner as to be -at liberty to assume the position which its polar action assigns to -them; (for instance, by strewing them upon a sheet of paper while -the two poles of the magnet are close below the paper;) they will -arrange themselves in certain curves, each proceeding from the N. to -the S. pole of the magnet, like the meridians in a map of the globe. -It is easily shown, on the supposition of magnetic attraction and -repulsion, that these _magnetic curves_, as they are termed, are each -a curve whose tangent at every point is the direction of a small line -or particle, as determined by the attraction and repulsion of the two -poles. But if we suppose a _magnetic vortex_ constantly to flow out -of one pole and into the other, in streams which follow such curves, -it is evident that such a vortex, being supposed to exercise material -pressure and impulse, would arrange the iron filings in corresponding -streams, and would thus produce the phenomenon which I have described. -And the hypothesis of _central torrents_ of Bernoulli or Le Sage which -I have referred to, would, in its application to magnets, really become -this hypothesis of a magnetic vortex, if we further suppose that the -matter of the torrents which proceed to one pole and from the other, -mingles its streams, so as at each point to produce a stream in the -resulting direction. Of course we shall have to suppose two sets of -magnetic torrents;--a boreal torrent, proceeding to the north pole, -and from the south pole of a magnet; and an austral torrent proceeding -to the south and from the north pole:--and with these suppositions, -we make a transition from the hypothesis of attraction and repulsion, -to the Cartesian hypothesis of vortices, or at least, torrents, which -determine bodies to their magnetic positions by impulse. - -Of course it is to be expected that, in this as in the other case, -when we follow the hypothesis of impulse into detail, it will need to -be loaded with so many subsidiary hypotheses, in order to accommodate -it to the phenomena, that it will no longer seem tenable. But the -plausibility of the hypothesis in its first application cannot be -denied:--for, it may be observed, the two _opposite_ streams would -counteract each other so as to produce no local _motion_, only -_direction_. And this case may put us on our guard against other -suggestions of forces acting in curve lines, which may at first sight -appear to be discerned in magnetic and electric phenomena. Probably -such curve lines will all be found to be only resulting lines, arising -from the direct action and combination of elementary attraction and -repulsion. - -5. There is another case in which it would not be difficult to devise -a mode of transition from one to the other of two rival theories; -namely, in the case of the emission theory and the undulation theory -of Light. Indeed several steps of such a transition have already -appeared in the history of optical speculation; and the conclusive -objection to the emission theory of light, as to the Cartesian theory -of vortices, is, that no amount of additional hypotheses will reconcile -it to the phenomena. Its defenders had to go on adding one piece of -machinery after another, as new classes of facts came into view, till -it became more complex and unmechanical than the theory of epicycles -and eccentrics at its worst period. Otherwise, as I have said, there -was nothing to prevent the emission theory from migrating into the -undulatory theory, and as the theory of vortices did into the theory -of attraction. For the emissionists allow that rays may _interfere_; -and that these interferences may be modified by alternate _fits_ in the -rays; now these fits are already a kind of _undulation_. Then again the -phenomena of polarized light show that the fits or undulations must -have a _transverse_ character: and there is no reason why emitted rays -should not be subject to _fits_ of _transverse_ modification as well -as to any other fits. In short, we may add to the emitted rays of the -one theory, all the properties which belong to the undulations of the -other, and thus account for all the phenomena on the emission theory; -with this limitation only, that the emission will have no share in the -explanation, and the undulations will have the whole. If, instead of -conceiving the universe full of a _stationary_ ether, we suppose it -to be full of etherial particles moving in every direction; and if we -suppose, in the one case and in the other, this ether to be susceptible -of undulations proceeding from every luminous point; the results of the -two hypotheses will be the same; and all we shall have to say is, that -the supposition of the emissive motion of the particles is superfluous -and useless. - -6. This view of the manner in which rival theories pass into one -another appears to be so unfamiliar to those who have only slightly -attended to the history of science, that I have thought it might be -worth while to illustrate it by a few examples. - -It might be said, for instance, by such persons[362], "Either the -planets are not moved by vortices, or they do not move by the law by -which heavy bodies fall. It is impossible that both opinions can be -true." But it appears, by what has been said above, that the Cartesians -did hold both opinions to be true; and one with just as much reason as -the other, on their assumptions. It might be said in the same manner, -"Either it is false that the planets are made to describe their orbits -by the above quasi-Cartesian theory of Bernoulli, or it is false that -they obey the Newtonian theory of gravitation." But this would be -said quite erroneously; for if the hypothesis of Bernoulli be true, -it is so because it agrees in its result with the theory of Newton. -It is not only possible that both opinions may be true, but it is -certain that if the first be so, the second is. It might be said again, -"Either the planets describe their orbits by an inherent virtue, or -according to the Newton theory." But this again would be erroneous, -for the Newtonian doctrine decided nothing as to whether the force of -gravitation was inherent or not. Cotes held that it was, though Newton -strongly protested against being supposed to hold such an opinion. -The word _inherent_ is no part of the physical theory, and will be -asserted or denied according to our metaphysical views of the essential -attributes of matter and force. - -Of course, the possibility of two rival hypotheses being true, one -of which takes the explanation a step higher than the other, is -not affected by the impossibility of two contradictory assertions -of the _same order_ of generality being both true. If there be a -new-discovered comet, and if one astronomer asserts that it will return -once in _every_ twenty years, and another, that it will return once in -every thirty years, both cannot be right. But if an astronomer says -that though its interval was in the last instance 30 years, it will -only be 20 years to the next return, in consequence of perturbation and -resistance, he may be perfectly right. - -And thus, when different and rival explanations of the same phenomena -are held, till one of them, though long defended by ingenious men, is -at last driven out of the field by the pressure of facts, the defeated -hypothesis is transformed before it is extinguished. Before it has -disappeared, it has been modified so as to have all palpable falsities -squeezed out of it, and subsidiary provisions added, in order to -reconcile it with the phenomena. It has, in short, been penetrated, -infiltrated, and metamorphosed by the surrounding medium of truth, -before the merely arbitrary and erroneous residuum has been finally -ejected out of the body of permanent and certain knowledge. - - -FOOTNOTES: - -[Footnote 352: These remarks were written in 1841. The accompanying -Memoir contains a further discussion of this problem.] - - -APPENDIX H. - -ON HEGEL'S CRITICISM OF NEWTON'S PRINCIPIA. - -(_Cam. Phil. Soc._ MAY 21, 1849.) - - -The Newtonian doctrine of universal gravitation, as the cause of -the motions which take place in the solar system, is so entirely -established in our minds, and the fallacy of all the ordinary arguments -against it is so clearly understood among us, that it would undoubtedly -be deemed a waste of time to argue such questions in this place, so far -as physical truth is concerned. But since in other parts of Europe, -there are teachers of philosophy whose reputation and influence are -very great, and who are sometimes referred to among our own countrymen -as the authors of new and valuable views of truth, and who yet reject -the Newtonian opinions, and deny the validity of the proofs commonly -given of them, it may be worth while to attend for a few minutes to the -declarations of such teachers, as a feature in the present condition -of European philosophy. I the more readily assume that the Cambridge -Philosophical Society will not think a communication on such a subject -devoid of interest, in consequence of the favourable reception which it -has given to philosophical speculations still more abstract, which I -have on previous occasions offered to it. I will therefore proceed to -make some remarks on the opinions concerning the Newtonian doctrine of -gravitation, delivered by the celebrated Hegel, of Berlin, than whom no -philosopher in modern, and perhaps hardly any even in ancient times, -has had his teaching received with more reverential submission by his -disciples, or been followed by a more numerous and zealous band of -scholars bent upon diffusing and applying his principles. - -The passages to which I shall principally refer are taken from one of -his works which is called the _Encyclopædia_ (Encyklopädie), of which -the First Part is _the Science of Logic_, the Second, the _Philosophy -of Nature_, the Third, the _Philosophy of Spirit_. The Second Part, -with which I am here concerned, has for an _aliter_ title, _Lectures -on Natural Philosophy_ (Vorlesungen über Natur-philosophie), and would -through its whole extent offer abundant material for criticism, by -referring it to principles with which we are here familiar: but I -shall for the present confine myself to that part which refers to the -subject which I have mentioned, the Newtonian Doctrine of Gravitation, -§ 269, 270, of the work. Nor shall I, with regard to this part, think -it necessary to give a continuous and complete criticism of all the -passages bearing upon the subject; but only such specimens, and such -remarks thereon, as may suffice to show in a general manner the value -and the character of Hegel's declarations on such questions. I do not -pretend to offer here any opinion upon the value and character of -Hegel's philosophy in general: but I think it not unlikely that some -impression on that head may be suggested by the examination, here -offered, of some points in which we can have no doubt where the truth -lies; and I am not at all persuaded that a like examination of many -other parts of the Hegelian _Encyclopædia_, would not confirm the -impression which we shall receive from the parts now to be considered. - -Hegel both criticises the Newtonian doctrines, or what he states as -such; and also, not denying the truth of the laws of phenomena which he -refers to, for instance Kepler's laws, offers his own proof of these -laws. I shall make a few brief remarks on each of these portions of the -pages before me. And I would beg it to be understood that where I may -happen to put my remarks in a short, and what may seem a peremptory -form, I do so for the sake of saving time; knowing that among us, upon -subjects so familiar, a few words will suffice. For the same reason, I -shall take passages from Hegel, not in the order in which they occur, -but in the order in which they best illustrate what I have to say. I -shall do Hegel no injustice by this mode of proceeding: for I will -annex a faithful translation, so far as I can make one, of the whole of -the passages referred to, with the context. - -No one will be surprised that a German, or indeed any lover of science, -should speak with admiration of the discovery of Kepler's laws, as a -great event in the history of Astronomy, and a glorious distinction to -the discoverer. But to say that the glory of the discovery of the proof -of these laws has been unjustly transferred from Kepler to Newton, is -quite another matter. This is what Hegel says (_a_)[363]. And we have -to consider the reasons which he assigns for saying so. - -He says (_b_) that "it is allowed by mathematicians that the Newtonian -Formula maybe derived from the Keplerian laws," and hence he seems to -infer that the Newtonian law is not an additional truth. That is, he -does not allow that the discovery of the cause which produces a certain -phenomenal law is anything additional to the discovery of the law -itself. - -"The Newtonian formula may be derived from the Keplerian law." It was -professedly so derived; but derived by introducing the Idea of _Force_, -which Idea and its consequences were not introduced and developed till -after Kepler's time. - -"The Newtonian formula may be derived from the Keplerian law." And the -Keplerian law may be derived, and was derived, from the observations of -the Greek astronomers and their successors; but was not the less a new -and great discovery on that account. - -But let us see what he says further of this derivation of the Newtonian -"formula" from the Keplerian Law. It is evident that by calling it a -_formula_, he means to imply, what he also asserts, that it is no new -law, but only a new form (and a bad one) of a previously known truth. - -How is the Newtonian "formula," that is, the law of the inverse squares -of the central force, derived from the Keplerian law of the cubes of -the distances proportional to the squares of the times? This, says -Hegel, is the "immediate derivation." (_c_).--By Kepler's law, _A_ -being the distance and _T_ the periodic time, _A_^3/_T_^2 is constant. -But Newton _calls_ _A_/_T_^2 universal gravitation; whence it easily -follows that gravitation is inversely as _A_^2. - -This is Hegel's way of representing Newton's proof. Reading it, any one -who had never read the _Principia_ might suppose that Newton _defined_ -gravitation to be _A_/_T_^2. We, who have read the _Principia_, know -that Newton _proves_ that in circles, the _central force_ (not the -_universal gravitation_) is as _A_/_T_^2: that he proves this, by -setting out from the idea of force, as that which deflects a body from -the tangent, and makes it describe a curved line: and that in this way, -he passes from Kepler's laws of mere motion to his own law of Force. - -But Hegel does not see any value in this. Such a mode of treating the -subject he says (_i_) "offers to us a tangled web, formed of the Lines -of the mere geometrical construction, to which a physical meaning of -independent forces is given." That a _measure_ of forces is _found_ in -such lines as the sagitta of the arc described in a given time, (not -such a _meaning_ arbitrarily _given_ to them,) is certainly true, and -is very distinctly proved in Newton, and in all our elementary books. - -But, says Hegel, as further showing the artificial nature of the -Newtonian formulæ, (_h_) "Analysis has long been able to derive the -Newtonian expression and the laws therewith connected out of the Form -of the Keplerian Laws;" an assertion, to verify which he refers to -Francœur's _Mécanique_. This is apparently in order to show that the -"lines" of the Newtonian construction are superfluous. We know very -well that analysis does not always refer to visible representations of -such lines: but we know too, (and Francœur would testify to this also,) -that the analytical proofs contain equivalents to the Newtonian lines. -We, in this place, are too familiar with the substitution of analytical -for geometrical proofs, to be led to suppose that such a substitution -affects the substance of the truth proved. The conversion of Newton's -geometrical proofs of his discoveries into analytical processes by -succeeding writers, has not made them cease to be discoveries: and -accordingly, those who have taken the most prominent share in such a -conversion, have been the most ardent admirers of Newton's genius and -good fortune. - -So much for Newton's comparison of the Forces in different circular -orbits, and for Hegel's power of understanding and criticising it. Now -let us look at the motion in different parts of the same elliptical -orbit, as a further illustration of the value of Hegel's criticism. In -an elliptical orbit the velocity alternately increases and diminishes. -This follows necessarily from Kepler's law of the equal description -of the areas, and so Newton explains it. Hegel, however, treats of -this acceleration and retardation as a separate fact, and talks of -another explanation of it, founded upon Centripetal and Centrifugal -Force (_o_). Where he finds this explanation, I know not; certainly -not in Newton, who in the second and third section of the _Principia_ -explains the variation of the velocity in a quite different manner, as -I have said; and nowhere, I think, employs centrifugal force in his -explanations. However, the notion of centrifugal as acting along with -centripetal force is introduced in some treatises, and may undoubtedly -be used with perfect truth and propriety. How far Hegel can judge -when it is so used, we may see from what he says of the confusion -produced by such an explanation, which is, he says, a maximum. In the -first place, he speaks of the motion being _uniformly_ accelerated and -retarded in an elliptical orbit, which, in any exact use of the word -_uniformly_, it is not. But passing by this, he proceeds to criticise -an explanation, not of the variable velocity of the body in its orbit, -but of the alternate access and recess of the body to and from the -center. Let us overlook this confusion also, and see what is the value -of his criticism on the explanation. He says (_p_), "according to -this explanation, in the motion of a planet from the aphelion to the -perihelion, the centrifugal is less than the centripetal force; and -in the perihelion itself the centripetal force is supposed suddenly -to become greater than the centrifugal;" and so, of course, the body -re-ascends to the aphelion. - -Now I will not say that this explanation has never been given in a book -professing to be scientific; but I have never seen it given; and it -never can have been given but by a very ignorant and foolish person. -It goes upon the utterly unmechanical supposition that the approach -of a body to the center at any moment depends solely upon the excess -of the centripetal over the centrifugal force; and reversely. But the -most elementary knowledge of mechanics shows us that when a body is -moving _obliquely_ to the distance from the center, it approaches to -or recedes from the center in virtue of this obliquity, even if no -force at all act. And the total approach to the center is the approach -due to this cause, _plus_ the approach due to the centripetal force, -_minus_ the recess due to the centrifugal force. At the aphelion, the -centripetal is greater than the centrifugal force; and _hence_ the -motion becomes oblique; and _then_, the body approaches to the center -on _both_ accounts, and approaches on account of the obliquity of the -path even when the centrifugal has become greater than the centripetal -force, which it becomes before the body reaches the perihelion. This -reasoning is so elementary, that when a person who cannot see this, -writes on the subject with an air of authority, I do not see what can -be done but to point out the oversight and leave it. - -But there is, says Hegel (_q_), another way of explaining the motion -by means of centripetal and centrifugal forces. The two forces are -supposed to increase and decrease gradually, according to different -laws. In this case, there must be a point where they are equal, and in -equilibrio; and this being the case, they will always continue equal, -for there will be no reason for their going out of equilibrium. - -This, which is put as _another_ mode of explanation, is, in fact, the -same mode; for, as I have already said, the centrifugal force, which is -less than the centripetal at the aphelion, becomes the greater of the -two before the perihelion; and there is an intermediate position, at -which the two forces are equal. But at this point, is there no reason -why, being equal, the forces should become unequal? Reason abundant: -for the body, being there, moves in a line oblique to the distance, and -so changes its distance; and the centripetal and centrifugal force, -depending upon the distance by different laws, they forthwith become -unequal. - -But these modes of explanation, by means of the centripetal and -centrifugal forces and their relation, are not necessary to Newton's -doctrine, and are nowhere used by Newton; and undoubtedly much -confusion has been produced in other minds, as well as Hegel's, -by speaking of the centrifugal force, which is a mere intrinsic -geometrical result of a body's curvilinear motion round a center, in -conjunction with centripetal force, which is an extrinsic force, acting -upon the body and urging it to the center. Neither Newton, nor any -intelligent Newtonian, ever spoke of the centripetal and centrifugal -force as two distinct forces both extrinsic to the motion, which Hegel -accuses them of doing. (_n_) - -I have spoken of the third and second of Kepler's laws; of Newton's -explanations of them, and of Hegel's criticism. Let us now, in the same -manner, consider the first law, that the planets move in ellipses. -Newton's proof that this was the result of a central force varying -inversely as the square of the distance, was the solution of a problem -at which his contemporaries had laboured in vain, and is commonly -looked upon as an important step. "But," says Hegel, (_d_) "the proof -gives a conic section generally, whereas the main point which ought -to be proved is, that the path of the body is an ellipse only, not a -circle or any other conic section." Certainly if Newton _had_ proved -that a planet cannot move in a circle, (which Hegel says he ought to -have done), his system would have perplexed astronomers, since there -are planets which move in orbits hardly distinguishable from circles, -and the variation of the extremity from planet to planet shows that -there is nothing to prevent the excentricity vanishing and the orbit -becoming a circle. - -"But," says Hegel again, (_e_) "the conditions which make the path to -be an ellipse rather than any other conic section, are empirical and -extraneous;--the supposed casual strength of the impulsion originally -received." Certainly the circumstances which determine the amount -of excentricity of a planet's orbit are derived from experience, or -rather, observation. It is not a part of Newton's system to determine -_à priori_ what the excentricity of a planet's orbit must be. A system -that professes to do this will undoubtedly be one very different -from his. And as our knowledge of the excentricity is derived from -observation, it is, in that sense, empirical and casual. The strength -of the original impulsion is a hypothetical and impartial way of -expressing this result of observation. And as we see no reason why the -excentricity should be of any certain magnitude, we see none why the -fraction which expresses the excentricity should not become as large -as unity, that is, why the orbit should not become a parabola; and -accordingly, some of the bodies which revolve about the same appear to -move in orbits of this form: so little is the motion in an ellipse, as -Hegel says, (_f_) "the only thing to be proved." - -But Hegel himself has offered proof of Kepler's laws, to which, -considering his objections to Newton's proofs, we cannot help turning -with some curiosity. - -And first, let us look at the proof of the Proposition which we have -been considering, that the path of a planet is necessarily an ellipse. -I will translate Hegel's language as well as I can; but without -answering for the correctness of my translation, since it does not -appear to me to conform to the first condition of translation, of -being intelligible. The translation however, such as it is, may help -us to form some opinion of the validity and value of Hegel's proofs as -compared with Newton's. (_r_) - -"For absolutely uniform motion, the circle is the only path.... The -circle is the line returning into itself in which all the radii are -equal; there is, for it, only one determining quantity, the radius. - -"But in free motion, the determination according to space and to -time come into view with differences. There must be a difference in -the spatial aspect in itself, and therefore the form requires two -determining quantities. Hence the form of the path returning into -itself is an ellipse." - -Now even if we could regard this as reasoning, the conclusion does -not in the smallest degree follow. A curve returning into itself and -determined by two quantities, may have innumerable forms besides the -ellipse; for instance, any _oval_ form whatever, besides that of the -conic section. - -But why must the curve be a curve returning into itself? Hegel has -professed to prove this previously (_m_) from "the determination of -particularity and individuality of the bodies in general, so that -they have partly a center in themselves, and partly at the same time -their center in another." Without seeking to find any precise meaning -in this, we may ask whether it proves the impossibility of the orbits -with moveable apses, (which do not return into themselves,) such as the -planets (affected by perturbations) really do describe, and such as -we know that bodies must describe in all cases, except when the force -varies exactly as the square of the distance? It appears to do so: -and it proves this impossibility of known facts at least as much as it -proves anything. - -Let us now look at Hegel's proof of Kepler's second law, that the -elliptical sectors swept by the radius vector are proportional to the -time. It is this: (_s_). - -"In the circle, the arc or angle which is included by the two radii is -independent of them. But in the motion [of a planet] as determined by -the conception, the distance from the center and the arc run over in a -certain time must be compounded in one determination, and must make out -a whole. This whole is the sector, a space of two dimensions. And hence -the arc is essentially a Function of the radius vector; and the former -(the arc) being unequal, brings with it the inequality of the radii." - -As was said in the former case, if we could regard this as reasoning, -it would not prove the conclusion, but only, that the arc is _some -function or other_ of the radii. - -Hegel indeed offers (_t_) a reason why there must be an arc involved. -This arises, he says, from "the determinateness [of the nature of -motion], at one while as time in the root, at another while as space in -the square. But here the quadratic character of the space is, by the -returning of the line of motion into itself, limited to a sector." - -Probably my readers have had a sufficient specimen of Hegel's mode of -dealing with these matters. I will however add his proof of Kepler's -third law, that the cubes of the distances are as the squares of the -times. - -Hegel's proof in this case (_u_) has a reference to a previous doctrine -concerning falling bodies, in which time and space have, he says, a -relation to each other as root and square. Falling bodies however -are the case of only _half-free_ motion, and the determination is -incomplete. - -"But in the case of absolute motion, the domain of _free_ masses, the -determination attains its totality. The time as the root is a mere -empirical magnitude: but as a component of the developed Totality, -it is a Totality in itself: it produces itself, and therein has a -reference to itself. And in this process, Time, being itself the -dimensionless element, only comes to a formal identity with itself and -reaches the square: Space, on the other hand, as a positive external -relation, comes to the full dimensions of the conception of space, -that is, the cube. The Realization of the two conceptions (space and -time) preserves their original difference. This is the third Keplerian -law, the relation of the Cubes of the distances to the squares of the -times." - -"And this," he adds, (_v_) with remarkable complacency, "represents -simply and immediately _the reason of the thing_:--while on the -contrary, the Newtonian Formula, by means of which the Law is changed -into a Law for the Force of Gravity, shows the distortion and inversion -of _Reflexion_, which stops half-way." - -I am not able to assign any precise meaning to the _Reflexion_, which -is here used as a term of condemnation, applicable especially to the -Newtonian doctrine. It is repeatedly applied in the same manner by -Hegel. Thus he says, (_g_) "that what Kepler expresses in a simple and -sublime manner in the form of Laws of the Celestial Motions, Newton has -metamorphosed into the _Reflexion-Form_ of the Force of Gravitation." - -Though Hegel thus denies Newton all merit with regard to the -explanation of Kepler's laws by means of the gravitation of the -planets to the sun, he allows that to the Keplerian Laws Newton added -the Principle of Perturbations (_k_). This Principle he accepts to a -certain extent, transforming the expression of it after his peculiar -fashion. "It lies," he says, (_l_) "in this: that matter in general -assigns a center for itself: the collective bodies of the system -recognise a reference to their sun, and all the individual bodies, -according to the relative positions into which they are brought by -their motions, form a momentary relation of their gravity towards each -other." - -This must appear to us a very loose and insufficient way of stating the -Principle of Perturbations, but loose as it is, it recognises that the -Perturbations depend upon the gravity of the planets one to another, -and to the sun. And if the Perturbations depend upon these forces, -one can hardly suppose that any one who allows this will deny that -the primary undisturbed motions depend upon these forces, and must be -explained by means of them; yet this is what Hegel denies. - -It is evident, on looking at Hegel's mode of reasoning on such -subjects, that his views approach towards those of Aristotle and the -Aristotelians; according to which motions were divided into _natural_ -and _unnatural_;--the _celestial motions_ were circular and uniform in -their nature;--and the like. Perhaps it may be worth while to show how -completely Hegel adheres to these ancient views, by an extract from -the additions to the Articles on Celestial Motions, made in the last -edition of the _Encyclopædia_. He says (_w_), - -"The motion of the heavenly bodies is not a being pulled this way -and that, as is imagined (by the Newtonians). _They go along, as the -ancients said, like blessed gods._ The celestial conformity is not -such a one as has the principle of rest or motion external to itself. -It is not right to say because a stone is inert, and the whole earth -consists of stones, and the other heavenly bodies are of the same -nature as the earth, therefore the heavenly bodies are inert. This -conclusion makes the properties of the whole the same as those of the -part. Impulse, Pressure, Resistance, Friction, Pulling, and the like, -are valid only for other than celestial matter." - -There can be no doubt that this is a very different doctrine from that -of Newton. - -I will only add to these specimens of Hegel's physics, a specimen of -the logic by which he refutes the Newtonian argument which has just -been adduced; namely, that the celestial bodies are matter, and that -matter, as we see in terrestrial matter, is inert. He says (_x_), - -"Doubtless both are matter, as a good thought and a bad thought are -both thoughts; but the bad one is not therefore good, because it is a -thought." - - -APPENDIX TO THE MEMOIR ON HEGEL'S CRITICISM OF NEWTON'S PRINCIPIA. - -HEGEL. _Encyclopædia_ (2nd Ed. 1827), Part XI. p. 250. - -C. _Absolute Mechanics._ - -§ 269. - -Gravitation is the true and determinate conception of material -Corporeity, which (Conception) is realized to the Idea (zur Idee). -_General_ Corporeity is separable essentially into _particular_ -Bodies, and connects itself with the Element of _Individuality_ or -subjectivity, as apparent (phenomenal) presence in the _Motion_, which -by this means is immediately a system of _several Bodies_. - -Universal gravitation must, as to itself, be recognised as a profound -thought, although it was principally as apprehended in the sphere -of Reflexion that it eminently attracted notice and confidence on -account of the quantitative determinations therewith connected, and -was supposed to find its confirmation in _Experiments_ (Erfahrung) -pursued from the Solar System down to the phenomena of Capillary -Tubes.--But Gravitation contradicts immediately the Law of Inertia, -for in virtue of it (Gravitation) matter tends _out of itself_ to the -other (matter).--In the _Conception of Weight_, there are, as has been -shown, involved the two elements--Self-existence, and Continuity, -which takes away self-existence. These elements of the Conception, -however, experience a fate, as particular forces, corresponding to -Attractive and Repulsive Force, and are thereby apprehended in nearer -determination, as _Centripetal_ and _Centrifugal Force_, which (Forces) -like weight, _act upon Bodies_, independent of each other, and are -supposed to come in contact accidentally in a third thing, Body. By -this means, what there is of profound in the thought of universal -weight is again reduced to nothing; and Conception and Reason cannot -make their way into the doctrine of absolute motion, so long as the -so highly-prized discoveries of Forces are dominant there. In the -conclusion which contains the _Idea_ of Weight, namely, [contains -this Idea] as the Conception which, in the case of motion, enters -into external Reality through the particularity of the Bodies, and -at the same time into this [Reality] and into their Ideality and -self-regarding Reflexion, (Reflexion-in-sich), the rational identity -and inseparability of the elements is involved, which at other times -are represented as independent. Motion itself, as such, has only its -meaning and existence in a system of _several_ bodies, and those, -such as stand in relation to each other according to different -determinations. - -§ 270. - -As to what concerns bodies in which the conception of gravity -(weight) is realized free by itself, we say that they have for the -determinations of their different nature the elements (momente) of -their conception. One [conception of this kind] is the _universal_ -center of the abstract reference [of a body] to itself. Opposite -to this [conception] stands the immediate, extrinsic, centerless -_Individuality_, appearing as _Corporeity_ similarly independent. Those -[Bodies] however which are particular, which stand in the determination -of extrinsic, and at the same time of intrinsic relation, are centers -for themselves, and [also] have a reference to the first as to their -essential unity. - - The Planetary Bodies, as the immediately concrete, are in their - existence the most complete. Men are accustomed to take the Sun - as the most excellent, inasmuch as the understanding prefers the - abstract to the concrete, and in like manner the fixed stars are - esteemed higher than the Bodies of the Solar System. Centerless - Corporeity, as belonging to externality, naturally separates itself - into the opposition of the lunar and the cometary Body. The laws - of absolutely free motion, as is well known, were discovered by - Kepler;--a discovery of immortal fame. Kepler has proved these - laws in this sense, that for the empirical data he found their -(_a_) general expression. Since then, (_a_) it has become a common way - of speaking to say that Newton first found out the proof of these - Laws. It has rarely happened that fame has been more unjustly - transferred from the first discoverer to another person. On this - subject I make the following remarks. - - 1. That it is allowed by Mathematicians that the Newtonian -(_b_) Formulæ may be derived from the Keplerian Laws. The - completely immediate derivation is this: In the third Keplerian -(_c_) Law, _A_^3/_T_^2 is the constant quantity. This being put - as _A.A_^2/_T_^2 and calling, with Newton, _A_/_T_^2 universal - Gravitation, his expression of the effect of gravity in the - reciprocal ratio of the square of the distances is obvious. - -(_d_) 2. That the Newtonian proof of the Proposition that a body - subjected to the Law of Gravitation moves about the central body - in an _Ellipse_, gives a _Conic Section_ generally, while the - main Proposition which ought to be proved is that the fall of - such a Body is _not_ a _Circle or any other Conic Section_, but - an _Ellipse only_. Moreover, there are objections which may be - made against this proof in itself (_Princ. Math._ I. 1. Sect. II. -(_e_) Prop. 1); and although it is the foundation of the Newtonian - Theory, analysis has no longer any need of it. The conditions which - in the sequel make the path of the Body to a determinate Conic - Section, are referred to an _empirical_ circumstance, namely, a - particular position of the Body at a determined moment of time, and -(_f_) the _casual_ strength of an _impulsion_ which it is supposed - to have received originally; so that the circumstance which makes - the Curve be an Ellipse, which alone ought to be the thing proved, - is extraneous to the Formula. - - 3. That the Newtonian Law of the so-called Force of Gravitation is - in like manner only proved from experience by Induction. - -(_g_) The sum of the difference is this, that what Kepler - expressed in a simple and sublime manner in the Form of _Laws_ - _of the Celestial Motions_, Newton has metamorphosed into the - _Reflection-Form_ of the _Force of Gravitation_. If the Newtonian - Form has not only its convenience but its necessity in reference -(_h_) to the analytical method, this is only a difference of the - mathematical formulæ; Analysis has long been able to derive the - Newtonian expression, and the Propositions therewith connected, - out of the Form of the Keplerian Laws; (on this subject I refer -(_i_) to the elegant exposition in _Francœur's Traité Elém. de - Mécanique_, Liv. II. Ch. xi. n. 4.)--The old method of so-called - proof is conspicuous as offering to us a tangled web, formed of - the _Lines_ of the mere geometrical construction, to which a - physical meaning of _independent Forces_ is given; and of empty - Reflexion-determinations of the already mentioned _Accelerating - Force_ and _Vis Inertiæ_, and especially of the relation of - the so-called gravitation itself to the centripetal force and - centrifugal force, and so on. - - The remarks which are here made would undoubtedly have need of - a further explication to show how well founded they are: in a - Compendium, propositions of this kind which do not agree with - that which is assumed, can only have the shape of assertions. - Indeed, since they contradict such high authorities, they must - appear as something worse, as presumptuous assertions. I will not, - on this subject, support myself by saying, by the bye, that an - interest in these subjects has occupied me for 25 years; but it - is more precisely to the purpose to remark, that the distinctions - and determinations which Mathematical Analysis introduces, - and the course which it must take according to its method, is - altogether different from that which a physical reality must - have. The Presuppositions, the Course, and the Results, which - the Analysis necessarily has and gives, remain quite extraneous - to the considerations which determine the physical value and the - signification of those determinations and of that course. To this - it is that attention should be directed. We have to do with a - consciousness relative to the deluging of physical Mechanics with - an _inconceivable_ (unsäglichen) _Metaphysic_, which--contrary to - experience and conception--has those mathematical determinations - alone for its source. - - It is recognized that what Newton--besides the foundation of the - analytical treatment, the development of which, by the bye, has - of itself rendered superfluous, or indeed rejected much which - belonged to Newton's essential Principles and glory--has added - to the Keplerian Laws is the Principle of _Perturbations_,--a - Principle whose importance we may here accept thus far (hier in -(_k_) sofern anzuführen ist); namely, so far as it rests upon the - Proposition that the so-called attraction is an operation of all -(_l_) the individual parts of bodies, as being material. It lies - in this, that matter in general assigns a center for itself (sich - das centrum setzt), and the figure of the body is an element in the - determination of its place; that collective bodies of the system - recognize a reference to their Sun (sich ihre Sonne setzen), but - also the individual bodies themselves, according to the relative - position with regard to each other into which they come by their - general motion, form a momentary relation of their gravity - (schwere) _towards each other_, and are related to each other not - only in abstract spatial relations, but at the same time assign to - themselves a joint center, which however is again resolved [into - the general center] in the universal system. - -(_m_) As to what concerns the features of the path, to show how - the fundamental determinations of Free Motion are connected _with - the Conception_, cannot here be undertaken in a satisfactory and - detailed manner, and must therefore be left to its fate. The proof - from reason of the quantitative determinations of free motion can - only rest upon the _determinations_ of _Conceptions_ of space and - time, the elements whose relation (intrinsic not extrinsic) motion - is. - - That, _in the first place_, the motion in general is a motion - _returning into itself_, is founded on the determination of - particularity and individuality of the bodies in general (§ 269), - so that partly they have a center in themselves, and partly at the - same time their center in another. These are the determinations of - Conceptions which form the basis of the false representatives of -(_n_) Centripetal Force and Centrifugal Force, as if each of these - were self-existing, extraneous to the other, and independent of - it; and as if they only came in contact in their operations and - consequently _externally_. They are, as has already been mentioned, - the Lines which must be drawn for the mathematical determinations, - transformed into physical realities. - - Further, this motion is _uniformly accelerated_, (and--as returning - into itself--in turn uniformly retarded). In motion as _free_, - Time and Space enter as _different_ things which are to make -(_o_) themselves effective in the determination of the motion - (§ 266, note). In the so-called _Explanation_ of the uniformly - accelerated and retarded motion, by means of the alternate - decrease and increase of the magnitude of the Centripetal Force - and Centrifugal Force, the _confusion_ which the assumption of -(_p_) such independent Forces produces is at its greatest height. - According to this explanation, in the motion of a Planet from the - Aphelion to the Perihelion, the centrifugal is _less_ than the - centripetal force, and on the contrary, in the Perihelion itself, - the centrifugal force is supposed to become greater than the - centripetal. For the motion from the Perihelion to the Aphelion, - this representation makes the forces pass into the opposite - relation in the same manner. It is apparent that such a sudden - conversion of the preponderance which a force has obtained over - another, into an inferiority to the other, cannot be anything taken - out of the nature of Forces. On the contrary it must be concluded, - that a preponderance which one Force has obtained over another - must not only be preserved, but must go onwards to the complete - annihilation of the other Force, and the motion must either, by - the Preponderance of the Centripetal Force, proceed till it ends - in rest, that is, in the Collision of the Planet with the Central -(_q_) Body, or till by the Preponderance of the Centrifugal Force - it ends in a straight line. But now, if in place of the suddenness - of the conversion, we suppose a gradual increase of the Force in - question, then, since rather the other Force ought to be assumed as - increasing, we lose the opposition which is assumed for the sake - of the explanation; and if the increase of the one is assumed to - be different from that of the other, (which is the case in some - representations,) then there is found at the mean distance between - the apsides a point in which the Forces are _in equilibrio_. And - the transition of the Forces out of Equilibrium is a thing just as - little without any sufficient reason as the aforesaid suddenness - of inversion. And in the whole of this kind of explanation, we see - that the mode of remedying a bad mode of dealing with a subject - leads to newer and greater confusion.--A similar confusion makes - its appearance in the explanation of the phænomenon that the - pendulum oscillates more slowly at the equator. This phænomenon is - ascribed to the Centrifugal Force, which it is asserted must then - be greater; but it is easy to see that we may just as well ascribe - it to the augmented gravity, inasmuch as that holds the pendulum - more strongly to the perpendicular line of rest. - - - § 240. - -(_r_) And now first, as to what concerns the _Form of the Path_, - the _Circle_ only can be conceived as the path of an _absolutely - uniform_ motion. _Conceivable_, as people express it, no doubt it - is, that an increasing and diminishing motion should take place in - a circle. But this conceivableness or possibility means only an - abstract capability of being represented, which leaves out of sight - that Determinate Thing on which the question turns. - - The Circle is the line returning into itself in which all the radii - are _equal_, that is, it is completely determined by means of the - radius. There is only _one_ Determination, and that is the _whole_ - Determination. - - But in free motion, in which the Determinations according to - space and according to time come into view with Differences, in a - qualitative relation to each other, this Relation appears in the - spatial aspect as a _Difference_ thereof in itself, which therefore - requires two Determinations. Hereby the Form of the path returning - into itself is essentially an _Ellipse_. - -(_s_) The abstract Determinations which produces the circle - appears also in this way, that the arc or angle which is included - by two Radii is independent of them, a magnitude with regard to - them completely empirical. But since in the motion as determined - by the Conception, the distance from the center, and the arc - which is run over in a certain time, must be comprehended in one - determinateness, [_and_] make out a whole, this is the sector, a - space-determination of two dimensions: in this way, the arc is - essentially a Function of the Radius Vector; and the former (the - arc) being unequal, brings with it the inequality of the Radii. - That the determination with regard to the space by means of the -(_t_) time appears as a Determination of two Dimensions,--as a - Superficies-Determination,--agrees with what was said before (§ - 266) respecting Falling Bodies, with regard to the exposition of - the same Determinateness, at one while as Time in the root, at - another while as Space in the Square. Here, however, the Quadratic - character of the space is, by the returning of the Line of motion - into itself, limited to a Sector. These are, as may be seen, the - general principles on which the Keplerian Law, that in equal times - equal sectors are cut off, rests. - - This Law becomes, as is clear, only the relation of the arc to - the Radius Vector, and the Time enters there as the abstract - Unity, in which the different Sectors are compared, because as - Unity it is the Determining Element. But the further relation is - that of the Time, not as Unity, but as a Quantity in general,--as - the time of Revolution--to the magnitude of the Path, or, what is - the same thing, the distance from the center. As Root and Square, - we saw that Time and Space had a relation to each other, in the - case of Falling Bodies, the case of half-free motion--because - that [_motion_] is determined on one side by the conception, on -(_u_) the other by external [_conditions_]. But in the case of - absolute motion--the domain of _free_ masses--the determination - attains its Totality. The Time as the Root is a mere empirical - magnitude; but as a component (moment) of the developed Totality, - it is a Totality in itself,--it produces itself, and therein has - a reference to itself; as the Dimensionless Element in itself, it - only comes to a formal identity with itself, the Square; Space, - on the other hand, as the positive Distribution (aussereinander) - [_comes_] to the Dimension of the Conception, _the_ CUBE. Their -(_v_) Realization preserves their original difference. This is the - third Keplerian Law, the relation of the _Cubes_ of the _Distances_ - to the _Squares_ of the _Times_;--a Law which is so great on this - account, that it represents so simply and immediately _Reason - as belonging to the thing_: while on the contrary the Newtonian - Formula, by means of which the Law is changed into a Law for the - Force of Gravity, shows the Distortion, Perversion and Inversion of - _Reflexion_ which stops half-way. - - Additions to new Edition. § 269. - - The center has no sense without the circumference, nor the - circumference without the center. This makes all physical - hypotheses vanish which sometimes proceed from the center, - sometimes from the particular bodies, and sometimes assign this, - sometimes that, as the original [cause of motion] ... It is silly - (läppisch) to suppose that the centrifugal force, as a tendency to - fly off in a Tangent, has been produced by a lateral projection, a - projectile force, an impulse which they have retained ever since - they set out on their journey (von Haus aus). Such casualty of the - motion produced by external causes belongs to inert matter; as when - a stone fastened to a thread which is thrown transversely tries to - fly from the thread. We are not to talk in this way of Forces. If - we will speak of Force, there is one Force, whose elements do not -(_w_) draw bodies to different sides as if they were two Forces. - The motion of the heavenly bodies is not a being pulled this way or - that, such as is thus imagined; it is free motion: they go along, - as the ancients said, as blessed Gods (sie gehen als selige Götter - einher). The celestial corporeity is not such a one as has the - principle of rest or motion external to itself. Because stone is - inert, and all the earth consists of stones, and the other heavenly - bodies are of the same nature,--is a conclusion which makes the - properties of the whole the same as those of the part. Impulse, - Pressure, Resistance, Friction, Pulling, and the like, are valid -(_x_) only for an existence of matter other than the celestial. - Doubtless that which is common to the two is matter, as a good - thought and a bad thought are both thoughts; but the bad one is not - therefore good, because it is a thought. - - -FOOTNOTES: - -[Footnote 353: Cartes. _Princip._ iv. 23.] - -[Footnote 354: Jac. Bernoulli, _Nouvelles Pensées sur le Système de M. -Descartes_, op. t. i. p. 239 (1686).] - -[Footnote 355: _De la Cause de la Pesanteur_ (1689), p. 135.] - -[Footnote 356: _Journal des Savans_, 1703. Mém. Acad. Par. 1709. - -Bulfinger, in 1726 (Acad. Petrop.), conceived that by making a sphere -revolve at the same time about two axes at right angles to each other, -every particle would describe a great circle; but this is not so.] - -[Footnote 357: Acad. Par. 1714, _Hist._ p. 106.] - -[Footnote 358: Acad. Par. 1733.] - -[Footnote 359: Acad. Sc. 1709. If we abandon the clear principles of -mechanics, the writer says, "toute la lumière que nous pouvons avoir -est éteinte, et nous voilà replongés de nouveau dans les anciennes -ténèbres du Peripatetisme, dont le Ciel nous veuille preserver!" - -It was also objected to the Newtonian system, that it did not account -for the remarkable facts, that all the motions of the primary planets, -all the motions of the satellites, and all the motions of rotation, -including that of the sun, are in the same direction, and nearly in -the same plane; facts which have been urged by Laplace as so strongly -recommending the Nebular Hypothesis; and that hypothesis is, in truth, -a hypothesis of vortices respecting the _origin_ of the system of the -world.] - -[Footnote 360: _Nouvelle Physique Céleste_, Op. t. iii. p. 163. - -The deviation of the orbits of the planets from the plane of the -sun's equator was of course a difficulty in the system which supposed -that they were carried round by the vortices which the sun's rotation -caused, or at least rendered evident. Bernoulli's explanation consists -in supposing the planets to have a sort of _leeway_ (_dérive des -vaisseaux_) in the stream of the vortex.] - -[Footnote 361: See _Hist. Sc. Ideas_, b. iii. c. ix. Art. 7.] - -[Footnote 362: See Mill's _Logic_, vol. i. p. 311, 2nd ed.] - -[Footnote 363: These letters refer to passages in the Translation -annexed to this Memoir.] - - -APPENDIX K. - -DEMONSTRATION THAT ALL MATTER IS HEAVY. - -(_Cam. Phil. Soc._ FEB. 22, 1841.) - - -The discussion of the nature of the grounds and proofs of the most -general propositions which the physical sciences include, belongs -rather to Metaphysics than to that course of experimental and -mathematical investigation by which the sciences are formed. But such -discussions seem by no means unfitted to occupy the attention of the -cultivators of physical science. The ideal, as well as the experimental -side of our knowledge must be carefully studied and scrutinized, -in order that its true import may be seen; and this province of -human speculation has been perhaps of late unjustly depreciated and -neglected by men of science. Yet it can be prosecuted in the most -advantageous manner by them only: for no one can speculate securely -and rightly respecting the nature and proofs of the truths of science -without a steady possession of some large and solid portions of such -truths. A man must be a mathematician, a mechanical philosopher, a -natural historian, in order that he may philosophize well concerning -mathematics, and mechanics, and natural history; and the mere -metaphysician who without such preparation and fitness sets himself -to determine the grounds of mathematical or mechanical truths, or the -principles of classification, will be liable to be led into error at -every step. He must speculate by means of general terms, which he -will not be able to use as instruments of discovering and conveying -philosophical truth, because he cannot, in his own mind, habitually and -familiarly, embody their import in special examples. - -Acting upon such views, I have already laid before the Philosophical -Society of Cambridge essays on such subjects as I here refer to; -especially a memoir "On the Nature of the Truth of the Laws of Motion," -which was printed by the Society in its Transactions. This memoir -appears to have excited in other places, notice of such a kind as to -show that the minds of many speculative persons are ready for and -inclined towards the discussion of such questions. I am therefore the -more willing to bring under consideration another subject of a kind -closely related to the one just mentioned. - -The general questions which all such discussions suggest, are (in -the existing phase of English philosophy) whether certain proposed -scientific truths, (as the laws of motion,) be _necessary_ truths; -and if they are necessary, (which I have attempted to show that in a -certain sense they are,) _on what ground_ their necessity rests. These -questions may be discussed in a general form, as I have elsewhere -attempted to show. But it may be instructive also to follow the general -arguments into the form which they assume in special cases; and to -exhibit, in a distinct shape, the incongruities into which the opposite -false doctrine leads us, when applied to particular examples. This -accordingly is what I propose to do in the present memoir, with regard -to the proposition stated at the head of this paper, namely, that _all -matter is heavy_. - -At first sight it may appear a doctrine altogether untenable to assert -that this proposition is a necessary truth: for, it may be urged, we -have no difficulty in conceiving matter which is not heavy; so that -matter without weight is a conception not inconsistent with itself; -which it must be if the reverse were a necessary truth. It may be -added, that the possibility of conceiving matter without weight -was shown in the controversy which ended in the downfall of the -phlogiston theory of chemical composition; for some of the reasoners -on this subject asserted phlogiston to be a body with positive levity -instead of gravity, which hypothesis, however false, shows that such -a supposition is possible. Again, it may be said that _weight_ and -_inertia_ are two separate properties of matter: that mathematicians -measure the quantity of matter by the inertia, and that we learn -by experiment only that the weight is proportional to the inertia; -Newton's experiments with pendulums of different materials having been -made with this very object. - -I proceed to reply to these arguments. And first, as to the possibility -of conceiving matter without weight, and the argument thence -deduced, that the universal gravity of matter is not a necessary -truth, I remark, that it is indeed just, to say that we cannot even -distinctly conceive the contrary of a necessary truth to be true; -but that this impossibility can be asserted only of those perfectly -distinct conceptions which result from a complete development of -the fundamental idea and its consequences. Till we reach this stage -of development, the obscurity and indistinctness may prevent our -perceiving absolute contradictions, though they exist. We have abundant -store of examples of this, even in geometry and arithmetic; where the -truths are universally allowed to be necessary, and where the relations -which are impossible, are also inconceivable, that is, not conceivable -distinctly. Such relations, though not distinctly conceivable, still -often appear conceivable and possible, owing to the indistinctness -of our ideas. Who, at the first outset of his geometrical studies, -sees any impossibility in supposing the side and the diagonal of a -square to have a common measure? Yet they can be rigorously proved to -be incommensurable, and therefore the attempt distinctly to conceive -a common measure of them must fail. The attempts at the geometrical -duplication of the cube, and the supposed solutions, (as that of -Hobbes,) have involved absolute contradictions; yet this has not -prevented their being long and obstinately entertained by men, even of -minds acute and clear in other respects. And the same might be shewn to -be the case in arithmetic. It is plain, therefore, that we cannot, from -the supposed possibility of conceiving matter without weight, infer -that the contrary may not be a necessary truth. - -Our power of judging, from the compatibility or incompatibility of our -conceptions, whether certain propositions respecting the relations of -ideas are true or not, must depend entirely, as I have said, upon the -degree of development which such ideas have undergone in our minds. -Some of the relations of our conceptions on any subject are evident -upon the first steady contemplation of the fundamental idea by a sound -mind: these are the _axioms_ of the subject. Other propositions may be -deduced from the axioms by strict logical reasoning. These propositions -are no less _necessary_ than the axioms, though to common minds their -_evidence_ is very different. Yet as we become familiar with the steps -by which these ulterior truths are deduced from the axioms, _their_ -truth also becomes evident, and the contrary becomes inconceivable. -When a person has familiarized himself with the first twenty-six -propositions of Euclid, and not till then, it becomes evident to him, -that parallelograms on the same base and between the same parallels -are equal; and he cannot even conceive the contrary. When he has a -little further cultivated his geometrical powers, the equality of the -square on the hypothenuse of a right-angled triangle to the squares on -the sides, becomes also evident; the steps by which it is demonstrated -being so familiar to the mind as to be apprehended without a conscious -act. And thus, the contrary of a necessary truth cannot be distinctly -conceived; but the incapacity of forming such a conception is a -condition which depends upon cultivation, being intimately connected -with the power of rapidly and clearly perceiving the connection of the -necessary truth under consideration with the elementary principles on -which it depends. And thus, again, it may be that there is an absolute -impossibility of conceiving matter without weight; but then, this -impossibility may not be apparent, till we have traced our fundamental -conceptions of matter into some of their consequences. - -The question then occurs, whether we can, by any steps of reasoning, -point out an inconsistency in the conception of matter without weight. -This I conceive we may do, and this I shall attempt to show. - -The general mode of stating the argument is this:--the quantity of -matter is measured by those sensible properties of matter which undergo -quantitative addition, subtraction and division, as the matter is -added, subtracted and divided. The quantity of matter cannot be known -in any other way. But this mode of measuring the quantity of matter, -in order to be true at all, must be universally true. If it were only -partially true, the limits within which it is to be applied would be -arbitrary; and therefore the whole procedure would be arbitrary, and, -as a method of obtaining philosophical truth, altogether futile. - -We may unfold this argument further. Let the contrary be supposed, of -that which we assert to be true: namely, let it be supposed that while -all other kinds of matter are heavy (and of course heavy in proportion -to the quantity of matter), there is one kind of matter which is -absolutely destitute of weight; as, for instance, phlogiston, or any -other element. Then where this _weightless_ element (as we may term -it) is mixed with _weighty_ elements, we shall have a compound, in -which the weight is no longer proportional to the quantity of matter. -If, for example, 2 measures of heavy matter unite with one measure -of phlogiston, the weight is as 2, and the quantity of matter as 3. -In all such cases, therefore, the weight ceases to be the measure of -the quantity of matter. And as the proportion of the weighty and the -weightless matter may vary in innumerable degrees in such compounds, -the weight affords no criterion at all of the quantity of matter -in them. And the smallest admixture of the weightless element is -sufficient to prevent the weight from being taken as the measure of the -quantity of matter. - -But on this hypothesis, how are we to distinguish such compounds from -bodies consisting purely of heavy matter? How are we to satisfy -ourselves that there is not, in every body, some admixture, small or -great, of the weightless element? If we call this element _phlogiston_, -how shall we know that the bodies with which we have to do are, any of -them, absolutely free from phlogiston? - -We cannot refer to the weight for any such assurance; for by -supposition the presence and absence of phlogiston makes no difference -in the weight. Nor can any other properties secure us at least from -a very small admixture; for to assert that a mixture of 1 in 100 or -1 in 10 of phlogiston would always manifest itself in the properties -of the body, must be an arbitrary procedure, till we have proved this -assertion by experiment: and we cannot do this till we have learnt -some mode of measuring the quantities of matter in bodies and parts of -bodies; which is exactly what we question the possibility of, in the -present hypothesis. - -Thus, if we assume the existence of an element, _phlogiston_, devoid of -weight, we cannot be sure that every body does not contain some portion -of this element; while we see that if there be an admixture of such -an element, the weight is no longer any criterion of the quantity of -matter. And thus we have proved, that if there be any kind of matter -which is not heavy, the weight can no longer avail us, _in any case or -to any extent_, as a measure of the quantity of matter. - -I may remark, that the same conclusion is easily extended to the case -in which phlogiston is supposed to have absolute levity; for in that -case, a certain mixture of phlogiston and of heavy matter would have -no weight, and might be substituted for phlogiston in the preceding -reasoning. - -I may remark, also, that the same conclusion would follow by the same -reasoning, if any kind of matter, instead of being void of weight, were -heavy, indeed, but not _so_ heavy, in proportion to its quantity of -matter, as other kinds. - -On all these hypotheses there would be no possibility of measuring -quantity of matter by weight at all, in any case, or to any extent. - -But it may be urged, that we have not yet reduced the hypothesis of -matter without weight to a contradiction; for that mathematicians -measure quantity of matter, not by weight, but by the other property, -of which we have spoken, inertia. - -To this I reply, that, practically speaking, quantity of matter is -always measured by weight, both by mechanicians and chemists: and as -we have proved that this procedure is utterly insecure in all cases, -on the hypothesis of weightless matter, the practice rests upon a -conviction that the hypothesis is false. And yet the practice is -universal. Every experimenter measures quantity of matter by the -balance. No one has ever thought of measuring quantity of matter by -its inertia practically: no one has constructed a measure of quantity -of matter in which the matter produces its indications of quantity by -its motion. When we have to take into account the inertia of a body, -we inquire what its weight is, and assume this as the measure of the -inertia; but we never take the contrary course, and ascertain the -inertia first in order to determine by that means the weight. - -But it may be asked, Is it not then true, and an important scientific -truth, that the _quantity of matter_ is measured by the _inertia_? -Is it not true, and proved by experiment, that the _weight_ is -_proportional_ to the _inertia_? If this be not the result of Newton's -experiments mentioned above, what, it may be demanded, do they prove? - -To these questions I reply: It is true that quantity of matter is -measured by the inertia, for it is true that inertia is as the quantity -of matter. This truth is indeed one of the laws of motion. That weight -is proportional to inertia is proved by experiment, as far as the laws -of motion are so proved: and Newton's experiments prove one of the laws -of motion, so far as any experiments can prove them, or are needed to -prove them. - -That inertia is proportional to weight, is a law equivalent to that -law which asserts, that when pressure produces motion in a given body, -the velocity produced in a given time is as the pressure. For if the -velocity be as the pressure, when the body is given, the velocity will -be constant if the inertia also be as the pressure. For the inertia is -understood to be that property of bodies to which, _ceteris paribus_, -the velocity impressed is _inversely_ proportional. One body has -twice as much inertia as another, if, when the same force acts upon -it for the same time, it acquires but half the velocity. This is the -fundamental conception of _inertia_. - -In Newton's pendulum experiments, the pressure producing motion was -a certain resolved part of the weight, and was proportional to the -weight. It appeared by the experiments, that whatever were the material -of which the pendulum was formed, the rate of oscillation was the same; -that is, the velocity acquired was the same. Hence the inertia of the -different bodies must have been in each case as the weight: and thus -this assertion is true of all different kinds of bodies. - -Thus it appears that the assertion, that inertia is universally -proportional to weight, is equivalent to the law of motion, that the -velocity is as the pressure. The conception of inertia (of which, -as we have said, the fundamental conception is, that the velocity -impressed is inversely proportional to the inertia,) connects the two -propositions so as to make them identical. - -Hence our argument with regard to the universal gravity of matter -brings us to the above law of motion, and is proved by Newton's -experiments in the same sense in which that law of motion is so proved. - -Perhaps some persons might conceive that the identity of weight -and inertia is obvious at once; for both are merely resistance -to motion;--inertia, resistance to all motion (or change of -motion)--weight, resistance to motion upwards. - -But there is a difference in these two kinds of resistance to motion. -Inertia is instantaneous, weight is continuous resistance. Any -momentary impulse which acts upon a free body overcomes its inertia, -for it changes its motion; and this change once effected, the inertia -opposes any return to the former condition, as well as any additional -change. The inertia is thus overcome by a momentary force. But the -weight can only be overcome by a continuous force like itself. If an -impulse act in opposition to the weight, it may for a moment neutralize -or overcome the weight; but if it be not continued, the weight resumes -its effect, and restores the condition which existed before the impulse -acted. - -But weight not only produces rest, when it is resisted, but motion, -when it is not resisted. Weight is measured by the reaction which would -balance it; but when unbalanced, it produces motion, and the velocity -of this motion increases constantly. Now what determines the velocity -thus produced in a given time, or its rate of increase? What determines -it to have one magnitude rather than another? To this we must evidently -reply, _the inertia_. When weight produces motion, the inertia is the -reaction which makes the motion determinate. The accumulated motion -produced by the action of unbalanced weight is as determinate a -condition as the equilibrium produced by balanced weight. In both cases -the condition of the body acted on is determined by the opposition of -the action and reaction. - -Hence inertia is the reaction which opposes the weight, when -unbalanced. But by the conception of action and reaction, (as mutually -determining and determined,) they are measured by each other: and hence -the inertia is necessarily proportional to the weight. - -But when we have reached this conclusion, the original objection may be -again urged against it. It may be said, that there must be some fallacy -in this reasoning, for it proves a state of things to be necessary when -we can so easily conceive a contrary state of things. Is it denied, -the opponent may ask, that we can readily imagine a state of things in -which bodies have no weight? Is not the uniform tendency of all bodies -in the same direction not only not necessary, but not even true? For -they do in reality tend, not with equal forces in parallel lines, but -to a center with unequal forces, according to their position: and we -can conceive these differences of intensity and direction in the force -to be greater than they really are; and can with equal ease suppose the -force to disappear altogether. - -To this I reply, that certainly we may conceive the weight of bodies -to vary in intensity and direction, and by an additional effort of -imagination, may conceive the weight to vanish: but that in all these -suppositions, even in the extreme one, we must suppose the rule to be -universal. If _any_ bodies have weight, _all_ bodies must have weight. -If the direction of weight be different in different points, this -direction must still vary according to the _law of continuity_; and the -same is true of the intensity of the weight. For if this were not so, -the rest and motion, the velocity and direction, the permanence and -change of bodies, as to their mechanical condition, would be arbitrary -and incoherent: they would not be subject to mechanical ideas; that -is, not to ideas at all: and hence these conditions of objects would -in fact be inconceivable. In order that the universe may be possible, -that is, may fall under the conditions of intelligible conceptions, we -must be able to conceive a body at rest. But the rest of bodies (except -in the absolute negation of all force) implies the equilibrium of -opposite forces. And one of these opposite forces must be a _general_ -force, as weight, in order that the universe may be governed by general -conditions. And this general force, by the conception of force, may -produce motion, as well as equilibrium; and this motion again must -be determined, and determined by general conditions; which cannot -be, except the communication of motion be regulated by an inertia -proportional to the weight. - -But it will be asked, Is it then pretended that Newton's experiment, -by which it was intended to prove inertia proportional to weight, -does really prove nothing but what may be demonstrated _à priori_? -Could we know, without experiment, that all bodies,--gold, iron, wood, -cork,--have inertia proportional to their weight? And to this we reply, -that experiment holds the same place in the establishment of this, as -of the other fundamental doctrines of mechanics. Intercourse with the -external world is requisite for developing our ideas; measurement of -phenomena is needed to fix our conceptions and to render them precise: -but the result of our experimental studies is, that we reach a -position in which our convictions do not rest upon experiment. We learn -by observation truths of which we afterwards see the necessity. This is -the case with the laws of motion, as I have repeatedly endeavoured to -show. The same will appear to be the case with the proposition, that -bodies of different kinds have their inertia proportional to their -weight. - -For bodies _of the same kind_ have their inertia proportional to their -weight, both quantities being proportional to the quantity of matter. -And if we compress the same quantity of matter into half the space, -neither the weight nor the inertia is altered, because these depend -on the quantity of matter alone. But in this way we obtain a body -of _twice the density_; and in the same manner we obtain a body of -any other density. Therefore whatever be the density, the inertia is -proportional to the quantity of matter. But the mechanical relations -of bodies cannot depend upon any difference of _kind_, _except_ a -difference of density. For if we suppose any fundamental difference of -mechanical nature in the particles or component elements of bodies, we -are led to the same conclusion, of arbitrary, and therefore impossible, -results, which we deduced from this supposition with regard to weight. -Therefore all bodies of different density, and hence, all bodies -whatever, must have their inertia proportional to their weight. - -Hence we see, that the propositions, that all bodies are heavy, and -that inertia is proportional to weight, necessarily follow from those -fundamental ideas which we unavoidably employ in all attempts to -reason concerning the mechanical relations of bodies. This conclusion -may perhaps appear the more startling to many, because they have -been accustomed to expect that fundamental ideas and their relations -should be self-evident at our first contemplation of them. This, -however, is far from being the case, as I have already shown. It is -not the _first_, but the most complete and developed condition of our -conceptions which enables us to see what are axiomatic truths in each -province of human speculation. Our fundamental ideas are necessary -conditions of knowledge, universal forms of intuition, inherent types -of mental development; they may even be termed, if any one chooses, -results of connate intellectual tendencies; but we cannot term them -_innate_ ideas, without calling up a large array of false opinions. For -innate ideas were considered as capable of composition, but by no means -of simplification: as most perfect in their original condition; as to -be found, if any where, in the most uneducated and most uncultivated -minds; as the same in all ages, nations, and stages of intellectual -culture; as capable of being referred to at once, and made the basis -of our reasonings, without any special acuteness or effort: in all -which circumstances the Fundamental Ideas of which we have spoken, are -opposed to Innate Ideas so understood. - -I shall not, however, here prosecute this subject. I will only remark, -that Fundamental Ideas, as we view them, are not only not innate, in -any usual or useful sense, but they are not necessarily _ultimate_ -elements of our knowledge. They are the results of our analysis so far -as we have yet prosecuted it; but they may themselves subsequently -be analysed. It may hereafter appear, that what we have treated as -different Fundamental Ideas have, in fact, a connexion, at some point -below the structure which we erect upon them. For instance, we treat of -the mechanical ideas of force, matter, and the like, as distinct from -the idea of substance. Yet the principle of measuring the quantity of -matter by its weight, which we have deduced from mechanical ideas, is -applied to determine the substances which enter into the composition -of bodies. The idea of substance supplies the axiom, that the whole -quantity of matter of a compound body is equal to the sum of the -quantities of matter of its elements. The mechanical ideas of force -and matter lead us to infer that the quantity both of the whole and -its parts must be measured by their weights. _Substance_ may, for some -purposes, be described as that to which properties belong; _matter_ -in like manner may be described as that which resists force. The -former involves the Idea of permanent Being; the latter, the Idea of -Causation. There may be some elevated point of view from which these -ideas may be seen to run together. But even if this be so, it will by -no means affect the validity of reasonings founded upon these notions, -when duly determined and developed. If we once adopt a view of the -nature of knowledge which makes necessary truth possible at all, we -need be little embarrassed by finding how closely connected different -necessary truths are; and how often, in exploring towards their roots, -different branches appear to spring from the same stem. - - -END OF THE APPENDIX. - - - - - Cambridge: - PRINTED BY C. J. CLAY, M.A. - AT THE UNIVERSITY PRESS. - - - - -WORKS BY - -WILLIAM WHEWELL, D.D. F.R.S. - -MASTER OF TRINITY COLLEGE, CAMBRIDGE. - - - HISTORY OF THE INDUCTIVE SCIENCES. Third and Cheaper Edition. 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- color: black; - font-size:smaller; - padding:0.5em; - margin-bottom:5em; - font-family:sans-serif, serif; } - </style> - </head> -<body> - - -<pre> - -The Project Gutenberg EBook of On the Philosophy of Discovery, Chapters -Historical and Critical, by William Whewell - -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/license - - -Title: On the Philosophy of Discovery, Chapters Historical and Critical - -Author: William Whewell - -Release Date: March 25, 2016 [EBook #51555] - -Language: English - -Character set encoding: UTF-8 - -*** START OF THIS PROJECT GUTENBERG EBOOK PHILOSOPHY OF DISCOVERY *** - - - - -Produced by Sonya Schermann, Les Galloway and the Online -Distributed Proofreading Team at http://www.pgdp.net (This -file was produced from images generously made available -by The Internet Archive) - - - - - - -</pre> - - - -<p class="half-title"> -<small>ON THE</small><br /> - -PHILOSOPHY<br /> - -<small>OF</small><br /> - -DISCOVERY. -</p> - - - - -<p class="center"> -Cambridge:<br /> -<br /> -PRINTED BY C. J. CLAY, M.A.<br /> -<br /> -AT THE UNIVERSITY PRESS.<br /> -</p> - -<hr class="chap" /> - - -<h1><small> -ON THE</small><br /> -<br /> -PHILOSOPHY OF DISCOVERY,<br /> -<br /> -<small>CHAPTERS HISTORICAL AND CRITICAL;</small></h1> - -<p class="center"> -<small>BY</small><br /> - -WILLIAM WHEWELL, D.D.</p> -<p class="center xs"> -MASTER OF TRINITY COLLEGE, CAMBRIDGE, AND<br /> -CORRESPONDING MEMBER OF THE INSTITUTE OF FRANCE.</p> -<p class="center small"> -INCLUDING THE COMPLETION OF THE THIRD EDITION<br /> -OF THE PHILOSOPHY OF THE INDUCTIVE SCIENCES.</p> - -<div class="figcenter" > -<img src="images/title-1.jpg" alt="Hand passing torch to hand" /> -</div> - -<p class="center small"> -ΛΑΜΠΑΔΙΑ ΕΧΟΝΤΕΣ ΔΙΑΔΩΣΟΥΣΙΝ ΑΛΛΗΛΟΙΣ</p> - -<p class="center"> -LONDON:<br /> - -JOHN W. PARKER AND SON, WEST STRAND.<br /> - -1860. -</p> - -<hr class="chap" /> - - -<p>The following are the latest editions of the series of works -which has been published connected with the present subject:</p> -<p class="pi2"> -<i>History of the Inductive Sciences</i>, 3 Vols. 1857.<br /> -<i>History of Scientific Ideas</i>, 2 Vols. 1858.<br /> -<i>Novum Organon Renovatum</i>, 1 Vol. 1858.<br /> -<i>On the Philosophy of Discovery</i>, 1 Vol. 1860.<br /> -</p> -<p>To the <i>History of the Inductive Sciences</i> are appended two -Indexes (in Vol. 1.), an Index of Proper Names, and an Index -of Technical Terms. These Indexes, and the Tables of Contents -of the other works, will enable the reader to refer to any person -or event included in this series.</p> - -<hr class="chap" /> - - -<h2><a name="PREFACE" id="PREFACE"></a>PREFACE</h2> - - -<p class="drop-cap"><span class="smcap">The</span> two works which I entitled <i>The History of -the Inductive Sciences</i>, and <i>The Philosophy of the -Inductive Sciences</i>, were intended to present to the -reader a view of the steps by which those portions -of human knowledge which are held to be most -certain and stable have been acquired, and of the -philosophical principles which are involved in those -steps. Each of these steps was a scientific <i>Discovery</i>, -in which a <i>new</i> conception was applied in order to -bind together observed facts. And though the conjunction -of the observed facts was in each case an -example of logical <i>Induction</i>, it was not the inductive -process merely, but the <i>novelty</i> of the result in -each case which gave its peculiar character to the -History; and the Philosophy at which I aimed was -not the Philosophy of Induction, but the <i>Philosophy -of Discovery</i>. In the present edition I have described -this as my object in my Title.</p> - -<p><span class="pagenum" id="Page_v">v</span></p> - -<p>A great part of the present volume consists of -chapters which composed the twelfth Book of the -Philosophy in former editions, which Book was then -described as a 'Review of Opinions on the nature of -Knowledge and the Method of seeking it.' I have -added to this part several new chapters, on Plato, -Aristotle, the Arabian Philosophers, Francis Bacon, -Mr. Mill, Mr. Mansel, the late Sir William Hamilton, -and the German philosophers Kant, Fichte, -Schelling and Hegel. I might, if time had allowed, -have added a new chapter on Roger Bacon, founded -on his <i>Opus Minus</i> and other works, recently published -for the first time under the direction of the Master of -the Rolls; a valuable contribution to the history of -philosophy. But the review of this work would not -materially alter the estimate of Roger Bacon which I -had derived from the <i>Opus Majus</i>.</p> - -<p>But besides these historical and critical surveys of -the philosophy of others, I have ventured to introduce -some new views of my own; namely, views -which bear upon the philosophy of religion. I have -done so under the conviction that no philosophy of -the universe can satisfy the minds of thoughtful men -which does not deal with such questions as inevitably -force themselves on our notice, respecting the -Author and the Object of the universe; and also -under the conviction that every philosophy of the<span class="pagenum" id="Page_vi">vi</span> -universe which has any consistency must suggest -answers, at least conjectural, to such questions. -No <i>Cosmos</i> is complete from which the question -of Deity is excluded; and all Cosmology has -a side turned towards Theology. Though I am aware -therefore how easy it is, on this subject, to give -offence and to incur obloquy, I have not thought it -right to abstain from following out my philosophical -principles to their results in this department of speculation. -The results do not differ materially from -those at which many pious and thoughtful speculators -have arrived in previous ages of the world; though -they have here, as seems to me, something of novelty -in their connection with the philosophy of science. -But this point I willingly leave to the calm decision -of competent judges.</p> - -<p>I have added in an Appendix various Essays, -previously published at different times, which may -serve perhaps to illustrate some points of the history -and philosophy of science.</p> - -<p class="pi"> -<span class="smcap">Trinity Lodge</span>,<br /> - <i>February 8, 1856</i>.<br /> -</p> - -<hr class="chap" /> - -<p><span class="pagenum"><a name="Page_vii" id="Page_vii">[Pg vii]</a><a name="Page_viii" id="Page_viii">[Pg viii]</a></span></p> - - - - -<p class="half-title"><small>ON</small><br /> - -THE PHILOSOPHY OF DISCOVERY.</p> - - - -<hr class="small" /> -<h2><a name="CONTENTS" id="CONTENTS"></a>CONTENTS.</h2> - -<blockquote> - -<p>The chapters marked thus * appear now for the first time.</p> - -<p>The chapters marked thus † have appeared in other works.</p></blockquote> - - - - -<div class="center"> -<table border="0" cellpadding="4" cellspacing="0" summary=""> -<tr><td class="tdh" colspan="3"><span class="smcap"><a href="#CHAPTER_I">Chap. I</a>. Introduction.</span></td> -</tr> -<tr><td class="tdh" colspan="3"><span class="smcap"><a href="#CHAPTER_II">Chap. II</a>. Plato.</span></td> -</tr> -<tr><td class="tdh" colspan="3"><span class="smcap"><a href="#CHAPTER_III">Chap. III</a>. *Additional Remarks on Plato.</span></td> -</tr> -<tr><td align="left"> </td><td class="tdrt"><a href="#III1">1</a>.</td> -<td class="tdhs">The Doctrine of Ideas.</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#III2">2</a>.</td> -<td class="tdhs">The Doctrine of the One and Many.</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#III3">3</a>.</td> -<td class="tdhs">The notion of the nature and aim of Science.</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#III4">4</a>.</td> -<td class="tdhs">The Survey of existing Sciences.</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#III5">5</a>.</td> -<td class="tdhs">The Constitution of the human Mind.</td> -</tr> -<tr><td class="tdh" colspan="3"><span class="smcap"><a href="#CHAPTER_IV">Chap. IV</a>. Aristotle.</span></td> -</tr> -<tr><td class="tdh" colspan="3"><span class="smcap"><a href="#CHAPTER_V">Chap. V</a>. *Additional Remarks on Aristotle.</span></td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#CHAPTER_V">1</a>.</td> -<td class="tdhs">Induction.</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#V2">2</a>.</td> -<td class="tdhs">Invention.</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#V3">3</a>.</td> -<td class="tdhs">The One in the Many.</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#V4">4</a>.</td> -<td class="tdhs">The "Five Words."</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#V5">5</a>.</td> -<td class="tdhs">Aristotle's contribution to the Physical Sciences.</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#V6">6</a>.</td> -<td class="tdhs">Aristotle's Astronomy.</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#V7">7</a>.</td> -<td class="tdhs">Aristotle on Classification.</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#V8">8</a>.</td> -<td class="tdhs">F. Bacon on Aristotle.</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#V9">9</a>.</td> -<td class="tdhs">Discovery of Causes.</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#V10">10</a>.</td> -<td class="tdhs">Plato and Aristotle.</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#V11">11</a>.</td> -<td class="tdhs">Aristotle against Plato's <i>Ideas</i>.<span class="pagenum" id="Page_ix">ix</span></td> -</tr> -<tr><td class="tdh" colspan="3"><span class="smcap"><a href="#CHAPTER_VI">Chap. VI</a>. The Later Greeks.</span></td> -</tr> -<tr><td class="tdh" colspan="3"><span class="smcap"><a href="#CHAPTER_VII">Chap. VII</a>. The Romans.</span></td> -</tr> -<tr><td class="tdh" colspan="3"><span class="smcap"><a href="#CHAPTER_VIII">Chap. VIII</a>. *Arabian Philosophers.</span></td> -</tr> -<tr><td class="tdh" colspan="3"><span class="smcap"><a href="#CHAPTER_IX">Chap. IX</a>. The Schoolmen of the Middle Ages.</span></td> -</tr> -<tr><td class="tdh" colspan="3"><span class="smcap"><a href="#CHAPTER_X">Chap. X</a>. The Innovators of the Middle Ages.</span></td> -</tr> -<tr><td align="left"></td><td class="tdrt"> </td> -<td class="tdhs">Raymond Lully.</td> -</tr> -<tr><td class="tdh" colspan="3"><span class="smcap"><a href="#CHAPTER_XI">Chap. XI</a>. The Innovators of the Middle Ages</span>—<i>continued</i>.</td> -</tr> -<tr><td align="left"></td><td class="tdrt"> </td> -<td class="tdhs">Roger Bacon.</td> -</tr> -<tr><td class="tdh" colspan="3"><span class="smcap"><a href="#CHAPTER_XII">Chap. XII</a>. The Revival of Platonism.</span></td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XII1">1</a>.</td> -<td class="tdhs">Causes of Delay in the Advance of Knowledge.</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XII2">2</a>.</td> -<td class="tdhs">Causes of Progress.</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XII3">3</a>.</td> -<td class="tdhs">Hermolaus Barbarus, &c.</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XII4">4</a>.</td> -<td class="tdhs">Nicolaus Cusanus.</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XII5">5</a>.</td> -<td class="tdhs">Manilius Ficinus.</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XII6">6</a>.</td> -<td class="tdhs">Francis Patricius.</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XII7">7</a>.</td> -<td class="tdhs">Picus, Agrippa, &c.</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XII8">8</a>.</td> -<td class="tdhs">Paracelsus, Fludd, &c.</td> -</tr> -<tr><td class="tdh" colspan="3"><span class="smcap"><a href="#CHAPTER_XIII">Chap. XIII</a>. The Theoretical Reformers of Science.</span></td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XIII1">1</a>.</td> -<td class="tdhs">Bernardinus Telesius.</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XIII2">2</a>.</td> -<td class="tdhs">Thomas Campanella.</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XIII3">3</a>.</td> -<td class="tdhs">Andrew Cæsalpinus.</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XIII4">4</a>.</td> -<td class="tdhs">Giordano Bruno.</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XIII5">5</a>.</td> -<td class="tdhs">Peter Ramus.</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XIII6">6</a>.</td> -<td class="tdhs">The Reformers in General.</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XIII7">7</a>.</td> -<td class="tdhs">Melancthon.</td> -</tr> -<tr><td class="tdh" colspan="3"><span class="smcap"><a href="#CHAPTER_XIV">Chap. XIV</a>. The Practical Reformers of Science.</span></td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XIV1">1</a>.</td> -<td class="tdhs">Character of the Practical Reformers.</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XIV2">2</a>.</td> -<td class="tdhs">Leonardo da Vinci.</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XIV3">3</a>.</td> -<td class="tdhs">Copernicus.</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XIV4">4</a>.</td> -<td class="tdhs">Fabricius.</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XIV5">5</a>.</td> -<td class="tdhs">Maurolycus.</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XIV6">6</a>.</td> -<td class="tdhs">Benedetti.</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XIV7">7</a>.</td> -<td class="tdhs">Gilbert.<span class="pagenum" id="Page_x">x</span></td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XIV8">8</a>.</td> -<td class="tdhs">Galileo.</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XIV9">9</a>.</td> -<td class="tdhs">Kepler.</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XIV10">10</a>.</td> -<td class="tdhs">Tycho.</td> -</tr> -<tr><td class="tdh" colspan="3"><span class="smcap"><a href="#CHAPTER_XV">Chap. XV</a>. Francis Bacon.</span></td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#CHAPTER_XV">1</a>.</td> -<td class="tdhs">(I.) General Remarks.</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XV2">2</a>.</td> -<td class="tdhs">Common estimate of him.</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XV3">3</a>.</td> -<td class="tdhs">We consider only Physical Science.</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XV4">4</a>.</td> -<td class="tdhs">He is placed at the head of the change:</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XV5">5</a>.</td> -<td class="tdhs">(II.) <i>He proclaims a New Era</i>;</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XV6">6</a>.</td> -<td class="tdhs">(III.) <i>By a Change of Method</i>;</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XV7">7</a>.</td> -<td class="tdhs">Including successive Steps;</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XV8">8</a>.</td> -<td class="tdhs">Gradually ascending.</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XV9">9</a>.</td> -<td class="tdhs">(IV.) <i>He contrasts the Old and the New Method.</i></td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XV10">10</a>.</td> -<td class="tdhs">(V.) <i>Has he neglected Ideas?</i></td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XV11">11</a>.</td> -<td class="tdhs">No.</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XV12">12</a>.</td> -<td class="tdhs">Examples of Ideas treated by him.</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XV13">13</a>.</td> -<td class="tdhs">He has failed in applying his Method;</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XV14">14</a>.</td> -<td class="tdhs">(VI.) <i>To the Cause of Heat.</i></td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XV15">15</a>.</td> -<td class="tdhs">He seeks Causes before Laws.</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XV16">16</a>.</td> -<td class="tdhs">(VII.) <i>His Technical Form worthless.</i></td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XV17">17</a>.</td> -<td class="tdhs">He is confused by words.</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XV18">18</a>.</td> -<td class="tdhs">His "Instances."</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XV19">19</a>.</td> -<td class="tdhs">Contain some good Suggestions.</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XV20">20</a>.</td> -<td class="tdhs">(VIII.) <i>His "Idols."</i></td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XV21">21</a>.</td> -<td class="tdhs">(IX.) <i>His view of Utility.</i></td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XV22">22</a>.</td> -<td class="tdhs">(X.) <i>His Hopefulness.</i></td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XV23">23</a>.</td> -<td class="tdhs">(XI.) <i>His Piety.</i></td> -</tr> -<tr><td class="tdh" colspan="3"><span class="smcap"><a href="#CHAPTER_XVI">Chap. XVI</a>. *Additional Remarks on Francis Bacon.</span></td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XVI1">1</a>.</td> -<td class="tdhs">Mr. Ellis's views.</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XVI2">2</a>.</td> -<td class="tdhs">Mr. Spedding's views.</td> -</tr> -<tr><td class="tdh" colspan="3"><span class="smcap"><a href="#CHAPTER_XVII">Chap. XVII</a>. From Bacon to Newton.</span></td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XVII1">1</a>.</td> -<td class="tdhs">Harvey.</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XVII2">2</a>.</td> -<td class="tdhs">Descartes.</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XVII3">3</a>.</td> -<td class="tdhs">Gassendi.</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XVII4">4</a>.</td> -<td class="tdhs">Actual Progress in Science.<span class="pagenum" id="Page_xi">xi</span></td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XVII5">5</a>.</td> -<td class="tdhs">Otto Guericke, &c.</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XVII6">6</a>.</td> -<td class="tdhs">Hooke.</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XVII7">7</a>.</td> -<td class="tdhs">Royal Society.</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XVII8">8</a>.</td> -<td class="tdhs">Bacon's <i>New Atalantis</i>.</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XVII9">9</a>.</td> -<td class="tdhs">Cowley.</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XVII10">10</a>.</td> -<td class="tdhs">Barrow.</td> -</tr> -<tr><td class="tdh" colspan="3"><span class="smcap"><a href="#CHAPTER_XVIII">Chap. XVIII</a>. Newton.</span></td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XVIII1">1</a>.</td> -<td class="tdhs">Animating effect of his Discoveries.</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XVIII2">2</a>.</td> -<td class="tdhs">They confirm Bacon's views.</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XVIII3">3</a>.</td> -<td class="tdhs">Newton shuns Hypotheses.</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XVIII4">4</a>.</td> -<td class="tdhs">His views of Inductive Philosophy.</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XVIII5">5</a>.</td> -<td class="tdhs">His "Rules of Philosophizing."</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XVIII6">6</a>.</td> -<td class="tdhs"><i>The First Rule.</i></td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XVIII7">7</a>.</td> -<td class="tdhs">What is a "True Cause"?</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XVIII8">8</a>.</td> -<td class="tdhs"><i>Such</i> as are real?</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XVIII9">9</a>.</td> -<td class="tdhs">Or <i>those</i> which are proved?</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XVIII10">10</a>.</td> -<td class="tdhs">Use of the Rule.</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XVIII11">11</a>.</td> -<td class="tdhs">Rule otherwise expressed.</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XVIII12">12</a>.</td> -<td class="tdhs"><i>The Second Rule.</i></td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XVIII13">13</a>.</td> -<td class="tdhs">What are Events "of the same kind"?</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XVIII14">14</a>.</td> -<td class="tdhs"><i>The Third Rule</i>:</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XVIII15">15</a>.</td> -<td class="tdhs">Not safe.</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XVIII16">16</a>.</td> -<td class="tdhs"><i>The Fourth Rule.</i></td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XVIII17">17</a>.</td> -<td class="tdhs">Occult Qualities.</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XVIII18">18</a>.</td> -<td class="tdhs">Ridiculed.</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XVIII19">19</a>.</td> -<td class="tdhs">Distinction of Laws and Causes.</td> -</tr> -<tr><td class="tdh" colspan="3"><span class="smcap"><a href="#CHAPTER_XIX">Chap. XIX</a>. Locke and his French Followers.</span></td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XIX1">1</a>.</td> -<td class="tdhs">Cause of Locke's popularity.</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XIX2">2</a>.</td> -<td class="tdhs">Sensational School.</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XIX3">3</a>.</td> -<td class="tdhs">His inconsistencies.</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XIX4">4</a>.</td> -<td class="tdhs">Condillac, &c.</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XIX5">5</a>.</td> -<td class="tdhs">Importance of Language.</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XIX6">6</a>.</td> -<td class="tdhs">Ground of this.</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XIX7">7</a>.</td> -<td class="tdhs">The Encyclopedists.</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XIX8">8</a>.</td> -<td class="tdhs">Helvetius.</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XIX9">9</a>.</td> -<td class="tdhs">Value of Arts.</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XIX10">10</a>.</td> -<td class="tdhs">Tendency to Reaction.<span class="pagenum" id="Page_xii">xii</span></td> -</tr> -<tr><td class="tdh" colspan="3"><span class="smcap"><a href="#CHAPTER_XX">Chap. XX</a>. The Reaction against the Sensational School.</span></td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XX1">1</a>.</td> -<td class="tdhs">"Nisi intellectus ipse."</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XX2">2</a>.</td> -<td class="tdhs">Price's "Review."</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XX3">3</a>.</td> -<td class="tdhs">Stewart defends Price.</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XX4">4</a>.</td> -<td class="tdhs">Archbishop Whately.</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XX5">5</a>.</td> -<td class="tdhs">Laromiguière.</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XX6">6</a>.</td> -<td class="tdhs">M. Cousin.</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XX7">7</a>.</td> -<td class="tdhs">M. Ampère.</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XX8">8</a>.</td> -<td class="tdhs">His Classification of Sciences.</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XX9">9</a>.</td> -<td class="tdhs">Kant's Reform of Philosophy.</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XX10">10</a>.</td> -<td class="tdhs">Its Effect in Germany.</td> -</tr> -<tr><td class="tdh" colspan="3"><span class="smcap"><a href="#CHAPTER_XXI">Chap. XXI</a>. Further Advance of the Sensational School.</span></td> -</tr> -<tr><td align="left"></td><td class="tdrt"> </td> -<td class="tdhs">M. Auguste Comte.</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XXI1">1</a>.</td> -<td class="tdhs">M. Comte on three States of Science.</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XXI2">2</a>.</td> -<td class="tdhs">M. Comte rejects the Search of Causes.</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XXI3">3</a>.</td> -<td class="tdhs">Causes in Physics.</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XXI4">4</a>.</td> -<td class="tdhs">Causes in other Sciences.</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XXI5">5</a>.</td> -<td class="tdhs">M. Comte's Practical Philosophy.</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XXI6">6</a>.</td> -<td class="tdhs">M. Comte on Hypotheses.</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XXI7">7</a>.</td> -<td class="tdhs">M. Comte's Classification of Sciences.</td> -</tr> -<tr><td class="tdh" colspan="3"><span class="smcap"><a href="#CHAPTER_XXII">Chap. XXII</a>. †Mr. Mill's Logic.</span></td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XXII1">(I.)</a></td> -<td class="tdhs">What is Induction? §§ 1-14.</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XXII2">(II.)</a></td> -<td class="tdhs">Induction or Description, §§ 15-23.</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XXII3">(III.)</a></td> -<td class="tdhs">In Discovery a new Conception is introduced, §§ 24-37.</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XXII4">(IV.)</a></td> -<td class="tdhs">Mr. Mill's Four Methods of Inquiry, §§ 38-40.</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XXII5">(V.)</a></td> -<td class="tdhs">His Examples, §§ 41-48.</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XXII6">(VI.)</a></td> -<td class="tdhs">Mr. Mill against Hypotheses, §§ 49, 50.</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XXII7">(VII.)</a></td> -<td class="tdhs">Against prediction of Facts, §§ 51-53.</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XXII8">(VIII.)</a></td> -<td class="tdhs">Newton's Vera Causa, §§ 54, 55.</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XXII9">(IX.)</a></td> -<td class="tdhs">Successive Generalizations, §§ 56-62.</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XXII10">(X.)</a></td> -<td class="tdhs">Mr. Mill's Hope from Deductions, §§ 63-67.</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XXII11">(XI.)</a></td> -<td class="tdhs">Fundamental opposition of our Doctrines, §§ 68-71.</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XXII12">(XII.)</a></td> -<td class="tdhs">Absurdities in Mr. Mill's Logic, §§ 72-74.<span class="pagenum" id="Page_xiii">xiii</span></td> -</tr> -<tr><td class="tdh" colspan="3"><span class="smcap"><a href="#CHAPTER_XXIII">Chap. XXIII</a>. *Political Economy as an Inductive Science.</span></td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XXIII1">1</a>.</td> -<td class="tdhs">Moral Sciences.</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XXIII2">2</a>.</td> -<td class="tdhs">Political Economy.</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XXIII3">3</a>.</td> -<td class="tdhs">Wages, Profits, and Rents.</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XXIII4">4</a>.</td> -<td class="tdhs">Premature Generalizations.</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XXIII5">5</a>.</td> -<td class="tdhs">Correction of these by Induction—Rent.</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XXIII6">6</a>.</td> -<td class="tdhs"> " Wages.</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XXIII7">7</a>.</td> -<td class="tdhs"> " Population.</td> -</tr> -<tr><td class="tdh" colspan="3"><span class="smcap"><a href="#CHAPTER_XXIV">Chap. XXIV</a>. †Modern German Philosophy.</span></td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XXIV1">(I.)</a></td> -<td class="tdhs">Science is the Idealization of Facts, §§ 1-8.</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XXIV2">(II.)</a></td> -<td class="tdhs">Successive German Philosophies.</td> -</tr> -<tr><td align="left"></td><td class="tdrt"> </td> -<td class="tdhs">Kant, Fichte, Schelling, Hegel, §§ 9-16.</td> -</tr> -<tr><td class="tdh" colspan="3"><span class="smcap"><a href="#CHAPTER_XXV">Chap. XXV</a>. †The Fundamental Antithesis as it exists in the Moral World.</span></td> -</tr> -<tr><td align="left"></td><td class="tdrt"> </td> -<td class="tdhs">Moral Progress is the Realization of Ideas.</td> -</tr> -<tr><td class="tdh" colspan="3"><span class="smcap"><a href="#CHAPTER_XXVI">Chap. XXVI</a>. *Of the "Philosophy of the Infinite."</span></td> -</tr> -<tr><td align="left"></td><td class="tdrt"> </td> -<td class="tdhs">God is Eternal.</td> -</tr> -<tr><td class="tdh" colspan="3"><span class="smcap"><a href="#CHAPTER_XXVII">Chap. XXVII</a>. *Sir William Hamilton on Inertia and Weight.</span></td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XXVII1">1</a>.</td> -<td class="tdhs">Primary and Secondary Qualities.</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XXVII2">2</a>.</td> -<td class="tdhs">Meaning of the Distinction.</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XXVII3">3</a>.</td> -<td class="tdhs">Sir W. Hamilton adds "Secundo-Primary."</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XXVII4">4</a>.</td> -<td class="tdhs">Inertia.</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XXVII5">5</a>.</td> -<td class="tdhs">Sir W. Hamilton's arguments and reply.</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XXVII6">6</a>.</td> -<td class="tdhs">Gravity.</td> -</tr> -<tr><td align="left"></td><td class="tdrt"> </td> -<td class="tdhs">Sir W. Hamilton's arguments and reply.</td> -</tr> -<tr><td class="tdh" colspan="3"><span class="smcap"><a href="#CHAPTER_XXVIII">Chap. XXVIII</a>. †Influence of German Systems of Philosophy in Britain.</span></td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XXVIII1">1</a>.</td> -<td class="tdhs">Stewart on Kant.</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XXVIII2">2</a>.</td> -<td class="tdhs">Mr. G. H. Lewes on Kant.</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XXVIII4">4—6</a>.</td> -<td class="tdhs">Mr. Mansel on Kant.</td> -</tr> -<tr><td align="left"></td><td class="tdrt"> </td> -<td class="tdhs">His objection to our Fundamental Ideas, and Reply.</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XXVIII7">7—10</a>.</td> -<td class="tdhs">New Axioms are possible.</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XXVIII11">11—13</a>.</td> -<td class="tdhs">Mr. Mansel's Kantianism.</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XXVIII14">14—16</a>.</td> -<td class="tdhs">Axioms are not from experience.<span class="pagenum" id="Page_xiv">xiv</span></td> -</tr> -<tr><td class="tdh" colspan="3"><span class="smcap"><a href="#CHAPTER_XXIX">Chap. XXIX</a>. *Necessary Truth is Progressive.</span></td> -</tr> -<tr><td align="left"></td><td class="tdrt"> </td> -<td class="tdhs">Objections considered.</td> -</tr> -<tr><td class="tdh" colspan="3"><span class="smcap"><a href="#CHAPTER_XXX">Chap. XXX</a>. *The Theological Bearing of the Philosophy of Discovery.</span></td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XXX1">1—4</a>.</td> -<td class="tdhs">How can necessary truths be actual?</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XXX5">5, 6</a>.</td> -<td class="tdhs">Small extent of necessary truth.</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XXX7">7</a>.</td> -<td class="tdhs">How did things come to be as they are?</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XXX8">8</a>.</td> -<td class="tdhs">View of the Theist.</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XXX9">9—12</a>.</td> -<td class="tdhs">Is this Platonism?</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XXX13">13</a>.</td> -<td class="tdhs">Idea of Time.</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XXX14">14, 15</a>.</td> -<td class="tdhs">Ideas of Force and Matter.</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XXX16">16</a>.</td> -<td class="tdhs">Creation of Matter.</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XXX17">17</a>.</td> -<td class="tdhs">Platonic Ideas.</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XXX18">18—21</a>.</td> -<td class="tdhs">Idea of Kind.</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XXX22">22</a>.</td> -<td class="tdhs">Idea of Substance.</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XXX23">23</a>.</td> -<td class="tdhs">Idea of Final Cause.</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XXX24">24, 25</a>.</td> -<td class="tdhs">Human immeasurably inferior to Divine.</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XXX26">26</a>.</td> -<td class="tdhs">Science advances towards the Divine Ideas.</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XXX27">27</a>.</td> -<td class="tdhs">Recapitulation.</td> -</tr> -<tr><td class="tdh" colspan="3"><span class="smcap"><a href="#CHAPTER_XXXI">Chap. XXXI</a>. *Man's Knowledge of God.</span></td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XXXI1">1, 2</a>.</td> -<td class="tdhs">Opinions.</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XXXI3">3</a>.</td> -<td class="tdhs">From Nature we learn something of God.</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XXXI1">4—6</a>.</td> -<td class="tdhs">Though but little.</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XXXI1">7, 8</a>.</td> -<td class="tdhs">From ourselves we learn something concerning God.</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XXXI1">9—11</a>.</td> -<td class="tdhs">Objections answered.</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XXXI12">12</a>.</td> -<td class="tdhs">Creation.</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XXXI13">13</a>.</td> -<td class="tdhs">End of the World.</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XXXI14">14</a>.</td> -<td class="tdhs">Moral and Theological views enter.</td> -</tr> -<tr><td class="tdh" colspan="3"><span class="smcap"><a href="#CHAPTER_XXXII">Chap. XXXII</a>. *Analogies of Physical and Religious Philosophy.</span></td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XXXII1">1, 2</a>.</td> -<td class="tdhs">Idealization of Facts and Realization of Ideas;</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XXXII3">3, 4</a>.</td> -<td class="tdhs">Both imperfect.</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XXXII5">5, 6</a>.</td> -<td class="tdhs">Divine Ideas perfect.</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XXXII7">7—9</a>.</td> -<td class="tdhs">Realization of Divine Love.</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XXXII10">10—13</a>.</td> -<td class="tdhs">Realization of Divine Justice.</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XXXII14">14</a>.</td> -<td class="tdhs">Analogy of Physical and Moral Philosophy.<span class="pagenum" id="Page_xv">xv</span></td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XXXII15">15, 16</a>.</td> -<td class="tdhs">Supernatural Beginning, Middle, and End indicated.</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XXXII17">17</a>.</td> -<td class="tdhs">Suggestion of a Future State.</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XXXII18">18—20</a>.</td> -<td class="tdhs">Confirmation from the Intellect of Man.</td> -</tr> -<tr><td align="left"></td><td class="tdrt"><a href="#XXXII21">21</a>.</td> -<td class="tdhs">From the Moral Nature of Man.</td> -</tr> -</table></div> - - <p class="center"><a href="#APPENDIX">APPENDIX</a>.</p> - - -<div class="center"> -<table border="0" cellpadding="6" cellspacing="0" summary=""> -<tr><td class="tdr" colspan="3"><span class="xs">PAGE</span></td></tr> -<tr><td class="tdrt"><span class="smcap">Append. <a href="#Appendix_A">A</a>.</span></td> -<td class="tdhs"><span class="smcap">Of the Platonic Theory of Ideas</span></td> -<td class="tdrb">403</td> -</tr> -<tr><td class="tdrt"><a href="#Appendix_B">B</a>.</td> -<td class="tdhs"><span class="smcap">On Plato's Survey of the Sciences</span></td> -<td class="tdrb">417</td> -</tr> -<tr><td class="tdrt"><a href="#Appendix_BB">BB</a>.</td> -<td class="tdhs"><span class="smcap">On Plato's Notion of Dialectic</span></td> -<td class="tdrb">429</td> -</tr> -<tr><td class="tdrt"><a href="#APPENDIX_C">C</a>.</td> -<td class="tdhs"><span class="smcap">Of the Intellectual Powers according to Plato</span></td> -<td class="tdrb">440</td> -</tr> -<tr><td class="tdrt"><a href="#Appendix_D">D</a>.</td> -<td class="tdhs"><span class="smcap">Criticism of Aristotle's Account of Induction</span></td> -<td class="tdrb">449</td> -</tr> -<tr><td class="tdrt"><a href="#Appendix_E">E</a>.</td> -<td class="tdhs"><span class="smcap">On the Fundamental Antithesis of Philosophy</span></td> -<td class="tdrb">462</td> -</tr> -<tr><td class="tdrt"><a href="#Appendix_F">F</a>.</td> -<td class="tdhs"><span class="smcap">Remarks on a Review of the Philosophy of the Inductive Sciences</span></td> -<td class="tdrb">482</td> -</tr> -<tr><td class="tdrt"><a href="#Appendix_G">G</a>.</td> -<td class="tdhs"><span class="smcap">On the Transformation of Hypotheses in the History of Science</span></td> -<td class="tdrb">492</td> -</tr> -<tr><td class="tdrt"><a href="#Appendix_H">H</a>.</td> -<td class="tdhs"><span class="smcap">On Hegel's Criticism of Newton's Principia</span></td> -<td class="tdrb">504</td> -</tr> -<tr><td class="tdrt"> </td> -<td class="tdhs"><a href="#APPENDIX_TO_THE_MEMOIR">Appendix to the Memoir on Hegel's Criticism of Newton's Principia</a></td> -<td class="tdrb">513</td> -</tr> -<tr><td class="tdrt"><a href="#Appendix_K">K</a>.</td> -<td class="tdhs"><span class="smcap">Demonstration that all Matter is Heavy</span></td> -<td class="tdrb">522</td> -</tr> -</table></div> - - -<p><span class="pagenum" id="Page_1">1</span></p> - - - - -<p class="half-title"> -ON THE<br /> -PHILOSOPHY<br /> -OF<br /> -DISCOVERY.<br /> -</p> - -<p><span class="pagenum" id="Page_2">2</span></p> - - -<div class="poetry-container"><div class="poetry"><div class="stanza"> - <div class="verse">Wär' nicht das Auge sonnenhaft</div> - <div class="verse">Wie könnten wir das Licht erblicken?</div> - <div class="verse">Lebt' nicht in uns des Gottes eigne Kraft</div> - <div class="verse">Wie könnte uns das Göttliche entzücken?</div> - <div class="verse indent16"><span class="smcap">Goethe.</span></div> -</div></div></div> - -<div class="poetry-container"><div class="poetry"><div class="stanza"> - <div class="verse">Were nothing sunlike in the Eye</div> - <div class="verse">How could we Light itself descry?</div> - <div class="verse">Were nothing godlike in the Mind</div> - <div class="verse">How could we God in Nature find?</div> -</div></div></div> - -<hr class="chap" /> -<p><span class="pagenum" id="Page_3">3</span></p> - - -<div class="chapter"> -<h2><a id="CHAPTER_I"></a>CHAPTER I.<br /> - -INTRODUCTION.</h2> - - -<p class="drop-cap"><span class="smcap">By</span> the examination of the elements of human -thought in which I have been engaged, and by -a consideration of the history of the most clear and -certain parts of our knowledge, I have been led to -doctrines respecting the progress of that exact and -systematic knowledge which we call Science; and -these doctrines I have endeavoured to lay before the -reader in the History of the Sciences and of Scientific -Ideas. The questions on which I have thus ventured -to pronounce have had a strong interest for man from -the earliest period of his intellectual progress, and -have been the subjects of lively discussion and bold -speculation in every age. I conceive that in the doctrines -to which these researches have conducted us, -we have a far better hope that we possess a body of -permanent truths than the earlier essays on the same -subjects could furnish. For we have not taken our -examples of knowledge at hazard, as earlier speculators -did, and were almost compelled to do; but have -drawn our materials from the vast store of unquestioned -truths which modern science offers to us: and -we have formed our judgment concerning the nature -and progress of knowledge by considering what such -science is, and how it has reached its present condition. -But though we have thus pursued our speculations -concerning knowledge with advantages which earlier -writers did not possess, it is still both interesting and -instructive for us to regard the opinions upon this -subject which have been delivered by the philosophers -of past times. It is especially interesting to see some -of the truths which we have endeavoured to expound, -gradually dawning in men's minds, and assuming the<span class="pagenum" id="Page_4">4</span> -clear and permanent form in which we can now contemplate -them. I shall therefore, in the ensuing -chapters, pass in review many of the opinions of the -writers of various ages concerning the mode by which -man best acquires the truest knowledge; and I shall -endeavour, as we proceed, to appreciate the real value -of such judgments, and their place in the progress of -sound philosophy.</p> - -<p>In this estimate of the opinions of others, I shall -be guided by those general doctrines which I have, as -I trust, established in the histories already published. -And without attempting here to give any summary -of these doctrines, I may remark that there are two -main principles by which speculations on such subjects -in all ages are connected and related to each -other; namely, the opposition of <i>Ideas</i> and <i>Sensations</i>, -and the distinction of <i>practical</i> and <i>speculative</i> knowledge. -The opposition of Ideas and Sensations is exhibited -to us in the antithesis of Theory and Fact, -which are necessarily considered as distinct and of -opposite natures, and yet necessarily identical, and -constituting Science by their identity. In like manner, -although practical knowledge is in substance -identical with speculative, (for all knowledge is speculation,) -there is a distinction between the two in their -history, and in the subjects by which they are exemplified, -which distinction is quite essential in judging -of the philosophical views of the ancients. The -alternatives of identity and diversity, in these two -antitheses,—the successive separation, opposition, and -reunion of principles which thus arise,—have produced, -(as they may easily be imagined capable of -doing,) a long and varied series of systems concerning -the nature of knowledge; among which we shall have -to guide our course by the aid of the views already -presented.</p> - -<p>I am far from undertaking, or wishing, to review -the whole series of opinions which thus come under -our notice; and I do not even attempt to examine all -the principal authors who have written on such subjects. -I merely wish to select some of the most con<span class="pagenum" id="Page_5">5</span>siderable -forms which, such opinions have assumed, -and to point out in some measure the progress of truth -from age to age. In doing this, I can only endeavour -to seize some of the most prominent features of each -time and of each step, and I must pass rapidly from -classical antiquity to those which we have called the -dark ages, and from them to modern times. At each -of these periods the modifications of opinion, and the -speculations with which they were connected, formed -a vast and tangled maze, the byways of which our -plan does not allow us to enter. We shall esteem -ourselves but too fortunate, if we can discover the -single track by which ancient led to modern philosophy.</p> - -<p>I must also repeat that my survey of philosophical -writers is here confined to this one point,—their opinions -on the nature of knowledge and the method of -science. I with some effort avoid entering upon other -parts of the philosophy of those authors of whom I -speak; I knowingly pass by those portions of their -speculations which are in many cases the most interesting -and celebrated;—their opinions concerning the -human soul, the Divine Governor of the world, the -foundations or leading doctrines of politics, religion, -and general philosophy. I am desirous that my -reader should bear this in mind, since he must otherwise -be offended with the scanty and partial view -which I give in this place of the philosophers whom -I enumerate.</p> - -<hr class="chap" /> -<p><span class="pagenum" id="Page_6">6</span></p> - - -</div><div class="chapter"> - - - -</div><div class="chapter"> -<h2><a name="CHAPTER_II" id="CHAPTER_II"></a>CHAPTER II.<br /> - -<span class="smcap medium">Plato.</span></h2> - - -<p class="drop-cap"><span class="smcap">There</span> would be small advantage in beginning our -examination earlier than the period of the Socratic -School at Athens; for although the spirit of inquiry -on such subjects had awakened in Greece at an earlier -period, and although the peculiar aptitude of the -Grecian mind for such researches had shown itself -repeatedly in subtle distinctions and acute reasonings, -all the positive results of these early efforts were contained -in a more definite form in the reasonings of the -Platonic age. Before that time, the Greeks did not -possess plain and familiar examples of exact knowledge, -such as the truths of Arithmetic, Geometry, -Astronomy and Optics became in the school of Plato; -nor were the antitheses of which we spoke above, so -distinctly and fully unfolded as we find them in Plato's -works.</p> - -<p>The question which hinges upon one of these antitheses, -occupies a prominent place in several of the -Platonic dialogues; namely, whether our knowledge -be obtained by means of Sensation or of Ideas. One -of the doctrines which Plato most earnestly inculcated -upon his countrymen was, that we do not <i>know</i> concerning -sensible objects, but concerning ideas. The -first attempts of the Greeks at metaphysical analysis -had given rise to a school which maintained that -material objects are the only realities. In opposition -to this, arose another school, which taught that material -objects have no permanent reality, but are ever -waxing and waning, constantly changing their substance. -"And hence," as Aristotle says<a id="FNanchor_1" href="#Footnote_1" class="fnanchor">1</a>, "arose the -doctrine of ideas which the Platonists held. For they<span class="pagenum" id="Page_7">7</span> -assented to the opinion of Heraclitus, that all sensible -objects are in a constant state of flux. So that if -there is to be any knowledge and science, it must -be concerning some permanent natures, different from -the sensible natures of objects; for there can be no -permanent science respecting that which is perpetually -changing. It happened that Socrates turned his -speculations to the moral virtues, and was the first -philosopher who endeavoured to give universal definitions -of such matters. He wished to reason systematically, -and therefore he tried to establish definitions, -for definitions are the basis of systematic -reasoning. There are two things which may justly -be looked upon as steps in philosophy due to Socrates; -inductive reasonings, and universal definitions;—both -of them steps which belong to the foundations of -science. Socrates, however, did not make universals, -or definitions separable from the objects; but his followers -separated them, and these essences they termed -<i>Ideas</i>." And the same account is given by other -writers<a name="FNanchor_2" id="FNanchor_2"></a><a href="#Footnote_2" class="fnanchor">[2]</a>. "Some existences are sensible, some intelligible: -and according to Plato, if we wish to understand -the principles of things, we must first separate -the <i>ideas</i> from the <i>things</i>, such as the ideas of Similarity, -Unity, Number, Magnitude, Position, Motion: -second, that we must assume an absolute Fair, Good, -Just, and the like: third, that we must consider the -ideas of relation, as Knowledge, Power: recollecting -that the Things which we perceive have this or that -appellation applied to them because they partake of -this or that Idea; those things being <i>just</i> which participate -in the idea of The Just, those being <i>beautiful</i>, -which contain the idea of The Beautiful." And many -of the arguments by which this doctrine was maintained -are to be found in the Platonic dialogues. Thus -the opinion that true knowledge consists in sensation, -which had been asserted by Protagoras and others, is -refuted in the <i>Theætetus</i>: and, we may add, so victoriously -refuted, that the arguments there put forth<span class="pagenum" id="Page_8">8</span> -have ever since exercised a strong influence upon the -speculative world. It may be remarked that in the -minds of Plato and of those who have since pursued -the same paths of speculation, the interest of such discussions -as those we are now referring to, was by no -means limited to their bearing upon mere theory; but -was closely connected with those great questions of -morals which have always a practical import. Those -who asserted that the only foundation of knowledge -was sensation, asserted also that the only foundation of -virtue was the desire of pleasure. And in Plato, the -metaphysical part of the disquisitions concerning knowledge -in general, though independent in its principles, -always seems to be subordinate in its purpose to the -questions concerning the knowledge of our duty.</p> - -<p>Since Plato thus looked upon the Ideas which were -involved in each department of knowledge as forming -its only essential part, it was natural that he should -look upon the study of Ideas as the true mode of pursuing -knowledge. This he himself describes in the -<i>Philebus</i><a name="FNanchor_3" id="FNanchor_3"></a><a href="#Footnote_3" class="fnanchor">[3]</a>. "The best way of arriving at truth is not -very difficult to point out, but most hard to pursue. -All the arts which have ever been discovered, were -revealed in this manner. It is a gift of the gods to -man, which, as I conceive, they sent down by some -Prometheus, as by Prometheus they gave us the light -of fire; and the ancients, more clear-sighted than we, -and less removed from the gods, handed down this -traditionary doctrine: that whatever is said to be, -comes of One and of Many, and comprehends in itself -the Finite and the Infinite in coalition (being -One Kind, and consisting of Infinite Individuals). -And this being the state of things, we must, in each -case, endeavour to seize the One Idea (the idea of the -Kind) as the chief point; for we shall find that it is -there. And when we have seized this one thing, we -may then consider how it comprehends in itself two, -or three, or any other number; and, again, examine -each of these ramifications separately; till at last we<span class="pagenum" id="Page_9">9</span> -perceive, not only that One is at the same time One -and Many, but also <i>how many</i>. And when we have -thus filled up the interval between the Infinite and -the One, we may consider that we have done with -each one. The gods then, as I have said, taught us -by tradition thus to contemplate, and to learn, and to -teach one another. But the philosophers of the present -day seize upon the One, at hazard, too soon or too -late, and then immediately snatch at the Infinite; but -the intermediate steps escape them, in which resides -the distinction between a truly logical and a mere -disputatious discussion."</p> - -<p>It would seem that what the author here describes -as the most perfect form of exposition, is that which -refers each object to its place in a classification containing -a complete series of subordinations, and which -gives a definition of each class. We have repeatedly -remarked that, in sciences of classification, each new -definition which gives a tenable and distinct separation -of classes is an important advance in our knowledge; -but that such definitions are rather the last than the -first step in each advance. In the progress of real -knowledge, these definitions are always the results of -a laborious study of individual cases, and are never -arrived at by a pure effort of thought, which is what -Plato appears to have imagined as the true mode of -philosophizing. And still less do the advances of other -sciences consist in seizing at once upon the highest -generality, and filling in afterwards all the intermediate -steps between that and the special instances. On -the contrary, as we have seen, the ascents from particular -to general are all successive; and each step of -this ascent requires time, and labour, and a patient -examination of actual facts and objects.</p> - -<p>It would, of course, be absurd to blame Plato for -having inadequate views of the nature of progressive -knowledge, at the time when knowledge could hardly -be said to have begun its progress. But we already -find in his speculations, as appears in the passages -just quoted from his writings, several points brought -into view which will require our continued attention<span class="pagenum" id="Page_10">10</span> -as we proceed. In overlooking the necessity of a -gradual and successive advance from the less general -to the more general truths, Plato shared in a dimness -of vision<a name="FNanchor_4" id="FNanchor_4"></a><a href="#Footnote_4" class="fnanchor">[4]</a> which prevailed among philosophers to the -time of Francis Bacon. In thinking too slightly -of the study of actual nature, he manifested a bias -from which the human intellect freed itself in the -vigorous struggles which terminated the dark ages. -In pointing out that all knowledge implies a unity of -what we observe as manifold, which unity is given by -the mind, Plato taught a lesson which has of late -been too obscurely acknowledged, the recoil by which -men repaired their long neglect of facts having carried -them for a while so far as to think that facts -were the whole of our knowledge. And in analysing -this principle of Unity, by which we thus connect -sensible things, into various Ideas, such as Number, -Magnitude, Position, Motion, he made a highly important -step, which it has been the business of philosophers -in succeeding times to complete and to follow -out.</p> - -<p>But the efficacy of Plato's speculations in their -bearing upon physical science, and upon theory in -general, was much weakened by the confusion of -practical with theoretical knowledge, which arose from -the ethical propensities of the Socratic school. In -the Platonic Dialogues, Art and Science are constantly -spoken of indiscriminately. The skill possessed by -the Painter, the Architect, the Shoemaker, is considered -as a just example of human science, no less -than the knowledge which the geometer or the astronomer -possesses of the theoretical truths with which -he is conversant. Not only so; but traditionary and -mythological tales, mystical imaginations and fantastical -etymologies, are mixed up, as no less choice ingredients, -with the most acute logical analyses, and -the most exact conduct of metaphysical controversies. -There is no distinction made between the knowledge -possessed by the theoretical psychologist and the<span class="pagenum" id="Page_11">11</span> -physician, the philosophical teacher of morals and the -legislator or the administrator of law. This, indeed, -is the less to be wondered at, since even in our own -time the same confusion is very commonly made by -persons not otherwise ignorant or uncultured.</p> - -<p>On the other hand, we may remark finally, that -Plato's admiration of Ideas was not a barren imagination, -even so far as regarded physical science. For, -as we have seen<a name="FNanchor_5" id="FNanchor_5"></a><a href="#Footnote_5" class="fnanchor">[5]</a>, he had a very important share in -the introduction of the theory of epicycles, having -been the first to propose to astronomers in a distinct -form, the problem of which that theory was the solution; -namely, "to explain the celestial phenomena by -the combination of equable circular motions." This -demand of an ideal hypothesis which should exactly -express the phenomena (as well as they could then be -observed), and from which, by the interposition of -suitable steps, all special cases might be deduced, falls -in well with those views respecting the proper mode -of seeking knowledge which we have quoted from the -<i>Philebus</i>. And the Idea which could thus represent -and replace all the particular Facts, being not only -sought but found, we may readily suppose that the -philosopher was, by this event, strongly confirmed in -his persuasion that such an Idea was indeed what the -inquirer ought to seek. In this conviction all his -genuine followers up to modern times have participated; -and thus, though they have avoided the error -of those who hold that facts alone are valuable as the -elements of our knowledge, they have frequently run -into the opposite error of too much despising and -neglecting facts, and of thinking that the business of -the inquirer after truth was only a profound and constant -contemplation of the conceptions of his own -mind. But of this hereafter.</p> -<p><span class="pagenum" id="Page_12">12</span></p> - - - - -<hr class="chap" /> - -</div><div class="chapter"> -<h2><a name="CHAPTER_III" id="CHAPTER_III"></a>CHAPTER III.<br /> - -<span class="smcap medium">Additional Remarks on Plato.</span></h2> - - -<p class="drop-cap"><span class="smcap">The</span> leading points in Plato's writings which bear -upon the philosophy of discovery are these:</p> - -<p> -1. The Doctrine of Ideas.<br /> -2. The Doctrine of the One and the Many.<br /> -3. The notion of the nature and aim of Science.<br /> -4. The survey of existing Sciences.<br /> -</p> - -<p><a id="III1"></a>1. The Doctrine of Ideas is an attempt to solve a -problem which in all ages forces itself upon the notice -of thoughtful men; namely, How can certain and -permanent knowledge be possible for man, since all -his knowledge must be derived from transient and -fluctuating sensations? And the answer given by this -doctrine is, that certain and permanent knowledge is -<i>not</i> derived from <i>Sensations</i>, but from <i>Ideas</i>. There -are in the mind certain elements of knowledge which -are not derived from sensation, and are only imperfectly -exemplified in sensible objects; and when we -reason concerning sensible things so as to obtain real -knowledge, we do so by considering such things as -partaking of the qualities of the Ideas concerning -which there can be truth. The sciences of Geometry -and Arithmetic show that there <i>are</i> truths which -man can know; and the Doctrine of Ideas explains -how this is possible.</p> - -<p>So far the Doctrine of Ideas answers its primary -purpose, and is a reply (by no means the least intelligible -and satisfactory reply) to a question still agitated -among philosophers: What is the ground of -geometrical (and other necessary) truth?</p> - -<p>But Plato seems, in many of his writings, to extend -this doctrine much further; and to assume, not only -Ideas of Space and its properties, from which geome<span class="pagenum" id="Page_13">13</span>trical -truths are derived; but of Relations, as the -Relations of Like and Unlike, Greater and Less; and -of mere material objects, as Tables and Chairs. Now -to assume Ideas of such things as these solves no difficulty -and is supported by no argument. In this -respect the Ideal theory is of no value in Science.</p> - -<p>It is curious that we have a very acute refutation -of the Ideal theory in this sense, not only in Aristotle, -the open opponent of Plato on this subject, but in the -Platonic writings themselves: namely, in the Dialogue -entitled <i>Parmenides</i>; which, on this and on other accounts, -I consider to be the work not of Plato, but of -an opponent of Plato<a name="FNanchor_6" id="FNanchor_6"></a><a href="#Footnote_6" class="fnanchor">[6]</a>.</p> - -<p><a id="III2"></a>2. I have spoken, in the preceding chapter, of -Plato's doctrine that truth is to be obtained by discerning -the One in the Many. This expression is -used, it would seem, in a somewhat large and fluctuating -way, to mean several things; as for instance, -finding the one <i>kind</i> in many <i>individuals</i> (for instance, -the one idea of dog in many dogs); or the -one <i>law</i> in many <i>phenomena</i> (for instance, the eccentrics -and epicycles in many planets). In any interpretation, -it is too loose and indefinite a rule to be of -much value in the formation of sciences, though it -has been recently again propounded as important in -modern times.</p> - -<p><a id="III3"></a>3. I have said, in the preceding chapter, that -Plato, though he saw that scientific truths of great -generality might be obtained and were to be arrived -at by philosophers, overlooked the necessity of a <i>gradual</i> -and <i>successive</i> advance from the less general to -the more general; and I have described this as a -'dimness of vision.' I must now acknowledge that this -is not a very appropriate phrase; for not only no -acuteness of vision could have enabled Plato to see -that gradual generalization in science of which, as yet, -no example had appeared; but it was very fortunate -for the progress of truth, at that time, that Plato had -imagined to himself the object of science to be general<span class="pagenum" id="Page_14">14</span> -and sublime truths which prove themselves to be true -by the light of their own generality and symmetry. -It is worth while to illustrate this notice of Plato by -some references to his writings.</p> - -<p>In the Sixth Book of the <i>Republic</i>, Plato treats of -the then existing sciences as the instruments of a -philosophical education. Among the most conspicuous -of these is astronomy. He there ridicules the -notion that astronomy is a sublime science because it -makes men look <i>upward</i>. He asserts that the really -sublime science is that which makes men look at the -<i>realities</i>, which are suggested by the appearances seen -in the heavens: namely, the spheres which revolve and -carry the luminaries in their revolutions. Now it was -no doubt the determined search for such "realities" -as these which gave birth to the Greek <i>Astronomy</i>, -that first and critical step in the progress of science. -Plato, by his exhortations, if not by his suggestions, -contributed effectually, as I conceive, to this step in -science. In the same manner he requires a science of -<i>Harmonics</i> which shall be free from the defects and -inaccuracies which occur in actual instruments. This -belief that the universe was full of mathematical relations, -and that these were the true objects of scientific -research, gave a vigour, largeness of mind, and confidence -to the Greek speculators which no more cautious -view of the problem of scientific discovery could -have supplied. It was well that this advanced guard -in the army of discoverers was filled with indomitable -courage, boundless hopes, and creative minds.</p> - -<p>But we must not forget that this disposition to -what Bacon calls <i>anticipation</i> was full of danger as -well as of hope. It led Plato into error, as it led -Kepler afterwards, and many others in all ages of -scientific activity. It led Plato into error, for instance, -when it led him to assert (in the <i>Timæus</i>) that -the four elements, Earth, Air, Fire and Water, have, -for the forms of their particles respectively, the Cube, -the Icosahedron, the Pyramid, and the Octahedron; -and again, when it led him to despise the practical -controversies of the musicians of his time; which con<span class="pagenum" id="Page_15">15</span>troversies -were, in fact, the proof of the truth of the -mathematical theory of Harmonics. And in like manner -it led Kepler into error when it led him to believe -that he had found the reason of the number, size and -motion of the planetary orbits in the application of -the five regular solids to the frame of the universe<a name="FNanchor_7" id="FNanchor_7"></a><a href="#Footnote_7" class="fnanchor">[7]</a>.</p> - -<p>How far the caution in forming hypotheses which -Bacon's writings urge upon us is more severe than -suits the present prospects of science, we may hereafter -consider; but it is plainly very conceivable that a -boldness in the invention and application of hypotheses -which was propitious to science in its infancy, -may be one of the greatest dangers of its more mature -period: and further, that the happy effect of such a -temper depended entirely upon the candour, skill and -labour with which the hypotheses were compared with -the observed phenomena.</p> - -<p><a id="III4"></a>4. Plato has given a survey of the sciences of his -time as Francis Bacon has of <i>his</i>. Indeed Plato has -given two such surveys: one, in the <i>Republic</i>, in -reviewing, as I have said, the elements of a philosophical -education; the other in the <i>Timæus</i>, as the -portions of a theological view of the universe—such -as has been called a <i>Theodicæa</i>, a justification of God. -In the former passage of Plato, the sciences enumerated -are Arithmetic, Plane Geometry, Solid Geometry, -Astronomy and Harmonics<a name="FNanchor_8" id="FNanchor_8"></a><a href="#Footnote_8" class="fnanchor">[8]</a>. In the <i>Timæus</i> we have -a further notice of many other subjects, in a way -which is intended, I conceive, to include such knowledge -as Plato had then arrived at on the various parts -of the universe. The subjects there referred to are, -as I have elsewhere stated<a name="FNanchor_9" id="FNanchor_9"></a><a href="#Footnote_9" class="fnanchor">[9]</a>, these: light and heat, -water, ice, gold, gems, rust and other natural objects:—odours, -taste, hearing, lights, colour, and the powers -of sense in general:—the parts and organs of the body, -as the bones, the marrow, the brain, flesh, muscles, -tendons, ligaments and nerves; the skin, the hair, the<span class="pagenum" id="Page_16">16</span> -nails; the veins and arteries; respiration; generation; -and in short, every obvious point of physiology. -But the opinions thus delivered in the <i>Timæus</i> on the -latter subject have little to do with the progress of -real knowledge. The doctrines, on the other hand, -which depend upon geometrical and arithmetical relations -are portions or preludes of the sciences which -the fulness of time brought forth.</p> - -<p><a id="III5"></a>5. I may, as further bearing upon the Platonic -notion of science, notice Plato's view of the constitution -of the human mind. According to him the Ideas -which are the constituents of science form an Intelligible -World, while the visible and tangible things -which we perceive by our senses form the Visible -World. In the visible world we have shadows and -reflections of actual objects, and by these shadows and -reflections we may judge of the objects, even when we -cannot do so directly; as when men in a dark cavern -judge of external objects by the shadows which they -cast into the cavern. In like manner in the Intelligible -World there are conceptions which are the usual -objects of human thought, and about which we reason; -but these are only shadows and reflections of the Ideas -which are the real sources of truth. And the Reasoning -Faculty, the Discursive Reason, the <i>Logos</i>, which -thus deals with conceptions, is subordinate to the Intuitive -Faculty, the Intuitive Reason, the <i>Nous</i>, which -apprehends Ideas<a name="FNanchor_10" id="FNanchor_10"></a><a href="#Footnote_10" class="fnanchor">[10]</a>. This recognition of a Faculty in -man which contemplates the foundations—the <i>Fundamental -Ideas</i>—of science, and by apprehending such -Ideas, makes science possible, is consentaneous to the -philosophy which I have all along presented, as the -view taught us by a careful study of the history and -nature of science. That new Fundamental Ideas are -unfolded, and the Intuitive Faculty developed and -enlarged by the progress of science and by an intimate -acquaintance with its reasonings, Plato appears to have -discerned in some measure, though dimly. And this -is the less wonderful, inasmuch as this gradual and<span class="pagenum" id="Page_17">17</span> -successive extension of the field of Intuitive Truth, in -proportion as we become familiar with a larger amount -of derived truth, is even now accepted by few, though -proved by the reasonings of the greatest scientific discoverers -in every age.</p> - -<p>The leading defect in Plato's view of the nature of -real science is his not seeing fully the extent to which -experience and observation are the basis of all our -knowledge of the universe. He considers the luminaries -which appear in the heavens to be not the true -objects of astronomy, but only some imperfect adumbration -of them;—mere diagrams which may assist us -in the study of a higher truth, as beautiful diagrams -might illustrate the truths of geometry, but would not -prove them. This notion of an astronomy which is an -astronomy of Theories and not of Facts, is not tenable, -for Theories <i>are</i> Facts. Theories and Facts are equally -<i>real</i>; true Theories are Facts, and Facts are familiar -Theories. But when Plato says that astronomy is a -series of problems suggested by visible things, he uses -expressions quite conformable to the true philosophy -of science; and the like is true of all other sciences.</p> - -<p><span class="pagenum" id="Page_18">18</span></p> - - - - - - -<hr class="chap" /> -</div><div class="chapter"> -<h2><a name="CHAPTER_IV" id="CHAPTER_IV"></a>CHAPTER IV.<br /> - -<span class="smcap medium">Aristotle.</span></h2> - - -<p class="drop-cap"><span class="smcap">The</span> views of Aristotle with regard to the foundations -of human knowledge are very different from -those of his tutor Plato, and are even by himself put -in opposition to them. He dissents altogether from -the Platonic doctrine that Ideas are the true materials -of our knowledge; and after giving, respecting the -origin of this doctrine, the account which we quoted -in the last chapter, he goes on to reason against it. -"Thus," he says<a name="FNanchor_11" id="FNanchor_11"></a><a href="#Footnote_11" class="fnanchor">[11]</a>, "they devised Ideas of all things -which are spoken of as universals: much as if any -one having to count a number of objects, should think -that he could not do it while they were few, and -should expect to count them by making them more -numerous. For the kinds of things are almost more -numerous than the special sensible objects, by seeking -the causes of which they were led to their Ideas." He -then goes on to urge several other reasons against the -assumption of Ideas and the use of them in philosophical -researches.</p> - -<p>Aristotle himself establishes his doctrines by trains -of reasoning. But reasoning must proceed from certain -First Principles; and the question then arises, -Whence are these First Principles obtained? To this -he replies, that they are the result of <i>Experience</i>, and -he even employs the same technical expression by -which we at this day describe the process of collecting -these principles from observed facts;—that they are -obtained by <i>Induction</i>. I have already quoted passages -in which this statement is made<a name="FNanchor_12" id="FNanchor_12"></a><a href="#Footnote_12" class="fnanchor">[12]</a>. "The way -of reasoning," he says<a name="FNanchor_13" id="FNanchor_13"></a><a href="#Footnote_13" class="fnanchor">[13]</a>, "is the same in philosophy,<span class="pagenum" id="Page_19">19</span> -and in any art or science: we must collect the <i>facts</i> -(τὰ ὑπὰρχοντα), and the things to which the facts happen, -and must have as large a supply of these as -possible, and then we must examine them according -to the terms of our syllogisms." ... "There are peculiar -principles in each science; and in each case these -principles must be obtained from <i>experience</i>. Thus -astronomical observation supplies the principles of -astronomical science. For the phenomena being -rightly taken, the demonstrations of astronomy were -discovered; and the same is the case with any other -Art or Science. So that if the facts in each case be -taken, it is our business to construct the demonstrations. -For if <i>in our natural history</i> (κατὰ τὰν ἱστορί αν) -we have omitted none of the facts and properties -which belong to the subject, we shall learn what we -can demonstrate and what we cannot." And again<a name="FNanchor_14" id="FNanchor_14"></a><a href="#Footnote_14" class="fnanchor">[14]</a>, -"It is manifest that if any sensation be wanting, -there must be some knowledge wanting, which we are -thus prevented from having. For we acquire knowledge -either <i>by Induction</i> (ἐπαγωγῆ) or by Demonstration: -and Demonstration is from universals, but Induction -from particulars. It is impossible to have -universal theoretical propositions except by Induction: -and we cannot make inductions without having sensation; -for sensation has to do with particulars."</p> - -<p>It is easy to show that Aristotle uses the term -<i>Induction</i>, as we use it, to express the process of -collecting a general proposition from particular cases -in which it is exemplified. Thus in a passage which -we have already quoted<a name="FNanchor_15" id="FNanchor_15"></a><a href="#Footnote_15" class="fnanchor">[15]</a>, he says, "Induction, and -Syllogism from Induction, is when we attribute one -extreme term to the middle by means of the other." -The import of this technical phraseology will further -appear by the example which he gives: "We find -that several animals which are deficient in bile are -long-lived, as man, the horse, the mule; hence we -infer that <i>all</i> animals which are deficient in bile are -long-lived."</p> -<p><span class="pagenum" id="Page_20">20</span></p> -<p>We may observe, however, that both Aristotle's -notion of induction, and many other parts of his -philosophy, are obscure and imperfect, in consequence -of his refusing to contemplate ideas as something -distinct from sensation. It thus happens that he -always assumes the ideas which enter into his proposition -as <i>given</i>; and considers it as the philosopher's -business to determine whether such propositions are -true or not: whereas the most important feature in -induction is, as we have said, the <i>introduction</i> of a -new idea, and not its employment when once introduced. -That the mind in this manner gives unity to -that which is manifold,—that we are thus led to speculative -principles which have an evidence higher than -any others,—and that a peculiar sagacity in some men -seizes upon the conceptions by which the facts may be -bound into true propositions,—are doctrines which -form no essential part of the philosophy of the Stagirite, -although such views are sometimes recognized, more -or less clearly, in his expressions. Thus he says<a name="FNanchor_16" id="FNanchor_16"></a><a href="#Footnote_16" class="fnanchor">[16]</a>, -"There can be no knowledge when the sensation does -not continue in the mind. For this purpose, it is -necessary both to perceive, and to have some <i>unity</i> in -the mind (αἰσθανομένοις εχειν ἔν τι<a name="FNanchor_17" id="FNanchor_17"></a><a href="#Footnote_17" class="fnanchor">[17]</a> ἐν τῇ ψυχῇ); and -many such perceptions having taken place, some -difference is then perceived: and from the remembrance -of these arises Reason. Thus from Sensation -comes Memory, and from Memory of the same thing -often repeated comes Experience: for many acts of -Memory make up one Experience. And from Experience, -or from any Universal Notion which takes a -permanent place in the mind,—from the <i>unity in the -manifold</i>, the same some one thing being found in -many facts,—springs the first principle of Art and of -Science; of Art, if it be employed about production; -of Science, if about existence."</p> - -<p><span class="pagenum" id="Page_21">21</span></p> - -<p>I will add to this, Aristotle's notice of <i>Sagacity</i>; -since, although little or no further reference is made -to this quality in his philosophy, the passage fixes our -attention upon an important step in the formation of -knowledge. "Sagacity" (ἀγχίνοια), he says<a name="FNanchor_18" id="FNanchor_18"></a><a href="#Footnote_18" class="fnanchor">[18]</a>, "is a -hitting by guess (εὐστοχία τις) upon the middle term -(the conception common to two cases) in an inappreciable -time. As for example, if any one seeing that the -bright side of the moon is always towards the sun, -suddenly perceives why this is; namely, because the -moon shines by the light of the sun:—or if he sees -a person talking with a rich man, he guesses that he -is borrowing money;—or conjectures that two persons -are friends, because they are enemies of the same -person."—To consider only the first of these examples;—the -conception here introduced, that of a body -shining by the light which another casts upon it, is -not contained in the observed facts, but introduced -by the mind. It is, in short, that conception which, -in the act of induction, the mind superadds to the phenomena -as they are presented by the senses: and to -invent such appropriate conceptions, such "eustochies," -is, indeed, the precise office of inductive sagacity.</p> - -<p>At the end of this work (the <i>Later Analytics</i>) -Aristotle ascribes our knowledge of principles to Intellect -(νοῦς), or, as it appears necessary to translate -the word, <i>Intuition</i><a name="FNanchor_19" id="FNanchor_19"></a><a href="#Footnote_19" class="fnanchor">[19]</a>. "Since, of our intellectual habits -by which we aim at truth, some are always true, but -some admit of being false, as Opinion and Reasoning, but -Science and Intuition are always true; and since there -is nothing which is more certain than Science except -Intuition; and since Principles are better known to -us than the Deductions from them; and since all -Science is connected by reasoning, we cannot have -Science respecting Principles. Considering this then, -and that the beginning of Demonstration cannot be -Demonstration, nor the beginning of Science, Science; -and since, as we have said, there is no other kind of -truth, Intuition must be the beginning of Science."</p> -<p><span class="pagenum" id="Page_22">22</span></p> -<p>What is here said, is, no doubt, in accordance with -the doctrines which we have endeavoured to establish -respecting the nature of Science, if by this <i>Intuition</i> -we understand that contemplation of certain Fundamental -Ideas, which is the basis of all rigorous knowledge. -But notwithstanding this apparent approximation, -Aristotle was far from having an habitual -and practical possession of the principles which he -thus touches upon. He did not, in reality, construct -his philosophy by giving Unity to that which was -manifold, or by seeking in Intuition principles which -might be the basis of Demonstration; nor did he collect, -in each subject, fundamental propositions by an -induction of particulars. He rather endeavoured to -divide than to unite; he employed himself, not in -combining facts, but in analysing notions; and the -criterion to which he referred his analysis was, not -the facts of our experience, but our habits of language. -Thus his opinions rested, not upon sound -inductions, gathered in each case from the phenomena -by means of appropriate Ideas; but upon the loose -and vague generalizations which are implied in the -common use of speech.</p> - -<p>Yet Aristotle was so far consistent with his own -doctrine of the derivation of knowledge from experience, -that he made in almost every province of human -knowledge, a vast collection of such special facts as -the experience of his time supplied. These collections -are almost unrivalled, even to the present day, especially -in Natural History; in other departments, when -to the facts we must add the right Inductive Idea, in -order to obtain truth, we find little of value in the -Aristotelic works. But in those parts which refer to -Natural History, we find not only an immense and -varied collection of facts and observations, but a sagacity -and acuteness in classification which it is impossible -not to admire. This indeed appears to have been -the most eminent faculty in Aristotle's mind.</p> - -<p>The influence of Aristotle in succeeding ages will -come under our notice shortly.</p> - -<p><span class="pagenum" id="Page_23">23</span></p> - - - - - - -<hr class="chap" /> -</div><div class="chapter"> -<h2><a name="CHAPTER_V" id="CHAPTER_V"></a>CHAPTER V.<br /> - -<span class="smcap medium">Additional Remarks on Aristotle.</span></h2> - - -<p> -<span class="dropcap"><span class="dsmall">1.</span> O</span>NE of the most conspicuous points in Aristotle's -doctrines as bearing upon the philosophy -of Science is his account of that mode of attaining -truth which is called <i>Induction</i>; for we are accustomed -to consider Induction as the process by which our -Sciences have been formed; and we call them collectively -the <i>Inductive Sciences</i>. Aristotle often speaks of -Induction, as for instance, when he says that Socrates -introduced the frequent use of it. But the cardinal -passage on this subject is in his <i>Analytics</i>, in which he -compares Syllogism and Induction as two modes of -drawing conclusions<a name="FNanchor_20" id="FNanchor_20"></a><a href="#Footnote_20" class="fnanchor">[20]</a>. He there says that all belief -arises either from Syllogism or from Induction: and -adds that Induction is, when by means of one extreme -term we infer the other extreme to be true of the -middle term. The example which he gives is this: -knowing that particular animals are long-lived, as -elephant, horse, mule; and finding that these animals -agree in having no gall-bladder; we infer, by <i>Induction</i>, -that <i>all</i> animals which have no gall-bladder -are long-lived. This may be done, he says, if the -middle and the second extreme are convertible: as -the following formal statement may show.</p> - -<p> -Elephant, horse, mule, &c. are long-lived.<br /> -Elephant, horse, mule, &c. are all gall-less.<br /> -</p> - -<p>If we might convert this proposition, and say</p> - -<p>All gall-less animals are as elephant, horse, mule, -&c.:</p> - -<p><span class="pagenum" id="Page_24">24</span></p> - -<p>we might infer <i>syllogistically</i> that</p> - -<p>All gall-less animals are long-lived.</p> - -<p>And though we cannot infer this syllogistically, we -infer it by Induction, when we have a sufficient -amount of instances<a name="FNanchor_21" id="FNanchor_21"></a><a href="#Footnote_21" class="fnanchor">[21]</a>.</p> - -<p>I have already elsewhere given this account of Induction, -as a process employed in the formation of our -knowledge<a name="FNanchor_22" id="FNanchor_22"></a><a href="#Footnote_22" class="fnanchor">[22]</a>. What I have now to remark concerning -Aristotle is, that it does not appear to have occurred -to him, that in establishing such a proposition as that -which he gives as his instance, the main difficulty is -the <i>discovery</i> of a <i>middle term</i> which will allow us to -frame such a proposition as we need. The zoologist -who wanted to know what kind of animals are long-lived, -might guess long before he guessed that the -absence of the gall-bladder supplied the requisite -middle term; (if the proposition were true; which it -is not.) And in like manner in other cases, it is difficult -to find a middle term, which enables us to collect -a proposition by Induction. And herein consists the -imperfection of his view of the subject; which considers -the main point to be the proof of the proposition -when the conceptions are <i>given</i>, whereas the main -point really is, the <i>discovery</i> of conceptions which will -make a true proposition possible.</p> - -<p><a id="V2"></a>2. Since the main characteristic of the steps -which have occurred in the formation of the physical -sciences, is not merely that they are propositions collected -by Induction, but by the introduction of a <i>new</i> -conception; it has been suggested that it is not a -characteristic designation of these Sciences to call them -<i>Inductive Sciences</i>. Almost every discovery involves -in it the introduction of a new conception, as the element -of a new proposition; and the novelty of the -conception is more characteristic of the stages of discovery -than the inductive application of it. Hence as<span class="pagenum" id="Page_25">25</span> -bearing upon the Philosophy of Discovery, the statements -of Aristotle concerning Induction, though acute -and valuable, are not so valuable as they might seem. -Even Francis Bacon, it has been asserted, erred in the -same way (and of course with less excuse) in asserting -Induction, of a certain kind, to be the great instrument -for the promotion of knowledge, and in overlooking -the necessity of the <i>Invention</i> which gives Induction -its value.</p> - -<p><a id="V3"></a>3. The invention or discovery of a conception by -which many facts of observation are conjoined so -as to make them the materials of a proposition, is -called in Plato, as we have seen, <i>finding the One in the -Many</i>.</p> - -<p>In the passage quoted from the <i>Later Analytics</i>, -Aristotle uses the same expression, and speaks very -justly respecting the formation of knowledge. Indeed -the <i>Titles</i> of the chapters of this and many parts of -Aristotle's works would lead us to expect just such a -Philosophy of Discovery as is the object of our study -at present. Thus we have, <i>Anal. Post.</i> B. <span class="smcap">II.</span> chap. 13: -"How we are to hunt (θηρεύειν) the predications of a -Definition." Chap. 14: "Precepts for the invention -of Problems and of a Middle Term:" and the like. -But when we come to read these chapters, they contain -little that is of value, and resolve themselves -mostly into permutations of Aristotle's logical phraseology.</p> - -<p><a id="V4"></a>4. The part of the Aristotelian philosophy which -has most permanently retained its place in modern -Sciences is a part of which a use has been made quite -different from that which was originally contemplated. -The "Five words" which are explained in the Introduction -to Aristotle's <i>Categories</i>: namely, the words -<i>Genus</i>, <i>Species</i>, <i>Difference</i>, <i>Property</i>, <i>Accident</i>, were introduced -mainly that they might be used in the propositions -of which Syllogisms consist, and might thus be -the elements of reasoning. But it has so happened -that these words are rarely used in Sciences of -Reasoning, but are abundantly and commonly used in<span class="pagenum" id="Page_26">26</span> -the Sciences of Classification, as I have explained in -speaking of the Classificatory Sciences<a name="FNanchor_23" id="FNanchor_23"></a><a href="#Footnote_23" class="fnanchor">[23]</a>.</p> - -<p><a id="V5"></a>5. Of Aristotle's actual contributions to the Physical -Sciences I have spoken in the History of those -Sciences<a name="FNanchor_24" id="FNanchor_24"></a><a href="#Footnote_24" class="fnanchor">[24]</a>. I have<a name="FNanchor_25" id="FNanchor_25"></a><a href="#Footnote_25" class="fnanchor">[25]</a> stated that he conceived the globular -form of the earth so clearly and gave so forcibly -the arguments for that doctrine, that we may look -upon him as the most effective teacher of it. Also in -the Appendix to that History, published in the third -edition, I have given Aristotle's account of the Rainbow, -as a further example of his industrious accumulation -of facts, and of his liability to error in his facts.</p> - -<p><a id="V6"></a>6. We do not find Aristotle so much impressed -as we might have expected by that great monument -of Grecian ingenuity, the theory of epicycles and excentrics -which his predecessor Plato urged so strongly -upon the attention of his contemporaries. Aristotle -proves, as I have said, the globular form of the -earth by good and sufficient arguments. He also -proves by arguments which seem to him quite conclusive<a name="FNanchor_26" id="FNanchor_26"></a><a href="#Footnote_26" class="fnanchor">[26]</a>, -that the earth is in the center of the universe, -and immoveable. As to the motions of the rest of -the planets, he says little. The questions of their -order, and their distances, and the like, belong, he says, -to Astrology<a name="FNanchor_27" id="FNanchor_27"></a><a href="#Footnote_27" class="fnanchor">[27]</a>. He remarks only that the revolution -of the heaven itself, the outermost revolution, is simple -and the quickest of all: that the revolutions of the -others are slower, each moving in a direction opposite -to the heaven in its own circle: and that it is reasonable -that those which are nearest to the first revolution -should take the longest time in describing their -own circle, and those that are furthest off, the least -time, and the intermediate ones in the order of their -distances, "as also the mathematicians show."</p> - -<p>In the <i>Metaphysics</i><a name="FNanchor_28" id="FNanchor_28"></a><a href="#Footnote_28" class="fnanchor">[28]</a> he enumerates the circular -movements which had been introduced by the astro<span class="pagenum" id="Page_27">27</span>nomers -Eudoxus and Calippus for the explanation of -the phenomena presented by the sun, moon and planets. -These, he says, amount to fifty-five; and this, he -says, must be the number of essences and principles -which exist in the universe.</p> - -<p><a id="V7"></a>7. In the Sciences of Classification, and especially -in the classification of animals, higher claims have -been made for Aristotle, which I have discussed in -the History<a name="FNanchor_29" id="FNanchor_29"></a><a href="#Footnote_29" class="fnanchor">[29]</a>. I have there attempted to show that -Aristotle's classification, inasmuch as it enumerates all -the parts of animals, may be said to contain the <i>materials</i> -of every subsequent classification: but that it cannot -be said to anticipate any modern system, because -the different grades of classification are not made <i>subordinate</i> -to one another as a <i>system</i> of classification -requires. I have the satisfaction of finding Mr. Owen -agreeing with me in these views<a name="FNanchor_30" id="FNanchor_30"></a><a href="#Footnote_30" class="fnanchor">[30]</a>.</p> - -<p><a id="V8"></a>8. Francis Bacon's criticism on Aristotle which I -have quoted in the Appendix to the History<a name="FNanchor_31" id="FNanchor_31"></a><a href="#Footnote_31" class="fnanchor">[31]</a>, is -severe, and I think evidently the result of prejudice. -He disparages Aristotle in comparison with the other -philosophers of Greece. 'Their systems,' he says, 'had -some savour of experience, and nature, and bodily -things; while the Physics of Aristotle, in general, -sound only of Logical Terms.</p> - -<p>'Nor let anyone be moved by this: that in his -books <i>Of Animals</i>, and in his <i>Problems</i>, and in others -of his tracts, there is often a quoting of experiments. -For he had made up his mind beforehand; and did not -consult experience in order to make right propositions -and axioms, but when he had settled his system to his -will, he twisted experience round and made her bend -to his system.'</p> - -<p>I do not think that this can be said with any truth. -I know no instances in which Aristotle has twisted experience -round, and made her bend to his system. In<span class="pagenum" id="Page_28">28</span> -his <i>Problems</i>, he is so far from giving dogmatical solutions -of the questions proposed, that in most cases, he -propounds two or three solutions as mere suggestions -and conjectures. And both in his History of Animals, -as I have said, and in others of his works, the want of -system gives them an incoherent and tumultuary character, -which even a false system would have advantageously -removed; for, as I have said elsewhere, it is -easier to translate a false system into a true one, than -to introduce system into a mass of confusion.</p> - -<p><a id="V9"></a>9. It is curious that a fundamental error into -which Aristotle fell in his view of the conditions -which determine the formation of Science is very -nearly the same as one of Francis Bacon's leading -mistakes. Aristotle says, that Science consists in -knowing the <i>causes</i> of things, as Bacon aims at acquiring -a knowledge of the <i>forms</i> or <i>essences</i> of things -and their qualities. But the history of all the sciences -teaches us that sciences do not begin with such knowledge, -and that in few cases only do they ever attain to -it. Sciences begin by a knowledge of the <i>laws</i> of <i>phenomena</i>, -and proceed by the discovery of the scientific -ideas by which the phenomena are colligated, as I -have shown in other works<a name="FNanchor_32" id="FNanchor_32"></a><a href="#Footnote_32" class="fnanchor">[32]</a>. The discovery of causes -is not beyond the human powers, as some have -taught. Those who thus speak disregard the lessons -taught by the history of Physical Astronomy, of -Geology, of Physical Optics, Thermotics and other -sciences. But the discovery of causes, and of the -essential forms of qualities, is a triumph reserved for -the later stages of each Science, when the knowledge -of the laws of phenomena has already made great -progress. It was not to be expected that Aristotle -would discern this truth, when, as yet, there was no -Science extant in which it had been exemplified. Yet -in Astronomy, the theory of epicycles and excentrics -had immense value, and even has still, as representing -the laws of phenomena; while the attempt to find in<span class="pagenum" id="Page_29">29</span> -it, as Aristotle wished to do, the ultimate causes of -the motions of the universe, could only mislead. The -Aristotelian maxim, which sounds so plausible, and -has been so generally accepted, that "to know truly is -to know the causes of things," is a bad guide in -scientific research. Instead of it we might substitute -this: that "though we may aspire to know at last -<i>why</i> things are, we must be content for a long time -with knowing <i>how</i> they are."</p> - -<p><a id="V10"></a>10. Hence if we are asked whether Plato or -Aristotle had the truer views of the nature and property -of Science, we must give the preference to Plato; -for though his notion of a real Intelligible World, of -which the Visible world was a fleeting and changeable -shadow, was extravagant, yet it led him to seek to -determine the forms of the Intelligible Things, which -are really the laws of visible phenomena; while Aristotle -was led to pass lightly over such laws, because -they did not at once reveal the causes which produced -the phenomena.</p> - -<p><a id="V11"></a>11. Aristotle, throughout his works, takes numerous -occasions to argue against Plato's doctrine of Ideas. -Yet these Ideas, so far as they were the Intelligible -Forms of Visible Things, were really fit objects of -philosophical research; and the search after them had -a powerful influence in promoting the progress of -Science. And we may see in the effect of this search -the answer to many of Aristotle's strongest arguments. -For instance, Aristotle says that Plato, by -way of explaining things, adds to them as many -Ideas, and that this is just as if a man having to -reckon a large number, were to begin by adding to it -another large number. It is plain that to this we -may reply, that the adopting the Ideas of Cycles, along -with the motions of the Planets, does really explain -the motions; and that the Cycles are not simply added -to the phenomena, but include and supersede the phenomena: -a finite number of Cycles include and represent -an infinite number of separate phenomena.</p> - -<p>To Aristotle's argument that Ideas cannot be the -Causes or Principles of Things, we should reply, that<span class="pagenum" id="Page_30">30</span> -though they cannot be this, they may nevertheless be, -and must be, the Conditions and Principles of our -Knowledge, which is what we want them to be.</p> - -<p>I have given an account of the main features of -Aristotle's philosophy, so far as it concerns the Physical -Sciences, in the History of the Inductive Sciences, -Book <span class="smcap">I</span>.</p> - -<p><span class="pagenum" id="Page_31">31</span></p> - - - - - - - -<hr class="chap" /> -</div><div class="chapter"> -<h2><a name="CHAPTER_VI" id="CHAPTER_VI"></a>CHAPTER VI.<br /> - -<span class="smcap medium">The Later Greeks.</span></h2> - - -<p class="drop-cap"><span class="smcap">Thus</span> while Plato was disposed to seek the essence -of our knowledge in Ideas alone, Aristotle, slighting -this source of truth, looked to Experience as the -beginning of Science; and he attempted to obtain, by -division and deduction, all that Experience did not -immediately supply. And thus, with these two great -names, began that struggle of opposite opinions which -has ever since that time agitated the speculative world, -as men have urged the claims of Ideas or of Experience -to our respect, and as alternately each of these -elements of knowledge has been elevated above its due -place, while the other has been unduly depressed. We -shall see the successive turns of this balanced struggle -in the remaining portions of this review.</p> - -<p>But we may observe that practically the influence -of Plato predominated rather than that of Aristotle, -in the remaining part of the history of ancient philosophy. -It was, indeed, an habitual subject of dispute -among men of letters, whether the sources of true -knowledge are to be found in the Senses or in the -Mind; the Epicureans taking one side of this alternative, -and the Academics another, while the Stoics in -a certain manner included both elements in their view. -But none of these sects showed their persuasion that -the materials of knowledge were to be found in the -domain of Sense, by seeking them there. No one -appears to have thought of following the example of -Aristotle, and gathering together a store of observed -facts. We may except, perhaps, assertions belonging -to some provinces of Natural History, which were -collected by various writers: but in these, the mixed<span class="pagenum" id="Page_32">32</span> -character of the statements, the want of discrimination -in the estimate of evidence, the credulity and love of -the marvellous which the authors for the most part -displayed, showed that instead of improving upon the -example of Aristotle, they were wandering further -and further from the path of real knowledge. And -while they thus collected, with so little judgment, -such statements as offered themselves, it hardly appears -to have occurred to any one to enlarge the stores -of observation by the aid of experiment; and to learn -what the laws of nature were, by trying what were -their results in particular cases. They used no instruments -for obtaining an insight into the constitution of -the universe, except logical distinctions and discussions; -and proceeded as if the phenomena familiar to their -predecessors must contain all that was needed as a -basis for natural philosophy. By thus contenting -themselves with the facts which the earlier philosophers -had contemplated, they were led also to confine -themselves to the ideas which those philosophers had -put forth. For all the most remarkable alternatives -of hypothesis, so far as they could be constructed with -a slight and common knowledge of phenomena, had -been promulgated by the acute and profound thinkers -who gave the first impulse to philosophy: and it was -not given to man to add much to the original inventions -of <i>their</i> minds till he had undergone anew a long -discipline of observation, and of thought employed -upon observation. Thus the later authors of the Greek -Schools became little better than commentators on -the earlier; and the commonplaces with which the -different schools carried on their debates,—the constantly -recurring argument, with its known attendant -answer,—the distinctions drawn finer and finer and -leading to nothing,—render the speculations of those -times a <i>scholastic</i> philosophy, in the same sense in -which we employ the term when we speak of the -labours of the middle ages. It will be understood -that I now refer to that which is here my subject, the -opinions concerning our knowledge of nature, and the -methods in use for the purpose of obtaining such<span class="pagenum" id="Page_33">33</span> -knowledge. Whether the moral speculations of the -ancient world were of the same stationary kind, going -their round in a limited circle, like their metaphysics -and physics, must be considered on some other occasion.<a name="FNanchor_33" id="FNanchor_33"></a><a href="#Footnote_33" class="fnanchor">[33]</a></p> - -<p>Mr. Grote, in his very interesting discussion of -Socrates's teaching, notices also<a name="FNanchor_34" id="FNanchor_34"></a><a href="#Footnote_34" class="fnanchor">[34]</a> the teaching of Hippocrates, -which he conceives to have in one respect -the same tendency as the philosophy of Socrates; -namely, to turn away from the vague aggregate of -doctrines and guesses which constituted the Physical -Philosophy of that time, and to pursue instead a special -and more practical course of inquiry: Hippocrates -selecting Medicine and Socrates selecting Ethics. By -this limitation of their subject, they avoided some of -the errors of their predecessors. For, as Mr. Grote -has also remarked, "the earlier speculators, Anaxagoras, -Empedocles, Democritus, the Pythagoreans, all -had still present to their minds the vast and undivided -problems which have been transmitted down from the -old poets; bending their minds to the invention of -some system which would explain them all at once, or -assist the imagination in conceiving both how the -Kosmos first began and how it continued to move on." -There could be no better remedy for this ambitious -error of the human mind than to have a definite subject -of study, such as the diseases and the health of -the human body. Accordingly, we see that the study -of medicine did draw its cultivators away from this -ancient but unprofitable field. Hippocrates<a name="FNanchor_35" id="FNanchor_35"></a><a href="#Footnote_35" class="fnanchor">[35]</a> condemns -those who, as Empedocles, set themselves to make out -what man was from the beginning, how he began first -to exist, and in what manner he was constructed. -This is, he says, no part of medicine. In like manner -he blames and refutes those who make some simple -element, Hot, or Cold, or Moist, or Dry, the cause of<span class="pagenum" id="Page_34">34</span> -diseases, and give medical precepts professing to be -founded on this hypothesis.</p> - -<p>These passages are marked by the prudence which -practical study suggests to a calm and clear-sighted -man. They can hardly be said to have opened the -way to a Science of Medicine; for in the sense in -which we here use the word <i>Science</i>, namely, a collection -of general truths inferred from facts by successive -discoverers, we have even yet no Science of Medicine. -The question with regard to the number and nature -of the Elements of which bodies are composed began -to be agitated, as we have seen, at a very early period -of Greek philosophy, and continued long to be regarded -as a chief point of physiological doctrine. In Galen's -work we have a treatise entitled, <i>On the Elements -according to Hippocrates</i>; and the writer explains<a name="FNanchor_36" id="FNanchor_36"></a><a href="#Footnote_36" class="fnanchor">[36]</a> -that though Hippocrates has not written any work -with the title <i>On the Elements</i>, yet that he has in his -<i>Treatise on the Nature of Man</i> shown his opinion on -that subject. That the doctrine of the Four Elements, -Hot, Cold, Moist, Dry, subsisted long in the schools, -we have evidence in Galen. He tells us<a name="FNanchor_37" id="FNanchor_37"></a><a href="#Footnote_37" class="fnanchor">[37]</a> that when -he was a student of nineteen years old a teacher urged -this lore upon him, and regarded him as very contentious -and perverse, because he offered objections to -it. His account of the Dialogue between him and the -teacher is curious. But in Hippocrates the doctrine -of these four elements is replaced, in a great measure, -by the doctrine of the Four Humours of which the -human body is constituted; namely, Blood, Phlegm, -Yellow Bile and Black Bile. Galen dwells with emphasis -upon Hippocrates's proof that there must be -more than one such element<a name="FNanchor_38" id="FNanchor_38"></a><a href="#Footnote_38" class="fnanchor">[38]</a>.</p> - -<p>"What," he asks, "is the method of finding the -Elements of bodies? There can, in my opinion, be -no other than that which was introduced by Hippocrates; -namely, we must inquire whether there be only -one element, everywhere the same in kind, or whether<span class="pagenum" id="Page_35">35</span> -there are more than one, various and unlike each -other. And if the Element be not one only, but -several, various and dissimilar, we must inquire in -the second place, how many elements there are, and -what, and of what kind they are, and how related in -their association.</p> - -<p>"Now that the First Element is not one only of -which both our bodies and those of all other creatures -were produced, Hippocrates shows from these considerations. -And it is better first to put down his own -expressions and then to expound them. 'I assert that -if man consisted of one element only he could not fall -sick; for there would be nothing which could derange -his health, if he were all of one Element.'"</p> - -<p>The doctrine of One Element did not prevail much -after the time of Hippocrates: the doctrine of Four -Elements continued, as I have said, long to hold possession -of the Schools, but does not appear as an -important part of the doctrine of Hippocrates. The -doctrine of the Four Humours (Blood, Phlegm, Yellow -Bile and Black Bile) is more peculiarly his, and -long retained its place as a principle of physiological -Science.</p> - -<p>But we are here not so much concerned with his -discoveries in medicine as with his views respecting -the method of acquiring sound knowledge, and in this -respect, as has been said, he recommends by his practice -a prudent limitation of the field of inquiry, a -rejection of wide, ambitious, general assertions, and a -practical study of his proper field.</p> - -<p>In ascribing these merits to Hippocrates's medical -speculations as to the ethical speculations of his contemporary -Socrates, we assign considerable philosophical -value to Hippocrates, no less than to Socrates. -These merits were at that time the great virtues of -physical as well as of ethical philosophy. But, as -Mr. Grote well observes, the community of character -which then subsisted between the physical and ethical -speculations prevailing at that time, ceased to obtain -in later times. Indeed, it ceased to exist just -at that time, in consequence of the establishment of<span class="pagenum" id="Page_36">36</span> -scientific astronomy by the exertions of Plato and his -contemporaries. From that time the Common Sense -(as we call it) of a man like Socrates, though it might -be a good guide in ethics, was not a good guide in physics. -I have shown elsewhere<a name="FNanchor_39" id="FNanchor_39"></a><a href="#Footnote_39" class="fnanchor">[39]</a> how the Common Sense -of Socrates was worthless in matters of astronomy. -From that time one of the great intellectual lessons -was, that in order to understand the external world, we -must indeed observe carefully, but we must also guess -boldly. Discovery here required an inventive mind -like Plato's to deal with and arrange new and varied -facts. But in ethics all the facts were old and familiar, -and the generalizations of language by which -they were grouped as Virtues and Vices, and the like, -were common and well-known words. Here was no -room for invention; and thus in the ethical speculations -of Socrates or of any other moral teacher, we -are not to look for any contributions to the Philosophy -of Discovery.</p> - -<p>Nor do I find anything on this subject among later -Greek writers, beyond the commendation of such intellectual -virtues as Hippocrates and Galen, and other -medical writers, schooled by the practice of their art, -enjoined and praised. But before we quit the ancients -I will point out some peculiarities which may be noticed -in the Roman disciples of the Greek philosophy.</p> - -<p><span class="pagenum" id="Page_37">37</span></p> - - - - - - - -<hr class="chap" /> -</div><div class="chapter"> -<h2><a name="CHAPTER_VII" id="CHAPTER_VII"></a>CHAPTER VII.<br /> - -<span class="smcap medium">The Romans.</span></h2> - - -<p class="drop-cap"><span class="smcap">The</span> Romans had no philosophy but that which -they borrowed from the Greeks; and what they -thus received, they hardly made entirely their own. -The vast and profound question of which we have -been speaking, the relation between Existence and -our Knowledge of what exists, they never appear to -have fathomed, even so far as to discern how wide -and deep it is. In the development of the ideas by -which nature is to be understood, they went no further -than their Greek masters had gone, nor indeed -was more to be looked for. And in the practical -habit of accumulating observed facts as materials for -knowledge, they were much less discriminating and -more credulous than their Greek predecessors. The -descent from Aristotle to Pliny, in the judiciousness -of the authors and the value of their collections of -facts, is immense.</p> - -<p>Since the Romans were thus servile followers of -their Greek teachers, and little acquainted with any -example of new truths collected from the world around -them, it was not to be expected that they could have -any just conception of that long and magnificent ascent -from one set of truths to others of higher order and -wider compass, which the history of science began to -exhibit when the human mind recovered its progressive -habits. Yet some dim presentiment of the splendid -career thus destined for the intellect of man appears -from time to time to have arisen in their minds. Perhaps -the circumstance which most powerfully contributed -to suggest this vision, was the vast intellectual -progress which they were themselves conscious of -having made, through the introduction of the Greek<span class="pagenum" id="Page_38">38</span> -philosophy; and to this may be added, perhaps, some -other features of national character. Their temper -was too stubborn to acquiesce in the absolute authority -of the Greek philosophy, although their minds were -not inventive enough to establish a rival by its side. -And the wonderful progress of their political power -had given them a hope in the progress of man which -the Greeks never possessed. The Roman, as he believed -the fortune of his State to be destined for -eternity, believed also in the immortal destiny and -endless advance of that Intellectual Republic of which -he had been admitted a denizen.</p> - -<p>It is easy to find examples of such feelings as I have -endeavoured to describe. The enthusiasm with which -Lucretius and Virgil speak of physical knowledge, -manifestly arises in a great measure from the delight -which they had felt in becoming acquainted with the -Greek theories.</p> - -<div class="poetry-container"><div class="poetry"><div class="stanza"> - <div class="verse">Me vero primum dulces ante omnia Musæ</div> - <div class="verse">Quarum sacra fero ingenti perculsus amore</div> - <div class="verse">Accipiant, cœlique vias et sidera monstrent,</div> - <div class="verse">Defectus Solis varios, Lunæque labores!...</div> - <div class="verse">Felix qui potuit rerum cognoscere causas!</div> -</div></div></div> - -<div class="poetry-container"><div class="poetry"><div class="stanza"> - <div class="verse">Ye sacred Muses, with whose beauty fir'd,</div> - <div class="verse">My soul is ravisht and my brain inspir'd:</div> - <div class="verse">Whose Priest I am, whose holy fillets wear,</div> - <div class="verse">Would you your Poet's first petition hear,</div> - <div class="verse">Give me the ways of wand'ring stars to know,</div> - <div class="verse">The depth of Heaven above and Earth below;</div> - <div class="verse">Teach me the various labours of the Moon,</div> - <div class="verse">And whence proceed th' eclipses of the Sun;</div> - <div class="verse">Why flowing Tides prevail upon the main,</div> - <div class="verse">And in what dark abyss they shrink again;</div> - <div class="verse">What shakes the solid Earth; what cause delays</div> - <div class="verse">The Summer Nights; and shortens Winter Days....</div> - <div class="verse indent2">Happy the man who, studying Nature's Laws,</div> - <div class="verse">Through known effects can trace the secret cause!</div> -</div></div></div> - -<p>Ovid<a name="FNanchor_40" id="FNanchor_40"></a><a href="#Footnote_40" class="fnanchor">[40]</a> expresses a similar feeling.</p> - -<div class="poetry-container"><div class="poetry"><div class="stanza"> - <div class="verse">Felices animos quibus hæc cognoscere primis</div> - <div class="verse indent2">Inque domos superas scandere cura fuit!...</div> - <div class="verse">Admovere oculis distantia sidera nostris</div><span class="pagenum" id="Page_39">39</span> - <div class="verse indent2">Ætheraque ingenio supposuere suo.</div> - <div class="verse">Sic petitur cœlum: non ut ferat Ossam Olympus</div> - <div class="verse indent2">Summaque Peliacus sidera tanget apex.</div> -</div></div></div> - -<div class="poetry-container"><div class="poetry"><div class="stanza"> - <div class="verse">Thrice happy souls! to whom 'twas given to rise</div> - <div class="verse">To truths like these, and scale the spangled skies!</div> - <div class="verse">Far distant stars to clearest view they brought,</div> - <div class="verse">And girdled ether with their chain of thought.</div> - <div class="verse">So heaven is reached:—not as of old they tried</div> - <div class="verse">By mountains piled on mountains in their pride.</div> -</div></div></div> - - -<p>And from the whole tenour of these and similar -passages, it is evident that the intellectual pleasure -which arises from our first introduction to a beautiful -physical theory had a main share in producing this -enthusiasm at the contemplation of the victories of -science; although undoubtedly the moral philosophy, -which was never separated from the natural philosophy, -and the triumph over superstitious fears, which a knowledge -of nature was supposed to furnish, added warmth -to the feeling of exultation.</p> - -<p>We may trace a similar impression in the ardent -expressions which Pliny<a name="FNanchor_41" id="FNanchor_41"></a><a href="#Footnote_41" class="fnanchor">[41]</a> makes use of in speaking of -the early astronomers, and which we have quoted in -the <i>History</i>. "Great men! elevated above the common -standard of human nature, by discovering the -laws which celestial occurrences obey, and by freeing -the wretched mind of man from the fears which -eclipses inspired."</p> - -<p>This exulting contemplation of what science had -done, naturally led the mind to an anticipation of -further achievements still to be performed. Expressions -of this feeling occur in Seneca, and are of the -most remarkable kind, as the following example will -show<a name="FNanchor_42" id="FNanchor_42"></a><a href="#Footnote_42" class="fnanchor">[42]</a>:</p> - -<p>"Why do we wonder that comets, so rare a phenomenon, -have not yet had their laws assigned?—that we -should know so little of their beginning and their end, -when their recurrence is at wide intervals? It is not -yet fifteen hundred years since Greece,</p> - -<p class="center"> -Stellis numeros et nomina fecit,<br /> -</p> - -<p><span class="pagenum" id="Page_40">40</span></p> - -<p>'reckoned the stars, and gave them names.' There -are still many nations which are acquainted with the -heavens by sight only; which do not yet know why the -moon disappears, why she is eclipsed. It is but lately -that among us philosophy has reduced these matters -to a certainty. The day shall come when the course -of time and the labour of a maturer age shall bring -to light what is yet concealed. One generation, even -if it devoted itself to the skies, is not enough for researches -so extensive. How then can it be so, when -we divide this scanty allowance of years into no equal -shares between our studies and our vices? These -things then must be explained by a long succession of -inquiries. We have but just begun to know how -arise the morning and evening appearances, the stations, -the progressions, and the retrogradations of the -fixed stars which put themselves in our way;—which -appearing perpetually in another and another place -compel us to be curious. Some one will hereafter -demonstrate in what region the comets wander; why -they move so far asunder from the rest; of what size -and nature they are. Let us be content with what we -have discovered: let posterity contribute its share to -truth." Again he adds<a name="FNanchor_43" id="FNanchor_43"></a><a href="#Footnote_43" class="fnanchor">[43]</a> in the same strain: "Let -us not wonder that what lies so deep is brought out -so slowly. How many animals have become known -for the first time in this age! And the members of -future generations shall know many of which we are -ignorant. Many things are reserved for ages to come, -when our memory shall have passed away. The world -would be a small thing indeed, if it did not contain -matter of inquiry <i>for</i> all the world. Eleusis reserves -something for the second visit of the worshipper. <i>So -too Nature does not at once disclose all</i> <span class="smcap">HER</span> <i>mysteries</i>. -We think ourselves initiated; we are but in the vestibule. -The arcana are not thrown open without -distinction and without reserve. This age will see -some things; that which comes after us, others."</p> -<p><span class="pagenum" id="Page_41">41</span></p> -<p>While we admire the happy coincidence of these -conjectures with the soundest views which the history -of science teaches us, we must not forget that they -are merely conjectures, suggested by very vague impressions, -and associated with very scanty conceptions -of the laws of nature. Seneca's <i>Natural Questions</i>, -from which the above extract is taken, contains a series -of dissertations on various subjects of Natural Philosophy; -as Meteors, Rainbows, Lightnings, Springs, -Rivers, Snow, Hail, Rain, Wind, Earthquakes and -Comets. In the whole of these dissertations, the -statements are loose, and the explanations of little or -no value. Perhaps it may be worth our while to -notice a case in which he refers to an observation of -his own, although his conclusion from it be erroneous. -He is arguing<a name="FNanchor_44" id="FNanchor_44"></a><a href="#Footnote_44" class="fnanchor">[44]</a> against the opinion that Springs arise -from the water which falls in rain. "In the first -place," he says, "I, a very diligent digger in my vineyard, -affirm that no rain is so heavy as to moisten the -earth to the depth of more than ten feet. All the -moisture is consumed in this outer crust, and descends -not to the lower part." We have here something of -the nature of an experiment; and indeed, as we may -readily conceive, the instinct which impels man to -seek truth by experiment can never be altogether extinguished. -Seneca's experiment was deprived of its -value by the indistinctness of his ideas, which led him -to rest in the crude conception of the water being -"consumed" in the superficial crust of the earth.</p> - -<p>It is unnecessary to pursue further the reasonings -of the Romans on such subjects, and we now proceed -to the ages which succeeded the fall of their empire.</p> - -<p><span class="pagenum" id="Page_42">42</span></p> - - - - - - - -<hr class="chap" /> -</div><div class="chapter"> -<h2><a name="CHAPTER_VIII" id="CHAPTER_VIII"></a>CHAPTER VIII.<br /> - -<span class="smcap medium">Arabian Philosophers.</span></h2> - - -<p class="drop-cap"><span class="smcap">I have</span> noticed certain additions to Physical Science -made by the Arabians; namely, in Astronomy<a name="FNanchor_45" id="FNanchor_45"></a><a href="#Footnote_45" class="fnanchor">[45]</a>. -The discovery of the motion of the Sun's Apogee by -Albategnius, and the discovery of the Moon's <i>Variation</i> -by Aboul-Wefa; and in Optics<a name="FNanchor_46" id="FNanchor_46"></a><a href="#Footnote_46" class="fnanchor">[46]</a> the assertion of Alhazen -that the angle of refraction is not proportional to the -angle of incidence, as Ptolemy had supposed: and certain -steps in the philosophy of vision. We must also -suppose, as the Arabic word <i>alkali</i> reminds us, that -the Arabians contributed to lay the foundations of chemistry. -The question which we have here to ask is, -whether the Arabians made any steps beyond their -predecessors in the philosophy of discovery. And to -this question, I conceive the answer must be this: -that among them as among the Greeks, those who -practically observed nature, and especially those who -made discoveries in Science, must have had a practical -acquaintance with some of the maxims which are -exemplified in the formation of Science. To discover -that the Apogee of the Sun was 17 degrees distant -from the point where Ptolemy had placed it, Albategnius -made careful observations, and referred them -to the theory of the eccentric, so as to verify or correct -that theory. And when, in the eleventh century, -Arzachel found the Apogee to be less advanced than -Albategnius had found it, he proceeded again to correct -the theory by introducing a new movement of the -equinoctial points, which was called the <i>Trepidation</i>.<span class="pagenum" id="Page_43">43</span> -It appeared afterwards, however, that, in doing this, -he had had too much confidence in the observations of -his predecessors, and that no such movement as the -Trepidation really existed. In like manner to correct -Ptolemy's law of refraction, Alhazen had recourse to -experiment: but he did not put his experiments in -the form of a Table, as Ptolemy had done. If he -had done this, he might possibly have discovered the -law of sines, which Snell afterwards discovered.</p> - -<p>But though the Arabian philosophers thus, in some -cases, observed facts, and referred those facts to -general mathematical laws, it does not appear that -they were led to put in any new or striking general -form such maxims as this: That the progress of Science -consists in the exact observation of facts and in -colligating them by ideas. Those of them who were -dissatisfied with the existing philosophy as barren and -useless (for instance Algazel<a name="FNanchor_47" id="FNanchor_47"></a><a href="#Footnote_47" class="fnanchor">[47]</a>), were led to point at -the faults and contradictions of that philosophy, but -did not attempt, so far as I know, to substitute for it -anything better. If they rejected Aristotle's <i>Organon</i>, -they did not attempt to construct a new Organon for -themselves.</p> - -<p>Indeed they do not appear even to have had sufficient -confidence in the real truth of the astronomical -theories which they had adopted from the Greeks, -always to correct and extend those where their observations -showed that they required correction and extension. -Sometimes they did this, but not generally -enough. When Arzachel found by observation the -Apogee of the Sun to be situated too far back, he ventured -to correct Ptolemy's statement of its motion. -But when Aboul-Wefa had really discovered the <i>Variation</i> -of the Moon's motion, he did not express it -by means of an epicycle. If he had done so, he would -have made it unnecessary for Tycho Brahe at a later -period to make the same discovery.</p> - -<p><span class="pagenum" id="Page_44">44</span></p> - -<p>The moral of this incident is the same moral which we -have perpetually to note as taught us at every step by -the history of Science:—namely, the necessity of constant, -careful and exact observation of Facts; and the -advantage of devising a Theory, (even if it have to be -afterwards rejected,) by which the Facts shall be -bound together into a coherent whole.</p> - -<p><span class="pagenum" id="Page_45">45</span></p> - - - - - - - -<hr class="chap" /> -</div><div class="chapter"> -<h2><a name="CHAPTER_IX" id="CHAPTER_IX"></a>CHAPTER IX.<br /> - -<span class="smcap medium">The Schoolmen of the Middle Ages.</span></h2> - - -<p class="drop-cap"><span class="smcap">In</span> the <i>History of the Sciences</i> I have devoted a Book -to the state of Science in the middle ages, and have -endeavoured to analyse the intellectual defects of that -period. Among the characteristic features of the human -mind during those times, I have noticed Indistinctness -of Ideas, a Commentatorial Spirit, Mysticism, -and Dogmatism. The account there given of this -portion of the history of man belongs, in reality, -rather to the History of Ideas than to the History of -Progressive Science. For, as we have there remarked, -theoretical Science was, during the period of which we -speak, almost entirely stationary; and the investigation -of the causes of such a state of things may be -considered as a part of that review in which we are -now engaged, of the vicissitudes of man's acquaintance -with the methods of discovery. But when we offered -to the world a history of science, to leave so large a -chasm unexplained, would have made the series of -events seem defective and broken; and the survey of -the Middle Ages was therefore inserted. I would beg -to refer to that portion of the former work the reader -who wishes for information in addition to what is here -given.</p> - -<p>The Indistinctness of Ideas and the Commentatorial -Disposition of those ages have already been here -brought under our notice. Viewed with reference to -the opposition between Experience and Ideas, on -which point, as we have said, the succession of opinions -in a great measure turns, it is clear that the commentatorial -method belongs to the ideal side of the question: -for the commentator seeks for such knowledge<span class="pagenum" id="Page_46">46</span> -as he values, by analysing and illustrating what his -author has said; and, content with this material of -speculation, does not desire to add to it new stores of -experience and observation. And with regard to the -two other features in the character which we gave to -those ages, we may observe that Dogmatism demands -for philosophical theories the submission of mind, due -to those revealed religious doctrines which are to guide -our conduct and direct our hopes: while Mysticism -elevates ideas into realities, and offers them to us as -the objects of our religious regard. Thus the Mysticism -of the middle ages and their Dogmatism alike -arose from not discriminating the offices of theoretical -and practical philosophy. Mysticism claimed for ideas -the dignity and reality of principles of moral action -and religious hope: Dogmatism imposed theoretical -opinions respecting speculative points with the imperative -tone of rules of conduct and faith.</p> - -<p>If, however, the opposite claims of theory and practice -interfered with the progress of science by the confusion -they thus occasioned, they did so far more -by drawing men away altogether from mere physical -speculations. The Christian religion, with its precepts, -its hopes, and its promises, became the leading -subject of men's thoughts; and the great active truths -thus revealed, and the duties thus enjoined, made all -inquiries of mere curiosity appear frivolous and unworthy -of man. The Fathers of the Church sometimes -philosophized ill; but far more commonly they -were too intent upon the great lessons which they had -to teach, respecting man's situation in the eyes of his -Heavenly Master, to philosophize at all respecting -things remote from the business of life and of no importance -in man's spiritual concerns.</p> - -<p>Yet man has his intellectual as well as his spiritual -wants. He has faculties which demand systems and -reasons, as well as precepts and promises. The Christian -doctor, who knew so much more than the heathen -philosopher respecting the Creator and Governor of the -universe, was not long content to know or to teach less, -respecting the universe itself. While it was still main<span class="pagenum" id="Page_47">47</span>tained -that Theology was the only really important -study, Theology was so extended and so fashioned as -to include all other knowledge: and after no long -time, the Fathers of the Church themselves became -the authors of systems of universal knowledge.</p> - -<p>But when this happened, the commentatorial spirit -was still in its full vigour. The learned Christians -could not, any more than the later Greeks or the -Romans, devise, by the mere force of their own invention, -new systems, full, comprehensive, and connected, -like those of the heroic age of philosophy. The same -mental tendencies which led men to look for speculative -coherence and completeness in the view of the -universe, led them also to admire and dwell upon the -splendid and acute speculations of the Greeks. They -were content to find, in those immortal works, the -answers to the questions which their curiosity prompted; -and to seek what further satisfaction they might -require, in analysing and unfolding the doctrines promulgated -by those great masters of knowledge. Thus -the Christian doctors became, as to general philosophy, -commentators upon the ancient Greek teachers.</p> - -<p>Among these, they selected Aristotle as their peculiar -object of admiration and study. The vast store, -both of opinions and facts, which his works contain, -his acute distinctions, his cogent reasons in some portions -of his speculations, his symmetrical systems in -almost all, naturally commended him to the minds of -subtle and curious men. We may add that Plato, -who taught men to contemplate Ideas separate from -Things, was not so well fitted for general acceptance -as Aristotle, who rejected this separation. For although -the due apprehension of this opposition of Ideas -and Sensations is a necessary step in the progress of -true philosophy, it requires a clearer view and a more -balanced mind than the common herd of students -possess; and Aristotle, who evaded the necessary perplexities -in which this antithesis involves us, appeared, -to the temper of those times, the easier and the -plainer guide of the two.</p> - -<p>The Doctors of the middle ages having thus adopted<span class="pagenum" id="Page_48">48</span> -Aristotle as their master in philosophy, we shall not be -surprised to find them declaring, after him, that experience -is the source of our knowledge of the visible -world. But though, like the Greeks, they thus talked -of experiment, like the Greeks, they showed little -disposition to discover the laws of nature by observation -of facts. This barren and formal recognition of -experience or sensation as one source of knowledge, -not being illustrated by a practical study of nature, -and by real theoretical truths obtained by such a -study, remained ever vague, wavering, and empty. -Such a mere acknowledgment cannot, in any times, -ancient or modern, be considered as indicating a just -apprehension of the true basis and nature of science.</p> - -<p>In imperfectly perceiving how, and how far, experience -is the source of our knowledge of the external -world, the teachers of the middle ages were in the -dark; but so, on this subject, have been almost all the -writers of all ages, with the exception of those who -in recent times have had their minds enlightened by -contemplating philosophically the modern progress of -science. The opinions of the doctors of the middle -ages on such subjects generally had those of Aristotle -for their basis; but the subject was often still further -analysed and systematized, with an acute and methodical -skill hardly inferior to that of Aristotle himself.</p> - -<p>The Stagirite, in the beginning of his <i>Physics</i>, had -made the following remarks. "In all bodies of doctrine -which involve principles, causes, or elements, -Science and Knowledge arise from the knowledge -of these; (for we then consider ourselves to <i>know</i> -respecting any subject, when we know its first cause, -its first principles, its ultimate elements.) It is evident, -therefore, that in seeking a knowledge of -nature, we must first know what are its principles. -But the course of our knowledge is, from the things -which are better known and more manifest to us, to -the things which are more certain and evident in -nature. For those things which are most evident in -truth, are not most evident to us. [And consequently -we must advance from things obscure in nature, but<span class="pagenum" id="Page_49">49</span> -manifest to us, towards the things which are really in -nature more clear and certain.] The things which -are first obvious and apparent to us are complex; and -from these we obtain, by analysis, principles and elements. -We must proceed from universals to particulars. -For the whole is better known to our senses -than the parts, and for the same reason, the universal -better known than the particular. And thus words -signify things in a large and indiscriminate way, -which is afterwards analysed by definition; as we see -that the children at first call all men <i>father</i>, and all -women <i>mother</i>, but afterwards learn to distinguish."</p> - -<p>There are various assertions contained in this extract -which came to be considered as standard maxims, -and which occur constantly in the writers of the middle -ages. Such are, for instance, the maxim, "Verè -scire est per causas scire;" the remark, that compounds -are known to us before their parts, and the -illustration from the expressions used by children. -Of the mode in which this subject was treated by the -schoolmen, we may judge by looking at passages of -Thomas Aquinas which treat of the subject of the -human understanding. In the <i>Summa Theologiæ</i>, the -eighty-fifth Question is <i>On the manner and order of -understanding</i>, which subject he considers in eight -Articles; and these must, even now, be looked upon -as exhibiting many of the most important and interesting -points of the subject. They are, <i>First</i>, Whether -our understanding understands by abstracting ideas -(<i>species</i>) from appearances; <i>Second</i>, Whether intelligible -species abstracted from appearances are related -to our understanding as that <i>which</i> we understand, or -that <i>by which</i> we understand; <i>Third</i>, Whether our -understanding does naturally understand universals -first; <i>Fourth</i>, Whether our understanding can understand -many things at once; <i>Fifth</i>, Whether our understanding -understands by compounding and dividing; -<i>Sixth</i>, Whether the understanding can err; <i>Seventh</i>, -Whether one person can understand the same thing -better than another; <i>Eighth</i>, Whether our understanding -understands the indivisible sooner than the<span class="pagenum" id="Page_50">50</span> -divisible. And in the discussion of the last point, for -example, reference is made to the passage of Aristotle -which we have already quoted. "It may seem," he -says, "that we understand the indivisible before the -divisible; for <i>the Philosopher</i> says that we understand -and know by knowing principles and elements; but -indivisibles are the principles and elements of divisible -things. But to this we may reply, that in our receiving -of science, principles and elements are not always -first; for sometimes from the sensible effects we go on -to the knowledge of intelligible principles and causes." -We see that both the objection and the answer are -drawn from Aristotle.</p> - -<p>We find the same close imitation of Aristotle in -Albertus Magnus, who, like Aquinas, flourished in the -thirteenth century. Albertus, indeed, wrote treatises -corresponding to almost all those of the Stagirite, and -was called the <i>Ape of Aristotle</i>. In the beginning of -his <i>Physics</i>, he says, "Knowledge does not always -begin from that which is first according to the nature -of things, but from that of which the knowledge is -easiest. For the human intellect, on account of its -relation to the senses (<i>propter reflexionem quam habet -ad sensum</i>), collects science from the senses; and thus -it is easier for our knowledge to begin from that which -we can apprehend by sense, imagination, and intellect, -than from that which we apprehend by intellect alone." -We see that he has somewhat systematized what he -has borrowed.</p> - -<p>This disposition to dwell upon and systematize the -leading doctrines of metaphysics assumed a more definite -and permanent shape in the opposition of the -Realists and Nominalists. The opposition involved in -this controversy is, in fact, that fundamental antithesis -of Sense and Ideas about which philosophy has always -been engaged; and of which we have marked the -manifestation in Plato and Aristotle. The question, -What is the object of our thoughts when we reason -concerning the external world? must occur to all -speculative minds: and the difficulties of the answer -are manifest. We must reply, either that our own<span class="pagenum" id="Page_51">51</span> -Ideas, or that Sensible Things, are the elements of -our knowledge of nature. And then the scruples -again occur,—how we have any <i>general</i> knowledge if -our thoughts are fixed on particular objects; and, on -the other hand,—how we can attain to any <i>true</i> knowledge -of nature by contemplating ideas which are not -identical with objects in nature. The two opposite -opinions maintained on this subject were, on the one -side,—that our general propositions refer to objects -which are <i>real</i>, though divested of the peculiarities of -individuals; and, on the other side,—that in such -propositions, individuals are not represented by any -reality, but bound together by a <i>name</i>. These two -views were held by the Realists and Nominalists respectively: -and thus the Realist manifested the adherence -to Ideas, and the Nominalist the adherence to -the impressions of Sense, which have always existed -as opposite yet correlative tendencies in man.</p> - -<p>The Realists were the prevailing sect in the Scholastic -times: for example, both Thomas Aquinas and -Duns Scotus, the <i>Angelical</i> and the <i>Subtle</i> Doctor, -held this opinion, although opposed to each other in -many of their leading doctrines on other subjects. -And as the Nominalist, fixing his attention upon sensible -objects, is obliged to consider what is the <i>principle -of generalization</i>, in order that the possibility of -any general proposition may be conceivable; so on the -other hand, the Realist, beginning with the contemplation -of universal ideas, is compelled to ask what is -the <i>principle of individuation</i>, in order that he may -comprehend the application of general propositions in -each particular instance. This inquiry concerning the -principle of individuation was accordingly a problem -which occupied all the leading minds among the -Schoolmen<a name="FNanchor_48" id="FNanchor_48"></a><a href="#Footnote_48" class="fnanchor">[48]</a>. It will be apparent from what has been -said, that it is only one of the many forms of the -fundamental antithesis of the Ideas and the Senses, -which we have constantly before us in this review.</p> -<p><span class="pagenum" id="Page_52">52</span></p> -<p>The recognition of the derivation of our knowledge, -in part at least, from Experience, though always loose -and incomplete, appears often to be independent of the -Peripatetic traditions. Thus Richard of St. Victor, -a writer of contemplative theology in the twelfth century, -says<a name="FNanchor_49" id="FNanchor_49"></a><a href="#Footnote_49" class="fnanchor">[49]</a>, that "there are three sources of knowledge, -experience, reason, faith. Some things we prove -by experiment, others we collect by reasoning, the -certainty of others we hold by believing. And with -regard to temporal matters, we obtain our knowledge -by actual experience; the other guides belong to -divine knowledge." Richard also propounds a division -of human knowledge which is clearly not derived -directly from the ancients, and which shows that considerable -attention must have been paid to such speculations. -He begins by laying down clearly and broadly -the distinction, which, as we have seen, is of primary -importance, between <i>practice</i> and <i>theory</i>. <i>Practice</i>, he -says, includes seven mechanical arts; those of the -clothier, the armourer, the navigator, the hunter, the -physician, and the player. <i>Theory</i> is threefold, divine, -natural, doctrinal; and is thus divided into Theology, -Physics, and Mathematics. <i>Mathematics</i>, he adds, -treats of the invisible <i>forms</i> of visible things. We -have seen that by many profound thinkers this word -<i>forms</i> has been selected as best fitted to describe those -relations of things which are the subject of mathematics. -Again, Physics discovers causes from their effects -and effects from their causes. It would not be easy -at the present day to give a better account of the object -of physical science. But Richard of St. Victor -makes this account still more remarkably judicious, -by the examples to which he alludes; which are -earthquakes, the tides, the virtues of plants, the instincts -of animals, the classification of minerals, plants -and reptiles.</p> - -<div class="poetry-container"><div class="poetry"><div class="stanza"> - <div class="verse">Unde tremor terris, quâ vi maria alta tumescant,</div> - <div class="verse">Herbarum vires, animos irasque ferarum,</div> - <div class="verse">Omne genus fruticum, lapidum quoque, reptiliumque.</div> -</div></div></div> -<p><span class="pagenum" id="Page_53">53</span></p> -<p>He further adds<a name="FNanchor_50" id="FNanchor_50"></a><a href="#Footnote_50" class="fnanchor">[50]</a>, "Physical science ascends from -effects to causes, and descends again from causes to -effects." This declaration Francis Bacon himself -might have adopted. It is true, that Richard would -probably have been little able to produce any clear -and definite instances of knowledge, in which this -ascent and descent were exemplified; but still the -statement, even considered as a mere conjectural -thought, contains a portion of that sagacity and comprehensive -power which we admire so much in Bacon.</p> - -<p>Richard of St. Victor, who lived in the twelfth -century, thus exhibits more vigour and independence -of speculative power than Thomas Aquinas, Albertus -Magnus, and Duns Scotus, in the thirteenth. In the -interval, about the end of the twelfth century, the -writings of Aristotle had become generally known in -the West; and had been elevated into the standard of -philosophical doctrine, by the divines mentioned above, -who felt a reverent sympathy with the systematizing -and subtle spirit of the Stagirite as soon as it was -made manifest to them. These doctors, following the -example of their great forerunner, reduced every part -of human knowledge to a systematic form; the systems -which they thus framed were presented to men's -minds as the only true philosophy, and dissent from -them was no longer considered to be blameless. It was -an offence against religion as well as reason to reject -the truth, and the truth could be but one. In this -manner arose that claim which the Doctors of the -Church put forth to control men's opinions upon all -subjects, and which we have spoken of in the <i>History -of Science</i> as the Dogmatism of the Middle Ages. -There is no difficulty in giving examples of this characteristic. -We may take for instance a Statute of -the University of Paris, occasioned by a Bull of Pope -John XXI., in which it is enacted, "that no Master -or Bachelor of any faculty, shall presume to read lectures -upon any author in a private room, on account -of the many perils which may arise therefrom; but<span class="pagenum" id="Page_54">54</span> -shall read in public places, where all may resort, and -may faithfully report what is there taught; excepting -only books of Grammar and Logic, in which there can -be no presumption." And certain errors of Brescian -are condemned in a Rescript<a name="FNanchor_51" id="FNanchor_51"></a><a href="#Footnote_51" class="fnanchor">[51]</a> of the papal Legate -Odo, with the following expressions: "Whereas, as -we have been informed, certain Logical professors -treating of Theology in their disputations, and Theologians -treating of Logic, contrary to the command of -the law are not afraid to mix and confound the lots -of the Lord's heritage; we exhort and admonish your -University, all and singular, that they be content with -the landmarks of the Sciences and Faculties which -our Fathers have fixed; and that having due fear of -the curse pronounced in the law against him who -removeth his neighbour's landmark, you hold such -sober wisdom according to the Apostles, that ye may -by no means incur the blame of innovation or presumption."</p> - -<p>The account which, in the <i>History of Science</i>, I gave -of Dogmatism as a characteristic of the middle ages, -has been indignantly rejected by a very pleasing -modern writer, who has, with great feeling and great -diligence, brought into view the merits and beauties -of those times, termed by him <i>Ages of Faith</i>. He -urges<a name="FNanchor_52" id="FNanchor_52"></a><a href="#Footnote_52" class="fnanchor">[52]</a> that religious authority was never claimed for -physical science: and he quotes from Thomas Aquinas, -a passage in which the author protests against the -practice of confounding opinions of philosophy with -doctrines of faith. We might quote in return the Rescript<a name="FNanchor_53" id="FNanchor_53"></a><a href="#Footnote_53" class="fnanchor">[53]</a> -of Stephen, bishop of Paris, in which he declares -that there can be but one truth, and rejects the distinction -of things being true according to philosophy -and not according to the Catholic faith; and it might -be added, that among the errors condemned in this -document are some of Thomas Aquinas himself. We -might further observe, that if no physical doctrines<span class="pagenum" id="Page_55">55</span> -were condemned in the times of which we now speak, -this was because, on such subjects, no new opinions -were promulgated, and not because opinion was free. -As soon as new opinions, even on physical subjects, -attracted general notice, they were prohibited by -authority, as we see in the case of Galileo<a name="FNanchor_54" id="FNanchor_54"></a><a href="#Footnote_54" class="fnanchor">[54]</a>.</p> - -<p>But this disinclination to recognize philosophy as -independent of religion, and this disposition to find in -new theories, even in physical ones, something contrary -to religion or scripture, are, it would seem, very natural -tendencies of theologians; and it would be unjust -to assert that these propensities were confined to the -periods when the authority of papal Rome was highest; -or that the spirit which has in a great degree controlled -and removed such habits was introduced by -the Reformation of religion in the sixteenth century. -We must trace to other causes, the clear and general -recognition of Philosophy, as distinct from Theology, -and independent of her authority. In the earlier ages -of the Church, indeed, this separation had been acknowledged. -St. Augustin says, "A Christian should -beware how he speaks on questions of natural philosophy, -as if they were doctrines of Holy Scripture; for<span class="pagenum" id="Page_56">56</span> -an infidel who should hear him deliver absurdities -could not avoid laughing. Thus the Christian would -be confused, and the infidel but little edified; for the -infidel would conclude that our authors really entertained -these extravagant opinions, and therefore they -would despise them, to their own eternal ruin. Therefore -the opinions of philosophers should never be proposed -as dogmas of faith, or rejected as contrary to -faith, when it is not certain that they are so." These -words are quoted with approbation by Thomas Aquinas, -and it is said<a name="FNanchor_55" id="FNanchor_55"></a><a href="#Footnote_55" class="fnanchor">[55]</a>, are cited in the same manner in -every encyclopedical work of the middle ages. This -warning of genuine wisdom was afterwards rejected, -as we have seen; and it is only in modern times that -its value has again been fully recognized. And this -improvement we must ascribe, mainly, to the progress -of physical science. For a great body of undeniable -truths on physical subjects being accumulated, such as -had no reference to nor connexion with the truths of -religion, and yet such as possessed a strong interest for -most men's minds, it was impossible longer to deny -that there were wide provinces of knowledge which -were not included in the dominions of Theology, and -over which she had no authority. In the fifteenth -and sixteenth centuries, the fundamental doctrines of -mechanics, hydrostatics, optics, magnetics, chemistry, -were established and promulgated; and along with -them, a vast train of consequences, attractive to the -mind by the ideal relations which they exhibited, and -striking to the senses by the power which they gave -man over nature. Here was a region in which philosophy -felt herself entitled and impelled to assert her -independence. From this region, there is a gradation -of subjects in which philosophy advances more and -more towards the peculiar domain of religion; and at -some intermediate points there have been, and probably -will always be, conflicts respecting the boundary<span class="pagenum" id="Page_57">57</span> -line of the two fields of speculation. For the limit is -vague and obscure, and appears to fluctuate and shift -with the progress of time and knowledge.</p> - -<p>Our business at present is not with the whole extent -and limits of philosophy, but with the progress of -physical science more particularly, and the methods by -which it may be attained: and we are endeavouring -to trace historically the views which have prevailed -respecting such methods, at various periods of man's -intellectual progress. Among the most conspicuous of -the revolutions which opinions on this subject have -undergone, is the transition from an implicit trust in -the internal powers of man's mind to a professed dependence -upon external observation; and from an unbounded -reverence for the wisdom of the past, to a -fervid expectation of change and improvement. The -origin and progress of this disposition of mind;—the -introduction of a state of things in which men not -only obtained a body of indestructible truths from -experience, and increased it from generation to generation, -but professedly, and we may say, ostentatiously, -declared such to be the source of their knowledge, -and such their hopes of its destined career;—the -rise, in short, of Experimental Philosophy, not -only as a habit, but as a Philosophy of Experience, is -what we must now endeavour to exhibit.</p> - -<p><span class="pagenum" id="Page_58">58</span></p> - - - - - - - -<hr class="chap" /> -</div><div class="chapter"> -<h2><a name="CHAPTER_X" id="CHAPTER_X"></a>CHAPTER X.<br /> - -<span class="smcap medium">The Innovators of the Middle Ages.</span></h2> - - -<p class="center"><i>Raymond Lully.</i></p> - -<p>1. <i>General Remarks.</i>—<span class="smcap">In</span> the rise of Experimental -Philosophy, understanding the term in the way just -now stated, two features have already been alluded to: -the disposition to cast off the prevalent reverence for -the opinions and methods of preceding teachers with -an eager expectation of some vast advantage to be derived -from a change; and the belief that this improvement -must be sought by drawing our knowledge from -external observation rather than from mere intellectual -efforts;—<i>the Insurrection against Authority</i>, and <i>the -Appeal to Experience</i>. These two movements were -closely connected; but they may easily be distinguished, -and in fact, persons were very prominent in the former -part of the task, who had no comprehension of the latter -principle, from which alone the change derives its -value. There were many Malcontents who had not -the temper, talent or knowledge, which fitted them to -be Reformers.</p> - -<p>The authority which was questioned, in the struggle -of which we speak, was that of the Scholastic System, -the combination of Philosophy with Theology; of which -Aristotle, presented in the form and manner which the -Doctors of the Church had imposed upon him, is to be -considered the representative. When there was demanded -of men a submission of the mind, such as this -system claimed, the natural love of freedom in man's -bosom, and the speculative tendencies of his intellect, -rose in rebellion, from time to time, against the ruling -oppression. We find in all periods of the scholastic -ages examples of this disposition of man to resist over<span class="pagenum" id="Page_59">59</span>strained -authority; the tendency being mostly, however, -combined with a want of solid thought, and -showing itself in extravagant pretensions and fantastical -systems put forwards by the insurgents. We have -pointed out one such opponent<a name="FNanchor_56" id="FNanchor_56"></a><a href="#Footnote_56" class="fnanchor">[56]</a> of the established systems, -even among the Arabian schoolmen, a more -servile race than ever the Europeans were. We may -here notice more especially an extraordinary character -who appeared in the thirteenth century, and who may -be considered as belonging to the Prelude of the Reform -in Philosophy, although he had no share in the -Reform itself.</p> - -<p>2. <i>Raymond Lully.</i>—Raymond Lully is perhaps -traditionally best known as an Alchemist, of which -art he appears to have been a cultivator. But this -was only one of the many impulses of a spirit ardently -thirsty of knowledge and novelty. He had<a name="FNanchor_57" id="FNanchor_57"></a><a href="#Footnote_57" class="fnanchor">[57]</a>, in his -youth, been a man of pleasure, but was driven by a -sudden shock of feeling to resolve on a complete change -of life. He plunged into solitude, endeavoured to still -the remorse of his conscience by prayer and penance, -and soon had his soul possessed by visions which he -conceived were vouchsafed to him. In the feeling of -religious enthusiasm thus excited, he resolved to devote -his life to the diffusion of Christian truth among -Heathens and Mahomedans. For this purpose, at the -age of thirty he betook himself to the study of Grammar, -and of the Arabic language. He breathed earnest -supplications for an illumination from above; and these -were answered by his receiving from heaven, as his -admirers declare, his <i>Ars Magna</i> by which he was able -without labour or effort to learn and apply all knowledge. -The real state of the case is, that he put himself -in opposition to the established systems, and propounded -a New Art, from which he promised the most -wonderful results; but that his Art really is merely a -mode of combining ideal conceptions without any reference -to real sources of knowledge, or any possibility<span class="pagenum" id="Page_60">60</span> -of real advantage. In a Treatise addressed, in <span class="smcap">A.D.</span> -1310, to King Philip of France, entitled <i>Liber Lamentationis -Duodecim Principiorum Philosophiæ contra -Averroistas</i>, Lully introduced Philosophy, accompanied -by her twelve Principles, (Matter, Form, Generation, -&c.) uttering loud complaints against the prevailing -system of doctrine; and represents her as presenting -to the king a petition that she may be upheld and -restored by her favourite, the Author. His <i>Tabula -Generalis ad omnes Scientias applicabilis</i> was begun -the 15th September, 1292, in the Harbour of Tunis, -and finished in 1293, at Naples. In order to frame an -Art of thus tabulating all existing sciences, and indeed -all possible knowledge, he divides into various classes -the conceptions with which he has to deal. The first -class contains nine <i>Absolute Conceptions</i>: Goodness, -Greatness, Duration, Power, Wisdom, Will, Virtue, -Truth, Majesty. The second class has nine <i>Relative -Conceptions</i>: Difference, Identity, Contrariety, Beginning, -Middle, End, Majority, Equality, Minority. The -third class contains nine <i>Questions</i>: Whether? What? -Whence? Why? How great? How circumstanced? -When? Where? and How? The fourth class contains -the nine <i>Most General Subjects</i>: God, Angel, Heaven, -Man, <i>Imaginativum</i>, <i>Sensitivum</i>, <i>Vegetativum</i>, <i>Elementativum</i>, -<i>Instrumentativum</i>. Then come nine <i>Prædicaments</i>, -nine <i>Moral Qualities</i>, and so on. These conceptions -are arranged in the compartments of certain -concentric moveable circles, and give various combinations -by means of triangles and other figures, and thus -propositions are constructed.</p> - -<p>It must be clear at once, that real knowledge, which -is the union of facts and ideas, can never result from -this machinery for shifting about, joining and disjoining, -empty conceptions. This, and all similar schemes, -go upon the supposition that the logical combinations of -notions do of themselves compose knowledge; and that -really existing things may be arrived at by a successive -system of derivation from our most general ideas. It -is imagined that by distributing the nomenclature of -abstract ideas according to the place which they can<span class="pagenum" id="Page_61">61</span> -hold in our propositions, and by combining them according -to certain conditions, we may obtain formulæ -including all possible truths, and thus fabricate a -science in which all sciences are contained. We thus -obtain the means of talking and writing upon all subjects, -without the trouble of thinking: the revolutions -of the emblematical figures are substituted for the -operations of the mind. Both exertion of thought, -and knowledge of facts, become superfluous. And this -reflection, adds an intelligent author<a name="FNanchor_58" id="FNanchor_58"></a><a href="#Footnote_58" class="fnanchor">[58]</a>, explains the -enormous number of books which Lully is said to have -written; for he might have written those even during -his sleep, by the aid of a moving power which should -keep his machine in motion. Having once devised -this invention for manufacturing science, Lully varied -it in a thousand ways, and followed it into a variety -of developments. Besides Synoptical Tables, he employs -Genealogical Trees, each of which he dignifies -with the name of the Tree of Science. The only requisite -for the application of his System was a certain -agreement in the numbers of the classes into which -different subjects were distributed; and as this symmetry -does not really exist in the operations of our -thoughts, some violence was done to the natural distinction -and subordination of conceptions, in order to -fit them for the use of the system.</p> - -<p>Thus Lully, while he professed to teach an Art -which was to shed new light upon every part of -science, was in fact employed in a pedantic and trifling -repetition of known truths or truisms; and while he -complained of the errors of existing methods, he proposed -in their place one which was far more empty, -barren, and worthless, than the customary processes of -human thought. Yet his method is spoken of<a name="FNanchor_59" id="FNanchor_59"></a><a href="#Footnote_59" class="fnanchor">[59]</a> with -<span class="pagenum" id="Page_62">62</span>some praise by Leibnitz, who indeed rather delighted -in the region of ideas and words, than in the world of -realities. But Francis Bacon speaks far otherwise and -more justly on this subject<a name="FNanchor_60" id="FNanchor_60"></a><a href="#Footnote_60" class="fnanchor">[60]</a>. "It is not to be omitted -that some men, swollen with emptiness rather than -knowledge, have laboured to produce a certain Method, -not deserving the name of a legitimate Method, since -it is rather a method of imposture: which yet is -doubtless highly grateful to certain would-be philosophers. -This method scatters about certain little drops -of science in such a manner that a smatterer may -make a perverse and ostentatious use of them with a -certain show of learning. Such was the art of Lully, -which consisted of nothing but a mass and heap of the -words of each science; with the intention that he who -can readily produce the words of any science shall be -supposed to know the science itself. Such collections -are like a rag shop, where you find a patch of everything, -but nothing which is of any value."</p> -<p><span class="pagenum" id="Page_63">63</span></p> - - - - - - -<hr class="chap" /> -</div><div class="chapter"> -<h2><a name="CHAPTER_XI" id="CHAPTER_XI"></a>CHAPTER XI.<br /> - -<span class="smcap medium">The Innovators of the Middle Ages—continued.</span></h2> - - -<p class="center"><i>Roger Bacon.</i></p> - -<p class="drop-cap"><span class="smcap">We</span> now come to a philosopher of a very different -character, who was impelled to declare his dissent -from the reigning philosophy by the abundance of his -knowledge, and by his clear apprehension of the mode -in which real knowledge had been acquired and must -be increased.</p> - -<p>Roger Bacon was born in 1214, near Ilchester, in -Somersetshire, of an old family. In his youth he was -a student at Oxford, and made extraordinary progress -in all branches of learning. He then went to the -University of Paris, as was at that time the custom -of learned Englishmen, and there received the degree -of Doctor of Theology. At the persuasion of Robert -Grostête, bishop of Lincoln, he entered the brotherhood -of Franciscans in Oxford, and gave himself up to -study with extraordinary fervour. He was termed by -his brother monks <i>Doctor Mirabilis</i>. We know from -his own works, as well as from the traditions concerning -him, that he possessed an intimate acquaintance -with all the science of his time which could be acquired -from books; and that he had made many remarkable -advances by means of his own experimental -labours. He was acquainted with Arabic, as well as -with the other languages common in his time. In -the title of his works, we find the whole range of -science and philosophy, Mathematics and Mechanics, -Optics, Astronomy, Geography, Chronology, Chemistry, -Magic, Music, Medicine, Grammar, Logic, Metaphysics, -Ethics, and Theology; and judging from those which -are published, these works are full of sound and exact<span class="pagenum" id="Page_64">64</span> -knowledge. He is, with good reason, supposed to -have discovered, or to have had some knowledge of, -several of the most remarkable inventions which were -made generally known soon afterwards; as gunpowder, -lenses, burning specula, telescopes, clocks, the -correction of the calendar, and the explanation of the -rainbow.</p> - -<p>Thus possessing, in the acquirements and habits of -his own mind, abundant examples of the nature of -knowledge and of the process of invention, Roger -Bacon felt also a deep interest in the growth and progress -of science, a spirit of inquiry respecting the -causes which produced or prevented its advance, and -a fervent hope and trust in its future destinies; and -these feelings impelled him to speculate worthily and -wisely respecting a Reform of the Method of Philosophizing. -The manuscripts of his works have existed -for nearly six hundred years in many of the libraries -of Europe, and especially in those of England; and -for a long period the very imperfect portions of them -which were generally known, left the character and -attainments of the author shrouded in a kind of mysterious -obscurity. About a century ago, however, his -<i>Opus Majus</i> was published<a name="FNanchor_61" id="FNanchor_61"></a><a href="#Footnote_61" class="fnanchor">[61]</a> by Dr. S. Jebb, principally -from a manuscript in the Library of Trinity -College, Dublin; and this contained most or all of the -separate works which were previously known to the -public, along with others still more peculiar and characteristic. -We are thus able to judge of Roger -Bacon's knowledge and of his views, and they are in -every way well worthy our attention.</p> -<p><span class="pagenum" id="Page_65">65</span></p> -<p>The <i>Opus Majus</i> is addressed to Pope Clement the -Fourth, whom Bacon had known when he was legate -in England as Cardinal-bishop of Sabina, and who -admired the talents of the monk, and pitied him for -the persecutions to which he was exposed. On his -elevation to the papal chair, this account of Bacon's -labours and views was sent, at the earnest request of -the pontiff. Besides the <i>Opus Majus</i>, he wrote two -others, the <i>Opus Minus</i> and <i>Opus Tertium</i>; which -were also sent to the pope, as the author says<a name="FNanchor_62" id="FNanchor_62"></a><a href="#Footnote_62" class="fnanchor">[62]</a>, "on -account of the danger of roads, and the possible loss -of the work." These works still exist unpublished, -in the Cottonian and other libraries. -The <i>Opus Majus</i> is a work equally wonderful with -regard to its general scheme, and to the special treatises -with which the outlines of the plan are filled up. -The professed object of the work is to urge the necessity -of a reform in the mode of philosophizing, to set -forth the reasons why knowledge had not made a -greater progress, to draw back attention to the sources -of knowledge which had been unwisely neglected, to -discover other sources which were yet almost untouched, -and to animate men in the undertaking, by a -prospect of the vast advantages which it offered. In -the development of this plan, all the leading portions -of science are expounded in the most complete shape -which they had at that time assumed; and improvements -of a very wide and striking kind are proposed -in some of the principal of these departments. Even -if the work had had no leading purpose, it would have -been highly valuable as a treasure of the most solid -knowledge and soundest speculations of the time; even -if it had contained no such details, it would have been -a work most remarkable for its general views and -scope. It may be considered as, at the same time, the -<i>Encyclopedia</i> and the <i>Novum Organon</i> of the thirteenth -century.</p> - -<p>Since this work is thus so important in the history -of Inductive Philosophy I shall give, in a note, a view<a name="FNanchor_63" id="FNanchor_63"></a><a href="#Footnote_63" class="fnanchor">[63]</a><span class="pagenum" id="Page_66">66</span> -of its divisions and contents. But I must now endeavour -to point out more especially the way in which -the various principles, which the reform of scientific -method involved, are here brought into view.</p> - -<p>One of the first points to be noticed for this purpose, -is the resistance to authority; and at the stage -of philosophical history with which we here have to -do, this means resistance to the authority of Aristotle, -as adopted and interpreted by the Doctors of the -Schools. Bacon's work<a name="FNanchor_64" id="FNanchor_64"></a><a href="#Footnote_64" class="fnanchor">[64]</a> is divided into Six Parts; and -of these Parts, the First is, Of the four universal -Causes of all Human Ignorance. The causes thus -enumerated<a name="FNanchor_65" id="FNanchor_65"></a><a href="#Footnote_65" class="fnanchor">[65]</a> are:—the force of unworthy authority;—traditionary -habit;—the imperfection of the undisciplined -senses;—and the disposition to conceal our -ignorance and to make an ostentatious show of our -knowledge. These influences involve every man, occupy -every condition. They prevent our obtaining -the most useful and large and fair doctrines of wisdom, -the secret of all sciences and arts. He then proceeds -to argue, from the testimony of philosophers themselves, -that the authority of antiquity, and especially -of Aristotle, is not infallible. "We find<a name="FNanchor_66" id="FNanchor_66"></a><a href="#Footnote_66" class="fnanchor">[66]</a> their books -full of doubts, obscurities, and perplexities. They -scarce agree with each other in one empty question or<span class="pagenum" id="Page_67">67</span> -one worthless sophism, or one operation of science, as -one man agrees with another in the practical operations -of medicine, surgery, and the like arts of Secular -men. Indeed," he adds, "not only the philosophers, -but the saints have fallen into errors which they have -afterwards retracted," and this he instances in Augustin, -Jerome, and others. He gives an admirable -sketch<a name="FNanchor_67" id="FNanchor_67"></a><a href="#Footnote_67" class="fnanchor">[67]</a> of the progress of philosophy from the Ionic -School to Aristotle; of whom he speaks with great -applause. "Yet," he adds<a name="FNanchor_68" id="FNanchor_68"></a><a href="#Footnote_68" class="fnanchor">[68]</a>, "those who came after -him corrected him in some things, and added many -things to his works, and shall go on adding to the end -of the world." Aristotle, he adds, is now called peculiarly<a name="FNanchor_69" id="FNanchor_69"></a><a href="#Footnote_69" class="fnanchor">[69]</a> -the Philosopher, "yet there was a time when -his philosophy was silent and unregarded, either on -account of the rarity of copies of his works, or their difficulty, -or from envy; till after the time of Mahomet,<span class="pagenum" id="Page_68">68</span> -when Avicenna and Averroes, and others, recalled -this philosophy into the full light of exposition. And -although the Logic and some other works were translated -by Boethius from the Greek, yet the philosophy -of Aristotle first received a quick increase among -the Latins at the time of Michael Scot; who, in the -year of our Lord 1230, appeared, bringing with him -portions of the books of Aristotle on Natural Philosophy -and Mathematics. And yet a small part only -of the works of this author is translated, and a still -smaller part is in the hands of common students." -He adds further<a name="FNanchor_70" id="FNanchor_70"></a><a href="#Footnote_70" class="fnanchor">[70]</a> (in the Third Part of the <i>Opus -Majus</i>, which is a Dissertation on language), that the -translations which are current of these writings, are -very bad and imperfect. With these views, he is -moved to express himself somewhat impatiently<a name="FNanchor_71" id="FNanchor_71"></a><a href="#Footnote_71" class="fnanchor">[71]</a> respecting -these works: "If I had," he says, "power -over the works of Aristotle, I would have them all -burnt; for it is only a loss of time to study in them, -and a cause of error, and a multiplication of ignorance -beyond expression." "The common herd of students," -he says, "with their heads, have no principle by which -they can be excited to any worthy employment; and -hence they mope and make asses of themselves over -their bad translations, and lose their time, and trouble, -and money."</p> - -<p>The remedies which he recommends for these evils, -are, in the first place, the study of that only perfect -wisdom which is to be found in the sacred Scripture<a name="FNanchor_72" id="FNanchor_72"></a><a href="#Footnote_72" class="fnanchor">[72]</a>, -in the next place, the study of mathematics and the -use of experiment<a name="FNanchor_73" id="FNanchor_73"></a><a href="#Footnote_73" class="fnanchor">[73]</a>. By the aid of these methods, -<span class="pagenum" id="Page_69">69</span>Bacon anticipates the most splendid progress for human -knowledge. He takes up the strain of hope and -confidence which we have noticed as so peculiar in -the Roman writers; and quotes some of the passages -of Seneca which we adduced in illustration of this:—that -the attempts in science were at first rude and -imperfect, and were afterwards improved;—that the -day will come, when what is still unknown shall be -brought to light by the progress of time and the -labours of a longer period;—that one age does not -suffice for inquiries so wide and various;—that the -people of future times shall know many things unknown -to us;—and that the time shall arrive when -posterity will wonder that we overlooked what was so -obvious. Bacon himself adds anticipations more peculiarly -in the spirit of his own time. "We have seen," -he says, at the end of the work, "how Aristotle, by -the ways which wisdom teaches, could give to Alexander -the empire of the world. And this the Church -ought to take into consideration against the infidels -and rebels, that there may be a sparing of Christian -blood, and especially on account of the troubles that -shall come to pass in the days of Antichrist; which -by the grace of God, it would be easy to obviate, if -prelates and princes would encourage study, and join -in searching out the secrets of nature and art."</p> - -<p>It may not be improper to observe here that this -belief in the appointed progress of knowledge, is not -combined with any overweening belief in the unbounded -and independent power of the human intellect. -On the contrary, one of the lessons which Bacon draws -from the state and prospects of knowledge, is the duty -of faith and humility. "To him," he says<a name="FNanchor_74" id="FNanchor_74"></a><a href="#Footnote_74" class="fnanchor">[74]</a>, "who -denies the truth of the faith because he is unable to -understand it, I will propose in reply the course of -nature, and as we have seen it in examples." And -after giving some instances, he adds, "These, and the -like, ought to move men and to excite them to the -reception of divine truths. For if, in the vilest objects<span class="pagenum" id="Page_70">70</span> -of creation, truths are found, before which the inward -pride of man must bow, and believe though it cannot -understand, how much more should man humble his -mind before the glorious truths of God!" He had -before said<a name="FNanchor_75" id="FNanchor_75"></a><a href="#Footnote_75" class="fnanchor">[75]</a>: "Man is incapable of perfect wisdom in -this life; it is hard for him to ascend towards perfection, -easy to glide downwards to falsehoods and vanities: -let him then not boast of his wisdom, or extol -his knowledge. What he knows is little and worthless, -in respect of that which he believes without knowing; -and still less, in respect of that which he is ignorant -of. He is mad who thinks highly of his wisdom; -he most mad, who exhibits it as something to be wondered -at." He adds, as another reason for humility, -that he has proved by trial, he could teach in one year, -to a poor boy, the marrow of all that the most diligent -person could acquire in forty years' laborious and expensive -study.</p> - -<p>To proceed somewhat more in detail with regard to -Roger Bacon's views of a Reform in Scientific Inquiry, -we may observe that by making Mathematics and Experiment -the two great points of his recommendation, -he directed his improvement to the two essential parts -of all knowledge, Ideas and Facts, and thus took the -course which the most enlightened philosophy would -have suggested. He did not urge the prosecution of -experiment, to the comparative neglect of the existing -mathematical sciences and conception; a fault which -there is some ground for ascribing to his great namesake -and successor Francis Bacon: still less did he -content himself with a mere protest against the authority -of the schools, and a vague demand for change, -which was almost all that was done by those who put -themselves forward as reformers in the intermediate -time. Roger Bacon holds his way steadily between -the two poles of human knowledge; which, as we have -seen, it is far from easy to do. "There are two modes -of knowing," says he<a name="FNanchor_76" id="FNanchor_76"></a><a href="#Footnote_76" class="fnanchor">[76]</a>; "by argument, and by experi<span class="pagenum" id="Page_71">71</span>ment. -Argument concludes a question; but it does -not make us feel certain, or acquiesce in the contemplation -of truth, except the truth be also found to be -so by experience." It is not easy to express more -decidedly the clearly seen union of exact conceptions -with certain facts, which, as we have explained, constitutes -real knowledge.</p> - -<p>One large division of the <i>Opus Majus</i> is "On the -Usefulness of Mathematics," which is shown by a copious -enumeration of existing branches of knowledge, as -Chronology, Geography, the Calendar and (in a separate -Part) Optics. There is a chapter<a name="FNanchor_77" id="FNanchor_77"></a><a href="#Footnote_77" class="fnanchor">[77]</a>, in which it -is proved by reason, that all science requires mathematics. -And the arguments which are used to establish -this doctrine, show a most just appreciation of -the office of mathematics in science. They are such as -follows:—That other sciences use examples taken from -mathematics as the most evident:—That mathematical -knowledge is, as it were, innate in us, on which point -he refers to the well-known dialogue of Plato, as -quoted by Cicero:—That this science, being the easiest, -offers the best introduction to the more difficult:—That -in mathematics, things as known to us are -identical with things as known to nature:—That we -can here entirely avoid doubt and error, and obtain -certainty and truth:—That mathematics is prior to -other sciences in nature, because it takes cognizance of -quantity, which is apprehended by intuition, (<i>intuitu -intellectus</i>). "Moreover," he adds<a name="FNanchor_78" id="FNanchor_78"></a><a href="#Footnote_78" class="fnanchor">[78]</a>, "there have been -found famous men, as Robert, bishop of Lincoln, and -Brother Adam Marshman (de Marisco), and many -others, who by the power of mathematics have been -able to explain the causes of things; as may be seen -in the writings of these men, for instance, concerning -the Rainbow and Comets, and the generation of heat, -and climates, and the celestial bodies."</p> - -<p><span class="pagenum" id="Page_72">72</span></p> - -<p>But undoubtedly the most remarkable portion of the -<i>Opus Majus</i> is the Sixth and last Part, which is entitled -"De Scientia experimentali." It is indeed an -extraordinary circumstance to find a writer of the -thirteenth century, not only recognizing experiment -as one source of knowledge, but urging its claims as -something far more important than men had yet been -aware of, exemplifying its value by striking and just -examples, and speaking of its authority with a dignity -of diction which sounds like a foremurmur of the Baconian -sentences uttered nearly four hundred years -later. Yet this is the character of what we here find<a name="FNanchor_79" id="FNanchor_79"></a><a href="#Footnote_79" class="fnanchor">[79]</a>. -"Experimental science, the sole mistress of speculative -sciences, has three great Prerogatives among other -parts of knowledge: First she tests by experiment the -noblest conclusions of all other sciences: Next she -discovers respecting the notions which other sciences -deal with, magnificent truths to which these sciences -of themselves can by no means attain: her Third dignity -is, that she by her own power and without respect -of other sciences, investigates the secret of nature."</p> - -<p>The examples which Bacon gives of these "Prerogatives" -are very curious, exhibiting, among some error -and credulity, sound and clear views. His leading -example of the First Prerogative, is the Rainbow, of -which the cause, as given by Aristotle, is tested by -reference to experiment with a skill which is, even to -us now, truly admirable. The examples of the Second -Prerogative are three:—<i>first</i>, the art of making an -artificial sphere which shall move with the heavens by -natural influences, which Bacon trusts may be done, -though astronomy herself cannot do it—"et tunc," he -says, "thesaurum unius regis valeret hoc instrumentum;"—<i>secondly</i>, -the art of prolonging life, which -experiment may teach, though medicine has no means -of securing it except by regimen<a name="FNanchor_80" id="FNanchor_80"></a><a href="#Footnote_80" class="fnanchor">[80]</a>;—<i>thirdly</i>, the art of<span class="pagenum" id="Page_73">73</span> -making gold finer than fine gold, which goes beyond -the power of alchemy. The Third Prerogative of experimental -science, arts independent of the received -sciences, is exemplified in many curious examples, many -of them whimsical traditions. Thus it is said that the -character of a people may be altered by altering the -air<a name="FNanchor_81" id="FNanchor_81"></a><a href="#Footnote_81" class="fnanchor">[81]</a>. Alexander, it seems, applied to Aristotle to -know whether he should exterminate certain nations -which he had discovered, as being irreclaimably barbarous; -to which the philosopher replied, "If you can -alter their air, permit them to live, if not, put them to -death." In this part, we find the suggestion that the -fire-works made by children, of saltpetre, might lead -to the invention of a formidable military weapon.</p> - -<p>It could not be expected that Roger Bacon, at a -time when experimental science hardly existed, could -give any <i>precepts</i> for the discovery of truth by experiment. -But nothing can be a better <i>example</i> of the -method of such investigation, than his inquiry concerning -the cause of the Rainbow. Neither Aristotle, -nor Avicenna, nor Seneca, he says, have given us any -clear knowledge of this matter, but experimental -science can do so. Let the experimenter (<i>experimentator</i>) -consider the cases in which he finds the same -colours, as the hexagonal crystals from Ireland and -India; by looking into these he will see colours like -those of the rainbow. Many think that this arises -from some special virtue of these stones and their hexagonal -figure; let therefore the experimenter go on, -and he will find the same in other transparent stones, -in dark ones as well as in light-coloured. He will find -the same effect also in other forms than the hexagon,<span class="pagenum" id="Page_74">74</span> -if they be furrowed in the surface, as the Irish crystals -are. Let him consider too, that he sees the same -colours in the drops which are dashed from oars in -the sunshine;—and in the spray thrown by a millwheel;—and -in the dew-drops which lie on the grass -in a meadow on a summer-morning;—and if a man -takes water in his mouth and projects it on one side -into a sunbeam;—and if in an oil-lamp hanging in the -air, the rays fall in certain positions upon the surface -of the oil;—and in many other ways, are colours produced. -We have here a collection of instances, which -are almost all examples of the same kind as the phenomenon -under consideration; and by the help of a -principle collected by induction from these facts, the -colours of the rainbow were afterwards really explained.</p> - -<p>With regard to the form and other circumstances of -the bow he is still more precise. He bids us measure -the height of the bow and of the sun, to show that the -center of the bow is exactly opposite to the sun. He -explains the circular form of the bow,—its being independent -of the form of the cloud, its moving when we -move, its flying when we follow,—by its consisting of -the reflections from a vast number of minute drops. -He does not, indeed, trace the course of the rays -through the drop, or account for the precise magnitude -which the bow assumes; but he approaches to -the verge of this part of the explanation; and must be -considered as having given a most happy example of -experimental inquiry into nature, at a time when such -examples were exceedingly scanty. In this respect, -he was more fortunate than Francis Bacon, as we shall -hereafter see.</p> - -<p>We know but little of the biography of Roger Bacon, -but we have every reason to believe that his influence -upon his age was not great. He was suspected of -magic, and is said to have been put into close confinement -in consequence of this charge. In his work he -speaks of Astrology as a science well worth cultivating. -"But," says he, "Theologians and Decretists, -not being learned in such matters and seeing that evil -as well as good may be done, neglect and abhor such<span class="pagenum" id="Page_75">75</span> -things, and reckon them among Magic Arts." We -have already seen, that at the very time when Bacon -was thus raising his voice against the habit of blindly -following authority, and seeking for all science in -Aristotle, Thomas Aquinas was employed in fashioning -Aristotle's tenets into that fixed form in which -they became the great impediment to the progress of -knowledge. It would seem, indeed, that something -of a struggle between the progressive and stationary -powers of the human mind was going on at this time. -Bacon himself says<a name="FNanchor_82" id="FNanchor_82"></a><a href="#Footnote_82" class="fnanchor">[82]</a>, "Never was there so great an -appearance of wisdom, nor so much exercise of study -in so many Faculties, in so many regions, as for this -last forty years. Doctors are dispersed everywhere, in -every castle, in every burgh, and especially by the students -of two Orders, (he means the Franciscans and -Dominicans, who were almost the only religious orders -that distinguished themselves by an application to -study<a name="FNanchor_83" id="FNanchor_83"></a><a href="#Footnote_83" class="fnanchor">[83]</a>,) which has not happened except for about -forty years. And yet there was never so much ignorance, -so much error." And in the part of his work -which refers to Mathematics, he says of that study<a name="FNanchor_84" id="FNanchor_84"></a><a href="#Footnote_84" class="fnanchor">[84]</a>, -that it is the door and the key of the sciences; and -that the neglect of it for thirty or forty years has entirely -ruined the studies of the Latins. According to -these statements, some change, disastrous to the fortunes -of science, must have taken place about 1230, -soon after the foundation of the Dominican and Franciscan -Orders<a name="FNanchor_85" id="FNanchor_85"></a><a href="#Footnote_85" class="fnanchor">[85]</a>. Nor can we doubt that the adoption -of the Aristotelian philosophy by these two Orders, -in the form in which the Angelical Doctor had systematized -it, was one of the events which most tended -to defer, for three centuries, the reform which Roger -Bacon urged as a matter of crying necessity in his -own time.</p> - -<p><span class="pagenum" id="Page_76">76</span></p> - - - - - -<hr class="chap" /> -</div><div class="chapter"> -<h2><a name="CHAPTER_XII" id="CHAPTER_XII"></a>CHAPTER XII.<br /> - -<span class="smcap medium">The Revival of Platonism.</span></h2> - - -<p><a id="XII1"></a>1. <i>Causes of Delay in the Advance of Knowledge.</i>—<span class="smcap">In</span> -the insight possessed by learned men into the -method by which truth was to be discovered, the fourteenth -and fifteenth centuries went backwards, rather -than forwards, from the point which had been reached -in the thirteenth. Roger Bacon had urged them to -have recourse to experiment; but they returned with -additional and exclusive zeal to the more favourite -employment of reasoning upon their own conceptions. -He had called upon them to look at the world without; -but their eyes forthwith turned back upon the world -within. In the constant oscillation of the human -mind between Ideas and Facts, after having for a -moment touched the latter, it seemed to swing back -more impetuously to the former. Not only was the -philosophy of Aristotle firmly established for a considerable -period, but when men began to question its -authority, they attempted to set up in its place a philosophy -still more purely ideal, that of Plato. It was -not till the actual progress of experimental knowledge -for some centuries had given it a vast accumulation of -force, that it was able to break its way fully into the -circle of speculative science. The new Platonist schoolmen -had to run their course, the practical discoverers -had to prove their merit by their works, the Italian -innovators had to utter their aspirations for a change, -before the second Bacon could truly declare that the -time for a fundamental reform was at length arrived.</p> - -<p>It cannot but seem strange, to any one who attempts -to trace the general outline of the intellectual progress -of man, and who considers him as under the guidance<span class="pagenum" id="Page_77">77</span> -of a Providential sway, that he should thus be permitted -to wander so long in a wilderness of intellectual -darkness; and even to turn back, by a perverse caprice -as it might seem, when on the very border of the -brighter and better land which was his destined inheritance. -We do not attempt to solve this difficulty: -but such a course of things naturally suggests the -thought, that a progress in physical science is not the -main object of man's career, in the eyes of the Power -who directs the fortunes of our race. We can easily -conceive that it may have been necessary to man's -general welfare that he should continue to turn his -eyes inwards upon his own heart and faculties, till -Law and Duty, Religion and Government, Faith and -Hope, had been fully incorporated with all the past -acquisitions of human intellect; rather than that he -should have rushed on into a train of discoveries tending -to chain him to the objects and operations of the -material world. The systematic Law<a name="FNanchor_86" id="FNanchor_86"></a><a href="#Footnote_86" class="fnanchor">[86]</a> and philosophical -Theology which acquired their ascendancy in -men's minds at the time of which we speak, kept -them engaged in a region of speculations which perhaps -prepared the way for a profounder and wider -civilization, for a more elevated and spiritual character, -than might have been possible without such a -preparation. The great Italian poet of the fourteenth -century speaks with strong admiration of the founders -of the system which prevailed in his time. Thomas, -Albert, Gratian, Peter Lombard, occupy distinguished -places in the Paradise. The first, who is the poet's -instructor, says,—</p> - -<div class="poetry-container"><div class="poetry"><div class="stanza"> - <div class="verse indent2">Io fui degli agni della santa greggia</div> - <div class="verse">Che Domenico mena per cammino</div> - <div class="verse">U' ben s'impingua se non si vaneggia.</div> - <div class="verse indent2">Questo che m'è a destra piu vicino</div> - <div class="verse">Frate e maestro fummi; ed esso Alberto</div> - <div class="verse">E di Cologna, ed io Tomas d'Aquino....</div> - <div class="verse indent2">Quell' altro fiammeggiar esce del riso</div><span class="pagenum" id="Page_78">78</span> - <div class="verse indent2">De Grazian, che l'uno et l'altro foro</div> - <div class="verse indent4">Ajutò si che piace in Paradiso.</div> -</div></div></div> - -<div class="poetry-container"><div class="poetry"><div class="stanza"> - <div class="verse indent2">I, then, was of the lambs that Dominic</div> - <div class="verse">Leads, for his saintly flock, along the way</div> - <div class="verse">Where well they thrive not swoln with vanity.</div> - <div class="verse">He nearest on my right-hand brother was</div> - <div class="verse">And master to me; Albert of Cologne</div> - <div class="verse">Is this; and of Aquinum Thomas, I....</div> - <div class="verse">That next resplendence issues from the smile</div> - <div class="verse">Of Gratian, who to either forum lent</div> - <div class="verse">Such help as favour wins in Paradise.</div> -</div></div></div> - -<p>It appears probable that neither poetry, nor painting, -nor the other arts which require for their perfection a -lofty and spiritualized imagination, would have appeared -in the noble and beautiful forms which they -assumed in the fourteenth and fifteenth century, if -men of genius had, at the beginning of that period, -made it their main business to discover the laws of -nature, and to reduce them to a rigorous scientific -form. Yet who can doubt that the absence of these -touching and impressive works would have left one of -the best and purest parts of man's nature without its -due nutriment and development? It may perhaps -be a necessary condition in the progress of man, that -the Arts which aim at beauty should reach their excellence -before the Sciences which seek speculative -truth; and if this be so, we inherit, from the middle -ages, treasures which may well reconcile us to the -delay which took place in their cultivation of experimental -science.</p> - -<p>However this may be, it is our business at present -to trace the circumstances of this very lingering advance. -We have already noticed the contest of the -Nominalists and Realists, which was one form, though, -with regard to scientific methods, an unprofitable one, -of the antithesis of Ideas and Things. Though, therefore, -this struggle continued, we need not dwell upon -it. The Nominalists denied the real existence of Ideas, -which doctrine was to a great extent implied in the -prevailing systems; but the controversy in which they -thus engaged, did not lead them to seek for knowledge -in a new field and by new methods. The arguments<span class="pagenum" id="Page_79">79</span> -which Occam the Nominalist opposes to those of Duns -Scotus the Realist, are marked with the stamp of the -same system, and consist only in permutations and -combinations of the same elementary conceptions. It -was not till the impulse of external circumstances was -added to the discontent, which the more stirring intellects -felt towards the barren dogmatism of their -age, that the activity of the human mind was again -called into full play, and a new career of progression -entered upon, till then undreamt of, except by a few -prophetic spirits.</p> - -<p><a id="XII2"></a>2. <i>Causes of Progress.</i>—These circumstances were -principally the revival of Greek and Roman literature, -the invention of Printing, the Protestant Reformation, -and a great number of curious discoveries and inventions -in the arts, which were soon succeeded by important -steps in speculative physical science. Connected -with the first of these events, was the rise of a -party of learned men who expressed their dissatisfaction -with the Aristotelian philosophy, as it was then -taught, and manifested a strong preference for the -views of Plato. It is by no means suitable to our plan -to give a detailed account of this new Platonic school; -but we may notice a few of the writers who belong to -it, so far at least as to indicate its influence upon the -Methods of pursuing science.</p> - -<p>In the fourteenth century<a name="FNanchor_87" id="FNanchor_87"></a><a href="#Footnote_87" class="fnanchor">[87]</a>, the frequent intercourse -of the most cultivated persons of the Eastern and -Western Empire, the increased study of the Greek language -in Italy, the intellectual activity of the Italian -States, the discovery of manuscripts of the classical -authors, were circumstances which excited or nourished -a new and zealous study of the works of Greek and -Roman genius. The genuine writings of the ancients, -when presented in their native life and beauty, instead -of being seen only in those lifeless fragments and dull -transformations which the scholastic system had exhibited, -excited an intense enthusiasm. Europe, at -that period, might be represented by Plato's beautiful<span class="pagenum" id="Page_80">80</span> -allegory, of a man who, after being long kept in a dark -cavern, in which his knowledge of the external world -is gathered from the images which stream through the -chinks of his prison, is at last led forth into the full -blaze of day. It was inevitable that such a change -should animate men's efforts and enlarge their faculties. -Greek literature became more and more known, -especially by the influence of learned men who came -from Constantinople into Italy: these teachers, though -they honoured Aristotle, reverenced Plato no less, and -had never been accustomed to follow with servile submission -of thought either these or any other leaders. -The effect of such influences soon reveals itself in the -works of that period. Dante has woven into his <i>Divina -Commedia</i> some of the ideas of Platonism. Petrarch, -who had formed his mind by the study of Cicero, and -had thus been inspired with a profound admiration for -the literature of Greece, learnt Greek from Barlaam, -a monk who came as ambassador from the Emperor of -the East to the Pope, in 1339. With this instructor, -the poet read the works of Plato; struck by their -beauty, he contributed, by his writings and his conversation, -to awake in others an admiration and love -for that philosopher, which soon became strongly and -extensively prevalent among the learned in Italy.</p> - - -<p><a id="XII3"></a>3. <i>Hermolaus Barbarus, &c.</i>—Along with the feeling -there prevailed also, among those who had learnt -to relish the genuine beauties of the Greek and Latin -writers, a strong disgust for the barbarisms in which -the scholastic philosophy was clothed. Hermolaus Barbarus<a name="FNanchor_88" id="FNanchor_88"></a><a href="#Footnote_88" class="fnanchor">[88]</a>, -who was born in 1454, at Venice, and had -formed his taste by the study of classical literature, -translated, among other learned works, Themistius's -paraphrastic expositions of the Physics of Aristotle; -with the view of trying whether the Aristotelian Natural -Philosophy could not be presented in good Latin, -which the scholastic teachers denied. In his Preface -he expresses great indignation against those philosophers -who have written and disputed on philosophical<span class="pagenum" id="Page_81">81</span> -subjects in barbarous Latin, and in an uncultured -style, so that all refined minds are repelled from these -studies by weariness and disgust. They have, he says, -by this barbarism, endeavoured to secure to themselves, -in their own province, a supremacy without rivals or -opponents. Hence they maintain that mathematics, -philosophy, jurisprudence, cannot be expounded in correct -Latin;—that between these sciences and the genuine -Latin language there is a great gulf, as between -things that cannot be brought together: and on this -ground they blame those who combine the study of philology -and eloquence with that of science. This opinion, -adds Hermolaus, perverts and ruins our studies; and is -highly prejudicial and unworthy in respect to the state. -Hermolaus awoke in others, as for instance, in John -Picus of Mirandula, the same dislike to the reigning -school philosophy. As an opponent of the same kind, -we may add Marius Nizolius of Bersallo, a scholar who -carried his admiration of Cicero to an exaggerated extent, -and who was led, by a controversy with the defenders -of the scholastic philosophy, to publish (1553) -a work <i>On the True Principles and True Method of -Philosophizing</i>. In the title of this work, he professes -to give "the true principles of almost all arts and -sciences, refuting and rejecting almost all the false -principles of the Logicians and Metaphysicians." But -although, in the work, he attacks the scholastic philosophy, -he does little or nothing to justify the large -pretensions of his title; and he excited, it is said, little -notice. It is therefore curious that Leibnitz should -have thought it worth his while to re-edit this work, -which he did in 1670, adding remarks of his own.</p> - - -<p><a id="XII4"></a>4. <i>Nicolaus Cusanus.</i>—Without dwelling upon -this opposition to the scholastic system on the ground -of taste, I shall notice somewhat further those writers -who put forwards Platonic views, as fitted to complete -or to replace the doctrines of Aristotle. Among these, -I may place Nicolaus Cusanus, (so called from Cus, a -village on the Moselle, where he was born in 1401;) -who was afterwards raised to the dignity of cardinal. -We might, indeed, at first be tempted to include<span class="pagenum" id="Page_82">82</span> -Cusanus among those persons who were led to reject -the old philosophy by being themselves agents in the -progressive movement of physical science. For he -published, before Copernicus, and independently of -him, the doctrine that the earth is in motion<a name="FNanchor_89" id="FNanchor_89"></a><a href="#Footnote_89" class="fnanchor">[89]</a>. But -it should be recollected that in order to see the possibility -of this doctrine, and its claims to acceptance, -no new reference to observation was requisite. The -Heliocentric System was merely a new mode of representing -to the mind facts, with which all astronomers -had long been familiar. The system might very easily -have been embraced and inculcated by Plato himself; -as indeed it is said to have been actually taught by -Pythagoras. The mere adoption of the Heliocentric -view, therefore, without attempting to realize the system -in detail, as Copernicus did, cannot entitle a -writer of the fifteenth century to be looked upon as -one of the authors of the discoveries of that period; -and we must consider Cusanus as a speculative anti-Aristotelian, -rather than as a practical reformer.</p> - -<p>The title of Cusanus's book, <i>De Doctâ Ignorantiâ</i>, -shows how far he was from agreeing with those who -conceived that, in the works of Aristotle, they had -a full and complete system of all human knowledge. -At the outset of this book<a name="FNanchor_90" id="FNanchor_90"></a><a href="#Footnote_90" class="fnanchor">[90]</a>, he says, after pointing out -some difficulties in the received philosophy, "If, therefore, -the case be so, (as even the very profound Aristotle, -in his <i>First Philosophy</i>, affirms,) that in things -most manifest by nature, there is a difficulty, no less -than for an owl to look at the sun; since the appetite -of knowledge is not implanted in us in vain, we ought -to desire to know that we are ignorant. If we can -fully attain to this, we shall arrive at <i>Instructed Ignorance</i>." -How far he was from placing the source of -knowledge in experience, as opposed to ideas, we may -see in the following passage<a name="FNanchor_91" id="FNanchor_91"></a><a href="#Footnote_91" class="fnanchor">[91]</a> from another work of -his, <i>On Conjectures</i>. "Conjectures must proceed from<span class="pagenum" id="Page_83">83</span> -our mind, as the real world proceeds from the infinite -Divine Reason. For since the human mind, the lofty -likeness of God, participates, as it may, in the fruitfulness -of the creative nature, it doth from itself, as the -image of the Omnipotent Form, bring forth reasonable -thoughts which have a similitude to real existences. -Thus the Human Mind exists as a conjectural form of -the world, as the Divine Mind is its real form." We -have here the Platonic or ideal side of knowledge put -prominently and exclusively forwards.</p> - - -<p><a id="XII5"></a>5. <i>Marsilius Ficinus, &c.</i>—A person who had much -more influence on the diffusion of Platonism was Marsilius -Ficinus, a physician of Florence. In that city -there prevailed, at the time of which we speak, the -greatest enthusiasm for Plato. George Gemistius Pletho, -when in attendance upon the Council of Florence, -had imparted to many persons the doctrines of the -Greek philosopher; and, among others, had infused a -lively interest on this subject into the elder Cosmo, -the head of the family of the Medici. Cosmo formed -the plan of founding a Platonic academy. Ficinus<a name="FNanchor_92" id="FNanchor_92"></a><a href="#Footnote_92" class="fnanchor">[92]</a>, -well instructed in the works of Plato, Plotinus, Proclus, -and other Platonists, was selected to further this -object, and was employed in translating the works of -these authors into Latin. It is not to our present -purpose to consider the doctrines of this school, except -so far as they bear upon the nature and methods of -knowledge; and therefore I must pass by, as I have -in other instances done, the greater part of their speculations, -which related to the nature of God, the immortality -of the soul, the principles of Goodness and -Beauty, and other points of the same order. The -object of these and other Platonists of this school, -however, was not to expel the authority of Aristotle -by that of Plato. Many of them had come to the conviction -that the highest ends of philosophy were to be -reached only by bringing into accordance the doctrines -of Plato and of Aristotle. Of this opinion was John -Picus, Count of Mirandula and Concordia; and under<span class="pagenum" id="Page_84">84</span> -this persuasion he employed the whole of his life in -labouring upon a work, <i>De Concordiâ Platonis et Aristotelis</i>, -which was not completed at the time of his -death, in 1494; and has never been published. But -about a century later, another writer of the same school, -Francis Patricius<a name="FNanchor_93" id="FNanchor_93"></a><a href="#Footnote_93" class="fnanchor">[93]</a>, pointing out the discrepancies between -the two Greek teachers, urged the propriety of -deposing Aristotle from the supremacy he had so long -enjoyed. "Now all these doctrines, and others not -a few," he says<a name="FNanchor_94" id="FNanchor_94"></a><a href="#Footnote_94" class="fnanchor">[94]</a>, "since they are Platonic doctrines, -philosophically most true, and consonant with the Catholic -faith, whilst the Aristotelian tenets are contrary -to the faith, and philosophically false, who will not, -both as a Christian and a Philosopher, prefer Plato to -Aristotle? And why should not hereafter, in all the -colleges and monasteries of Europe, the reading and -study of Plato be introduced? Why should not the -philosophy of Aristotle be forthwith exiled from such -places? Why must men continue to drink the mortal -poison of impiety from that source?" with much more -in the same strain.</p> - -<p>The Platonic school, of which we have spoken, had, -however, reached its highest point of prosperity before -this time, and was already declining. About 1500, -the Platonists appeared to triumph over the Peripatetics<a name="FNanchor_95" id="FNanchor_95"></a><a href="#Footnote_95" class="fnanchor">[95]</a>; -but the death of their great patron, Cardinal -Bessarion, about this time, and we may add, the hollowness -of their system in many points, and its want -of fitness for the wants and expectations of the age, -turned men's thoughts partly back to the established -Aristotelian doctrines, and partly forwards to schemes -of bolder and fresher promise.</p> - - -<p><a id="XII6"></a>6. <i>Francis Patricius.</i>—Patricius, of whom we have -just spoken, was one of those who had arrived at the -conviction that the formation of a new philosophy, -and not merely the restoration of an old one, was -needed. In 1593, appeared his <i>Nova de Universis<span class="pagenum" id="Page_85">85</span> -Philosophia</i>; and the mode in which it begins<a name="FNanchor_96" id="FNanchor_96"></a><a href="#Footnote_96" class="fnanchor">[96]</a> can -hardly fail to remind us of the expressions which -Francis Bacon soon afterwards used in the opening of -a work of the same nature. "Francis Patricius, being -about to found anew the true philosophy of the universe, -dared to begin by announcing the following -indisputable principles." Here, however, the resemblance -between Patricius and true inductive philosophers -ends. His principles are barren <i>à priori</i> axioms; -and his system has one main element, <i>Light</i>, (<i>Lux</i>, or -<i>Lumen</i>,) to which all operations of nature are referred. -In general cultivation, and practical knowledge of -nature, he was distinguished among his contemporaries. -In various passages of his works he relates<a name="FNanchor_97" id="FNanchor_97"></a><a href="#Footnote_97" class="fnanchor">[97]</a> observations -which he had made in the course of his -travels, in Cyprus, Corfu, Spain, the mountains of the -Modenese, and Dalmatia, which was his own country; -his observations relate to light, the saltness of the sea, -its flux and reflux, and other points of astronomy, -meteorology, and natural history. He speaks of the -sex of plants<a name="FNanchor_98" id="FNanchor_98"></a><a href="#Footnote_98" class="fnanchor">[98]</a>; rejects judicial astrology; and notices -the astronomical systems of Copernicus, Tycho, Fracastoro, -and Torre. But the mode in which he speaks -of experiments proves, what indeed is evident from -the general scheme of his system, that he had no due -appreciation of the place which observation must hold -in real and natural philosophy.</p> - - -<p><a id="XII7"></a>7. <i>Picus, Agrippa, &c.</i>—It had been seen in the -later philosophical history of Greece, how readily the -ideas of the Platonic school lead on to a system of -unfathomable and unbounded mysticism. John Picus, -of Mirandula<a name="FNanchor_99" id="FNanchor_99"></a><a href="#Footnote_99" class="fnanchor">[99]</a>, added to the study of Plato and the<span class="pagenum" id="Page_86">86</span> -Neoplatonists, a mass of allegorical interpretations of -the Scriptures, and the dreams of the Cabbala, a Jewish -system<a name="FNanchor_100" id="FNanchor_100"></a><a href="#Footnote_100" class="fnanchor">[100]</a>, which pretends to explain how all things -are an emanation of the Deity. To this his nephew, -Francis Picus, added a reference to inward illumination<a name="FNanchor_101" id="FNanchor_101"></a><a href="#Footnote_101" class="fnanchor">[101]</a>, -by which knowledge is obtained, independently -of the progress of reasoning. John Reuchlin, or Capnio, -born 1455; John Baptist Helmont, born 1577; -Francis Mercurius Helmont, born 1618, and others, -succeeded John Picus in his admiration of the Cabbala: -while others, as Jacob Bœhmen, rested upon -internal revelations like Francis Picus. And thus -we have a series of mystical writers, continued into -modern times, who may be considered as the successors -of the Platonic school; and who all exhibit views altogether -erroneous with regard to the nature and origin -of knowledge. Among the various dreams of this -school are certain wide and loose analogies of terrestrial -and spiritual things. Thus in the writings of -Cornelius Agrippa (who was born 1487, at Cologne) -we have such systems as the following<a name="FNanchor_102" id="FNanchor_102"></a><a href="#Footnote_102" class="fnanchor">[102]</a>:—"Since -there is a threefold world, elemental, celestial, and intellectual, -and each lower one is governed by that -above it, and receives the influence of its powers: so -that the very Archetype and Supreme Author transfuses -the virtues of his omnipotence into us through -angels, heavens, stars, elements, animals, plants, stones,—into -us, I say, for whose service he has framed and -created all these things;—the Magi do not think it -irrational that we should be able to ascend by the -same degrees, the same worlds, to this Archetype of -the world, the Author and First Cause of all, of whom -all things are, and from whom they proceed; and -should not only avail ourselves of those powers which -exist in the nobler works of creation, but also should -be able to attract other powers, and add them to -these."</p> - -<p>Agrippa's work, <i>De Vanitate Scientiarum</i>, may be<span class="pagenum" id="Page_87">87</span> -said rather to have a skeptical and cynical, than a -Platonic, character. It is a declamation<a name="FNanchor_103" id="FNanchor_103"></a><a href="#Footnote_103" class="fnanchor">[103]</a>, in a melancholy -mood, against the condition of the sciences in -his time. His indignation at the worldly success of -men whom he considered inferior to himself, had, he -says, metamorphosed him into a dog, as the poets -relate of Hecuba of Troy, so that his impulse was to -snarl and bark. His professed purpose, however, was -to expose the dogmatism, the servility, the self-conceit, -and the neglect of religious truth which prevailed in -the reigning Schools of philosophy. His views of the -nature of science, and the modes of improving its cultivation, -are too imperfect and vague to allow us to -rank him among the reformers of science.</p> - - -<p><a id="XII8"></a>8. <i>Paracelsus, Fludd, &c.</i>—The celebrated Paracelsus<a name="FNanchor_104" id="FNanchor_104"></a><a href="#Footnote_104" class="fnanchor">[104]</a> -put himself forwards as a reformer in philosophy, -and obtained no small number of adherents. -He was, in most respects, a shallow and impudent -pretender; and had small knowledge of the literature -or science of his time: but by the tone of his speaking -and writing he manifestly belongs to the mystical -school of which we are now speaking. Perhaps by -the boldness with which he proposed new systems, -and by connecting these with the practical doctrines -of medicine, he contributed something to the introduction -of a new philosophy. We have seen in the -History of Chemistry that he was the author of the -system of Three Principles, (salt, sulphur, and mercury,) -which replaced the ancient doctrine of Four -Elements, and prepared the way for a true science of -chemistry. But the salt, sulphur, and mercury of -Paracelsus were not, he tells his disciples, the visible -bodies which we call by those names, but certain invisible, -astral, or sidereal elements. The astral salt is -the basis of the solidity and incombustible parts in -bodies; the astral sulphur is the source of combustion<span class="pagenum" id="Page_88">88</span> -and vegetation; the astral mercury is the origin of -fluidity and volatility. And again, these three elements -are analogous to the three elements of man,—Body, -Spirit, and Soul.</p> - -<p>A writer of our own country, belonging to this -mystical school, is Robert Fludd, or De Fluctibus, -who was born in 1571, in Kent, and after pursuing -his studies at Oxford, travelled for several years. Of -all the Theosophists and Mystics, he is by much the -most learned; and was engaged in various controversies -with Mersenne, Gassendi, Kepler, and others. -He thus brings us in contact with the next class of -philosophers whom we have to consider, the practical -reformers of philosophy;—those who furthered the -cause of science by making, promulgating, or defending -the great discoveries which now began to occupy -men. He adopted the principle, which we have noticed -elsewhere<a name="FNanchor_105" id="FNanchor_105"></a><a href="#Footnote_105" class="fnanchor">[105]</a>, of the analogy of the Macrocosm and -Microcosm, the world of nature and the world of man. -His system contains such a mixture and confusion of -physical and metaphysical doctrines as might be expected -from his ground-plan, and from his school. -Indeed his object, the general object of mystical speculators, -is to identify physical with spiritual truths. -Yet the influence of the practical experimental philosophy -which was now gaining ground in the world -may be traced in him. Thus he refers to experiments -on distillation to prove the existence and relation of -the regions of water, air, and fire, and of the spirits -which correspond to them; and is conceived, by some -persons<a name="FNanchor_106" id="FNanchor_106"></a><a href="#Footnote_106" class="fnanchor">[106]</a>, to have anticipated Torricelli in the invention -of the Barometer.</p> - -<p>We need no further follow the speculations of this -school. We see already abundant reason why the reform -of the methods of pursuing science could not -proceed from the Platonists. Instead of seeking knowledge -by experiment, they immersed themselves deeper -than even the Aristotelians had done in traditionary<span class="pagenum" id="Page_89">89</span> -lore, or turned their eyes inwards in search of an internal -illumination. Some attempts were made to -remedy the defects of philosophy by a recourse to the -doctrines of other sects of antiquity, when men began -to feel more distinctly the need of a more connected -and solid knowledge of nature than the established -system gave them. Among these attempts were those -of Berigard<a name="FNanchor_107" id="FNanchor_107"></a><a href="#Footnote_107" class="fnanchor">[107]</a>, Magernus, and especially Gassendi, to -bring into repute the philosophy of the Ionian school, -of Democritus and of Epicurus. But these endeavours -were posterior in time to the new impulse given to -knowledge by Copernicus, Kepler, and Galileo, and -were influenced by views arising out of the success of -these discoveries, and they must, therefore, be considered -hereafter. In the mean time, some independent -efforts (arising from speculative rather than practical -reformers) were made to cast off the yoke of the -Aristotelian dogmatism, and to apprehend the true -form of that new philosophy which the most active -and hopeful minds saw to be needed; and we must -give some account of these attempts, before we can -commit ourselves to the full stream of progressive -philosophy.</p> - - - - -<hr class="chap" /> -</div><div class="chapter"> - -<p><span class="pagenum" id="Page_90">90</span></p> - - -<h2><a name="CHAPTER_XIII" id="CHAPTER_XIII"></a>CHAPTER XIII.<br /> - -<span class="smcap medium">The Theoretical Reformers of Science.</span></h2> - - -<p class="drop-cap"><span class="smcap">We</span> have already seen that Patricius, about the -middle of the sixteenth century, announced his -purpose of founding anew the whole fabric of philosophy; -but that, in executing this plan, he ran into wide -and baseless hypotheses, suggested by <i>à priori</i> conceptions -rather than by external observation; and that he -was further misled by fanciful analogies resembling -those which the Platonic mystics loved to contemplate. -The same time, and the period which followed it, produced -several other essays which were of the same -nature, with the exception of their being free from the -peculiar tendencies of the Platonic school: and these -insurrections against the authority of the established -dogmas, although they did not directly substitute a -better positive system in the place of that which they -assailed, shook the authority of the Aristotelian system, -and led to its overthrow; which took place as soon -as these theoretical reformers were aided by practical -reformers.</p> - - -<p><a id="XIII1"></a>1. <i>Bernardinus Telesius.</i>—Italy, always, in modern -times, fertile in the beginnings of new systems, was -the soil on which these innovators arose. The earliest -and most conspicuous of them is Bernardinus -Telesius, who was born in 1508, at Cosenza, in the -kingdom of Naples. His studies, carried on with -great zeal and ability, first at Milan and then at -Rome, made him well acquainted with the knowledge -of his times; but his own reflections convinced him -that the basis of science, as then received, was altogether -erroneous; and led him to attempt a reform, -with which view, in 1565, he published, at Rome, his<span class="pagenum" id="Page_91">91</span> -work<a name="FNanchor_108" id="FNanchor_108"></a><a href="#Footnote_108" class="fnanchor">[108]</a>, "<i>Bernardinus Telesius, of Cosenza, on the Nature -of Things, according to principles of his own</i>." -In the preface of this work he gives a short account<a name="FNanchor_109" id="FNanchor_109"></a><a href="#Footnote_109" class="fnanchor">[109]</a> -of the train of reflection by which he was led to put -himself in opposition to the Aristotelian philosophy. -This kind of autobiography occurs not unfrequently -in the writings of theoretical reformers; and shows -how livelily they felt the novelty of their undertaking. -After the storm and sack of Rome in 1527, Telesius -retired to Padua, as a peaceful seat of the muses; -and there studied philosophy and mathematics, with -great zeal, under the direction of Jerome Amalthæus -and Frederic Delphinus. In these studies he made -great progress; and the knowledge which he thus -acquired threw a new light upon his view of the -Aristotelian philosophy. He undertook a closer examination -of the Physical Doctrines of Aristotle; and -as the result of this, he was astonished how it could -have been possible that so many excellent men, so -many nations, and even almost the whole human race, -should, for so long a time, have allowed themselves to -be carried away by a blind reverence for a teacher, -who had committed errors so numerous and grave -as he perceived to exist in "the philosopher." -Along with this view of the insufficiency of the Aristotelian -philosophy, arose, at an early period, the -thought of erecting a better system in its place. With -this purpose he left Padua, when he had received the -degree of Doctor, and went to Rome, where he was -encouraged in his design by the approval and friendly -exhortations of distinguished men of letters, amongst -whom were Ubaldino Bandinelli and Giovanni della -Casa. From Rome he went to his native place, when the -incidents and occupations of a married life for a while -interrupted his philosophical project. But after his<span class="pagenum" id="Page_92">92</span> -wife was dead, and his eldest son grown to manhood, -he resumed with ardour the scheme of his youth; -again studied the works of Aristotle and other philosophers, -and composed and published the first two -books of his treatise. The opening to this work sufficiently -exhibits the spirit in which it was conceived. -Its object is stated in the title to be to show, that -"the construction of the world, the magnitude and -nature of the bodies contained in it, are not to be -investigated by reasoning, which was done by the -ancients, but are to be apprehended by the senses, and -collected from the things themselves." And the Proem -is in the same strain. "They who before us have inquired -concerning the construction of this world and -of the things which it contains, seem indeed to have -prosecuted their examination with protracted vigils -and great labour, but <i>never to have looked at it</i>." And -thus, he observes, they found nothing but error. -This he ascribes to their presumption. "For, as it -were, attempting to rival God in wisdom, and venturing -to seek for the principles and causes of the -world by the light of their own reason, and thinking -they had found what they had only invented, they -made an arbitrary world of their own." "<i>We</i> then," -he adds, "not relying on ourselves, and of a duller -intellect than they, propose to ourselves to turn our -regards to the world itself and its parts."</p> - -<p>The execution of the work, however, by no means -corresponds to the announcement. The doctrines of -Aristotle are indeed attacked; and the objections to -these, and to other received opinions, form a large part -of the work. But these objections are supported by -<i>à priori</i> reasoning, and not by experiments. And thus, -rejecting the Aristotelian physics, he proposes a system -at least equally baseless; although, no doubt, grateful -to the author from its sweeping and apparently simple -character. He assumes three principles, Heat, Cold, -and Matter: Heat is the principle of motion, Cold of -immobility, and Matter is the corporeal substratum, in -which these incorporeal and active principles produce -their effects. It is easy to imagine that, by combining<span class="pagenum" id="Page_93">93</span> -and separating these abstractions in various ways, a -sort of account of many natural phenomena may be -given; but it is impossible to ascribe any real value to -such a system. The merit of Telesius must be considered -to consist in his rejection of the Aristotelian -errors, in his perception of the necessity of a reform in -the method of philosophizing, and in his persuasion that -this reform must be founded on experiments rather -than on reasoning. When he said<a name="FNanchor_110" id="FNanchor_110"></a><a href="#Footnote_110" class="fnanchor">[110]</a>, "We propose to -ourselves to turn our eyes to the world itself, and its -parts, their passions, actions, operations, and species," -his view of the course to be followed was right; but -his purpose remained but ill fulfilled, by the arbitrary -edifice of abstract conceptions which his system exhibits.</p> - -<p>Francis Bacon, who, about half a century later, -treated the subject of a reform of philosophy in a far -more penetrating and masterly manner, has given us -his judgment of Telesius. In his view, he takes -Telesius as the restorer of the Atomic philosophy, -which Democritus and Parmenides taught among the -ancients; and according to his custom, he presents an -image of this philosophy in an adaptation of a portion -of ancient mythology<a name="FNanchor_111" id="FNanchor_111"></a><a href="#Footnote_111" class="fnanchor">[111]</a>. The Celestial Cupid, who with -Cœlus, was the parent of the Gods and of the Universe, -is exhibited as a representation of matter and -its properties, according to the Democritean philosophy. -"Concerning Telesius," says Bacon, "we think -well, and acknowledge him as a lover of truth, a useful -contributor to science, an amender of some tenets, -the first of recent men. But we have to do with him -as the restorer of the philosophy of Parmenides, to -whom much reverence is due." With regard to this -philosophy, he pronounces a judgment which very -truly expresses the cause of its rashness and emptiness. -"It is," he says, "such a system<a name="FNanchor_112" id="FNanchor_112"></a><a href="#Footnote_112" class="fnanchor">[112]</a> as naturally<span class="pagenum" id="Page_94">94</span> -proceeds from the intellect, abandoned to its own impulse, -and not rising from experience to theory continuously -and successively." Accordingly, he says that, -"Telesius, although learned in the Peripatetic philosophy -(if that were anything), which indeed, he has -turned against the teachers of it, is hindered by his -affirmations, and is more successful in destroying than -in building."</p> - -<p>The work of Telesius excited no small notice, and -was placed in the <i>Index Expurgatorius</i>. It made many -disciples, a consequence probably due to its spirit of -system-making, no less than to its promise of reform, -or its acuteness of argument; for till trial and reflection -have taught man modesty and moderation, he can -never be content to receive knowledge in the small -successive instalments in which nature gives it forth -to him. It is the makers of large systems, arranged -with an <i>appearance</i> of completeness and symmetry, -who, principally, give rise to Schools of philosophy.</p> - - -<p><a id="XIII2"></a>2. (<i>Thomas Campanella</i>).—Accordingly, Telesius -may be looked upon as the founder of a School. His -most distinguished successor was Thomas Campanella, -who was born in 1568, at Stilo, in Calabria. He showed -great talents at an early age, prosecuting his studies -at Cosenza, the birth-place of the great opponent of -Aristotle and reformer of philosophy. He, too, has -given us an account<a name="FNanchor_113" id="FNanchor_113"></a><a href="#Footnote_113" class="fnanchor">[113]</a> of the course of thought by which -he was led to become an innovator. "Being afraid -that not genuine truth, but falsehood in the place of -truth, was the tenant of the Peripatetic School, I examined -all the Greek, Latin, and Arabic commentators -of Aristotle, and hesitated more and more, as I -sought to learn whether what they have said were also -to be read in the world itself, which I had been taught -by learned men was the living book of God. And as -my doctors could not satisfy my scruples, I resolved to -read all the books of Plato, Pliny, Galen, the Stoics,<span class="pagenum" id="Page_95">95</span> -and the Democriteans, and especially those of Telesius; -and to compare them with that <i>first and original -writing, the world</i>; that thus from the primary autograph, -I might learn if the copies contained anything -false." Campanella probably refers here to an expression -of Plato, who says, "the world is God's epistle -to mankind." And this image, of the natural world -as an original manuscript, while human systems of -philosophy are but copies, and may be false ones, -became a favourite thought of the reformers, and appears -repeatedly in their writings from this time. -"When I held my public disputation at Cosenza," -Campanella proceeds, "and still more, when I conversed -privately with the brethren of the monastery, -I found little satisfaction in their answers; but Telesius -delighted me, on account of his freedom in philosophizing, -and because he rested upon the nature of -things, and not upon the assertions of men."</p> - -<p>With these views and feelings, it is not wonderful -that Campanella, at the early age of twenty-two (1590,) -published a work remarkable for the bold promise of -its title: "<i>Thomas Campanella's Philosophy demonstrated -to the senses, against those who have philosophized -in an arbitrary and dogmatical manner, not taking -nature for their guide; in which the errors of Aristotle -and his followers are refuted from their own assertions -and the laws of nature: and all the imaginations -feigned in the place of nature by the Peripatetics are -altogether rejected; with a true defence of Bernardin -Telesius of Cosenza, the greatest of philosophers; confirmed -by the opinions of the ancients, here elucidated -and defended, especially those of the Platonists</i>."</p> - -<p>This work was written in answer to a book published -against Telesius by a Neapolitan professor named -Marta; and it was the boast of the young author that -he had only employed eleven months in the composition -of his defence, while his adversary had been -engaged eleven years in preparing his attack. Campanella -found a favourable reception in the house of the -Marchese Lavelli, and there employed himself in the -composition of an additional work, entitled <i>On the<span class="pagenum" id="Page_96">96</span> -Sense of Things and Magic</i>, and in other literary -labours. These, however, are full of the indications of -an enthusiastic temper, inclined to mystical devotion, -and of opinions bearing the cast of pantheism. For -instance, the title of the book last quoted sets forth as -demonstrated in the course of the work, that "the -world is the living and intelligent statue of God; and -that all its parts, and particles of parts, are endowed some -with a clearer, some with a more obscure sense, such as -suffices for the preservation of each and of the whole." -Besides these opinions, which could not fail to make -him obnoxious to the religious authorities, Campanella<a name="FNanchor_114" id="FNanchor_114"></a><a href="#Footnote_114" class="fnanchor">[114]</a> -engaged in schemes of political revolution, which -involved him in danger and calamity. He took part -in a conspiracy, of which the object was to cast off the -tyranny of Spain, and to make Calabria a republic. -This design was discovered; and Campanella, along -with others, was thrown into prison and subjected to -torture. He was kept in confinement twenty-seven -years; and at last obtained his liberation by the interposition -of Pope Urban VIII. He was, however, still -in danger from the Neapolitan Inquisition; and escaped -in disguise to Paris, where he received a pension from -the king, and lived in intercourse with the most eminent -men of letters. He died there in 1639.</p> - -<p>Campanella was a contemporary of Francis Bacon, -whom we must consider as belonging to an epoch to -which the Calabrian school of innovators was only a -prelude. I shall not therefore further follow the connexion -of writers of this order. Tobias Adami, a Saxon -writer, an admirer of Campanella's works, employed -himself, about 1620, in adapting them to the German -public, and in recommending them strongly to German -philosophers. Descartes, and even Bacon, may be considered -as successors of Campanella; for they too were -theoretical reformers; but they enjoyed the advantage -of the light which had, in the mean time, been thrown -upon the philosophy of science, by the great practical -advances of Kepler, Galileo, and others. To these<span class="pagenum" id="Page_97">97</span> -practical reformers we must soon turn our attention: -but we may first notice one or two additional circumstances -belonging to our present subject.</p> - -<p>Campanella remarks that both the Peripatetics and -the Platonists conducted the learner to knowledge by a -long and circuitous path, which he wished to shorten -by setting out from the sense. Without speaking of -the methods which he proposed, we may notice one -maxim<a name="FNanchor_115" id="FNanchor_115"></a><a href="#Footnote_115" class="fnanchor">[115]</a> of considerable value which he propounds, and -to which we have already been led. "We begin to -reason from sensible objects, and definition is the end -and epilogue of science. It is not the beginning of our -knowing, but only of our teaching."</p> - - -<p><a id="XIII3"></a>3. (<i>Andrew Cæsalpinus.</i>)—The same maxim had already -been announced by Cæsalpinus, a contemporary -of Telesius; (he was born at Arezzo in 1520, and died -at Rome in 1603). Cæsalpinus is a great name in -science, though professedly an Aristotelian. It has -been seen in the <i>History of Science</i><a name="FNanchor_116" id="FNanchor_116"></a><a href="#Footnote_116" class="fnanchor">[116]</a>, that he formed -the first great epoch of the science of botany by his -systematic arrangement of plants, and that in this -task he had no successor for nearly a century. He -also approached near to the great discovery of the -circulation of the blood<a name="FNanchor_117" id="FNanchor_117"></a><a href="#Footnote_117" class="fnanchor">[117]</a>. He takes a view of science -which includes the remark that we have just quoted -from Campanella: "We reach perfect knowledge by -three steps: Induction, Division, Definition. By Induction, -we collect likeness and agreement from observation; -by Division, we collect unlikeness and disagreement; -by Definition, we learn the proper substance -of each object. Induction makes universals -from particulars, and offers to the mind all intelligible -matter; Division discovers the difference of universals, -and leads to species; Definition resolves species -into their principles and elements<a name="FNanchor_118" id="FNanchor_118"></a><a href="#Footnote_118" class="fnanchor">[118]</a>." Without asserting -this to be rigorously correct, it is incomparably -more true and philosophical than the opposite view,<span class="pagenum" id="Page_98">98</span> -which represents definition as the beginning of our -knowledge; and the establishment of such a doctrine -is a material step in inductive philosophy<a name="FNanchor_119" id="FNanchor_119"></a><a href="#Footnote_119" class="fnanchor">[119]</a>.</p> - - -<p><a id="XIII4"></a>4. (<i>Giordano Bruno.</i>)—Among the Italian innovators -of this time we must notice the unfortunate Giordano -Bruno, who was born at Nola about 1550 and -burnt at Rome in 1600. He is, however, a reformer of -a different school from Campanella; for he derives his -philosophy from Ideas and not from Observation. He -represents himself as the author of a new doctrine, -which he terms the <i>Nolan Philosophy</i>. He was a -zealous promulgator and defender of the Copernican -system of the universe, as we have noticed in the -<i>History of Science</i><a name="FNanchor_120" id="FNanchor_120"></a><a href="#Footnote_120" class="fnanchor">[120]</a>. Campanella also wrote in defence -of that system.</p> - -<p>It is worthy of remark that a thought which is -often quoted from Francis Bacon, occurs in Bruno's -<i>Cena di Cenere</i>, published in 1584; I mean, the notion -that the later times are more aged than the earlier. -In the course of the dialogue, the Pedant, who is one -of the interlocutors, says, "In antiquity is wisdom;" -to which the Philosophical Character replies, "If you -knew what you were talking about, you would see -that your principle leads to the opposite result of that -which you wish to infer;—I mean, that <i>we</i> are older, -and have lived longer, than our predecessors." He -then proceeds to apply this, by tracing the course of -astronomy through the earlier astronomers up to Copernicus.</p> - - -<p><a id="XIII5"></a>5.(<i>Peter Ramus.</i>)—I will notice one other reformer -of this period, who attacked the Aristotelian system on -another side, on which it was considered to be most -impregnable. This was Peter Ramus,(born in Picardy -in 1515,) who ventured to denounce the <i>Logic</i> of Aristotle -as unphilosophical and useless. After showing -an extraordinary aptitude for the acquirement of knowledge -in his youth, when he proceeded to the degree -of Master of Arts, he astonished his examiners by<span class="pagenum" id="Page_99">99</span> -choosing for the subject of the requisite disputation -the thesis<a name="FNanchor_121" id="FNanchor_121"></a><a href="#Footnote_121" class="fnanchor">[121]</a>, "that what Aristotle has said is all -wrong." This position, so startling in 1535, he defended -for the whole day, without being defeated. -This was, however, only a formal academical exercise, -which did not necessarily imply any permanent conviction -of the opinion thus expressed. But his mind -was really labouring to detect and remedy the errors -which he thus proclaimed. From him, as from the -other reformers of this time, we have an account of -this mental struggle<a name="FNanchor_122" id="FNanchor_122"></a><a href="#Footnote_122" class="fnanchor">[122]</a>. He says, in a work on this -subject, "I will candidly and simply explain how I -was delivered from the darkness of Aristotle. When, -according to the laws of our university, I had spent -three years and a half in the Aristotelian philosophy, -and was now invested with the philosophical laurel as -a Master of Arts, I took an account of the time which -I had consumed in this study, and considered on what -subjects I should employ this logical art of Aristotle, -which I had learnt with so much labour and noise, -I found it made me not more versed in history or antiquities, -more eloquent in discourse, more ready in -verse, more wise in any subject. Alas for me! how -was I overpowered, how deeply did I groan, how did -I deplore my lot and my nature, how did I deem -myself to be by some unhappy and dismal fate and -frame of mind abhorrent from the Muses, when I -found that I was one who, after all my pains, could -reap no benefit from that wisdom of which I heard so -much, as being contained in the Logic of Aristotle." -He then relates that he was led to the study of the -Dialogues of Plato, and was delighted with the kind -of analysis of the subjects discussed which Socrates is -there represented as executing. "Well," he adds, "I -began thus to reflect within myself—(I should have -thought it impious to say it to another)—What, I<span class="pagenum" id="Page_100">100</span> -pray you, prevents me from <i>socratizing</i>; and from asking, -without regard to Aristotle's authority, whether -Aristotle's Logic be true and correct? It may be that -that philosopher leads us wrong; and if so, no wonder -that I cannot find in his books the treasure which is -not there. What if his dogmas be mere figments? Do -I not tease and torment myself in vain, trying to get -a harvest from a barren soil?" He convinced himself -that the Aristotelian logic was worthless: and constructed -a new system of Logic, founded mainly on the -Platonic process of exhausting a subject by analytical -classification of its parts. Both works, his <i>Animadversions -on Aristotle</i>, and his <i>Logic</i>, appeared in 1543. -The learned world was startled and shocked to find a -young man, on his first entrance into life, condemning -as faulty, fallacious, and useless, that part of Aristotle's -works which had always hitherto been held as -a masterpiece of philosophical acuteness, and as the -Organon of scientific reasoning. And in truth, it -must be granted that Ramus does not appear to have -understood the real nature and object of Aristotle's -Logic; while his own system could not supply the -place of the old one, and was not of much real value. -This dissent from the established doctrines was, however, -not only condemned but punished. The printing -and selling of his books was forbidden through France; -and Ramus was stigmatized by a sentence<a name="FNanchor_123" id="FNanchor_123"></a><a href="#Footnote_123" class="fnanchor">[123]</a> which -declared him rash, arrogant, impudent, and ignorant, -and prohibited from teaching logic and philosophy. -He was, however, afterwards restored to the office of -professor: and though much attacked, persisted in his -plan of reforming, not only Logic but Physics and -Metaphysics. He made his position still more dangerous -by adopting the reformed religion; and during -the unhappy civil wars of France, he was deprived of -his professorship, driven from Paris, and had his -library plundered. He endeavoured, but in vain, to -engage a German professor, Schegk, to undertake the<span class="pagenum" id="Page_101">101</span> -reform of the Aristotelian Physics; a portion of knowledge -in which he felt himself not to be strong. Unhappily -for himself, he afterwards returned to Paris, -where he perished in the massacre of St. Bartholomew -in 1572.</p> - -<p>Ramus's main objection to the Aristotelian Logic -is, that it is not the image of the natural process of -thought; an objection which shows little philosophical -insight; for the course by which we obtain knowledge -may well differ from the order in which our knowledge, -when obtained, is exhibited. We have already -seen that Ramus's contemporaries, Cæsalpinus and -Campanella, had a wiser view; placing definition as -the last step in knowing, but the first in teaching. -But the effect which Ramus produced was by no -means slight. He aided powerfully in turning the -minds of men to question the authority of Aristotle -on all points; and had many followers, especially -among the Protestants. Among the rest, Milton, our -great poet, published "Artis Logicæ plenior Institutio -<i>ad Petri Rami methodum concinnata</i>;" but this -work, appearing in 1672, belongs to a succeeding -period.</p> - - -<p><a id="XIII6"></a>6.(<i>The Reformers in general</i>).—It is impossible not to -be struck with the series of misfortunes which assailed -the reformers of philosophy of the period we have had -to review. Roger Bacon was repeatedly condemned -and imprisoned; and, not to speak of others who suffered -under the imputation of magical arts, Telesius is -said<a name="FNanchor_124" id="FNanchor_124"></a><a href="#Footnote_124" class="fnanchor">[124]</a> to have been driven from Naples to his native -city by calumny and envy; Cæsalpinus was accused -of atheism<a name="FNanchor_125" id="FNanchor_125"></a><a href="#Footnote_125" class="fnanchor">[125]</a>; Campanella was imprisoned for twenty-seven -years and tortured; Giordano Bruno was burnt -at Rome as a heretic; Ramus was persecuted during -his life, and finally murdered by his personal enemy -Jacques Charpentier, in a massacre of which the plea -was religion. It is true, that for the most part these -misfortunes were not principally due to the attempts<span class="pagenum" id="Page_102">102</span> -at philosophical reform, but were connected rather -with politics or religion. But we cannot doubt that -the spirit which led men to assail the received philosophy, -might readily incline them to reject some tenets -of the established religion; since the boundary line of -these subjects is difficult to draw. And as we have -seen, there was in most of the persons of whom we -have spoken, not only a well-founded persuasion of -the defects of existing systems, but an eager spirit of -change, and a sanguine anticipation of some wide and -lofty philosophy, which was soon to elevate the minds -and conditions of men. The most unfortunate were, -for the most part, the least temperate and judicious -reformers. Patricius, who, as we have seen, declared -himself against the Aristotelian philosophy, lived and -died at Rome in peace and honour<a name="FNanchor_126" id="FNanchor_126"></a><a href="#Footnote_126" class="fnanchor">[126]</a>.</p> - - -<p><a id="XIII7"></a>7.(<i>Melancthon.</i>)—It is not easy to point out with -precision the connexion between the efforts at a Reform -in Philosophy, and the great Reformation of Religion -in the sixteenth century. The disposition to assert -(practically at least) a freedom of thinking, and to -reject the corruptions which tradition had introduced -and authority maintained, naturally extended its influence -from one subject to another; and especially in -subjects so nearly connected as theology and philosophy. -The Protestants, however, did not reject the -Aristotelian system; they only reformed it, by going -back to the original works of the author, and by reducing -it to a conformity with Scripture. In this -reform, Melancthon was the chief author, and wrote -works on Logic, Physics, Morals, and Metaphysics, -which were used among Protestants. On the subject -of the origin of our knowledge, his views contained a -very philosophical improvement of the Aristotelian -doctrines. He recognized the importance of Ideas, as -well as of Experience. "We could not," he says<a name="FNanchor_127" id="FNanchor_127"></a><a href="#Footnote_127" class="fnanchor">[127]</a>, -"proceed to reason at all, except there were by nature<span class="pagenum" id="Page_103">103</span> -innate in man certain fixed points, that is, principles -of science;—as Number, the recognition of Order and -Proportion, logical, geometrical, physical and moral -Principles. Physical principles are such as these,—everything -which exists proceeds from a cause,—a -body cannot be in two places at once,—time is a continued -series of things or of motions,—and the like." -It is not difficult to see that such Principles partake -of the nature of the Fundamental Ideas which we -have attempted to arrange and enumerate in a previous -part of this work.</p> - -<p>Before we proceed to the next chapter, which treats -of the Practical Reformers of Scientific Method, let -us for an instant look at the strong persuasion implied -in the titles of the works of this period, that the -time of a philosophical revolution was at hand. Telesius -published <i>De Rerum Natura juxta propria principia</i>; -Francis Helmont, <i>Philosophia vulgaris refutata</i>; -Patricius, <i>Nova de Universis Philosophia</i>; Campanella, -<i>Philosophia sensibus demonstrata, adversus -errores Aristotelis</i>; Bruno professed himself the author -of a <i>Nolan Philosophy</i>; and Ramus of a <i>New Logic</i>. -The age announced itself pregnant; and the eyes of -all who took an interest in the intellectual fortunes of -the race, were looking eagerly for the expected offspring.</p> - - - - -<hr class="chap" /> - -<p><span class="pagenum" id="Page_104">104</span></p> - - -</div><div class="chapter"> -<h2><a name="CHAPTER_XIV" id="CHAPTER_XIV"></a>CHAPTER XIV.<br /> - -<span class="smcap medium">The Practical Reformers of Science.</span></h2> - - -<p><a id="XIV1"></a>1. <i>Character of the Practical Reformers.</i>—<span class="smcap">We</span> now -come to a class of speculators who had perhaps a -greater share in bringing about the change from stationary -to progressive knowledge, than those writers -who so loudly announced the revolution. The mode -in which the philosophers of whom we now speak -produced their impressions on men's minds, was very -different from the procedure of the theoretical reformers. -What these talked of, they did; what these -promised, they performed. While the theorists concerning -knowledge proclaimed that great advances -were to be made, the practical discoverers went steadily -forwards. While one class spoke of a complete -Reform of scientific Methods, the other, boasting little, -and often thinking little of Method, proved the novelty -of their instrument by obtaining new results. While -the metaphysicians were exhorting men to consult experience -and the senses, the physicists were examining -nature by such means with unparalleled success. And -while the former, even when they did for a moment -refer to facts, soon rushed back into their own region -of ideas, and tried at once to seize the widest generalizations, -the latter, fastening their attention upon the -phenomena, and trying to reduce them to laws, were -carried forwards by steps measured and gradual, such -as no conjectural view of scientific method had suggested; -but leading to truths as profound and comprehensive -as any which conjecture had dared to -anticipate. The theoretical reformers were bold, self-confident, -hasty, contemptuous of antiquity, ambitious -of ruling all future speculations, as they whom they<span class="pagenum" id="Page_105">105</span> -sought to depose had ruled the past. The practical -reformers were cautious, modest, slow, despising no -knowledge, whether borrowed from tradition or observation, -confident in the ultimate triumph of science, -but impressed with the conviction that each single -person could contribute a little only to its progress. -Yet though thus working rather than speculating,—dealing -with particulars more than with generals,—employed -mainly in adding to knowledge, and not in -defining what knowledge is, or how additions are to -be made to it,—these men, thoughtful, curious, and of -comprehensive minds, were constantly led to important -views on the nature and methods of science. And -these views, thus suggested by reflections on their own -mental activity, were gradually incorporated with the -more abstract doctrines of the metaphysicians, and -had a most important influence in establishing an improved -philosophy of science. The indications of such -views we must now endeavour to collect from the -writings of the discoverers of the times preceding the -seventeenth century.</p> - -<p>Some of the earliest of these indications are to be -found in those who dealt with Art rather than with -Science. I have already endeavoured to show that the -advance of the arts which give us a command over the -powers of nature, is generally prior to the formation -of exact and speculative knowledge concerning those -powers. But Art, which is thus the predecessor of -Science, is, among nations of acute and active intellects, -usually its parent. There operates, in such a case, a -speculative spirit, leading men to seek for the reasons -of that which they find themselves able to do. How -slowly, and with what repeated deviations men follow -this leading, when under the influence of a partial and -dogmatical philosophy, the late birth and slow growth -of sound physical theory shows. But at the period of -which we now speak, we find men, at length, proceeding -in obedience to the impulse which thus drives them -from practice to theory;—from an acquaintance with -phenomena to a free and intelligent inquiry concerning -their causes.</p> - -<p><span class="pagenum" id="Page_106">106</span></p> - - -<p><a id="XIV2"></a>2. <i>Leonardo da Vinci.</i>—I have already noted, in -the History of Science, that the Indistinctness of Ideas, -which was long one main impediment to the progress -of science in the middle ages, was first remedied among -architects and engineers. These men, so far at least as -mechanical ideas were concerned, were compelled by -their employments to judge rightly of the relations and -properties of the materials with which they had to deal; -and would have been chastised by the failure of their -works, if they had violated the laws of mechanical truth. -It was not wonderful, therefore, that these laws became -known to <i>them</i> first. We have seen, in the <i>History</i>, -that Leonardo da Vinci, the celebrated painter, who -was also an engineer, is the first writer in whom we -find the true view of the laws of equilibrium of the -lever in the most general case. This artist, a man of -a lively and discursive mind, is led to make some remarks<a name="FNanchor_128" id="FNanchor_128"></a><a href="#Footnote_128" class="fnanchor">[128]</a> -on the formation of our knowledge, which may -show the opinions on that subject that already offered -themselves at the beginning of the sixteenth century<a name="FNanchor_129" id="FNanchor_129"></a><a href="#Footnote_129" class="fnanchor">[129]</a>. -He expresses himself as follows:—"Theory is the general, -Experiments are the soldiers. The interpreter of -the artifices of nature is Experience: she is never deceived. -Our judgment sometimes is deceived, because -it expects effects which Experience refuses to allow." -And again, "We must consult Experience, and vary -the circumstances till we have drawn from them general -rules; for it is she who furnishes true rules. But -of what use, you ask, are these rules; I reply, that -they direct us in the researches of nature and the -operations of art. They prevent our imposing upon -ourselves and others by promising ourselves results -which we cannot obtain.</p> - -<p>"In the study of the sciences which depend on mathematics, -those who do not consult nature but authors, -are not the children of nature, they are only her grand<span class="pagenum" id="Page_107">107</span>children. -She is the true teacher of men of genius. -But see the absurdity of men! They turn up their -noses at a man who prefers to learn from nature herself -rather than from authors who are only her clerks."</p> - -<p>In another place, in reference to a particular case, -he says, "Nature begins from the Reason and ends in -Experience; but for all that, we must take the opposite -course; begin from the Experiment and try to discover -the Reason."</p> - -<p>Leonardo was born forty-six years before Telesius; -yet we have here an estimate of the value of experience -far more just and substantial than the Calabrian school -ever reached. The expressions contained in the above -extracts, are well worthy our notice;—that experience -is never deceived;—that we must vary our experiments, -and draw from them general rules;—that nature -is the original source of knowledge, and books -only a derivative substitute;—with a lively image of -the sons and grandsons of nature. Some of these -assertions have been deemed, and not without reason, -very similar to those made by Bacon a century later. -Yet it is probable that the import of such expressions, -in Leonardo's mind, was less clear and definite than -that which they acquired by the progress of sound philosophy. -When he says that theory is the general -and experiments the soldiers, he probably meant that -theory directs men what experiments to make; and -had not in his mind the notion of a theoretical Idea -ordering and brigading the Facts. When he says that -Experience is the interpreter of Nature, we may recollect, -that in a more correct use of this image, Experience -and Nature are the writing, and the Intellect -of man the interpreter. We may add, that the clear -apprehension of the importance of Experience led, in -this as in other cases, to an unjust depreciation of the -value of what science owed to books. Leonardo would -have made little progress, if he had attempted to master -a complex science, astronomy for instance, by means of -observation alone, without the aid of books.</p> - -<p>But in spite of such criticism, Leonardo's maxims -show extraordinary sagacity and insight; and they<span class="pagenum" id="Page_108">108</span> -appear to us the more remarkable, when we see how -rare such views are for a century after his time.</p> - - -<p><a id="XIV3"></a>3. <i>Copernicus.</i>—For we by no means find, even in -those practical discoverers to whom, in reality, the revolution -in science, and consequently in the philosophy -of science, was due, this prompt and vigorous recognition -of the supreme authority of observation as a ground of -belief; this bold estimate of the probable worthlessness -of traditional knowledge; and this plain assertion of -the reality of theory founded upon experience. Among -such discoverers, Copernicus must ever hold a most -distinguished place. The heliocentric theory of the -universe, established by him with vast labour and -deep knowledge, was, for the succeeding century, the -field of discipline and exertion of all the most active -speculative minds. Men, during that time, proved -their freedom of thought, their hopeful spirit, and -their comprehensive view, by adopting, inculcating, -and following out the philosophy which this theory -suggested. But in the first promulgation of the theory, -in the works of Copernicus himself, we find a far -more cautious and reserved temper. He does not, -indeed, give up the reality of his theory, but he expresses -himself so as to avoid shocking those who might -(as some afterwards did) think it safe to speak of it as -an <i>hypothesis</i> rather than a truth. In his preface addressed -to the Pope<a name="FNanchor_130" id="FNanchor_130"></a><a href="#Footnote_130" class="fnanchor">[130]</a>, after speaking of the difficulties -in the old and received doctrines, by which he was led -to his own theory, he says, "Hence I began to think -of the mobility of the earth; and although the opinion -seemed absurd, yet because I knew that to others before -me this liberty had been conceded, of imagining -any kinds of circles in order to explain the phenomena -of the stars, I thought it would also be readily granted -me, that I might try whether, by supposing the earth -to be in motion, I might not arrive at a better explanation -than theirs, of the revolutions of the celestial -orbs." Nor does he anywhere assert that the seeming<span class="pagenum" id="Page_109">109</span> -absurdity had become a certain truth, or betray any -feeling of triumph over the mistaken belief of his -predecessors. And, as I have elsewhere shown, his -disciples<a name="FNanchor_131" id="FNanchor_131"></a><a href="#Footnote_131" class="fnanchor">[131]</a> indignantly and justly defended him from -the charge of disrespect towards Ptolemy and other -ancient astronomers. Yet Copernicus is far from compromising -the value or evidence of the great truths -which he introduced to general acceptance; and from -sinking in his exposition of his discoveries below the -temper which had led to them. His quotation from -Ptolemy, that "He who is to follow philosophy must -be a freeman in mind," is a grand and noble maxim, -which it well became him to utter.</p> - - -<p><a id="XIV4"></a>4. <i>Fabricius.</i>—In another of the great discoverers -of this period, though employed on a very different subject, -we discern much of the same temper. Fabricius -of Acquapendente<a name="FNanchor_132" id="FNanchor_132"></a><a href="#Footnote_132" class="fnanchor">[132]</a>, the tutor and forerunner of our -Harvey, and one of that illustrious series of Paduan -professors who were the fathers of anatomy<a name="FNanchor_133" id="FNanchor_133"></a><a href="#Footnote_133" class="fnanchor">[133]</a>, exhibits -something of the same respect for antiquity, in the -midst of his original speculations. Thus in a dissertation<a name="FNanchor_134" id="FNanchor_134"></a><a href="#Footnote_134" class="fnanchor">[134]</a> -<i>On the Action of the Joints</i>, he quotes Aristotle's -Mechanical Problems to prove that in all animal -motion there must be some quiescent fulcrum; -and finds merit even in Aristotle's ignorance. "Aristotle," -he says<a name="FNanchor_135" id="FNanchor_135"></a><a href="#Footnote_135" class="fnanchor">[135]</a>, "did not know that motion was -produced by the muscle; and after staggering about -from one supposition to another, at last is compelled -by the facts themselves to recur to an innate spirit, -which, he conceives, is contrasted, and which pulls -and pushes. And here we cannot help admiring the -genius of Aristotle, who, though ignorant of the muscle, -invents something which produces nearly the same -effect as the muscle, namely, contraction and pulling." -He then, with great acuteness, points out the distinction -between Aristotle's opinions, thus favourably -interpreted, and those of Galen. In all this, we see<span class="pagenum" id="Page_110">110</span> -something of the wish to find all truths in the writings -of the ancients, but nothing which materially interferes -with freedom of inquiry. The anatomists have -in all ages and countries been practically employed in -seeking knowledge from observation. Facts have ever -been to them a subject of careful and profitable study; -while the ideas which enter into the wider truths of -the science, are, as we have seen, even still involved -in obscurity, doubt, and contest.</p> - - -<p><a id="XIV5"></a>5. <i>Maurolycus.</i>—Francis Maurolycus of Messana, -whose mathematical works were published in 1575, was -one of the great improvers of the science of optics in his -time. In his Preface to his Treatise on the Spheres, -he speaks of previous writers on the same subject; and -observes that as they have not superseded one another, -they have not rendered it unfit for any one to treat -the subject afresh. "Yet," he says, "it is impossible -to amend the errors of all who have preceded us. -This would be a task too hard for Atlas, although he -supports the heavens. Even Copernicus is tolerated, -who makes the sun to be fixed, and the earth to move -round it in a circle, and who is more worthy of a -whip or a scourge than of a refutation." The mathematicians -and astronomers of that time were not the -persons most sensible of the progress of physical knowledge; -for the basis of their science, and a great part -of its substance, were contained in the writings of the -ancients; and till the time of Kepler, Ptolemy's work -was, very justly, looked upon as including all that was -essential in the science.</p> - - -<p><a id="XIV6"></a>6. <i>Benedetti.</i>—But the writers on Mechanics were -naturally led to present themselves as innovators and -experimenters; for all that the ancients had taught -concerning the doctrine of motion was erroneous; -while those who sought their knowledge from experiment, -were constantly led to new truths. John Baptist -Benedetti, a Venetian nobleman, in 1599, published -his <i>Speculationum Liber</i>, containing, among other -matter, a treatise on Mechanics, in which several of -the Aristotelian errors were refuted. In the Preface -to this Treatise, he says, "Many authors have written<span class="pagenum" id="Page_111">111</span> -much, and with great ability, on Mechanics; but since -nature is constantly bringing to light something either -new, or before unnoticed, I too wished to put forth a -few things hitherto unattempted, or not sufficiently -explained." In the doctrine of motion he distinctly -and at some length condemns and argues against all -the Aristotelian doctrines concerning motion, weight, -and many other fundamental principles of physics. -Benedetti is also an adherent of the Copernican doctrine. -He states<a name="FNanchor_136" id="FNanchor_136"></a><a href="#Footnote_136" class="fnanchor">[136]</a> the enormous velocity which the -heavenly bodies must have, if the earth be the centre -of their motions; and adds, "which difficulty does not -occur according to the beautiful theory of the Samian -Aristarchus, expounded in a divine manner by Nicolas -Copernicus; against which the reasons alleged by Aristotle -are of no weight." Benedetti throughout shows -no want of the courage or ability which were needed -in order to rise in opposition against the dogmas of -the Peripatetics. He does not, however, refer to experiment -in a very direct manner; indeed most of the -facts on which the elementary truths of mechanics -rest, were known and admitted by the Aristotelians; -and therefore could not be adduced as novelties. On -the contrary, he begins with <i>à priori</i> maxims, which -experience would not have confirmed. "Since," he -says<a name="FNanchor_137" id="FNanchor_137"></a><a href="#Footnote_137" class="fnanchor">[137]</a>, "we have undertaken the task of proving that -Aristotle is wrong in his opinions concerning motion, -there are certain absolute truths, the objects of the -intellect known of themselves, which we must lay -down in the first place." And then, as an example of -these truths, he states this: "Any two bodies of equal -size and figure, but of different materials, will have -their natural velocities in the same proportion as their -weights;" where by their natural velocities, he means -the velocities with which they naturally fall downwards.</p> - - -<p><a id="XIV7"></a>7. <i>Gilbert.</i>—The greatest of these practical reformers -of science is our countryman, William Gilbert; if,<span class="pagenum" id="Page_112">112</span> -indeed, in virtue of the clear views of the prospects -which were then opening to science, and of the -methods by which her future progress was to be secured, -while he exemplified those views by physical -discoveries, he does not rather deserve the still higher -praise of being at the same time a theoretical and a -practical reformer. Gilbert's physical researches and -speculations were employed principally upon subjects -on which the ancients had known little or nothing; -and on which therefore it could not be doubtful whether -tradition or observation was the source of knowledge. -Such was magnetism; for the ancients were -barely acquainted with the attractive property of the -magnet. Its polarity, including repulsion as well as -attraction, its direction towards the north, its limited -variation from this direction, its declination from the -horizontal position, were all modern discoveries. Gilbert's -work<a name="FNanchor_138" id="FNanchor_138"></a><a href="#Footnote_138" class="fnanchor">[138]</a> on the magnet and on the magnetism of -the earth, appeared in 1600; and in this, he repeatedly -maintains the superiority of experimental knowledge -over the physical philosophy of the ancients. His -preface opens thus: "Since in making discoveries and -searching out the hidden causes of things, stronger -reasons are obtained from trustworthy experiments -and demonstrable arguments, than from probable conjectures -and the dogmas of those who philosophize in -the usual manner," he has, he says, "endeavoured to -proceed from common magnetical experiments to the -inward constitution of the earth." As I have stated -in the History of Magnetism<a name="FNanchor_139" id="FNanchor_139"></a><a href="#Footnote_139" class="fnanchor">[139]</a>, Gilbert's work contains -all the fundamental facts of that science, so fully -stated, that we have, at this day, little to add to them. -He is not, however, by the advance which he thus -made, led to depreciate the ancients, but only to claim -for himself the same liberty of philosophizing which<span class="pagenum" id="Page_113">113</span> -they had enjoyed<a name="FNanchor_140" id="FNanchor_140"></a><a href="#Footnote_140" class="fnanchor">[140]</a>. "To those ancient and first parents -of philosophy, Aristotle, Theophrastus, Ptolemy, Hippocrates, -Galen, be all due honour; from them it was -that the stream of wisdom has been derived down to -posterity. But our age has discovered and brought -to light many things which they, if they were yet -alive, would gladly embrace. Wherefore we also shall -not hesitate to expound, by probable hypotheses, those -things which by long experience we have ascertained."</p> - -<p>In this work the author not only adopts the Copernican -doctrine of the earth's motion, but speaks<a name="FNanchor_141" id="FNanchor_141"></a><a href="#Footnote_141" class="fnanchor">[141]</a> of -the contrary supposition as utterly absurd, founding -his argument mainly on the vast velocities which such -a supposition requires us to ascribe to the celestial -bodies. Dr. Gilbert was physician to Queen Elizabeth -and to James the First, and died in 1603. Some time -after his death the executors of his brother published -another work of his, <i>De Mundo nostro Sublunari Philosophia -Nova</i>, in which similar views are still more -comprehensively presented. In this he says, "The -two lords of philosophy, Aristotle and Galen, are held -in worship like gods, and rule the schools;—the former -by some destiny obtained a sway and influence -among philosophers, like that of his pupil Alexander -among the kings of the earth;—Galen, with like success, -holds his triumph among the physicians of Europe." -This comparison of Aristotle to Alexander -was also taken hold of by Bacon. Nor is Gilbert an -unworthy precursor of Bacon in the view he gives of -the History of Science, which occupies the first three -chapters of his Philosophy. He traces this history -from "the simplicity and ignorance of the ancients," -through "the fabrication of the fable of the four elements," -to Aristotle and Galen. He mentions with -due disapproval the host of commentators which succeeded, -the alchemists, the "shipwreck of science in -the deluge of the Goths," and the revival of letters -and genius in the time of "our grandfathers." "This<span class="pagenum" id="Page_114">114</span> -later age," he says, "has exploded the Barbarians, and -restored the Greeks and Latins to their pristine grace -and honour. It remains, that if they have written -aught in error, this should be remedied by better and -more productive processes (<i>frugiferis</i> institutis), not -to be contemned for their novelty; (for nothing which -is true is really new, but is perfect from eternity, -though to weak man it may be unknown;) and that -thus Philosophy may bear her fruit." The reader of -Bacon will not fail to recognize, in these references to -"fruit-bearing" knowledge, a similarity of expression -with the <i>Novum Organon</i>.</p> - -<p>Bacon does not appear to me to have done justice to -his contemporary. He nowhere recognizes in the labours -of Gilbert a community of purpose and spirit -with his own. On the other hand, he casts upon him -a reflection which he by no means deserves. In the -<i>Advancement of Learning</i><a name="FNanchor_142" id="FNanchor_142"></a><a href="#Footnote_142" class="fnanchor">[142]</a>, he says, "Another error -is, that men have used to infect their meditations, -opinions, and doctrines, with some conceits which they -have most admired, or some sciences to which they -have most applied; and given all things else a tincture -according to them, utterly untrue and improper.... -So have the alchemists made a philosophy out of a -few experiments of the furnace; and Gilbertus, our -countryman, hath made a philosophy out of the observations -of a loadstone," (in the Latin, philosophiam -etiam e magnete elicuit). And in the same manner -he mentions him in the <i>Novum Organon</i><a name="FNanchor_143" id="FNanchor_143"></a><a href="#Footnote_143" class="fnanchor">[143]</a>, as affording -an example of an empirical kind of philosophy, -which appears to those daily conversant with the experiments, -probable, but to other persons incredible -and empty. But instead of blaming Gilbert for disturbing -and narrowing science by a too constant reference -to magnetical rules, we might rather censure -Bacon, for not seeing how important in all natural -philosophy are those laws of attraction and repulsion -of which magnetical phenomena are the most obvious<span class="pagenum" id="Page_115">115</span> -illustration. We may find ground for such a judgment -in another passage in which Bacon speaks of -Gilbert. In the Second Book<a name="FNanchor_144" id="FNanchor_144"></a><a href="#Footnote_144" class="fnanchor">[144]</a> of the <i>Novum Organon</i>, -having classified motions, he gives, as one kind, -what he calls, in his figurative language, <i>motion for -gain</i>, or <i>motion of need</i>, by which a body shuns heterogeneous, -and seeks cognate bodies. And he adds, -"The Electrical operation, concerning which Gilbert -and others since him have made up such a wonderful -story, is nothing less than the appetite of a body, -which, excited by friction, does not well tolerate the -air, and prefers another tangible body if it be found -near." Bacon's notion of an appetite in the body is -certainly much less philosophical than Gilbert's, who -speaks of light bodies as drawn towards amber by -certain material radii<a name="FNanchor_145" id="FNanchor_145"></a><a href="#Footnote_145" class="fnanchor">[145]</a>; and we might perhaps venture -to say that Bacon here manifests a want of clear -mechanical ideas. Bacon, too, showed his inferior -aptitude for physical research in rejecting the Copernican -doctrine which Gilbert adopted. In the <i>Advancement -of Learning</i><a name="FNanchor_146" id="FNanchor_146"></a><a href="#Footnote_146" class="fnanchor">[146]</a>, suggesting a history of the -opinions of philosophers, he says that he would have -inserted in it even recent theories, as those of Paracelsus; -of Telesius, who restored the philosophy of -Parmenides; or Patricius, who resublimed the fumes -of Platonism; or Gilbert, who brought back the dogmas -of Philolaus. But Bacon quotes<a name="FNanchor_147" id="FNanchor_147"></a><a href="#Footnote_147" class="fnanchor">[147]</a> with pleasure -Gilbert's ridicule of the Peripatetics' definition of -heat. They had said, that heat is that which separates -heterogeneous and unites homogeneous matter; -which, said Gilbert, is as if any one were to define -<i>man</i> as that which sows wheat and plants vines.</p> - -<p>Galileo, another of Gilbert's distinguished contemporaries, -had a higher opinion of him. He says<a name="FNanchor_148" id="FNanchor_148"></a><a href="#Footnote_148" class="fnanchor">[148]</a>, "I -extremely admire and envy this author. I think him -worthy of the greatest praise for the many new and -true observations which he has made, to the disgrace<span class="pagenum" id="Page_116">116</span> -of so many vain and fabling authors; who write, not -from their own knowledge only, but repeat everything -they hear from the foolish and vulgar, without attempting -to satisfy themselves of the same by experience; -perhaps that they may not diminish the size of -their books."</p> - - -<p><a id="XIV8"></a>8. <i>Galileo.</i>—Galileo was content with the active and -successful practice of experimental inquiry; and did -not demand that such researches should be made expressly -subservient to that wider and more ambitious -philosophy, on which the author of the <i>Novum Organon</i> -employed his powers. But still it now becomes our -business to trace those portions of Galileo's views which -have reference to the theory, as well as the practice, -of scientific investigation. On this subject, Galileo did -not think more profoundly, perhaps, than several of his -contemporaries; but in the liveliness of expression and -illustration with which he recommended his opinions -on such topics, he was unrivalled. Writing in the language -of the people, in the attractive form of dialogue, -with clearness, grace, and wit, he did far more than -any of his predecessors had done to render the new -methods, results, and prospects of science familiar to a -wide circle of readers, first in Italy, and soon, all over -Europe. The principal points inculcated by him were -already becoming familiar to men of active and inquiring -minds; such as,—that knowledge was to be sought -from observation, and not from books;—that it was -absurd to adhere to, and debate about, the physical -tenets of Aristotle and the rest of the ancients. On -persons who followed this latter course, Galileo fixed -the epithet of Paper Philosophers<a name="FNanchor_149" id="FNanchor_149"></a><a href="#Footnote_149" class="fnanchor">[149]</a>; because, as he -wrote in a letter to Kepler, this sort of men fancied -that philosophy was to be studied like the <i>Æneid</i> or -<i>Odyssey</i>, and that the true reading of nature was to be -detected by the collation of texts. Nothing so much -shook the authority of the received system of Physics -as the experimental discoveries, directly contradicting<span class="pagenum" id="Page_117">117</span> -it, which Galileo made. By experiment, as I have -elsewhere stated<a name="FNanchor_150" id="FNanchor_150"></a><a href="#Footnote_150" class="fnanchor">[150]</a>, he disproved the Aristotelian doctrine -that bodies fall quickly or slowly in proportion -to their weight. And when he had invented the telescope, -a number of new discoveries of the most striking -kind (the inequalities of the moon's surface, the spots -in the sun, the moon-like phases of Venus, the satellites -of Jupiter, the ring of Saturn,) showed, by the -evidence of the eyes, how inadequate were the conceptions, -and how erroneous the doctrines of the ancients, -respecting the constitution of the universe. How severe -the blow was to the disciples of the ancient schools, we -may judge by the extraordinary forms of defence in -which they tried to intrench themselves. They would -not look through Galileo's glasses; they maintained -that what was seen was an illusion of witchcraft; and -they tried, as Galileo says<a name="FNanchor_151" id="FNanchor_151"></a><a href="#Footnote_151" class="fnanchor">[151]</a>, with logical arguments, as if -with magical incantations, to charm the new planets -out of the sky. No one could be better fitted than -Galileo for such a warfare. His great knowledge, clear -intellect, gaiety, and light irony, (with the advantage -of being in the right,) enabled him to play with his -adversaries as he pleased. Thus when an Aristotelian<a name="FNanchor_152" id="FNanchor_152"></a><a href="#Footnote_152" class="fnanchor">[152]</a> -rejected the discovery of the irregularities in the moon's -surface, because, according to the ancient doctrine, her -form was a perfect sphere, and held that the apparent -cavities were filled with an invisible crystal substance, -Galileo replied, that he had no objection to assent to -this, but that then he should require his adversary in -return to believe that there were on the same surface -invisible crystal mountains ten times as high as -those visible ones which he had actually observed and -measured.</p> - -<p>We find in Galileo many thoughts which have -since become established maxims of modern philosophy. -"Philosophy," he says<a name="FNanchor_153" id="FNanchor_153"></a><a href="#Footnote_153" class="fnanchor">[153]</a>, "is written in that -great book, I mean the Universe, which is constantly -open before our eyes; but it cannot be understood,<span class="pagenum" id="Page_118">118</span> -unless we first know the language and learn the -characters in which it is written." With this thought -he combines some other lively images. One of his -interlocutors says concerning another, "Sarsi perhaps -thinks that philosophy is a book made up of the fancies -of men, like the <i>Iliad</i> or <i>Orlando Furioso</i>, in -which the matter of least importance is, that what -is written be true." And again, with regard to the -system of authority, he says, "I think I discover in -him a firm belief that, in philosophizing, it is necessary -to lean upon the opinion of some celebrated author; -as if our mind must necessarily remain unfruitful and -barren till it be married to another man's reason."—"No," -he says, "the case is not so.—When we have -the decrees of Nature, authority goes for nothing; -reason is absolute<a name="FNanchor_154" id="FNanchor_154"></a><a href="#Footnote_154" class="fnanchor">[154]</a>."</p> - -<p>In the course of Galileo's controversies, questions of -the logic of science came under discussion. Vincenzio -di Grazia objected to a proof from induction which -Galileo adduced, because <i>all</i> the particulars were not -enumerated; to which the latter justly replies<a name="FNanchor_155" id="FNanchor_155"></a><a href="#Footnote_155" class="fnanchor">[155]</a>, that if -induction were required to pass through all the cases, -it would be either useless or impossible;—impossible -when the cases are innumerable; useless when they -have each already been verified, since then the general -proposition adds nothing to our knowledge.</p> - -<p>One of the most novel of the characters which -Science assumes in Galileo's hands is, that she becomes -cautious. She not only proceeds leaning upon Experience, -but she is content to proceed a little way at a -time. She already begins to perceive that she must -rise to the heights of knowledge by many small and -separate steps. The philosopher is desirous to know -much, but resigned to be ignorant for a time of that -which cannot yet be known. Thus when Galileo discovered -the true law of the motion of a falling body<a name="FNanchor_156" id="FNanchor_156"></a><a href="#Footnote_156" class="fnanchor">[156]</a>, -that the velocity increases proportionally to the time -from the beginning of the fall, he did not insist upon<span class="pagenum" id="Page_119">119</span> -immediately assigning the cause of this law. "The -cause of the acceleration of the motions of falling -bodies is not," he says, "a necessary part of the investigation." -Yet the conception of this acceleration, -as the result of the continued action of the force of -gravity upon the falling body, could hardly fail to -suggest itself to one who had formed the idea of force. -In like manner, the truth that the velocities, acquired -by bodies falling down planes of equal heights, are all -equal, was known to Galileo and his disciples, long -before he accounted for it<a name="FNanchor_157" id="FNanchor_157"></a><a href="#Footnote_157" class="fnanchor">[157]</a>, by the principle, apparently -so obvious, that the momentum generated -is as the moving force which generates it. He was -not tempted to rush at once, from an experimental -truth to a universal system. Science had learnt that -she must move step by step; and the gravity of her -pace already indicated her approaching maturity and -her consciousness of the long path which lay before -her.</p> - -<p>But besides the genuine philosophical prudence which -thus withheld Galileo from leaping hastily from one -inference to another, he had perhaps a preponderating -inclination towards facts; and did not feel, so much as -some other persons of his time, the need of reducing -them to ideas. He could bear to contemplate laws of -motion without being urged by an uncontrollable desire -to refer them to conceptions of force.</p> - - -<p><a id="XIV9"></a>9. <i>Kepler.</i>—In this respect his friend Kepler differed -from him; for Kepler was restless and unsatisfied till -he had reduced facts to laws, and laws to causes; and -never acquiesced in ignorance, though he tested with -the most rigorous scrutiny that which presented itself -in the shape of knowledge to fill the void. It may be -seen in the History of Astronomy<a name="FNanchor_158" id="FNanchor_158"></a><a href="#Footnote_158" class="fnanchor">[158]</a> with what perseverance, -energy, and fertility of invention, Kepler -pursued his labours, (enlivened and relieved by the -most curious freaks of fancy,) with a view of discovering -the rules which regulate the motions of the planet<span class="pagenum" id="Page_120">120</span> -Mars. He represents this employment under the image -of a warfare; and describes<a name="FNanchor_159" id="FNanchor_159"></a><a href="#Footnote_159" class="fnanchor">[159]</a> his object to be "to -triumph over Mars, and to prepare for him, as for one -altogether vanquished, tabular prisons and equated -eccentric fetters;" and when, "the enemy, left at -home a despised captive, had burst all the chains of -the equations, and broken forth of the prisons of the -tables;"—when "it was buzzed here and there that the -victory is vain, and that the war is raging anew as -violently as before;"—that is, when the rules which -he had proposed did not coincide with the facts;—he -by no means desisted from his attempts, but "suddenly -sent into the field a reserve of new physical reasonings -on the rout and dispersion of the veterans," that is, -tried new suppositions suggested by such views as he -then entertained of the celestial motions. His efforts -to obtain the formal laws of the planetary motions -resulted in some of the most important discoveries -ever made in astronomy; and if his physical reasonings -were for the time fruitless, this arose only from -the want of that discipline in mechanical ideas which -the minds of mathematicians had still to undergo; for -the great discoveries of Newton in the next generation -showed that, in reality, the next step of the advance -was in this direction. Among all Kepler's fantastical -expressions, the fundamental thoughts were sound and -true; namely, that it was his business, as a physical -investigator, to discover a mathematical rule which -governed and included all the special facts; and that -the rules of the motions of the planets must conform -to some conception of causation.</p> - -<p>The same characteristics,—the conviction of rule and -cause, perseverance in seeking these, inventiveness in -devising hypotheses, love of truth in trying and rejecting -them, and a lively Fancy playing with the -Reason without interrupting her,—appear also in his -work on Optics; in which he tried to discover the -exact law of optical refraction<a name="FNanchor_160" id="FNanchor_160"></a><a href="#Footnote_160" class="fnanchor">[160]</a>. In this undertaking<span class="pagenum" id="Page_121">121</span> -he did not succeed entirely; nor does he profess to -have done so. He ends his numerous attempts by -saying, "Now, reader, you and I have been detained -sufficiently long while I have been attempting to <i>collect -into one fagot</i> the measures of different refractions."</p> - -<p>In this and in other expressions, we see how clearly -he apprehended that <i>colligation of facts</i> which is the -main business of the practical discoverer. And by his -peculiar endowments and habits, Kepler exhibits an -essential portion of this process, which hardly appears -at all in Galileo. In order to bind together facts, -theory is requisite as well as observation,—the cord as -well as the fagots. And the true theory is often, if -not always, obtained by trying several and selecting -the right. Now of this portion of the discoverer's -exertions, Kepler is a most conspicuous example. His -fertility in devising suppositions, his undaunted industry -in calculating the results of them, his entire honesty -and candour in resigning them if these results disagreed -with the facts, are a very instructive spectacle; -and are fortunately exhibited to us in the most lively -manner in his own garrulous narratives. Galileo urged -men by precept as well as example to begin their philosophy -from observation; Kepler taught them by his -practice that they must proceed from observation by -means of hypotheses. The one insisted upon facts; -the other dealt no less copiously with ideas. In the -practical, as in the speculative portion of our history, -this antithesis shows itself; although in the practical -part we cannot have the two elements separated, as in -the speculative we sometimes have.</p> - -<p>In the <i>History of Science</i><a name="FNanchor_161" id="FNanchor_161"></a><a href="#Footnote_161" class="fnanchor">[161]</a>, I have devoted several -pages to the intellectual character of Kepler, inasmuch -as his habit of devising so great a multitude of hypotheses, -so fancifully expressed, had led some writers to -look upon him as an inquirer who transgressed the -most fixed rules of philosophical inquiry. This opinion -has arisen, I conceive, among those who have<span class="pagenum" id="Page_122">122</span> -forgotten the necessity of Ideas as well as Facts for -all theory; or who have overlooked the impossibility -of selecting and explicating our ideas without a good -deal of spontaneous play of the mind. It must, however, -always be recollected that Kepler's genius and -fancy derived all their scientific value from his genuine -and unmingled love of truth. These qualities appeared, -not only in the judgment he passed upon hypotheses, -but also in matters which more immediately concerned -his reputation. Thus when Galileo's discovery of the -telescope disproved several opinions which Kepler had -published and strenuously maintained, he did not hesitate -a moment to retract his assertions and range himself -by the side of Galileo, whom he vigorously supported -in his warfare against those who were incapable -of thus cheerfully acknowledging the triumph of new -facts over their old theories.</p> - - -<p><a id="XIV10"></a>10. <i>Tycho.</i>—There remains one eminent astronomer, -the friend and fellow-labourer of Kepler, whom we must -not separate from him as one of the practical reformers -of science. I speak of Tycho Brahe, who is, I think, -not justly appreciated by the literary world in general, -in consequence of his having made a retrograde step -in that portion of astronomical theory which is most -familiar to the popular mind. Though he adopted the -Copernican view of the motion of the planets about -the sun, he refused to acknowledge the annual and -diurnal motion of the earth. But notwithstanding -this mistake, into which he was led by his interpretation -of Scripture rather than of nature, Tycho must -ever be one of the greatest names in astronomy. In -the philosophy of science also, the influence of what -he did is far from inconsiderable; and especially its -value in bringing into notice these two points:—that -not only are observations the beginning of science, but -that the progress of science may often depend upon -the observer's pursuing his task regularly and carefully -for a long time, and with well devised instruments; -and again, that observed facts offer a <i>succession</i> of -laws which we discover as our observations become -better, and as our theories are better adapted to the<span class="pagenum" id="Page_123">123</span> -observations. With regard to the former point, Tycho's -observatory was far superior to all that had preceded -it<a name="FNanchor_162" id="FNanchor_162"></a><a href="#Footnote_162" class="fnanchor">[162]</a>, not only in the optical, but in the mechanical -arrangements; a matter of almost equal consequence. -And hence it was that his observations inspired in -Kepler that confidence which led him to all his labours -and all his discoveries. "Since," he says<a name="FNanchor_163" id="FNanchor_163"></a><a href="#Footnote_163" class="fnanchor">[163]</a>, "the -divine goodness has given us in Tycho Brahe an exact -observer, from whose observations this error of eight -minutes in the calculations of the Ptolemaic hypothesis -is detected, let us acknowledge and make use of this -gift of God: and since this error cannot be neglected, -these eight minutes alone have prepared the way for -an entire reform of Astronomy, and are to be the -main subject of this work."</p> - -<p>With regard to Tycho's discoveries respecting the -moon, it is to be recollected that besides the first inequality -of the moon's motion, (the <i>equation of the -centre</i>, arising from the elliptical form of her orbit,) -Ptolemy had discovered a second inequality, the <i>evection</i>, -which, as we have observed in the History of -this subject<a name="FNanchor_164" id="FNanchor_164"></a><a href="#Footnote_164" class="fnanchor">[164]</a>, might have naturally suggested the suspicion -that there were still other inequalities. In the -middle ages, however, such suggestions, implying a -constant progress in science, were little attended to; -and, we have seen, that when an Arabian astronomer<a name="FNanchor_165" id="FNanchor_165"></a><a href="#Footnote_165" class="fnanchor">[165]</a> -had really discovered another inequality of the -moon, it was soon forgotten, because it had no place in -the established systems. Tycho not only rediscovered -the lunar inequality, (the <i>variation</i>,) thus once before -won and lost, but also two other inequalities; namely<a name="FNanchor_166" id="FNanchor_166"></a><a href="#Footnote_166" class="fnanchor">[166]</a>, -the <i>change of inclination</i> of the moon's orbit as the -line of nodes moves round, and an inequality in the -motion of the line of nodes. Thus, as I have elsewhere -said, it appeared that the discovery of a rule -is a step to the discovery of deviations from that -rule, which require to be expressed in other rules. It<span class="pagenum" id="Page_124">124</span> -became manifest to astronomers, and through them to -all philosophers, that in the application of theory to -observation, we find, not only the stated phenomena, -for which the theory does account, but also <i>residual -phenomena</i>, which are unaccounted for, and remain -over and above the calculation. And it was seen further, -that these residual phenomena might be, altogether -or in part, exhausted by new theories.</p> - -<p>These were valuable lessons; and the more valuable -inasmuch as men were now trying to lay down maxims -and methods for the conduct of science. A revolution -was not only at hand, but had really taken place, in -the great body of real cultivators of science. The -occasion now required that this revolution should be -formally recognized;—that the new intellectual power -should be clothed with the forms of government;—that -the new philosophical republic should be acknowledged -as a sister state by the ancient dynasties of -Aristotle and Plato. There was needed some great -Theoretical Reformer, to speak in the name of the -Experimental Philosophy; to lay before the world a -declaration of its rights and a scheme of its laws. And -thus our eyes are turned to Francis Bacon, and others -who like him attempted this great office. We quit -those august and venerable names of discoverers, whose -appearance was the prelude and announcement of the -new state of things then opening; and in doing so, we -may apply to them the language which Bacon applies -to himself<a name="FNanchor_167" id="FNanchor_167"></a><a href="#Footnote_167" class="fnanchor">[167]</a>:—</p> - -<p class="center"> -Χαίρετε Κήρυκες Διὸ ς ἄγγελοι ἠδὲ καὶ ἀνδρῶν.<br /> -<br /> -Hail, Heralds, Messengers of Gods and Men!<br /> -</p> - - - -<hr class="chap" /> - -<p><span class="pagenum" id="Page_125">125</span></p> - - -</div><div class="chapter"> -<h2><a name="CHAPTER_XV" id="CHAPTER_XV"></a>CHAPTER XV.<br /> - -<span class="smcap medium">Francis Bacon.</span></h2> - - -<p>(I.) 1. <i>General Remarks.</i>—<span class="smcap">It</span> is a matter of some -difficulty to speak of the character and merits of this -illustrious man, as regards his place in that philosophical -history with which we are here engaged. If we were to -content ourselves with estimating him according to the -office which, as we have just seen, he claims for himself<a name="FNanchor_168" id="FNanchor_168"></a><a href="#Footnote_168" class="fnanchor">[168]</a>, -as merely the harbinger and announcer of a sounder -method of scientific inquiry than that which was recognized -before him, the task would be comparatively -easy. For we might select from his writings those -passages in which he has delivered opinions and pointed -out processes, then novel and strange, but since -confirmed by the experience of actual discoverers, and -by the judgments of the wisest of succeeding philosophers; -and we might pass by, without disrespect, but -without notice, maxims and proposals which have not -been found available for use;—views so indistinct and -vague, that we are even yet unable to pronounce upon -their justice;—and boundless anticipations, dictated by -the sanguine hopes of a noble and comprehensive intellect. -But if we thus reduce the philosophy of -Bacon to that portion which the subsequent progress -of science has rigorously verified, we shall have to pass -over many of those declarations which have excited -most notice in his writings, and shall lose sight of -many of those striking thoughts which his admirers -most love to dwell upon. For he is usually spoken<span class="pagenum" id="Page_126">126</span> -of, at least in this country, as a teacher who not only -commenced, but in a great measure completed, the -Philosophy of Induction. He is considered, not only -as having asserted some general principles, but laid -down the special rules of scientific investigation; as -not only one of the Founders, but the supreme Legislator -of the modern Republic of Science; not only the -Hercules who slew the monsters that obstructed the -earlier traveller, but the Solon who established a constitution -fitted for all future time.</p> - - -<p><a id="XV2"></a>2. Nor is it our purpose to deny that of such -praise he deserves a share which, considering the period -at which he lived, is truly astonishing. But it is -necessary for us in this place to discriminate and select -that portion of his system which, bearing upon <i>physical</i> -science, has since been confirmed by the actual history -of science. Many of Bacon's most impressive and captivating -passages contemplate the extension of the new -methods of discovering truth to intellectual, to moral, -to political, as well as to physical science. And how -far, and how, the advantages of the inductive method -may be secured for those important branches of speculation, -it will at some future time be a highly interesting -task to examine. But our plan requires us at -present to omit the consideration of these; for our -purpose is to learn what the genuine course of the formation -of science is, by tracing it in those portions of -human knowledge, which, by the confession of all, are -most exact, most certain, most complete. Hence we -must here deny ourselves the dignity and interest -which float about all speculations in which the great -moral and political concerns of men are involved. It -cannot be doubted that the commanding position which -Bacon occupies in men's estimation arises from his -proclaiming a reform in philosophy of so comprehensive -a nature;—a reform which was to infuse a new -spirit into every part of knowledge. Physical Science -has tranquilly and noiselessly adopted many of his -suggestions; which were, indeed, her own natural impulses, -not borrowed from him; and she is too deeply -and satisfactorily absorbed in contemplating her re<span class="pagenum" id="Page_127">127</span>sults, -to talk much about the methods of obtaining -them which she has thus instinctively pursued. But -the philosophy which deals with mind, with manners, -with morals, with polity, is conscious still of much obscurity -and perplexity; and would gladly borrow aid -from a system in which aid is so confidently promised. -The aphorisms and phrases of the <i>Novum Organon</i> are -far more frequently quoted by metaphysical, ethical, -and even theological writers, than they are by the authors -of works on physics.</p> - - -<p><a id="XV3"></a>3. Again, even as regards physics, Bacon's fame -rests upon something besides the novelty of the maxims -which he promulgated. That a revolution in the -method of scientific research was going on, all the -greatest physical investigators of the sixteenth century -were fully aware, as we have shown in the last chapter. -But their writings conveyed this conviction to -the public at large somewhat slowly. Men of letters, -men of the world, men of rank, did not become familiar -with the abstruse works in which these views -were published; and above all, they did not, by such -occasional glimpses as they took of the state of physical -science, become aware of the magnitude and consequences -of this change. But Bacon's lofty eloquence, -wide learning, comprehensive views, bold pictures of -the coming state of things, were fitted to make men -turn a far more general and earnest gaze upon the -passing change. When a man of his acquirements, of -his talents, of his rank and position, of his gravity and -caution, poured forth the strongest and loftiest expressions -and images which his mind could supply, in -order to depict the "Great Instauration" which he -announced;—in order to contrast the weakness, the -blindness, the ignorance, the wretchedness, under -which men had laboured while they followed the long -beaten track, with the light, the power, the privileges, -which they were to find in the paths to which he -pointed;—it was impossible that readers of all classes -should not have their attention arrested, their minds -stirred, their hopes warmed; and should not listen -with wonder and with pleasure to the strains of<span class="pagenum" id="Page_128">128</span> -prophetic eloquence in which so great a subject was -presented. And when it was found that the prophecy -was verified; when it appeared that an immense -change in the methods of scientific research really <i>had</i> -occurred;—that vast additions to man's knowledge -and power had been acquired, in modes like those -which had been spoken of;—that further advances -might be constantly looked for;—and that a progress, -seemingly boundless, was going on in the direction in -which the seer had thus pointed;—it was natural that -men should hail him as the leader of the revolution; -that they should identify him with the event which he -was the first to announce; that they should look upon -him as the author of that which he had, as they perceived, -so soon and so thoroughly comprehended.</p> - - -<p><a id="XV4"></a>4. For we must remark, that although (as we -have seen) he was not the only, nor the earliest -writer, who declared that the time was come for such -a change, he not only proclaimed it more emphatically, -but understood it, in its general character, much more -exactly, than any of his contemporaries. Among the -maxims, suggestions and anticipations which he threw -out, there were many of which the wisdom and the -novelty were alike striking to his immediate successors;—there -are many which even now, from time to -time, we find fresh reason to admire, for their acuteness -and justice. Bacon stands far above the herd of -loose and visionary speculators who, before and about -his time, spoke of the establishment of new philosophies. -If we must select some one philosopher as the -Hero of the revolution in scientific method, beyond all -doubt Francis Bacon must occupy the place of honour.</p> - -<p>We shall, however, no longer dwell upon these -general considerations, but shall proceed to notice some -of the more peculiar and characteristic features of -Bacon's philosophy; and especially those views, which, -occurring for the first time in his writings, have been -fully illustrated and confirmed by the subsequent progress -of science, and have become a portion of the permanent -philosophy of our times.</p> - - -<p>(II.) <a id="XV5"></a>5. <i>A New Era announced.</i>—The first great<span class="pagenum" id="Page_129">129</span> -feature which strikes us in Bacon's philosophical views -is that which we have already noticed;—his confident -and emphatic announcement of a <i>New Era</i> in the progress -of science, compared with which the advances of -former times were poor and trifling. This was with -Bacon no loose and shallow opinion, taken up on light -grounds and involving only vague, general notions. -He had satisfied himself of the justice of such a view -by a laborious course of research and reflection. In -1605, at the age of forty-four, he published his Treatise -of the <i>Advancement of Learning</i>, in which he -takes a comprehensive and spirited survey of the condition -of all branches of knowledge which had been -cultivated up to that time. This work was composed -with a view to that reform of the existing philosophy -which Bacon always had before his eyes; and in the -Latin edition of his works, forms the First Part of the -<i>Instauratio Magna</i>. In the Second Part of the Instauratio, -the <i>Novum Organon</i>, published in 1620, he -more explicitly and confidently states his expectations -on this subject. He points out how slightly and feebly -the examination of nature had been pursued up to his -time, and with what scanty fruit. He notes the indications -of this in the very limited knowledge of the -Greeks who had till then been the teachers of Europe, -in the complaints of authors concerning the subtilty -and obscurity of the secrets of nature, in the dissensions -of sects, in the absence of useful inventions resulting -from theory, in the fixed form which the sciences -had retained for two thousand years. Nor, he -adds<a name="FNanchor_169" id="FNanchor_169"></a><a href="#Footnote_169" class="fnanchor">[169]</a>, is this wonderful; for how little of his thought -and labour has man bestowed upon science! Out of -twenty-five centuries scarce six have been favourable -to the progress of knowledge. And even in those -favoured times, natural philosophy received the smallest -share of man's attention; while the portion so -given was marred by controversy and dogmatism; and -even those who have bestowed a little thought upon<span class="pagenum" id="Page_130">130</span> -this philosophy, have never made it their main study, -but have used it as a passage or drawbridge to serve -other objects. And thus, he says, the great Mother of -the Sciences is thrust down with indignity to the offices -of a handmaid; is made to minister to the labours -of medicine or mathematics, or to give the first preparatory -tinge to the immature minds of youth. For -these and similar considerations of the errors of past -time, he draws hope for the future, employing the -same argument which Demosthenes uses to the Athenians: -"That which is worst in the events of the past, -is the best as a ground of trust in the future. For -if you had done all that became you, and still had -been in this condition, your case might be desperate; -but since your failure is the result of your own mistakes, -there is good hope that, correcting the error of -your course, you may reach a prosperity yet unknown -to you."</p> - - -<p>(III.) <a id="XV6"></a>6. <i>A change of existing Method.</i>—All Bacon's -hope of improvement indeed was placed in an entire -<i>change of the Method</i> by which science was pursued; -and the boldness, and at the same time (the then -existing state of science being considered), the definiteness -of his views of the change that was requisite, are -truly remarkable.</p> - -<p>That all knowledge must begin with observation, is -one great principle of Bacon's philosophy; but I hardly -think it necessary to notice the inculcation of this -maxim as one of his main services to the cause of sound -knowledge, since it had, as we have seen, been fully -insisted upon by others before him, and was growing -rapidly into general acceptance without his aid. But -if he was not the first to tell men that they must collect -their knowledge from observation, he had no rival -in his peculiar office of teaching them <i>how</i> science -must thus be gathered from experience.</p> - -<p>It appears to me that by far the most extraordinary -parts of Bacon's works are those in which, with extreme -earnestness and clearness, he insists upon a <i>graduated -and successive induction</i>, as opposed to a hasty transit -from special facts to the highest generalizations. The<span class="pagenum" id="Page_131">131</span> -nineteenth Axiom of the First Book of the <i>Novum -Organon</i> contains a view of the nature of true science -most exact and profound, and, so far as I am aware, -at the time perfectly new. "There are two ways, and -can only be two, of seeking and finding truth. The one, -from sense and particulars, takes a flight to the most -general axioms, and from those principles and their -truth, settled once for all, invents and judges of intermediate -axioms. The other method collects axioms -from sense and particulars, ascending <i>continuously and -by degrees</i>, so that in the end it arrives at the most -general axioms; this latter way is the true one, but -hitherto untried."</p> - -<p>It is to be remarked, that in this passage Bacon -employs the term <i>axioms</i> to express any propositions -collected from facts by induction, and thus fitted to -become the starting-point of deductive reasonings. -How far propositions so obtained may approach to the -character of axioms in the more rigorous sense of the -term, we have already in some measure examined; -but that question does not here immediately concern -us. The truly remarkable circumstance is to find this -recommendation of a continuous advance from observation, -by limited steps, through successive gradations of -generality, given at a time when speculative men in -general had only just begun to perceive that they must -begin their course from experience in some way or -other. How exactly this description represents the -general structure of the soundest and most comprehensive -physical theories, all persons who have studied -the progress of science up to modern times can bear -testimony; but perhaps this structure of science cannot -in any other way be made so apparent as by those -Tables of successive generalizations in which we have -exhibited the history and constitution of some of the -principal physical sciences, in the Chapter of a preceding -work which treats of the Logic of Induction. -And the view which Bacon thus took of the true progress -of science was not only new, but, so far as I am -aware, has never been adequately illustrated up to the -present day.</p> - -<p><span class="pagenum" id="Page_132">132</span></p> - - -<p><a id="XV7"></a>7. It is true, as I observed in the last chapter, that -Galileo had been led to see the necessity, not only of -proceeding from experience in the pursuit of knowledge, -but of proceeding cautiously and gradually; and -he had exemplified this rule more than once, when, -having made one step in discovery, he held back his -foot, for a time, from the next step, however tempting. -But Galileo had not reached this wide and commanding -view of the successive subordination of many steps, -all leading up at last to some wide and simple general -truth. In catching sight of this principle, and in -ascribing to it its due importance, Bacon's sagacity, so -far as I am aware, wrought unassisted and unrivalled.</p> - - -<p><a id="XV8"></a>8. Nor is there any wavering or vagueness in Bacon's -assertion of this important truth. He repeats it over -and over again; illustrates it by a great number of -the most lively metaphors and emphatic expressions. -Thus he speaks of the successive <i>floors</i> (<i>tabulata</i>) of -induction; and speaks of each science as a <i>pyramid</i><a name="FNanchor_170" id="FNanchor_170"></a><a href="#Footnote_170" class="fnanchor">[170]</a> -which has observation and experience for its basis. -No images can better exhibit the relation of general -and particular truths, as our own Inductive Tables -may serve to show.</p> - - -<p>(IV.) <a id="XV9"></a>9. <i>Comparison of the New and Old Method.</i> -Again; not less remarkable is his contrasting this -true Method of Science (while it was almost, as he -says, yet untried) with the ancient and <i>vicious Method</i>, -which began, indeed, with facts of observation, but -rushed at once and with no gradations, to the most -general principles. For this was the course which had -been actually followed by all those speculative reformers -who had talked so loudly of the necessity of -beginning our philosophy from experience. All these -men, if they attempted to frame physical doctrines at -all, had caught up a few facts of observation, and had<span class="pagenum" id="Page_133">133</span> -erected a universal theory upon the suggestions which -these offered. This process of illicit generalization, or, -as Bacon terms it, Anticipation of Nature (<i>anticipatio -naturæ</i>), in opposition to the Interpretation of Nature, -he depicts with singular acuteness, in its character and -causes. "These two ways," he says<a name="FNanchor_171" id="FNanchor_171"></a><a href="#Footnote_171" class="fnanchor">[171]</a> "both begin from -sense and particulars; but their discrepancy is immense. -The one merely skims over experience and particulars -in a cursory transit; the other deals with them in a -due and orderly manner. The one, at its very outset, -frames certain general abstract principles, but useless; -the other gradually rises to those principles which have -a real existence in nature."</p> - -<p>"The former path," he adds<a name="FNanchor_172" id="FNanchor_172"></a><a href="#Footnote_172" class="fnanchor">[172]</a>, "that of illicit and -hasty generalization, is one which the intellect follows -when abandoned to its own impulse; and this it does -from the requisitions of logic. For the mind has a -yearning which makes it dart forth to generalities, -that it may have something to rest in; and after a -little dallying with experience, becomes weary of it; -and all these evils are augmented by logic, which requires -these generalities to make a show with in its -disputations."</p> - -<p>"In a sober, patient, grave intellect," he further adds, -"the mind, by its own impulse, (and more especially if -it be not impelled by the sway of established opinions) -attempts in some measure that other and true way, of -gradual generalization; but this it does with small -profit; for the intellect, except it be regulated and -aided, is a faculty of unequal operation, and altogether -unapt to master the obscurity of things."</p> - -<p>The profound and searching wisdom of these remarks -appears more and more, as we apply them to the various -attempts which men have made to obtain knowledge; -when they begin with the contemplation of a -few facts, and pursue their speculations, as upon most -subjects they have hitherto generally done; for almost -all such attempts have led immediately to some process<span class="pagenum" id="Page_134">134</span> -of illicit generalization, which introduces an interminable -course of controversy. In the physical sciences, -however, we have the further inestimable advantage -of seeing the other side of the contrast exemplified: -for many of them, as our inductive Tables show us, -have gone on according to the most rigorous conditions -of gradual and successive generalization; and in consequence -of this circumstance in their constitution, -possess, in each part of their structure, a solid truth, -which is always ready to stand the severest tests of -reasoning and experiment.</p> - -<p>We see how justly and clearly Bacon judged concerning -the mode in which facts are to be employed in -the construction of science. This, indeed, has ever -been deemed his great merit: insomuch that many -persons appear to apprehend the main substance of -his doctrine to reside in the maxim that facts of observation, -and such facts alone, are the essential elements -of all true science.</p> - - -<p>(V.) <a id="XV10"></a>10. <i>Ideas are necessary.</i>—Yet we have endeavoured -to establish the doctrine that facts are -but one of two ingredients of knowledge both equally -necessary;—that <i>Ideas</i> are no less indispensable than -facts themselves; and that except these be duly unfolded -and applied, facts are collected in vain. Has -Bacon then neglected this great portion of his subject? -Has he been led by some partiality of view, or some -peculiarity of circumstances, to leave this curious and -essential element of science in its pristine obscurity? -Was he unaware of its interest and importance?</p> - -<p>We may reply that Bacon's philosophy, in its effect -upon his readers in general, does <i>not</i> give due weight -or due attention to the ideal element of our knowledge. -He is considered as peculiarly and eminently -the asserter of the value of experiment and observation. -He is always understood to belong to the experiential, -as opposed to the ideal school. He is held -up in contrast to Plato and others who love to dwell -upon that part of knowledge which has its origin in -the intellect of man.</p> - -<p><a id="XV11"></a>11. Nor can it be denied that Bacon has, in the<span class="pagenum" id="Page_135">135</span> -finished part of his <i>Novum Organon</i>, put prominently -forwards the necessary dependence of all our knowledge -upon Experience, and said little of its dependence, -equally necessary, upon the Conceptions which -the intellect itself supplies. It will appear, however, -on a close examination, that he was by no means insensible -or careless of this internal element of all connected -speculation. He held the balance, with no -partial or feeble hand, between phenomena and ideas. -He urged the Colligation of Facts, but he was not the -less aware of the value of the Explication of Conceptions.</p> - -<p><a id="XV12"></a>12. This appears plainly from some remarkable -Aphorisms in the <i>Novum Organon</i>. Thus, in noticing -the causes of the little progress then made by science<a name="FNanchor_173" id="FNanchor_173"></a><a href="#Footnote_173" class="fnanchor">[173]</a>, -he states this:—"In the current Notions, all is unsound, -whether they be logical or physical. <i>Substance</i>, -<i>quality</i>, <i>action</i>, <i>passion</i>, even <i>being</i>, are not good Conceptions; -still less are <i>heavy</i>, <i>light</i>, <i>dense</i>, <i>rare</i>, <i>moist</i>, -<i>dry</i>, <i>generation</i>, <i>corruption</i>, <i>attraction</i>, <i>repulsion</i>, <i>element</i>, -<i>matter</i>, <i>form</i>, and others of that kind; all are -fantastical and ill-defined." And in his attempt to -exemplify his own system, he hesitates<a name="FNanchor_174" id="FNanchor_174"></a><a href="#Footnote_174" class="fnanchor">[174]</a> in accepting -or rejecting the notions of <i>elementary</i>, <i>celestial</i>, <i>rare</i>, -as belonging to fire, since, as he says, they are vague -and ill-defined notions (<i>notiones vagæ nec bene terminatæ</i>). -In that part of his work which appears to be -completed, there is not, so far as I have noticed, any -attempt to fix and define any notions thus complained -of as loose and obscure. But yet such an undertaking -appears to have formed part of his plan; and in the -<i>Abecedarium Naturæ</i><a name="FNanchor_175" id="FNanchor_175"></a><a href="#Footnote_175" class="fnanchor">[175]</a>, which consists of the heads of -various portions of his great scheme, marked by letters -of the alphabet, we find the titles of a series of dissertations -"On the Conditions of Being," which must -have had for their object the elucidation of divers -Notions essential to science, and which would have<span class="pagenum" id="Page_136">136</span> -been contributions to the Explication of Conceptions, -such as we have attempted in a former part of this -work. Thus some of the subjects of these dissertations -are;—Of Much and Little;—Of Durable and -Transitory;—Of Natural and Monstrous;—Of Natural -and Artificial. When the philosopher of induction -came to discuss these, considered as <i>conditions of existence</i>, -he could not do otherwise than develope, limit, -methodize, and define the Ideas involved in these -Notions, so as to make them consistent with themselves, -and a fit basis of demonstrative reasoning. His -task would have been of the same nature as ours has -been, in that part of this work which treats of the -Fundamental Ideas of the various classes of sciences.</p> - - -<p><a id="XV13"></a>13. Thus Bacon, in his speculative philosophy, -took firmly hold of both the handles of science; and -if he had completed his scheme, would probably have -given due attention to Ideas, no less than to Facts, as -an element of our knowledge; while in his view of -the general method of ascending from facts to principles, -he displayed a sagacity truly wonderful. But -we cannot be surprised, that in attempting to exemplify -the method which he recommended, he should -have failed. For the method could be exemplified -only by some important discovery in physical science; -and great discoveries, even with the most perfect -methods, do not come at command. Moreover, although -the general structure of his scheme was correct, -the precise import of some of its details could -hardly be understood, till the actual progress of science -had made men somewhat familiar with the kind of -steps which it included.</p> - - -<p>(VI.) <a id="XV14"></a>14. <i>Bacon's Example.</i>—Accordingly, Bacon's -<i>Inquisition into the Nature of Heat</i>, which is given in -the Second Book of the <i>Novum Organon</i> as an example -of the mode of interrogating Nature, cannot be -looked upon otherwise than as a complete failure. -This will be evident if we consider that, although the -exact nature of heat is still an obscure and controverted -matter, the science of Heat now consists of -many important truths; and that to none of these<span class="pagenum" id="Page_137">137</span> -truths is there any approximation in Bacon's essay. -From his process he arrives at this, as the "forma or -true definition" of heat;—"that it is an expansive, -restrained motion, modified in certain ways, and exerted -in the smaller particles of the body." But the -steps by which the science of Heat really advanced -were (as may be seen in the history<a name="FNanchor_176" id="FNanchor_176"></a><a href="#Footnote_176" class="fnanchor">[176]</a> of the subject) -these;—The discovery of a <i>measure</i> of heat or temperature -(the thermometer); the establishment of the -<i>laws</i> of conduction and radiation; of the <i>laws</i> of specific -heat, latent heat, and the like. Such steps have -led to Ampère's <i>hypothesis</i><a name="FNanchor_177" id="FNanchor_177"></a><a href="#Footnote_177" class="fnanchor">[177]</a>, that heat consists in the -vibrations of an imponderable fluid; and to Laplace's -<i>hypothesis</i>, that temperature consists in the internal -radiation of such a fluid. These hypotheses cannot -yet be said to be even probable; but at least they are -so modified as to include some of the preceding laws -which are firmly established; whereas Bacon's hypothetical -motion includes no laws of phenomena, explains -no process, and is indeed itself an example of -illicit generalization.</p> - - -<p><a id="XV15"></a>15. One main ground of Bacon's ill fortune in this -undertaking appears to be, that he was not aware of -an important maxim of inductive science, that we -must first obtain the <i>measure</i> and ascertain the <i>laws</i> -of phenomena, before we endeavour to discover their -<i>causes</i>. The whole history of thermotics up to the -present time has been occupied with the <i>former</i> step, -and the task is not yet completed: it is no wonder, -therefore, that Bacon failed entirely, when he so prematurely -attempted the <i>second</i>. His sagacity had -taught him that the progress of science must be gradual; -but it had not led him to judge adequately how -gradual it must be, nor of what different kinds of -inquiries, taken in due order, it must needs consist, -in order to obtain success.</p> - -<p>Another mistake, which could not fail to render -it unlikely that Bacon should really exemplify his<span class="pagenum" id="Page_138">138</span> -precepts by any actual advance in science, was, that -he did not justly appreciate the sagacity, the inventive -genius, which all discovery requires. He conceived -that he could supersede the necessity of such peculiar -endowments. "Our method of discovery in science," -he says<a name="FNanchor_178" id="FNanchor_178"></a><a href="#Footnote_178" class="fnanchor">[178]</a>, "is of such a nature, that there is not much -left to acuteness and strength of genius, but all degrees -of genius and intellect are brought nearly to the -same level." And he illustrates this by comparing -his method to a pair of compasses, by means of which -a person with no manual skill may draw a perfect -circle. In the same spirit he speaks of proceeding by -<i>due rejections</i>; and appears to imagine that when we -have obtained a collection of facts, if we go on successively -rejecting what is false, we shall at last find -that we have, left in our hands, that scientific truth -which we seek. I need not observe how far this view -is removed from the real state of the case. The necessity -of a <i>conception</i> which must be furnished by the -mind in order to bind together the facts, could hardly -have escaped the eye of Bacon, if he had cultivated -more carefully the ideal side of his own philosophy. -And any attempts which he could have made to construct -such conceptions by mere rule and method, -must have ended in convincing him that nothing but -a peculiar inventive talent could supply that which -was thus not contained in the facts, and yet was needed -for the discovery.</p> - - -<p>(VII.) <a id="XV16"></a>16. <i>His Failure.</i>—Since Bacon, with all his -acuteness, had not divined circumstances so important -in the formation of science, it is not wonderful that -his attempt to reduce this process to a <i>Technical Form</i> -is of little value. In the first place, he says<a name="FNanchor_179" id="FNanchor_179"></a><a href="#Footnote_179" class="fnanchor">[179]</a>, we -must prepare a natural and experimental history, good -and sufficient; in the next place, the instances thus -collected are to be arranged in Tables in some orderly -way; and then we must apply a legitimate and true -induction. And in his example<a name="FNanchor_180" id="FNanchor_180"></a><a href="#Footnote_180" class="fnanchor">[180]</a>, he first collects a<span class="pagenum" id="Page_139">139</span> -great number of cases in which heat appears under -various circumstances, which he calls "a Muster of -Instances before the intellect," (<i>comparentia instantiarum -ad intellectum</i>,) or a <i>Table of the Presence</i> of -the thing sought. He then adds a <i>Table of its Absence</i> -in proximate cases, containing instances where -heat does not appear; then a <i>Table of Degrees</i>, in -which it appears with greater or less intensity. He -then adds<a name="FNanchor_181" id="FNanchor_181"></a><a href="#Footnote_181" class="fnanchor">[181]</a>, that we must try to exclude several obvious -suppositions, which he does by reference to some -of the instances he has collected; and this step he calls -the <i>Exclusive</i>, or the <i>Rejection of Natures</i>. He then -observes, (and justly,) that whereas truth emerges more -easily from error than from confusion, we may, after -this preparation, <i>give play to the intellect</i>, (fiat permissio -intellectus,) and make an attempt at induction, -liable afterwards to be corrected; and by this step, -which he terms his <i>First Vindemiation</i>, or <i>Inchoate -Induction</i>, he is led to the proposition concerning -heat, which we have stated above.</p> - - -<p><a id="XV17"></a>17. In all the details of his example he is unfortunate. -By proposing to himself to examine at once -into the <i>nature</i> of heat, instead of the laws of special -classes of phenomena, he makes, as we have said, a -fundamental mistake; which is the less surprising -since he had before him so few examples of the right -course in the previous history of science. But further, -his collection of instances is very loosely brought -together; for he includes in his list the <i>hot</i> taste of -aromatic plants, the <i>caustic</i> effects of acids, and many -other facts which cannot be ascribed to heat without a -studious laxity in the use of the word. And when he -comes to that point where he permits his intellect its -range, the conception of <i>motion</i> upon which it at once -fastens, appears to be selected with little choice or -skill, the suggestion being taken from flame<a name="FNanchor_182" id="FNanchor_182"></a><a href="#Footnote_182" class="fnanchor">[182]</a>, boiling -liquids, a blown fire, and some other cases. If from -such examples we could imagine heat to be motion, we<span class="pagenum" id="Page_140">140</span> -ought at least to have some gradation to cases of heat -where no motion is visible, as in a red-hot iron. It -would seem that, after a large collection of instances -had been looked at, the intellect, even in its first attempts, -ought not to have dwelt upon such an hypothesis -as this.</p> - - -<p><a id="XV18"></a>18. After these steps, Bacon speaks of several -classes of instances which, singling them out of the -general and indiscriminate collection of facts, he terms -<i>Instances with Prerogative</i>: and these he points out as -peculiar aids and guides to the intellect in its task. -These Instances with Prerogative have generally been -much dwelt upon by those who have commented on -the <i>Novum Organon</i>. Yet, in reality, such a classification, -as has been observed by one of the ablest -writers of the present day<a name="FNanchor_183" id="FNanchor_183"></a><a href="#Footnote_183" class="fnanchor">[183]</a>, is of little service in the -task of induction. For the instances are, for the most -part, classed, not according to the ideas which they involve, -or to any obvious circumstance in the facts of -which they consist, but according to the extent or -manner of their influence upon the inquiry in which -they are employed. Thus we have Solitary Instances, -Migrating Instances, Ostensive Instances, Clandestine -Instances, so termed according to the degree in which -they exhibit, or seem to exhibit, the property whose -nature we would examine. We have Guide-Post Instances, -(<i>Instantiæ Crucis</i>,) Instances of the Parted -Road, of the Doorway, of the Lamp, according to the -guidance they supply to our advance. Such a classification -is much of the same nature as if, having to -teach the art of building, we were to describe tools -with reference to the amount and place of the work -which they must do, instead of pointing out their construction -and use:—as if we were to inform the pupil -that we must have tools for lifting a stone up, tools -for moving it sideways, tools for laying it square, -tools for cementing it firmly. Such an enumeration of -ends would convey little instruction as to the means.<span class="pagenum" id="Page_141">141</span> -Moreover, many of Bacon's classes of instances are -vitiated by the assumption that the "form," that is, -the general law and cause of the property which is the -subject of investigation, is to be looked for directly in -the instances; which, as we have seen in his inquiry -concerning heat, is a fundamental error.</p> - - -<p><a id="XV19"></a>19. Yet his phraseology in some cases, as in the -<i>instantia crucis</i>, serves well to mark the place which -certain experiments hold in our reasonings: and many -of the special examples which he gives are full of -acuteness and sagacity. Thus he suggests swinging a -pendulum in a mine, in order to determine whether -the attraction of the earth arises from the attraction of -its parts; and observing the tide at the same moment -in different parts of the world, in order to ascertain -whether the motion of the water is expansive or progressive; -with other ingenious proposals. These marks -of genius may serve to counterbalance the unfavourable -judgment of Bacon's aptitude for physical science -which we are sometimes tempted to form, in consequence -of his false views on other points; as his rejection -of the Copernican system, and his undervaluing -Gilbert's magnetical speculations. Most of these errors -arose from a too ambitious habit of intellect, which -would not be contented with any except very wide -and general truths; and from an indistinctness of -mechanical, and perhaps, in general, of mathematical -ideas:—defects which Bacon's own philosophy was directed -to remedy, and which, in the progress of time, -it has remedied in others.</p> - - -<p><a id="XV20"></a>(VIII.) 20. <i>His Idols.</i>—Having thus freely given -our judgment concerning the most exact and definite -portion of Bacon's precepts, it cannot be necessary for -us to discuss at any length the value of those more -vague and general <i>Warnings</i> against prejudice and partiality, -against intellectual indolence and presumption, -with which his works abound. His advice and exhortations -of this kind are always expressed with energy -and point, often clothed in the happiest forms of imagery; -and hence it has come to pass, that such passages -are perhaps more familiar to the general reader<span class="pagenum" id="Page_142">142</span> -than any other part of his writings. Nor are Bacon's -counsels without their importance, when we have to -do with those subjects in which prejudice and partiality -exercise their peculiar sway. Questions of politics -and morals, of manners, taste, or history, cannot -be subjected to a scheme of rigorous induction; and -though on such matters we venture to assert general -principles, these are commonly obtained with some degree -of insecurity, and depend upon special habits of -thought, not upon mere logical connexion. Here, -therefore, the intellect may be perverted, by mixing, -with the pure reason, our gregarious affections, or our -individual propensities; the false suggestions involved -in language, or the imposing delusions of received -theories. In these dim and complex labyrinths of -human thought, <i>the Idol of the Tribe</i>, or <i>of the Den</i>, <i>of -the Forum</i>, or <i>of the Theatre</i>, may occupy men's minds -with delusive shapes, and may obscure or pervert their -vision of truth. But in that Natural Philosophy with -which we are here concerned, there is little opportunity -for such influences. As far as a physical theory -is completed through all the steps of a just induction, -there is a clear daylight diffused over it which leaves -no lurking-place for prejudice. Each part can be examined -separately and repeatedly; and the theory is -not to be deemed perfect till it will bear the scrutiny -of all sound minds alike. Although, therefore, Bacon, -by warning men against the idols of fallacious images -above spoken of, may have guarded them from dangerous -error, his precepts have little to do with Natural -Philosophy: and we cannot agree with him when he -says<a name="FNanchor_184" id="FNanchor_184"></a><a href="#Footnote_184" class="fnanchor">[184]</a>, that the doctrine concerning these idols bears -the same relation to the interpretation of nature as -the doctrine concerning sophistical paralogisms bears -to common logic.</p> - - -<p><a id="XV21"></a>(IX.) 21. <i>His Aim, Utility.</i>—There is one very -prominent feature in Bacon's speculations which we -must not omit to notice; it is a leading and constant<span class="pagenum" id="Page_143">143</span> -object with him to apply his knowledge to <i>Use</i>. The -insight which he obtains into nature, he would employ -in commanding nature for the service of man. He -wishes to have not only principles but works. The -phrase which best describes the aim of his philosophy -is his own<a name="FNanchor_185" id="FNanchor_185"></a><a href="#Footnote_185" class="fnanchor">[185]</a>, "Ascendendo ad <i>axiomata</i>, descendendo -ad <i>opera</i>." This disposition appears in the first aphorism -of the <i>Novum Organon</i>, and runs through the -work. "Man, the <i>minister</i> and interpreter of nature, -<i>does</i> and understands, so far as he has, in fact or in -thought, observed the course of nature; and he cannot -know or <i>do</i> more than this." It is not necessary for -us to dwell much upon this turn of mind; for the -whole of our present inquiry goes upon the supposition -that an acquaintance with the laws of nature is -worth our having for its own sake. It may be universally -true, that Knowledge is Power; but we have -to do with it not as Power, but as Knowledge. It is -the formation of Science, not of Art, with which we -are here concerned. It may give a peculiar interest -to the history of science, to show how it constantly -tends to provide better and better for the wants and -comforts of the body; but <i>that</i> is not the interest -which engages us in our present inquiry into the nature -and course of philosophy. The consideration of -the means which promote man's material well-being -often appears to be invested with a kind of dignity, by -the discovery of general laws which it involves; and -the satisfaction which rises in our minds at the contemplation -of such cases, men sometimes ascribe, with -a false ingenuity, to the love of mere bodily enjoyment. -But it is never difficult to see that this baser -and coarser element is not the real source of our admiration. -Those who hold that it is the main business -of science to construct instruments for the uses of life, -appear sometimes to be willing to accept the consequence -which follows from such a doctrine, that the -first shoemaker was a philosopher worthy of the highest<span class="pagenum" id="Page_144">144</span> -admiration<a name="FNanchor_186" id="FNanchor_186"></a><a href="#Footnote_186" class="fnanchor">[186]</a>. But those who maintain such paradoxes, -often, by a happy inconsistency, make it their -own aim, not to devise some improved covering for the -feet, but to delight the mind with acute speculations, -exhibited in all the graces of wit and fancy.</p> - -<p>It has been said<a name="FNanchor_187" id="FNanchor_187"></a><a href="#Footnote_187" class="fnanchor">[187]</a> that the key of the Baconian -doctrine consists in two words, Utility and Progress. -With regard to the latter point, we have already seen -that the hope and prospect of a boundless progress in -human knowledge had sprung up in men's minds, even -in the early times of imperial Rome; and were most -emphatically expressed by that very Seneca who disdained -to reckon the worth of knowledge by its value -in food and clothing. And when we say that Utility -was the great business of Bacon's philosophy, we forget -one-half of his characteristic phrase: "Ascendendo ad -aximomata," no less than "descendendo ad opera," was, -he repeatedly declared, the scheme of his path. He -constantly spoke, we are told by his secretary<a name="FNanchor_188" id="FNanchor_188"></a><a href="#Footnote_188" class="fnanchor">[188]</a>, of two -kinds of experiments, <i>experimenta fructifera</i>, and <i>experimenta -lucifera</i>.</p> - -<p>Again; when we are told by modern writers that -Bacon merely recommended such induction as all men -instinctively practise, we ought to recollect his own -earnest and incessant declarations to the contrary. The -induction hitherto practised is, he says, of no use for -obtaining solid science. There are two ways<a name="FNanchor_189" id="FNanchor_189"></a><a href="#Footnote_189" class="fnanchor">[189]</a>, "hæc -via in usu est," "altera vera, sed intentata." Men -have constantly been employed in <i>anticipation</i>; in illicit -induction. The intellect left to itself rushes on in this -road<a name="FNanchor_190" id="FNanchor_190"></a><a href="#Footnote_190" class="fnanchor">[190]</a>; the conclusions so obtained are persuasive<a name="FNanchor_191" id="FNanchor_191"></a><a href="#Footnote_191" class="fnanchor">[191]</a>; -far more persuasive than inductions made with due -caution<a name="FNanchor_192" id="FNanchor_192"></a><a href="#Footnote_192" class="fnanchor">[192]</a>. But still this method must be rejected if -we would obtain true knowledge. We shall then at -length have ground of good hope for science when we<span class="pagenum" id="Page_145">145</span> -proceed in another manner<a name="FNanchor_193" id="FNanchor_193"></a><a href="#Footnote_193" class="fnanchor">[193]</a>. We must rise, not by a -leap, but by small steps, by successive advances, by a -gradation of ascents, trying our facts, and clearing our -notions at every interval. The scheme of true philosophy, -according to Bacon, is not obvious and simple, but -long and technical, requiring constant care and self-denial -to follow it. And we have seen that, in this -opinion, his judgment is confirmed by the past history -and present condition of science.</p> - -<p>Again; it is by no means a just view of Bacon's -character to place him in contrast to Plato. Plato's -philosophy was the philosophy of Ideas; but it was -not left for Bacon to set up the philosophy of Facts in -opposition to that of Ideas. That had been done fully -by the speculative reformers of the sixteenth century. -Bacon had the merit of showing that Facts and Ideas -must be combined; and not only so, but of divining -many of the special rules and forms of this combination, -when as yet there were no examples of them, -with a sagacity hitherto quite unparalleled.</p> - - -<p><a id="XV22"></a>(X.) 22. <i>His Perseverance.</i>—With Bacon's unhappy -political life we have here nothing to do. But -we cannot but notice with pleasure how faithfully, -how perseveringly, how energetically he discharged -his great philosophical office of a Reformer of Methods. -He had conceived the purpose of making this his object -at an early period. When meditating the continuation -of his <i>Novum Organon</i>, and speaking of his -reasons for trusting that his work will reach some -completeness of effect, he says<a name="FNanchor_194" id="FNanchor_194"></a><a href="#Footnote_194" class="fnanchor">[194]</a>, "I am by two arguments -thus persuaded. First, I think thus from the -zeal and constancy of my mind, which has not waxed -old in this design, nor, after so many years, grown cold -and indifferent; I remember that about forty years ago -I composed a juvenile work about these things, which -with great contrivance and a pompous title I called -<i>temporis partum maximum</i>, or the most considerable<span class="pagenum" id="Page_146">146</span> -birth of time; Next, that on account of its usefulness, -it may hope the Divine blessing." In stating the -grounds of hope for future progress in the sciences, he -says<a name="FNanchor_195" id="FNanchor_195"></a><a href="#Footnote_195" class="fnanchor">[195]</a>: "Some hope may, we conceive, be ministered -to men by our own example: and this we say, not for -the sake of boasting, but because it is useful to be said. -If any despond, let them look at me, a man among all -others of my age most occupied with civil affairs, nor -of very sound health, (which brings a great loss of -time;) also in this attempt the first explorer, following -the footsteps of no man, nor communicating on these -subjects with any mortal; yet, having steadily entered -upon the true road and made my mind submit to -things themselves, one who has, in this undertaking, -made, (as we think,) some progress." He then proceeds -to speak of what may be done by the combined -and more prosperous labours of others, in that strain -of noble hope and confidence, which rises again and -again, like a chorus, at intervals in every part of his -writings. In the <i>Advancement of Learning</i> he had -said, "I could not be true and constant to the argument -I handle, if I were not willing to go beyond -others, but yet not more willing than to have others -go beyond me again." In the Preface to the <i>Instauratio -Magna</i>, he had placed among his postulates those -expressions which have more than once warmed the -breast of a philosophical reformer<a name="FNanchor_196" id="FNanchor_196"></a><a href="#Footnote_196" class="fnanchor">[196]</a>. "Concerning ourselves -we speak not; but as touching the matter which -we have in hand, this we ask;—that men be of good -hope, neither feign and imagine to themselves this -our Reform as something of infinite dimension and -beyond the grasp of mortal man, when in truth it -is the end and true limit of infinite error; and is by -no means unmindful of the condition of mortality and -humanity, not confiding that such a thing can be -carried to its perfect close in the space of a single age, -but assigning it as a task to a succession of generations." -In a later portion of the <i>Instauratio</i> he<span class="pagenum" id="Page_147">147</span> -says: "We bear the strongest love to the <i>human republic</i> -our common country; and we by no means -abandon the hope that there will arise and come forth -some man among posterity, who will be able to receive -and digest all that is best in what we deliver; and -whose care it will be to cultivate and perfect such -things. Therefore, by the blessing of the Deity, to -tend to this object, to open up the fountains, to discover -the useful, to gather guidance for the way, shall -be our task; and from this we shall never, while we -remain in life, desist."</p> - - -<p><a id="XV23"></a>(XI.) 23. <i>His Piety.</i>—We may add, that the spirit -of piety as well as of hope which is seen in this passage, -appears to have been habitual to Bacon at all periods -of his life. We find in his works several drafts of portions -of his great scheme, and several of them begin -with a prayer. One of these entitled, in the edition -of his works, "The Student's Prayer," appears to me -to belong probably to his early youth. Another, entitled -"The Writer's Prayer," is inserted at the end -of the Preface of the <i>Instauratio</i>, as it was finally published. -I will conclude my notice of this wonderful -man by inserting here these two prayers.</p> - -<p>"To God the Father, God the Word, God the Spirit, -we pour forth most humble and hearty supplications; -that he, remembering the calamities of mankind, and -the pilgrimage of this our life, in which we wear out -days few and evil, would please to open to us new -refreshments out of the fountains of his goodness for -the alleviating of our miseries. This also we humbly -and earnestly beg, that human things may not prejudice -such as are divine; neither that, from the unlocking -of the gates of sense, and the kindling of a greater -natural light, anything of incredulity, or intellectual -night, may arise in our minds towards divine mysteries. -But rather, that by our mind thoroughly cleansed and -purged from fancy and vanities, and yet subject and -perfectly given up to the Divine oracles, there may be -given unto faith the things that are faith's."</p> - -<p>"Thou, O Father, who gavest the visible light as -the first-born of thy creatures, and didst pour into<span class="pagenum" id="Page_148">148</span> -man the intellectual light as the top and consummation -of thy workmanship, be pleased to protect and -govern this work, which coming from thy goodness, -returneth to thy glory. Thou, after thou hadst reviewed -the works which thy hands had made, beheldest -that everything was very good, and thou didst -rest with complacency in them. But man, reflecting -on the works which he had made, saw that all was -vanity and vexation of spirit, and could by no means -acquiesce in them. Wherefore, if we labour in thy -works with the sweat of our brows, thou wilt make -us partakers of thy vision and thy Sabbath. We -humbly beg that this mind may be steadfastly in us; -and that thou, by our hands, and also by the hands of -others on whom thou shalt bestow the same spirit, wilt -please to convey a largess of new alms to thy family of -mankind. These things we commend to thy everlasting -love, by our Jesus, thy Christ, God with us. Amen."</p> - - - -<hr class="chap" /> - -<p><span class="pagenum" id="Page_149">149</span></p> - - -</div><div class="chapter"> -<h2><a name="CHAPTER_XVI" id="CHAPTER_XVI"></a>CHAPTER XVI.<br /> - -<span class="smcap small">Additional Remarks on Francis Bacon.</span></h2> - - -<p class="drop-cap"><span class="smcap">Francis Bacon</span> and his works have recently -been discussed and examined by various writers -in France and Germany as well as England<a name="FNanchor_197" id="FNanchor_197"></a><a href="#Footnote_197" class="fnanchor">[197]</a>. Not to -mention smaller essays, M. Bouillet has published a -valuable edition of his philosophical works; Count -Joseph de Maistre wrote a severe critique of his philosophy, -which has been published since the death of -the author; M. Charles Remusat has written a lucid -and discriminating Essay on the subject; and in England -we have had a new edition of the works published, -with a careful and thoughtful examination of -the philosophy which they contain, written by one of -the editors: a person especially fitted for such an examination -by an acute intellect, great acquaintance -with philosophical literature, and a wide knowledge -of modern science. Robert Leslie Ellis, the editor -of whom I speak, died during the publication of the -edition, and before he had done full justice to his -powers; but he had already written various dissertations -on Bacon's philosophy, which accompany the -different Treatises in the new edition.</p> - -<p><a id="XVI1"></a>Mr. Ellis has given a more precise view than any of -his predecessors had done of the nature of Bacon's<span class="pagenum" id="Page_150">150</span> -induction and of his philosophy of discovery. Bacon's -object was to discover the 'natures' or essences of -things, in order that he might reproduce these natures -or essences at will; he conceived that these natures -were limited in number, and manifested in various -combinations in the bodies which exist in the universe; -so that by accumulating observations of them -in a multitude of cases, we may learn by induction in -what they do and in what they do not consist; the <i>Induction</i> -which is to be used for this purpose consists -in a great measure of <i>excluding</i> the cases which do -not exhibit the 'nature' in question; and by such -exclusion, duly repeated, we have at last left in our -hands the elements of which the proposed nature consists. -And the knowledge which is thus obtained may -be applied to reproduce the things so analysed. As -exhibiting this view clearly we may take a passage in -the <i>Sylva Sylvarum</i>: "Gold has these natures: greatness -of weight, closeness of parts, fixation, pliantness or -softness, immunity from rust, colour or tincture of -yellow. Therefore the sure way, though most about, to -make gold, is to know the causes of the several natures -before rehearsed, and the axioms concerning the -same. For if a man can make a metal, that hath all -these properties, let men dispute whether it be gold -or no." He means that however they dispute, it is -gold for all practical purposes.</p> - -<p>For such an Induction as this, Bacon claims the -merit both of being certain, and of being nearly independent -of the ingenuity of the inquirer. It is a -method which enables all men to make exact discoveries, -as a pair of compasses enables all men to -draw an exact circle.</p> - -<p>Now it is necessary for us, who are exploring the -progress of the true philosophy of discovery, to say -plainly that this part of Bacon's speculation is erroneous -and valueless. No scientific discovery ever has -been made in this way. Men have not obtained truths -concerning the natural world by seeking for the natures -of things, and by extracting them from phenomena -by rejecting the cases in which they were not.<span class="pagenum" id="Page_151">151</span> -On the contrary, they have begun by ascertaining the -<i>laws of the phenomena</i>; and have then gone on, not -by a mechanical method which levels all intellect, but -by special efforts of the brightest intellects to catch -hold of the ideas by which these laws of phenomena -might be interpreted and expressed in more general -terms. These two steps, the finding the laws of phenomena, -and finding the conceptions by which those -laws can be expressed, are really the course of discovery, -as the history of science exhibits it to us.</p> - -<p>Bacon, therefore, according to the view now presented, -was wrong both as to his object and as to his -method. He was wrong in taking for his object the -essences of things,—the causes of abstract properties: -for these man cannot, or can very rarely discover; -and all Bacon's ingenuity in enumerating and classifying -these essences and abstract properties has led, and -could lead, to no result. The vast results of modern -science have been obtained, not by seeking and finding -the essences of things, but by exploring the laws of -phenomena and the causes of those laws.</p> - -<p>And Bacon's method, as well as his object, is vitiated -by a pervading error:—the error of supposing that to be -done by method which must be done by mind;—that -to be done by rule which must be done by a flight -beyond rule;—that to be mainly negative which is -eminently positive;—that to depend on other men -which must depend on the discoverer himself;—that -to be mere prose which must have a dash of poetry;—that -to be a work of mere labour which must be also -a work of genius.</p> - -<p>Mr. Ellis has seen very clearly and explained very -candidly that this method thus recommended by Bacon -has not led to discovery. "It is," he says, "neither to -the technical part of his method nor to the details of -his view of the nature and progress of science, that his -great fame is justly owing. His merits are of another -kind. They belong to the spirit rather than to the -positive precepts of his philosophy."</p> - -<p>As the reader of the last chapter will see, this -amounts to much the same as the account which I<span class="pagenum" id="Page_152">152</span> -had given of the positive results of Bacon's method, and -the real value of that portion of his philosophy which -he himself valued most. But still there remain, as I -have also noted, portions of Bacon's speculations which -have a great and enduring value, namely, his doctrine -that Science is the Interpretation of Nature, his distinction -of this Interpretation of Nature from the -vicious and premature Anticipation of Nature which -had generally prevailed till then; and the recommendation -of a graduated and successive induction by -which alone the highest and most general truths were -to be reached. These are points which he urges with -great clearness and with great earnestness; and these -are important points in the true philosophy of discovery.</p> - -<p>I may add that Mr. Ellis agrees with me in noting -the invention of the conception by which the laws of -phenomena are interpreted as something additional to -<i>Induction</i>, both in the common and in the Baconian -sense of the word. He says (General Preface, Art. 9), -"In all cases this process [scientific discovery] involves -an element to which nothing corresponds in the -Tables of Comparence and Exclusion; namely the -application to the facts of a <i>principle</i> of arrangement, -an <i>idea</i>, existing in the mind of the discoverer antecedently -to the act of induction." It may be said -that this principle or idea is aimed at in the Baconian -analysis. "And this is in one sense true: but it -must be added, that this <i>analysis</i>, if it be thought -right to call it so, is of the essence of the discovery -which results from it. To take for granted that it -has been already effected is simply a <i>petitio principii</i>. -In most cases the mere act of induction follows as a -matter of course as soon as the <i>appropriate idea</i> has -been introduced." And as an example he takes Kepler's -invention of the ellipse, as the idea by which -Mars's motions could be reduced to law; making the -same use of this example which we have repeatedly -made of it.</p> - -<p>Mr. Ellis may at first sight appear to express himself -more favourably than I have done, with regard to<span class="pagenum" id="Page_153">153</span> -the value of Bacon's <i>Inquisitio in Naturam Calidi</i> in -the Second Book of the <i>Novum Organon</i>. He says of -one part of it<a name="FNanchor_198" id="FNanchor_198"></a><a href="#Footnote_198" class="fnanchor">[198]</a>: "Bacon here anticipates not merely -the essential character of the most recent theory of -heat, but also the kind of evidence by which it has -been established.... The merit of having perceived the -true significance of the production of heat by friction -belongs of right to Bacon."</p> - -<p>But notwithstanding this, Mr. Ellis's general judgment -on this specimen of Bacon's application of his -own method does not differ essentially from mine. -He examines the <i>Inquisitio</i> at some length, and finally -says: "If it were affirmed that Bacon, after having -had a glimpse of the truth suggested by some obvious -phenomena, had then recourse, as he himself expresses -it, to certain 'differentiæ inanes' in order to save the -phenomena, I think it would be hard to dispute the -truth of the censure."</p> - -<p><a id="XVI2"></a>Another of the Editors of this edition (Mr. Spedding) -fixes his attention upon another of the features -of the method of discovery proposed by Bacon, and is -disposed to think that the proposed method has never -yet had justice done it, because it has not been tried -in the way and on the scale that Bacon proposes<a name="FNanchor_199" id="FNanchor_199"></a><a href="#Footnote_199" class="fnanchor">[199]</a>. -Bacon recommended that a great collection of facts -should be at once made and accumulated, regarding -every branch of human knowledge; and conceived -that, when this had been done by common observers, -philosophers might extract scientific truths from this -mass of facts by the application of a right method. -This separation of the offices of the observer and discoverer, -Mr. Spedding thinks is shown to be possible -by such practical examples as meteorological observations, -made by ordinary observers, and reduced to -tables and laws by a central calculator; by hydrographical -observations made by ships provided with proper -instructions, and reduced to general laws by the<span class="pagenum" id="Page_154">154</span> -man of science in his study; by magnetical observations -made by many persons in every part of the world, -and reduced into subservience to theory by mathematicians -at home.</p> - -<p>And to this our reply will be, in the terms which -the history of all the Sciences has taught us, that such -methods of procedure as this do not belong to the -<i>Epoch of Discovery</i>, but to the Period of <i>verification</i> -and <i>application</i> of the discovery which follows. When -a theory has been established in its general form, our -knowledge of the distribution of its phenomena in -time and space can be much promoted by ordinary observers -scattered over the earth, and succeeding each -other in time, provided they are furnished with instruments -and methods of observation, duly constructed -on the principles of science; but such observers cannot -in any degree supersede the discoverer who is first -to establish the theory, and to introduce into the facts -a new principle of order. When the laws of nature -have been caught sight of, much may be done, even -by ordinary observers, in verifying and exactly determining -them; but when a real discovery is to be made, -this separation of the observer and the theorist is not -possible. In those cases, the questioning temper, the -busy suggestive mind, is needed at every step, to direct -the operating hand or the open gaze. No possible -accumulation of facts about mixture and heat, collected -in the way of blind trial, could have led to the doctrines -of chemistry, or crystallography, or the atomic -theory, or voltaic and chemical and magnetic polarity, -or physiology, or any other science. Indeed not only -is an existing theory requisite to supply the observer -with instruments and methods, but without theory he -cannot even describe his observations. He says that -he mixes an acid and an alkali; but what is an acid? -What is an alkali? How does he know them? He -classifies crystals according to their forms: but till he -has learnt what is distinctive in the form of a crystal, -he cannot distinguish a cube from a square prism, even -if he had a goniometer and could use it. And the like -impossibility hangs over all the other subjects. To<span class="pagenum" id="Page_155">155</span> -report facts for scientific purposes without some aid -from theory, is not only useless, but impossible.</p> - -<p>When Mr. Spedding says, "I could wish that men -of science would apply themselves earnestly to the -solution of this practical problem: What measures -are to be taken in order that the greatest variety of -judicious observations of nature all over the world -may be carried on in concert upon a common plan and -brought to a common centre:"—he is urging upon men -of science to do what they have always done, so far as -they have had any power, and in proportion as the -state of science rendered such a procedure possible and -profitable to science. In Astronomy, it has been done -from the times of the Greeks and even of the Chaldeans, -having been begun <i>as soon as</i> the heavens were -reduced to law at all. In meteorology, it has been -done extensively, though to little purpose, because the -weather has <i>not yet</i> been reduced to rule. Men of science -have shown how barometers, thermometers, hygrometers, -and the like, may be constructed; and these -may be now read by any one as easily as a clock; but -of ten thousand meteorological registers thus kept by -ordinary observers, what good has come to science? -Again: The laws of the tides have been in a great -measure determined by observations in all parts of the -globe, <i>because</i> theory pointed out what was to be observed. -In like manner the facts of terrestrial magnetism -were ascertained with tolerable completeness -by extended observations, <i>then</i>, and then only, when a -most recondite and profound branch of mathematics -had pointed out what was to be observed, and most -ingenious instruments had been devised by men of -science for observing. And even with these, it requires -an education to use the instruments. But in -many cases no education in the use of instruments devised -by others can supersede the necessity of a theoretical -and suggestive spirit in the inquirer himself. -He must devise his own instruments and his own methods, -if he is to make any discovery. What chemist, -or inquirer about polarities, or about optical laws yet -undiscovered, can make any progress by using another<span class="pagenum" id="Page_156">156</span> -man's experiments and observations? He must invent -at every step of his observation; and the observer and -theorist can no more be dissevered, than the body and -soul of the inquirer.</p> - -<p>That persons of moderate philosophical powers may, -when duly educated, make observations which may be -used by greater discoverers than themselves, is true. -We have examples of such a subordination of scientific -offices in astronomy, in geology, and in many other -departments. But still, as I have said, a very considerable -degree of scientific education is needed even -for the subordinate labourers in science; and the more -considerable in proportion as science advances further -and further; since every advance implies a knowledge -of what has already been done, and requires a new -precision or generality in the new points of inquiry.</p> - - - -<hr class="chap" /> - -<p><span class="pagenum" id="Page_157">157</span></p> - - -</div><div class="chapter"> -<h2><a name="CHAPTER_XVII" id="CHAPTER_XVII"></a>CHAPTER XVII.<br /> - -<span class="smcap medium">From Bacon to Newton.</span></h2> - - -<p><a id="XVII1"></a>1. <i>Harvey.</i>—<span class="smcap">We</span> have already seen that Bacon -was by no means the first mover or principal author of -the revolution in the method of philosophizing which -took place in his time; but only the writer who proclaimed -in the most impressive and comprehensive -manner, the scheme, the profit, the dignity, and the -prospects of the new philosophy. Those, therefore, -who after him, took up the same views are not to be -considered as his successors, but as his fellow-labourers; -and the line of historical succession of opinions must -be pursued without special reference to any one leading -character, as the principal figure of the epoch. I -resume this line, by noticing a contemporary and -fellow-countryman of Bacon, Harvey, the discoverer of -the circulation of the blood. This discovery was not -published and generally accepted till near the end of -Bacon's life; but the anatomist's reflections on the -method of pursuing science, though strongly marked -with the character of the revolution that was taking -place, belong to a very different school from the Chancellor's. -Harvey was a pupil of Fabricius of Acquapendente, -whom we noticed among the practical reformers -of the sixteenth century. He entertained, -like his master, a strong reverence for the great names -which had ruled in philosophy up to that time, Aristotle -and Galen; and was disposed rather to recommend -his own method by exhibiting it as the true -interpretation of ancient wisdom, than to boast of its -novelty. It is true, that he assigns, as his reason for<span class="pagenum" id="Page_158">158</span> -publishing some of his researches<a name="FNanchor_200" id="FNanchor_200"></a><a href="#Footnote_200" class="fnanchor">[200]</a>, "that by revealing -the method I use in searching into things, I might -propose to studious men, a new and (if I mistake not) -a surer path to the attainment of knowledge<a name="FNanchor_201" id="FNanchor_201"></a><a href="#Footnote_201" class="fnanchor">[201]</a>;" but -he soon proceeds to fortify himself with the authority -of Aristotle. In doing this, however, he has the very -great merit of giving a living and practical character -to truths which exist in the Aristotelian works, but -which had hitherto been barren and empty professions. -We have seen that Aristotle had asserted the importance -of experience as one root of knowledge; and -in this had been followed by the schoolmen of the -middle ages: but this assertion came with very different -force and effect from a man, the whole of whose -life had been spent in obtaining, by means of experience, -knowledge which no man had possessed before. -In Harvey's general reflections, the necessity of both -the elements of knowledge, sensations and ideas, experience -and reason, is fully brought into view, and -rightly connected with the metaphysics of Aristotle. -He puts the antithesis of these two elements with<span class="pagenum" id="Page_159">159</span> -great clearness. "Universals are chiefly known to us, -for science is begot by reasoning from universals to -particulars; yet that very comprehension of universals -in the understanding springs from the perception of -singulars in our sense." Again, he quotes Aristotle's -apparently opposite assertions:—that made in his <i>Physics</i><a name="FNanchor_202" id="FNanchor_202"></a><a href="#Footnote_202" class="fnanchor">[202]</a>, -"that we must advance from things which are -first known to us, though confusedly, to things more -distinctly intelligible in themselves; from the whole -to the part; from the universal to the particular;" -and that made in the <i>Analytics</i><a name="FNanchor_203" id="FNanchor_203"></a><a href="#Footnote_203" class="fnanchor">[203]</a>; that "Singulars are -more known to us and do first exist according to -sense: for nothing is in the understanding which was -not before in the sense." Both, he says, are true, -though at first they seem to clash: for "though in -knowledge we begin with sense, sensation itself is a -universal thing." This he further illustrates; and -quotes Seneca, who says, that "Art itself is nothing -but the <i>reason</i> of the work, implanted in the Artist's -mind:" and adds, "the same way by which we gain -an Art, by the very same way we attain any kind of -science or knowledge whatever; for as Art is a habit -whose object is something to be done, so Science is a -habit whose object is something to be known; and as -the former proceedeth from the imitation of examples, -so this latter, from the knowledge of things natural. -The source of both is from sense and experience; since -[but?] it is impossible that Art should be rightly purchased -by the one or Science by the other without -a direction from ideas." Without here dwelling on -the relation of Art and Science, (very justly stated by -Harvey, except that ideas exist in a very different -form in the mind of the Artist and the Scientist) it will -be seen that this doctrine, of science springing from -experience with a direction from ideas, is exactly that -which we have repeatedly urged, as the true view of -the subject. From this view, Harvey proceeds to infer -the importance of a reference to sense in his own<span class="pagenum" id="Page_160">160</span> -subject, not only for first discovering, but for receiving -knowledge: "Without experience, not other men's but -our own, no man is a proper disciple of any part of -natural knowledge; without experimental skill in anatomy, -he will no better apprehend what I shall deliver -concerning generation, than a man born blind can -judge of the nature and difference of colours, or one -born deaf, of sounds." "If we do otherwise, we may -get a humid and floating opinion, but never a solid -and infallible knowledge: as is happenable to those -who see foreign countries only in maps, and the bowels -of men falsely described in anatomical tables. And -hence it comes about, that in this rank age, we have -many sophisters and bookwrights, but few wise men -and philosophers." He had before declared "how -unsafe and degenerate a thing it is, to be tutored by -other men's commentaries, without making trial of the -things themselves; especially since Nature's book is -so open and legible." We are here reminded of Galileo's -condemnation of the "paper philosophers." The -train of thought thus expressed by the practical discoverers, -spread rapidly with the spread of the new -knowledge that had suggested it, and soon became -general and unquestioned.</p> - - -<p><a id="XVII2"></a>2. <i>Descartes.</i>—Such opinions are now among the -most familiar and popular of those which are current -among writers and speakers; but we should err much -if we were to imagine that after they were once propounded -they were never resisted or contradicted. Indeed, -even in our own time, not only are such maxims -very often practically neglected or forgotten, but -the opposite opinions, and views of science quite inconsistent -with those we have been explaining, are -often promulgated and widely accepted. The philosophy -of pure ideas has its commonplaces, as well as the -philosophy of experience. And at the time of which -we speak, the former philosophy, no less than the -latter, had its great asserter and expounder; a man in -his own time more admired than Bacon, regarded -with more deference by a large body of disciples all -over Europe, and more powerful in stirring up men's<span class="pagenum" id="Page_161">161</span> -minds to a new activity of inquiry. I speak of Descartes, -whose labours, considered as a philosophical -system, were an endeavour to revive the method of -obtaining knowledge by reasoning from our own ideas -only, and to erect it in opposition to the method of -observation and experiment. The Cartesian philosophy -contained an attempt at a counter-revolution. -Thus in this author's <i>Principia Philosophiæ</i><a name="FNanchor_204" id="FNanchor_204"></a><a href="#Footnote_204" class="fnanchor">[204]</a>, he says -that "he will give a short account of the principal -phenomena of the world, not that he may use them as -reasons to prove anything; for," adds he, "we desire -to deduce effects from causes, not causes from effects; -but only in order that out of the innumerable effects -which we learn to be capable of resulting from the -same causes, we may determine our mind to consider -some rather than others." He had before said, "The -principles which we have obtained [by pure <i>à priori</i> -reasoning] are so vast and so fruitful, that many more -consequences follow from them than we see contained -in this visible world, and even many more than our -mind can ever take a full survey of." And he professes -to apply this method in detail. Thus in attempting -to state the three fundamental laws of motion, -he employs only <i>à priori</i> reasonings, and is in -fact led into error in the third law which he thus obtains<a name="FNanchor_205" id="FNanchor_205"></a><a href="#Footnote_205" class="fnanchor">[205]</a>. -And in his <i>Dioptrics</i><a name="FNanchor_206" id="FNanchor_206"></a><a href="#Footnote_206" class="fnanchor">[206]</a> he pretends to deduce -the laws of reflection and refraction of light from certain -comparisons (which are, in truth, arbitrary,) in -which the radiation of light is represented by the motion -of a ball impinging upon the reflecting or refracting -body. It might be represented as a curious instance -of the caprice of fortune, which appears in scientific -as in other history, that Kepler, professing to -derive all his knowledge from experience, and exerting -himself with the greatest energy and perseverance, -failed in detecting the law of refraction; while Descartes, -who professed to be able to despise experiment, -obtained the true law of sines. But as we have stated<span class="pagenum" id="Page_162">162</span> -in the <i>History</i><a name="FNanchor_207" id="FNanchor_207"></a><a href="#Footnote_207" class="fnanchor">[207]</a>, Descartes appears to have learnt this -law from Snell's papers. And whether this be so or -not, it is certain that notwithstanding the profession of -independence which his philosophy made, it was in -reality constantly guided and instructed by experience. -Thus in explaining the Rainbow (in which his portion -of the discovery merits great praise) he speaks<a name="FNanchor_208" id="FNanchor_208"></a><a href="#Footnote_208" class="fnanchor">[208]</a> of -taking a globe of glass, allowing the sun to shine on -one side of it, and noting the colours produced by rays -after two refractions and one reflection. And in many -other instances, indeed in all that relates to physics, -the reasonings and explanations of Descartes and his -followers were, consciously or unconsciously, directed -by the known facts, which they had observed themselves -or learnt from others.</p> - -<p>But since Descartes thus, speculatively at least, set -himself in opposition to the great reform of scientific -method which was going on in his time, how, it may -be asked, did he acquire so strong an influence over -the most active minds of his time? How is it that he -became the founder of a large and distinguished school -of philosophers? How is it that he not only was -mainly instrumental in deposing Aristotle from his intellectual -throne, but for a time appeared to have established -himself with almost equal powers, and to have -rendered the Cartesian school as firm a body as the -Peripatetic had been?</p> - -<p>The causes to be assigned for this remarkable result -are, I conceive, the following. In the first place, the -physicists of the Cartesian school did, as I have just -stated, found their philosophy upon experiment, and -did not practically, or indeed, most of them, theoretically, -assent to their master's boast of showing -what the phenomena <i>must be</i>, instead of looking to see -what they <i>are</i>. And as Descartes had really incorporated -in his philosophy all the chief physical discoveries -of his own and preceding times, and had delivered, -in a more general and systematic shape than<span class="pagenum" id="Page_163">163</span> -any one before him, the principles which he thus established, -the physical philosophy of his school was in -reality far the best then current; and was an immense -improvement upon the Aristotelian doctrines, which -had not yet been displaced as a system. Another circumstance -which gained him much favour, was the -bold and ostentatious manner in which he professed -to begin his philosophy by liberating himself from all -preconceived prejudice. The first sentence of his philosophy -contains this celebrated declaration: "Since," -he says, "we begin life as infants, and have contracted -various judgments concerning sensible things before -we possess the entire use of our reason, we are turned -aside from the knowledge of truth by many prejudices: -from which it does not appear that we can be any -otherwise delivered, than if once in our life we make -it our business to doubt of everything in which we -discern the smallest suspicion of uncertainty." In the -face of this sweeping rejection or unhesitating scrutiny -of all preconceived opinions, the power of the ancient -authorities and masters in philosophy must obviously -shrink away; and thus Descartes came to be considered -as the great hero of the overthrow of the Aristotelian -dogmatism. But in addition to these causes, -and perhaps more powerful than all in procuring the -assent of men to his doctrines, came the deductive and -systematic character of his philosophy. For although -all knowledge of the external world is in reality only -to be obtained from observation, by inductive steps,—minute, -perhaps, and slow, and many, as Galileo and -Bacon had already taught;—the human mind conforms -to these conditions reluctantly and unsteadily, and is -ever ready to rush to general principles, and then to -employ itself in deducing conclusions from these by -synthetical reasonings; a task grateful, from the distinctness -and certainty of the result, and the accompanying -feeling of our own sufficiency. Hence men -readily overlooked the precarious character of Descartes' -fundamental assumptions, in their admiration -of the skill with which a varied and complex Universe -was evolved out of them. And the complete and<span class="pagenum" id="Page_164">164</span> -systematic character of this philosophy attracted men -no less than its logical connexion. I may quote here -what a philosopher<a name="FNanchor_209" id="FNanchor_209"></a><a href="#Footnote_209" class="fnanchor">[209]</a> of our own time has said of another -writer: "He owed his influence to various causes; at -the head of which may be placed that genius for system -which, though it cramps the growth of knowledge, -perhaps finally atones for that mischief by the -zeal and activity which it rouses among followers and -opponents, who discover truth by accident when in -pursuit of weapons for their warfare. A system which -attempts a task so hard as that of subjecting vast provinces -of human knowledge to one or two principles, -if it presents some striking instances of conformity to -superficial appearances, is sure to delight the framer; -and for a time to subdue and captivate the student too -entirely for sober reflection and rigorous examination. -In the first instance consistency passes for truth. When -principles in some instances have proved sufficient to -give an unexpected explanation of facts, the delighted -reader is content to accept as true all other deductions -from the principles. Specious premises being assumed -to be true, nothing more can be required than logical -inference. Mathematical forms pass current as the -equivalent of mathematical certainty. The unwary -admirer is satisfied with the completeness and symmetry -of the plan of his house, unmindful of the need -of examining the firmness of the foundation and the -soundness of the materials. The system-maker, like -the conqueror, long dazzles and overawes the world; -but when their sway is past, the vulgar herd, unable -to measure their astonishing faculties, take revenge -by trampling on fallen greatness." Bacon showed -his wisdom in his reflections on this subject, when -he said that "Method, carrying a show of total and -perfect knowledge, hath a tendency to generate acquiescence."</p> - -<p>The main value of Descartes' physical doctrines -consisted in their being arrived at in a way incon<span class="pagenum" id="Page_165">165</span>sistent -with his own professed method, namely, by a -reference to observation. But though he did in reality -begin from facts, his system was nevertheless a glaring -example of that error which Bacon had called <i>Anticipation</i>; -that illicit generalization which leaps at once -from special facts to principles of the widest and -remotest kind; such, for instance, as the Cartesian -doctrine, that the world is an absolute <i>plenum</i>, every -part being full of matter of some kind, and that all -natural effects depend on the laws of motion. Against -this fault, to which the human mind is so prone, Bacon -had lifted his warning voice in vain, so far as the -Cartesians were concerned; as indeed, to this day, one -theorist after another pursues his course, and turns -a deaf ear to the Verulamian injunctions; perhaps -even complacently boasts that he founds his theory -upon observation; and forgets that there are, as the -aphorism of the <i>Novum Organon</i> declares, two ways -by which this may be done;—the one hitherto in -use and suggested by our common tendencies, but -barren and worthless; the other almost untried, to -be pursued only with effort and self-denial, but alone -capable of producing true knowledge.</p> - - -<p><a id="XVII3"></a>3. <i>Gassendi.</i>—Thus the lessons which Bacon -taught were far from being generally accepted and -applied at first. The amount of the influence of these -two men, Bacon and Descartes, upon their age, has -often been a subject of discussion. The fortunes of -the Cartesian school have been in some measure traced -in the History of Science. But I may mention the -notice taken of these two philosophers by Gassendi, -a contemporary and countryman of Descartes. Gassendi, -as I have elsewhere stated<a name="FNanchor_210" id="FNanchor_210"></a><a href="#Footnote_210" class="fnanchor">[210]</a>, was associated with -Descartes in public opinion, as an opponent of the -Aristotelian dogmatism; but was not in fact a follower -or profound admirer of that writer. In a Treatise -on Logic, Gassendi gives an account of the Logic of -various sects and authors; treating, in order, of the<span class="pagenum" id="Page_166">166</span> -Logic of Zeno (the Eleatic), of Euclid (the Megarean), -of Plato, of Aristotle, of the Stoics, of Epicurus, of -Lullius, of Ramus; and to these he adds the Logic -of Verulam, and the Logic of Cartesius. "We must -not," he says, "on account of the celebrity it has -obtained, pass over the Organon or Logic of Francis -Bacon Lord Verulam, High Chancellor of England, -whose noble purpose in our time it has been, to make -an Instauration of the Sciences." He then gives a -brief account of the <i>Novum Organon</i>, noticing the principal -features in its rules, and especially the distinction -between the vulgar induction which leaps at once from -particular experiments to the more general axioms, -and the chastised and gradual induction, which the -author of the <i>Organon</i> recommends. In his account -of the Cartesian Logic, he justly observes, that "He -too imitated Verulam in this, that being about to build -up a new philosophy from the foundation, he wished -in the first place to lay aside all prejudice: and -having then found some solid principle, to make that -the groundwork of his whole structure. But he proceeds -by a very different path from that which Verulam -follows; for while Verulam seeks aid from things, -to perfect the cogitation of the intellect, Cartesius conceives, -that when we have laid aside all knowledge of -things, there is, in our thoughts alone, such a resource, -that the intellect may by its own power arrive at a perfect -knowledge of all, even the most abstruse things."</p> - -<p>The writings of Descartes have been most admired, -and his method most commended, by those authors -who have employed themselves upon metaphysical rather -than physical subjects of inquiry. Perhaps we -might say that, in reference to such subjects, this -method is not so vicious as at first, when contrasted -with the Baconian induction, it seems to be: for it -might be urged that the <i>thoughts</i> from which Descartes -begins his reasonings are, in reality, <i>experiments</i> of the -kind which the subject requires us to consider: each -such thought is a fact in the intellectual world; and -of such facts, the metaphysician seeks to discover the -laws. I shall not here examine the validity of this<span class="pagenum" id="Page_167">167</span> -plea; but shall turn to the consideration of the actual -progress of physical science, and its effect on men's -minds.</p> - - -<p><a id="XVII4"></a>4. <i>Actual progress in Science.</i>—The practical discoverers -were indeed very active and very successful -during the seventeenth century, which opened with -Bacon's survey and exhortations. The laws of nature, -of which men had begun to obtain a glimpse in the -preceding century, were investigated with zeal and -sagacity, and the consequence was that the foundations -of most of the modern physical sciences were laid. -That mode of research by experiment and observation, -which had, a little time ago, been a strange, and to -many, an unwelcome innovation, was now become the -habitual course of philosophers. The revolution from -the philosophy of tradition to the philosophy of experience -was completed. The great discoveries of Kepler -belonged to the preceding century. They are not, -I believe, noticed, either by Bacon or by Descartes; -but they gave a strong impulse to astronomical and -mechanical speculators, by showing the necessity of a -sound science of motion. Such a science Galileo had -already begun to construct. At the time of which I -speak, his disciples<a name="FNanchor_211" id="FNanchor_211"></a><a href="#Footnote_211" class="fnanchor">[211]</a> were still labouring at this task, -and at other problems which rapidly suggested themselves. -They had already convinced themselves that -air had weight; in 1643 Torricelli proved this practically -by the invention of the Barometer; in 1647 Pascal -proved it still further by sending the Barometer to -the top of a mountain. Pascal and Boyle brought into -clear view the fundamental laws of fluid equilibrium; -Boyle and Mariotte determined the law of the compression -of air as regulated by its elasticity. Otto -Guericke invented the air-pump, and by his "Madgeburg -Experiments" on a vacuum, illustrated still further -the effects of the air. Guericke pursued what -Gilbert had begun, the observation of electrical pheno<span class="pagenum" id="Page_168">168</span>mena; -and these two physicists made an important -step, by detecting repulsion as well as attraction in -these phenomena. Gilbert had already laid the foundations -of the science of Magnetism. The law of refraction, -at which Kepler had laboured in vain, was, as -we have seen, discovered by Snell (about 1621), and -published by Descartes. Mersenne had discovered -some of the more important parts of the theory of -Harmonics. In sciences of a different kind, the same -movement was visible. Chemical doctrines tended to -assume a proper degree of generality, when Sylvius in -1679 taught the opposition of acid and alkali, and -Stahl, soon after, the phlogistic theory of combustion. -Steno had remarked the most important law of crystallography -in 1669, that the angles of the same kind of -crystals are always equal. In the sciences of classification, -about 1680, Ray and Morison in England -resumed the attempt to form a systematic botany, -which had been interrupted for a hundred years, from -the time of the memorable essay of Cæsalpinus. The -grand discovery of the circulation of the blood by -Harvey about 1619, was followed in 1651 by Pecquet's -discovery of the course of the chyle. There could now -no longer be any question whether science was progressive, -or whether observation could lead to new -truths.</p> - -<p>Among these cultivators of science, such sentiments -as have been already quoted became very familiar;—that -knowledge is to be sought from nature herself by -observation and experiment;—that in such matters -tradition is of no force when opposed to experience, -and that mere reasonings without facts cannot lead to -solid knowledge. But I do not know that we find in -these writers any more special rules of induction and -scientific research which have since been confirmed -and universally adopted. Perhaps too, as was natural -in so great a revolution, the writers of this time, especially -the second-rate ones, were somewhat too prone -to disparage the labours and talents of Aristotle and -the ancients in general, and to overlook the ideal -element of our knowledge, in their zealous study of<span class="pagenum" id="Page_169">169</span> -phenomena. They urged, sometimes in an exaggerated -manner, the superiority of modern times in all -that regards science, and the supreme and sole importance -of facts in scientific investigations. There -prevailed among them also a lofty and dignified tone -of speaking of the condition and prospects of science, -such as we are accustomed to admire in the Verulamian -writings; for this, in a less degree, is epidemic -among those who a little after his time speak of the -new philosophy.</p> - - -<p><a id="XVII5"></a>5. <i>Otto Guericke, &c.</i>—I need not illustrate these -characteristics at any great length. I may as an example -notice Otto Guericke's Preface to his <i>Experimenta -Magdeburgica</i> (1670). He quotes a passage -from Kircher's Treatise on the Magnetic Art, in which -the author says, "Hence it appears how all philosophy, -except it be supported by experiments, is empty, fallacious, -and useless; what monstrosities philosophers, -in other respects of the highest and subtlest genius, -may produce in philosophy by neglecting experiment. -Thus Experience alone is the Dissolver of Doubts, the -Reconciler of Difficulties, the sole Mistress of Truth, -who holds a torch before us in obscurity, unties our -knots, teaches us the true causes of things." Guericke -himself reiterates the same remark, adding that "philosophers, -insisting upon their own thoughts and arguments -merely, cannot come to any sound conclusion -respecting the natural constitution of the world." Nor -were the Cartesians slow in taking up the same train -of reflection. Thus Gilbert Clark who, in 1660, published<a name="FNanchor_212" id="FNanchor_212"></a><a href="#Footnote_212" class="fnanchor">[212]</a> -a defence of Descartes' doctrine of a <i>plenum</i> -in the universe, speaks in a tone which reminds us -of Bacon, and indeed was very probably caught from -him: "Natural philosophy formerly consisted entirely -of loose and most doubtful controversies, carried on in -high-sounding words, fit rather to delude than to instruct -men. But at last (by the favour of the Deity)<span class="pagenum" id="Page_170">170</span> -there shone forth some more divine intellects, who -taking as their counsellors reason and experience together, -exhibited a new method of philosophizing. -Hence has been conceived a strong hope that philosophers -may embrace, not a shadow or empty image of -Truth, but Truth herself: and that Physiology (Physics) -scattering these controversies to the winds, will contract -an alliance with Mathematics. Yet this is hardly -the work of one age; still less of one man. Yet let -not the mind despond, or doubt not that, one party of -investigators after another following the same method -of philosophizing, at last, under good auguries, the -mysteries of nature being daily unlocked as far as -human feebleness will allow, Truth may at last appear -in full, and these nuptial torches may be lighted."</p> - -<p>As another instance of the same kind, I may quote -the preface to the First volume of the Transactions -of the Academy of Sciences at Paris: "It is only -since the present century," says the writer, "that we -can reckon the revival of Mathematics and Physics. -M. Descartes and other great men have laboured at -this work with so much success, that in this department -of literature, the whole face of things has been -changed. Men have quitted a sterile system of physics, -which for several generations had been always at the -same point; the reign of words and terms is passed; -men will have things; they establish principles which -they understand, they follow those principles; and -thus they make progress. Authority has ceased to -have more weight than Reason: that which was received -without contradiction because it had been long -received, is now examined, and often rejected: and -philosophers have made it their business to consult, -respecting natural things, Nature herself rather than -the Ancients." These had now become the commonplaces -of those who spoke concerning the course and -method of the Sciences.</p> - - -<p><a id="XVII6"></a>6. <i>Hooke.</i>—In England, as might be expected, the -influence of Francis Bacon was more directly visible. -We find many writers, about this time, repeating the -truths which Bacon had proclaimed, and in almost<span class="pagenum" id="Page_171">171</span> -every case showing the same imperfections in their -views which we have noticed in him. We may take -as an example of this Hooke's Essay, entitled "A -General Scheme or Idea of the present state of Natural -Philosophy, and how its defects may be remedied by a -Methodical proceeding in the making Experiments and -collecting Observations; whereby to compile a Natural -History as a solid basis for the superstructure of -true Philosophy." This Essay may be looked upon as -an attempt to adapt the <i>Novum Organon</i> to the age -which succeeded its publication. We have in this -imitation, as in the original, an enumeration of various -mistakes and impediments which had in preceding -times prevented the progress of knowledge; exhortations -to experiment and observation as the only solid -basis of Science; very ingenious suggestions of trains of -inquiry, and modes of pursuing them; and a promise -of obtaining scientific truths when facts have been -duly accumulated. This last part of his scheme the -author calls <i>a Philosophical Algebra</i>; and he appears -to have imagined that it might answer the purpose of -finding unknown causes from known facts, by means -of certain regular processes, in the same manner as -Common Algebra finds unknown from known quantities. -But this part of the plan appears to have remained -unexecuted. The suggestion of such a method -was a result of the Baconian notion that invention -in a discoverer might be dispensed with. We find -Hooke adopting the phrases in which this notion is -implied: thus he speaks of the understanding as "being -very prone to run into the affirmative way of judging, -and wanting patience to follow and prosecute the negative -way of inquiry, by rejection of disagreeing natures." -And he follows Bacon also in the error of attempting -at once to obtain from the facts the discovery of a -"nature," instead of investigating first the measures -and the laws of phenomena. I return to more general -notices of the course of men's thoughts on this subject.</p> - - -<p><a id="XVII7"></a>7. <i>Royal Society.</i>—Those who associated themselves -together for the prosecution of science quoted -Bacon as their leader, and exulted in the progress<span class="pagenum" id="Page_172">172</span> -made by the philosophy which proceeded upon his -principles. Thus in Oldenburg's Dedication of the -Transactions of the Royal Society of London for 1670, -to Robert Boyle, he says; "I am informed by such -as well remember the best and worst days of the -famous Lord Bacon, that though he wrote his <i>Advancement -of Learning</i> and his <i>Instauratio Magna</i> in -the time of his greatest power, yet his greatest reputation -rebounded first from the most intelligent -foreigners in many parts of Christendom:" and after -speaking of his practical talents and his public employments, -he adds, "much more justly still may we -wonder how, without any great skill in Chemistry, -without much pretence to the Mathematics or Mechanics, -without optic aids or other engines of late -invention, he should so much transcend the philosophers -then living, in judicious and clear instructions, -in so many useful observations and discoveries, I think -I may say beyond the records of many ages." And -in the end of the Preface to the same volume, he -speaks with great exultation of the advance of science -all over Europe, referring undoubtedly to facts then -familiar. "And now let envy snarl, it cannot stop -the wheels of active philosophy, in no part of the -known world;—not in France, either in Paris or in -Caen;—not in Italy, either in Rome, Naples, Milan, -Florence, Venice, Bononia or Padua;—in none of the -Universities either on this or on that side of the seas, -Madrid and Lisbon, all the best spirits in Spain and -Portugal, and the spacious and remote dominions to -them belonging;—the Imperial Court and the Princes -of Germany; the Northern Kings and their best luminaries; -and even the frozen Muscovite and Russian -have all taken the operative ferment: and it works -high and prevails every way, to the encouragement -of all sincere lovers of knowledge and virtue."</p> - -<p>Again, in the Preface for 1672, he pursues the -same thought into detail: "We must grant that in -the last age, when operative philosophy began to recover -ground, and to tread on the heels of triumphant -Philology; emergent adventures and great successes<span class="pagenum" id="Page_173">173</span> -were encountered by dangerous oppositions and strong -obstructions. Galilæus and others in Italy suffered -extremities for their celestial discoveries; and here in -England Sir Walter Raleigh, when he was in his -greatest lustrous, was notoriously slandered to have -erected a school of atheism, because he gave countenance -to chemistry, to practical arts, and to curious -mechanical operations, and designed to form the best -of them into a college. And Queen Elizabeth's Gilbert -was a long time esteemed extravagant for his magnetisms; -and Harvey for his diligent researches in pursuance -of the circulation of the blood. But when our -renowned Lord Bacon had demonstrated the methods -for a perfect restoration of all parts of real knowledge; -and the generous and philosophical Peireskius had, -soon after, agitated in all parts to redeem the most -instructive antiquities, and to excite experimental -essays and fresh discoveries; the success became on a -sudden stupendous; and effective philosophy began to -sparkle, and even to flow into beams of shining light -all over the world."</p> - -<p>The formation of the Royal Society of London and -of the Academy of Sciences of Paris, from which proceeded -the declamations just quoted, were among many -indications, belonging to this period, of the importance -which states as well as individuals had by this time -begun to attach to the cultivation of science. The -English Society was established almost immediately -when the restoration of the monarchy appeared to -give a promise of tranquillity to the nation (in 1660), -and the French Academy very soon afterwards (in -1666). These measures were very soon followed by -the establishment of the Observatories of Paris and -Greenwich (in 1667 and 1675); which may be considered -to be a kind of public recognition of the astronomy -of observation, as an object on which it was the -advantage and the duty of nations to bestow their -wealth.</p> - - -<p><a id="XVII8"></a>8. <i>Bacon's New Atalantis.</i>—When philosophers -had their attention turned to the boundless prospect of -increase to the knowledge and powers and pleasures of<span class="pagenum" id="Page_174">174</span> -man which the cultivation of experimental philosophy -seemed to promise, it was natural that they should -think of devising institutions and associations by which -such benefits might be secured. Bacon had drawn a -picture of a society organized with a view to such purpose, -in his fiction of the "New Atalantis." The -imaginary teacher who explains this institution to the -inquiring traveller, describes it by the name of <i>Solomon's -House</i>; and says<a name="FNanchor_213" id="FNanchor_213"></a><a href="#Footnote_213" class="fnanchor">[213]</a>, "The end of our foundation -is the knowledge of causes and secret motions of -things; and the enlarging the bounds of the human -empire to effecting of things possible." And, as parts -of this House, he describes caves and wells, chambers -and towers, baths and gardens, parks and pools, dispensatories -and furnaces, and many other contrivances, -provided for the purpose of making experiments of -many kinds. He describes also the various employments -of the Fellows of this College, who take a share -in its researches. There are <i>merchants of light</i>, who -bring books and inventions from foreign countries; -<i>depredators</i>, who gather the experiments which exist -in books; <i>mystery-men</i>, who collect the experiments of -the mechanical arts; <i>pioneers</i> or <i>miners</i>, who invent -new experiments; and <i>compilers</i>, "who draw the experiments -of the former into titles and tables, to give -the better light for the drawing of observations and -axioms out of them." There are also <i>dowry-men</i> or -<i>benefactors</i>, that cast about how to draw out of the -experiments of their fellows things of use and practice -for man's life; <i>lamps</i>, that direct new experiments -of a more penetrating light than the former; <i>inoculators</i>, -that execute the experiments so directed. -Finally, there are the <i>interpreters of nature</i>, that raise -the former discoveries by experiments into greater observations -(that is, more general truths), axioms and -aphorisms. Upon this scheme we may remark, that -fictitious as it undisguisedly is, it still serves to exhibit -very clearly some of the main features of the author's<span class="pagenum" id="Page_175">175</span> -philosophy:—namely, his steady view of the necessity -of ascending from facts to the most general truths by -several stages;—an exaggerated opinion of the aid that -could be derived in such a task from technical separation -of the phenomena and a distribution of them -into tables;—a belief, probably incorrect, that the -offices of experimenter and interpreter may be entirely -separated, and pursued by different persons with a -certainty of obtaining success!—and a strong determination -to make knowledge constantly subservient to -the uses of life.</p> - - -<p><a id="XVII9"></a>9. <i>Cowley.</i>—Another project of the same kind, -less ambitious but apparently more directed to practice, -was published a little later (1657) by another -eminent man of letters in this country. I speak of -Cowley's "Proposition for the Advancement of Experimental -Philosophy." He suggests that a College should -be established at a short distance from London, endowed -with a revenue of four thousand pounds, and -consisting of twenty professors with other members. -The objects of the labours of these professors he describes -to be, first, to examine all knowledge of nature -delivered to us from former ages and to pronounce it -sound or worthless; second, to recover the lost inventions -of the ancients; third, to improve all arts that -we now have; lastly, to discover others that we yet -have not. In this proposal we cannot help marking -the visible declension from Bacon's more philosophical -view. For we have here only a very vague indication -of improving old arts and discovering new, instead of -the two clear Verulamian antitheses, Experiments and -Axioms deduced from them, on the one hand, and on -the other an ascent to general Laws, and a derivation, -from these, of Arts for daily use. Moreover the prominent -place which Cowley has assigned to the verifying -the knowledge of former ages and recovering "the -lost inventions and drowned lands of the ancients," -implies a disposition to think too highly of traditionary -knowledge; a weakness which Bacon's scheme shows -<i>him</i> to have fully overcome. And thus it has been up -to the present day, that with all Bacon's mistakes, in<span class="pagenum" id="Page_176">176</span> -the philosophy of scientific method few have come up -to him, and perhaps none have gone beyond him.</p> - -<p>Cowley exerted himself to do justice to the new -philosophy in verse as well as prose, and his Poem to -the Royal Society expresses in a very noble manner -those views of the history and prospects of philosophy -which prevailed among the men by whom the Royal -Society was founded. The fertility and ingenuity of -comparison which characterize Cowley's poetry are -well known; and these qualities are in this instance -largely employed for the embellishment of his subject. -Many of the comparisons which he exhibits are apt -and striking. Philosophy is a ward whose estate (human -knowledge) is, in his nonage, kept from him by -his guardians and tutors; (a case which the ancient -rhetoricians were fond of taking as a subject of declamation;) -and these wrong-doers retain him in unjust -tutelage and constraint for their own purposes; until</p> - -<div class="poetry-container"><div class="poetry"><div class="stanza"> - <div class="verse indent2">Bacon at last, a mighty man, arose,</div> - <div class="verse indent2">(Whom a wise King, and Nature, chose</div> - <div class="verse indent2">Lord Chancellor of both their laws,)</div> - <div class="verse">And boldly undertook the injured pupil's cause.</div> -</div></div></div> - -<p>Again, Bacon is one who breaks a scarecrow Priapus -which stands in the garden of knowledge. Again, -Bacon is one who, instead of a picture of painted -grapes, gives us real grapes from which we press "the -thirsty soul's refreshing wine." Again, Bacon is like -Moses, who led the Hebrews forth from the barren -wilderness, and ascended Pisgah;—</p> - -<div class="poetry-container"><div class="poetry"><div class="stanza"> - <div class="verse indent4">Did on the very border stand</div> - <div class="verse indent4">Of the blest promised land,</div> - <div class="verse">And from the mountain's top of his exalted wit</div> - <div class="verse">Saw it himself and showed us it.</div> -</div></div></div> - -<p>The poet however adds, that Bacon discovered, but -did not conquer this new world; and that the men -whom he addresses must subdue these regions. These -"champions" are then ingeniously compared to Gideon's -band:</p> - -<div class="poetry-container"><div class="poetry"><div class="stanza"> - <div class="verse">Their old and empty pitchers first they brake,</div> - <div class="verse">And with their hands then lifted up the light.</div> -</div></div></div> -<p><span class="pagenum" id="Page_177">177</span></p> -<p>There were still at this time some who sneered at or -condemned the new philosophy; but the tide of popular -opinion was soon strongly in its favour. I have elsewhere<a name="FNanchor_214" id="FNanchor_214"></a><a href="#Footnote_214" class="fnanchor">[214]</a> -noticed a pasquinade of the poet Boileau in -1682, directed against the Aristotelians. At this time, -and indeed for long afterwards, the philosophers of -France were Cartesians. The English men of science, -although partially and for a time they accepted some -of Descartes' opinions, for the most part carried on -the reform independently, and in pursuance of their -own views. And they very soon found a much greater -leader than Descartes to place at their head, and to -take as their authority, so far as they acknowledged -authority, in their speculations. I speak of Newton, -whose influence upon the philosophy of science I must -now consider.</p> - - -<p><a id="XVII10"></a>10. <i>Barrow.</i>—I will, however, first mention one other -writer who may, in more than one way, be regarded -as the predecessor of Newton. I speak of Isaac Barrow, -whom Newton succeeded as Professor of Mathematics -in the University of Cambridge, and who in his -mathematical speculations approached very near to -Newton's method of Fluxions. He afterwards (in 1673) -became Master of Trinity College, which office he held -till his death in 1677. But the passages which I -shall quote belong to an earlier period, (when Barrow -was about 22 years old,) and may be regarded as expressions -of the opinions which were then current -among active-minded and studious young men. They -manifest a complete familiarity with the writings both -of Bacon and of Descartes, and a very just appreciation -of both. The discourse of which I speak is an academical -exercise delivered in 1652, on the thesis <i>Cartesiana -hypothesis haud satisfacit præcipuis naturæ -phænomenis</i>. By the "Cartesian hypothesis," he does -not mean the hypothesis that the planets are moved -by vortices of etherial matter: I believe that this Cartesian -tenet never had any disciples in England; it<span class="pagenum" id="Page_178">178</span> -certainly never took any hold of Cambridge. By the -Cartesian hypothesis, Barrow means the doctrine that -all the phenomena of nature can be accounted for by -matter and motion; and allowing that the motions of -the planets are to be so accounted for, (which is Newtonian -as well as Cartesian doctrine,) he denies that -the Cartesian hypothesis accounts for "the generations, -properties, and specific operations of animals, plants, -minerals, stones, and other natural bodies," in doing -which he shows a sound philosophical judgment. But -among the parts of this discourse most bearing on our -present purpose are those where he mentions Bacon. -"Against Cartesius," he says, "I pit the chymists and -others, but especially as the foremost champion of this -battle, our Verulam, a man of great name and of great -judgment, who condemned this philosophy before it -was born." "He," adds Barrow, "several times in his -<i>Organon</i>, warned men against all hypotheses of this -kind, and noticed beforehand that there was not much -to be expected from those principles which are brought -into being by violent efforts of argumentation from the -brains of particular men: for that, as upon the phenomena -of the stars, various constructions of the heavens -may be devised, so also upon the phenomena of the -Universe, still more dogmas may be founded and constructed; -and yet all such are mere inventions: and as -many philosophies of this kind as are or shall be extant, -so many fictitious and theatrical worlds are made." -The reference is doubtless to Aphorism <span class="smcap">LXII.</span> of the First -Book of the <i>Novum Organon</i>, in which Bacon is -speaking of his "Idols of the Theatre." After making -the remark which Barrow has adopted, Bacon adds, -"Such theatrical fables have also this in common with -those of dramatic poets, that the dramatic story is -more regular and elegant than true histories are, and -is made so as to be agreeable." Barrow, having this -in his mind, goes on to say: "And though Cartesius -has dressed up the stage of his theatre more prettily -than any other person, and made his drama more like -history, still he is not exempt from the like censure." -And he then refers to Cartesius's own declaration, that<span class="pagenum" id="Page_179">179</span> -he did not learn his system from things themselves, -but tried to impose his own laws upon things; thus inverting -the order of true philosophy.</p> - -<p>Other parts of Bacon's work to which Barrow refers -are those where he speaks of the Form, or Formal -Cause of a body, and says that in comparison with -that, the Efficient Cause and the Material Cause are -things unimportant and superficial, and contribute -little to true and active science<a name="FNanchor_215" id="FNanchor_215"></a><a href="#Footnote_215" class="fnanchor">[215]</a>. And again, his -classification of the various kinds of motions<a name="FNanchor_216" id="FNanchor_216"></a><a href="#Footnote_216" class="fnanchor">[216]</a>,—the -motus libertatis, motus nexus, motus continuitatis, -motus ad lucrum, fugæ, unionis, congregationis; and -the explanation of electrical attraction (about which -Gilbert and others had written) as <i>motus ad lucrum</i>.</p> - -<p>These passages show that Barrow had read the -<i>Novum Organon</i> in a careful and intelligent manner, -and presumed his Cambridge hearers to be acquainted -with the work. Nor is his judgment of Descartes -less wise and philosophical. He rejects, as we have -seen, his system as a true scheme of the universe, and -condemns altogether his <i>à priori</i> mode of philosophizing; -but this does not prevent his accepting Descartes' -real discoveries, and admiring the boldness and vigour -of his attempts to reform philosophy. There is, in -Barrow's works, academic verse, as well as prose, on -the subject of the Cartesian hypothesis. In this, Descartes -himself is highly praised, though his doctrines -are very partially accepted. The writer says: "Pardon -us, great Cartesius, if the Muse resists you. Pardon! -We follow you, Inquiring Spirit that you are, -while we reject your system. As you have taught us -free thought, and broken down the rule of tyranny, -we undauntedly speculate, even in opposition to you."</p> - -<p>Descartes is even yet spoken of, especially by French -writers, as the person who first asserted and established -the freedom of inquiry which is the boast of -modern philosophy; but this is said with reference to -metaphysics, not to physics. In physical philosophy,<span class="pagenum" id="Page_180">180</span> -though he caught hold of some of the discoveries -which were then coming into view, the method in -which he reasoned or professed to reason was altogether -vicious; and was, as I have already said, an -attempt to undo what the reformers, both theoretical -and practical, had been doing:—to discredit the philosophy -of experience, and to restore the reign of <i>à priori</i> -systems.</p> - -<p>It was, however, now, too late to make any such -attempt; and nothing came of it to interrupt the progress -of a better philosophy of discovery.</p> - - - -<hr class="chap" /> - -<p><span class="pagenum" id="Page_181">181</span></p> - - -</div><div class="chapter"> -<h2><a name="CHAPTER_XVIII" id="CHAPTER_XVIII"></a>CHAPTER XVIII.<br /> - -<span class="smcap medium">Newton.</span></h2> - - -<p><a id="XVIII1"></a> -<span class="dropcap"><span class="dsmall">1.</span> B</span>OLD and extensive as had been the anticipations -of those whose minds were excited -by the promise of the new philosophy, the discoveries -of Newton respecting the mechanics of the universe, -brought into view truths more general and profound -than those earlier philosophers had hoped or imagined. -With these vast accessions to human knowledge, men's -thoughts were again set in action; and philosophers -made earnest and various attempts to draw, from these -extraordinary advances in science, the true moral with -regard to the conduct and limits of the human understanding. -They not only endeavoured to verify and -illustrate, by these new portions of science, what had -recently been taught concerning the methods of obtaining -sound knowledge; but they were also led to -speculate concerning many new and more interesting -questions relating to this subject. They saw, for the -first time, or at least far more clearly than before, the -distinction between the inquiry into the <i>laws</i>, and into -the <i>causes</i> of phenomena. They were tempted to ask, -how far the discovery of causes could be carried; and -whether it would soon reach, or clearly point to, the -ultimate cause. They were driven to consider whether -the properties which they discovered were essential -properties of all matter, necessarily and primarily involved -in its essence, though revealed to us at a late -period by their derivative effects. These questions -even now agitate the thoughts of speculative men. -Some of them have already, in this work, been discussed, -or arranged in the places which our view of the -philosophy of these subjects assigns to them. But we<span class="pagenum" id="Page_182">182</span> -must here notice them as they occurred to Newton -himself and his immediate followers.</p> - - -<p><a id="XVIII2"></a>2. The general Baconian notion of the method of -philosophizing,—that it consists in ascending from phenomena, -through various stages of generalization, to -truths of the highest order,—received, in Newton's discovery -of the universal mutual gravitation of every -particle of matter, that pointed actual exemplification, -for want of which it had hitherto been almost overlooked, -or at least very vaguely understood. That -great truth, and the steps by which it was established, -afford, even now, by far the best example of the successive -ascent, from one scientific truth to another,—of -the repeated transition from less to more general propositions,—which -we can yet produce; as may be seen -in the Table which exhibits the relation of these steps -in Book <span class="smcap">II.</span> of the <i>Novum Organon Renovatum</i>. Newton -himself did not fail to recognize this feature in the -truths which he exhibited. Thus he says<a name="FNanchor_217" id="FNanchor_217"></a><a href="#Footnote_217" class="fnanchor">[217]</a>, "By the -way of Analysis we proceed from compounds to ingredients, -as from motions to the forces producing them; -and in general, from effects to their causes, and from -particular causes to more general ones, till the argument -ends in the most general." And in like manner in another -Query<a name="FNanchor_218" id="FNanchor_218"></a><a href="#Footnote_218" class="fnanchor">[218]</a>: "The main business of natural philosophy -is to argue from phenomena without feigning hypotheses, -and to deduce causes from effects, till we come -to the First Cause, which is certainly not mechanical."</p> - - -<p><a id="XVIII3"></a>3. Newton appears to have had a horror of the -term <i>hypothesis</i>, which probably arose from his acquaintance -with the rash and illicit general assumptions -of Descartes. Thus in the passage just quoted, -after declaring that gravity must have some other -cause than matter, he says, "Later philosophers banish -the consideration of such a cause out of Natural Philosophy, -feigning hypotheses for explaining all things -mechanically, and referring other causes to metaphysics." -In the celebrated Scholium at the end of<span class="pagenum" id="Page_183">183</span> -the <i>Principia</i> he says, "Whatever is not deduced -from the phenomena, is to be termed <i>hypothesis</i>; and -hypotheses, whether metaphysical or physical, or occult -causes, or mechanical, have no place in experimental -philosophy. In this philosophy, propositions -are deduced from phenomena, and rendered general by -induction." And in another place, he arrests the -course of his own suggestions, saying, "Verum hypotheses -non fingo." I have already attempted to show -that this is, in reality, a superstitious and self-destructive -spirit of speculation. Some hypotheses are necessary, -in order to connect the facts which are observed; -some new principle of unity must be applied to the -phenomena, before induction can be attempted. What -is requisite is, that the hypothesis should be close to -the facts, and not connected with them by the intermediation -of other arbitrary and untried facts; and that -the philosopher should be ready to resign it as soon as -the facts refuse to confirm it. We have seen in the -<i>History</i><a name="FNanchor_219" id="FNanchor_219"></a><a href="#Footnote_219" class="fnanchor">[219]</a>, that it was by such a use of hypotheses, that -both Newton himself, and Kepler, on whose discoveries -those of Newton were based, made their discoveries. -The suppositions of a force tending to the sun and varying -inversely as the square of the distance; of a mutual -force between all the bodies of the solar system; of the -force of each body arising from the attraction of all its -parts; not to mention others, also propounded by -Newton,—were all hypotheses before they were verified -as theories. It is related that when Newton was -asked how it was that he saw into the laws of nature -so much further than other men, he replied, that if it -were so, it resulted from his keeping his thoughts -steadily occupied upon the subject which was to be -thus penetrated. But what is this occupation of the -thoughts, if it be not the process of keeping the phenomena -clearly in view, and trying, one after another, -all the plausible hypotheses which seem likely to connect -them, till at last the true law is discovered? Hypotheses -so used are a necessary element of discovery.</p> - -<p><span class="pagenum" id="Page_184">184</span></p> - - -<p><a id="XVIII4"></a>4. With regard to the details of the process of -discovery, Newton has given us some of his views, -which are well worthy of notice, on account of their -coming from him; and which are real additions to the -philosophy of this subject. He speaks repeatedly of -the <i>analysis</i> and <i>synthesis</i> of observed facts; and thus -marks certain steps in scientific research, very important, -and not, I think, clearly pointed out by his predecessors. -Thus he says<a name="FNanchor_220" id="FNanchor_220"></a><a href="#Footnote_220" class="fnanchor">[220]</a>, "As in Mathematics, so in -Natural Philosophy, the investigation of difficult things -by the method of analysis ought ever to precede the -method of composition. This analysis consists in making -experiments and observations, and in drawing -general conclusions from them by induction, and admitting -of no objections against the conclusions, but -such as are taken from experiments or other certain -truths. And although the arguing from experiments -and observations by induction be no demonstration of -general conclusions; yet it is the best way of arguing -which the nature of things admits of, and may be looked -upon as so much the stronger, by how much the -induction is more general." And he then observes, as -we have quoted above, that by this way of analysis we -proceed from compounds to ingredients, from motions -to forces, from effects to causes, and from less to more -general causes. The <i>analysis</i> here spoken of includes -the steps which in <i>our</i> Novum Organon we call the -<i>decomposition</i> of facts, the exact <i>observation</i> and <i>measurement</i> -of the phenomena, and the <i>colligation</i> of facts; -the necessary intermediate step, the <i>selection</i> and <i>explication</i> -of the appropriate conception, being passed over -by Newton, in the fear of seeming to encourage the -fabrication of hypotheses. The <i>synthesis</i> of which Newton -here speaks consists of those steps of <i>deductive reasoning</i>, -proceeding from the conception once assumed, -which are requisite for the comparison of its consequences -with the observed facts. This, his statement -of the process of research, is, as far as it goes, perfectly -exact.</p> - -<p><span class="pagenum" id="Page_185">185</span></p> - - -<p><a id="XVIII5"></a>5. In speaking of Newton's precepts on the subject, -we are naturally led to the celebrated "Rules of Philosophizing," -inserted in the second edition of the <i>Principia</i>. -These rules have generally been quoted and -commented on with an almost unquestioning reverence. -Such Rules, coming from such an authority, cannot -fail to be highly interesting to us; but at the same -time, we cannot here evade the necessity of scrutinizing -their truth and value, according to the principles -which our survey of this subject has brought into view. -The Rules stand at the beginning of that part of the -<i>Principia</i> (the Third Book) in which he infers the mutual -gravitation of the sun, moon, planets, and all parts -of each. They are as follows:</p> - -<p>"Rule I. We are not to admit other causes of natural -things than such as both are true, and suffice for -explaining their phenomena.</p> - -<p>"Rule II. Natural effects of the same kind are -to be referred to the same causes, as far as can be -done.</p> - -<p>"Rule III. The qualities of bodies which cannot -be increased or diminished in intensity, and which belong -to all bodies in which we can institute experiments, -are to be held for qualities of all bodies whatever.</p> - -<p>"Rule IV. In experimental philosophy, propositions -collected from phenomena by induction, are to -be held as true either accurately or approximately, notwithstanding -contrary hypotheses; till other phenomena -occur by which they may be rendered either -more accurate or liable to exception."</p> - -<p>In considering these Rules, we cannot help remarking, -in the first place, that they are constructed with -an intentional adaptation to the case with which Newton -has to deal,—the induction of Universal Gravitation; -and are intended to protect the reasonings before -which they stand. Thus the first Rule is designed to -strengthen the inference of gravitation from the celestial -phenomena, by describing it as a <i>vera causa</i>, a true -cause; the second Rule countenances the doctrine that -the planetary motions are governed by mechanical<span class="pagenum" id="Page_186">186</span> -forces, as terrestrial motions are; the third rule appears -intended to justify the assertion of gravitation, -as a <i>universal</i> quality of bodies; and the fourth contains, -along with a general declaration of the authority -of induction, the author's usual protest against hypotheses, -levelled at the Cartesian hypotheses especially.</p> - - -<p><a id="XVIII6"></a>6. <i>Of the First Rule.</i>—We, however, must consider -these Rules in their general application, in which -point of view they have often been referred to, and -have had very great authority allowed them. One of -the points which has been most discussed, is that -maxim which requires that the causes of phenomena -which we assign should be true causes, <i>veræ causæ</i>. -Of course this does not mean that they should be <i>the</i> -true or right cause; for although it is the philosopher's -aim to discover such causes, he would be little aided -in his search of truth, by being told that it is truth -which he is to seek. The rule has generally been understood -to prescribe that in attempting to account for -any class of phenomena, we must assume such causes -only, as <i>from other considerations</i>, we know to exist. -Thus gravity, which was employed in explaining the -motions of the moon and planets, was already known -to exist and operate at the earth's surface.</p> - -<p>Now the Rule thus interpreted is, I conceive, an -injurious limitation of the field of induction. For it -forbids us to look for a cause, except among the causes -with which we are already familiar. But if we follow -this rule, how shall we ever become acquainted with -any new cause? Or how do we know that the phenomena -which we contemplate do really arise from some -cause which we already truly know? If they do not, -must we still insist upon making them depend upon -some of our known causes; or must we abandon the -study of them altogether? Must we, for example, -resolve to refer the action of radiant heat to the air, -rather than to any peculiar fluid or ether, because the -former is known to exist, the latter is merely assumed -for the purpose of explanation? But why should we -do this? Why should we not endeavour to learn the -cause from the effects, even if it be not already known<span class="pagenum" id="Page_187">187</span> -to us? We can infer causes, which are new when we -first become acquainted with them. Chemical Forces, -Optical Forces, Vital Forces, are known to us only by -chemical and optical and vital phenomena; must we, -therefore, reject their existence or abandon their study? -They do not conform to the double condition, that they -shall be sufficient and <i>also</i> real: they are true, only so -far as they explain the facts, but are they, therefore, -unintelligible or useless? Are they not highly important -and instructive subjects of speculation? And -if the gravitation which rules the motions of the planets -had not existed at the earth's surface;—if it had -been there masked and concealed by the superior effect -of magnetism, or some other extraneous force,—might -not Newton still have inferred, from Kepler's laws, -the tendency of the planets to the sun; and from their -perturbations, their tendency to each other? His discoveries -would still have been immense, if the cause -which he assigned had not been a <i>vera causa</i> in the -sense now contemplated.</p> - - -<p><a id="XVIII7"></a>7. But what do we mean by calling gravity a "true -cause"? How do we learn its reality? Of course, by -its effects, with which we are familiar;—by the weight -and fall of bodies about us. These strike even the -most careless observer. No one can fail to see that all -bodies which we come in contact with are heavy;—that -gravity acts in our neighbourhood here upon -earth. Hence, it may be said, this cause is at any -rate a true cause, whether it explains the celestial -phenomena or not.</p> - -<p>But if this be what is meant by a <i>vera causa</i>, it -appears strange to require that in all cases we should -find such a one to account for all classes of phenomena. -Is it reasonable or prudent to demand that we -shall reduce every set of phenomena, however minute, -or abstruse, or complicated, to causes so obviously existing -as to strike the most incurious, and to be familiar -among men? How can we expect to find <i>such -veræ causæ</i> for the delicate and recondite phenomena -which an exact and skilful observer detects in chemical, -or optical, or electrical experiments? The facts<span class="pagenum" id="Page_188">188</span> -themselves are too fine for vulgar apprehension; their -relations, their symmetries, their measures require a -previous discipline to understand them. How then -can their causes be found among those agencies with -which the common unscientific herd of mankind are -familiar? What likelihood is there that causes held -for real by such persons, shall explain facts which such -persons cannot see or cannot understand?</p> - -<p>Again: if we give authority to such a rule, and -require that the causes by which science explains the -facts which she notes and measures and analyses, shall -be causes which men, without any special study, have -already come to believe in, from the effects which they -casually see around them, what is this, except to make -our first rude and unscientific persuasions the criterion -and test of our most laborious and thoughtful inferences? -What is it, but to give to ignorance and -thoughtlessness the right of pronouncing upon the convictions -of intense study and long-disciplined thought? -"Electrical atmospheres" surrounding electrized bodies, -were at one time held to be a "true cause" of -the effects which such bodies produce. These atmospheres, -it was said, are obvious to the senses; we -feel them like a spider's web on the hands and face. -Æpinus had to answer such persons, by proving that -there are no atmospheres, no effluvia, but only repulsion. -He thus, for a <i>true cause</i> in the vulgar sense of -the term, substituted an <i>hypothesis</i>; yet who doubts -that what he did was an advance in the science of -electricity?</p> - - -<p><a id="XVIII8"></a>8. Perhaps some persons may be disposed to say, -that Newton's Rule does not enjoin us to take those -causes only which we clearly know, or suppose we -know, to be really existing and operating, but only -causes <i>of such kinds</i> as we have already satisfied ourselves -do exist in nature. It may be urged that we -are entitled to infer that the planets are governed in -their motions by an attractive force, because we find, -in the bodies immediately subject to observation and -experiment, that such motions are produced by attractive -forces, for example, by that of the earth. It may<span class="pagenum" id="Page_189">189</span> -be said that we might on similar grounds infer forces -which unite particles of chemical compounds, or deflect -particles of light, because we see adhesion and deflection -produced by forces.</p> - -<p>But it is easy to show that the Rule, thus laxly understood, -loses all significance. It prohibits no hypothesis; -for all hypotheses suppose causes <i>such as</i>, in -some case or other, we have seen in action. No one -would think of explaining phenomena by referring -them to forces and agencies altogether different from -any which are known; for on this supposition, how -could he pretend to reason about the effects of the -assumed causes, or undertake to prove that they would -explain the facts? Some close similarity with some -known kind of cause is requisite, in order that the -hypothesis may have the appearance of an explanation. -No forces, or virtues, or sympathies, or fluids, -or ethers, would be excluded by <i>this</i> interpretation of -<i>veræ causæ</i>. Least of all, would such an interpretation -reject the Cartesian hypothesis of vortices; which -undoubtedly, as I conceive, Newton intended to condemn -by his Rule. For that <i>such</i> a case as a whirling -fluid, carrying bodies round a centre in orbits, does -occur, is too obvious to require proof. Every eddying -stream, or blast that twirls the dust in the road, exhibits -examples of such action, and would justify the -assumption of the vortices which carry the planets in -their courses; as indeed, without doubt, such facts -suggested the Cartesian explanation of the solar system. -The vortices, in this mode of considering the -subject, are at the least as <i>real</i> a cause of motion as -gravity itself.</p> - - -<p><a id="XVIII9"></a>9. Thus the Rule which enjoins "true causes," is -nugatory, if we take <i>veræ causæ</i> in the extended sense -of any causes of a real <i>kind</i>, and unphilosophical, if we -understand the term of <i>those very</i> causes which we -familiarly suppose to exist. But it may be said that -we are to designate as "true causes," not those which -are collected in a loose, confused and precarious manner, -by undisciplined minds, from obvious phenomena, -but those which are justly and rigorously inferred.<span class="pagenum" id="Page_190">190</span> -Such a cause, it may be added, gravity is; for the -facts of the downward pressures and downward motions -of bodies at the earth's surface lead us, by the -plainest and strictest induction, to the assertion of -such a force. Now to this interpretation of the Rule -there is no objection; but then, it must be observed, -that on this view, terrestrial gravity is inferred by the -same process as celestial gravitation; and the cause is -no more entitled to be called "true," because it is -obtained from the former, than because it is obtained -from the latter class of facts. We thus obtain an intelligible -and tenable explanation of a <i>vera causa</i>; -but then, by this explanation, its <i>verity</i> ceases to be -distinguishable from its other condition, that it "suffices -for the explanation of the phenomena." The -assumption of universal gravitation accounts for the -fall of a stone; it also accounts for the revolutions of -the Moon or of Saturn; but since both these explanations -are of the same kind, we cannot with justice -make the one a criterion or condition of the admissibility -of the other.</p> - - -<p><a id="XVIII10"></a>10. But still, the Rule, so understood, is so far -from being unmeaning or frivolous, that it expresses -one of the most important tests which can be given of -a sound physical theory. It is true, the explanation -of one set of facts may be of the same nature as the -explanation of the other class: but then, that the -cause explains <i>both</i> classes, gives it a very different -claim upon our attention and assent from that which -it would have if it explained one class only. The -very circumstance that the two explanations coincide, -is a most weighty presumption in their favour. It is -the testimony of two witnesses in behalf of the hypothesis; -and in proportion as these two witnesses are -separate and independent, the conviction produced by -their agreement is more and more complete. When -the explanation of two kinds of phenomena, distinct, -and not apparently connected, leads us to the same -cause, such a coincidence does give a reality to the -cause, which it has not while it merely accounts for -those appearances which suggested the supposition.<span class="pagenum" id="Page_191">191</span> -This coincidence of propositions inferred from separate -classes of facts, is exactly what we noticed in the -<i>Novum Organon Renovatum</i> (b. ii. c. 5, sect. 3), as -one of the most decisive characteristics of a true -theory, under the name of <i>Consilience of Inductions</i>.</p> - -<p>That Newton's First Rule of Philosophizing, so understood, -authorizes the inferences which he himself -made, is really the ground on which they are so firmly -believed by philosophers. Thus when the doctrine of -a gravity varying inversely as the square of the distance -from the body, accounted at the same time for -the relations of times and distances in the planetary -orbits and for the amount of the moon's deflection -from the tangent of her orbit, such a doctrine became -most convincing: or again, when the doctrine of the -universal gravitation of all parts of matter, which -explained so admirably the inequalities of the moon's -motions, also gave a satisfactory account of a phenomenon -utterly different, the precession of the equinoxes. -And of the same kind is the evidence in -favour of the undulatory theory of light, when the -assumption of the length of an undulation, to which -we are led by the colours of thin plates, is found to be -identical with that length which explains the phenomena -of diffraction; or when the hypothesis of transverse -vibrations, suggested by the facts of polarization, -explains also the laws of double refraction. When -such a convergence of two trains of induction points -to the same spot, we can no longer suspect that we -are wrong. Such an accumulation of proof really -persuades us that we have to do with a <i>vera causa</i>. -And if this kind of proof be multiplied;—if we again -find other facts of a sort uncontemplated in framing -our hypothesis, but yet clearly accounted for when we -have adopted the supposition;—we are still further -confirmed in our belief; and by such accumulation of -proof we may be so far satisfied, as to believe without -conceiving it possible to doubt. In this case, when -the validity of the opinion adopted by us has been -repeatedly confirmed by its sufficiency in unforeseen -cases, so that all doubt is removed and forgotten, the<span class="pagenum" id="Page_192">192</span> -theoretical cause takes its place among the realities of -the world, and becomes <i>a true cause</i>.</p> - - -<p><a id="XVIII11"></a>11. Newton's Rule then, to avoid mistakes, might -be thus expressed: That "we may, provisorily, assume -such hypothetical cause as will account for any given -class of natural phenomena; but that when two different -classes of facts lead us to the same hypothesis, -we may hold it to be a <i>true cause</i>." And this Rule -will rarely or never mislead us. There are no instances, -in which a doctrine recommended in this -manner has afterwards been discovered to be false. -There have been hypotheses which have explained -many phenomena, and kept their ground long, and -have afterwards been rejected. But these have been -hypotheses which explained only one class of phenomena; -and their fall took place when another kind of -facts was examined and brought into conflict with the -former. Thus the system of eccentrics and epicycles -accounted for all the observed <i>motions</i> of the planets, -and was the means of expressing and transmitting all -astronomical knowledge for two thousand years. But -then, how was it overthrown? By considering the -<i>distances</i> as well as motions of the heavenly bodies. -Here was a second class of facts; and when the system -was adjusted so as to agree with the one class, it -was at variance with the other. These cycles and -epicycles could not be true, because they could not be -made a just representation of the facts. But if the -measures of distance as well as of position had conspired -in pointing out the cycles and epicycles, as the -paths of the planets, the paths so determined could -not have been otherwise than their real paths; and -the epicyclical theory would have been, at least geometrically, -true.</p> - - -<p><a id="XVIII12"></a>12. <i>Of the Second Rule.</i>—Newton's Second Rule -directs that "natural events of the <i>same kind</i> are to -be referred to the <i>same causes</i>, so far as can be done." -Such a precept at first appears to help us but little; -for all systems, however little solid, profess to conform -to such a rule. When any theorist undertakes to explain -a class of facts, he assigns causes which, according<span class="pagenum" id="Page_193">193</span> -to him, will by their natural action, as seen in other -cases, produce the effects in question. The events -which he accounts for by his hypothetical cause, are, -he holds, of the same kind as those which such a cause -is known to produce. Kepler, in ascribing the planetary -motions to magnetism, Descartes, in explaining -them by means of vortices, held that they were referring -celestial motions to the causes which give rise -to terrestrial motions of the same kind. The question -is, <i>Are</i> the effects of the same kind? This once settled, -there will be no question about the propriety of assigning -them to the same cause. But the difficulty is, to -determine <i>when</i> events are of the same kind. Are -the motions of the planets of the same kind with the -motion of a body moving freely in a curvilinear -path, or do they not rather resemble the motion of a -floating body swept round by a whirling current? The -Newtonian and the Cartesian answered this question -differently. How then can we apply this Rule with -any advantage?</p> - - -<p><a id="XVIII13"></a>13. To this we reply, that there is no way of escaping -this uncertainty and ambiguity, but by obtaining -a clear possession of the ideas which our hypothesis -involves, and by reasoning rigorously from them. -Newton asserts that the planets move in free paths, -acted on by certain forces. The most exact calculation -gives the closest agreement of the results of this -hypothesis with the facts. Descartes asserts that the -planets are carried round by a fluid. The more rigorously -the conceptions of force and the laws of motion are -applied to this hypothesis, the more signal is its failure -in reconciling the facts to one another. Without such -calculation, we can come to no decision between the -two hypotheses. If the Newtonian hold that the -motions of the planets are <i>evidently</i> of the <i>same kind</i> -as those of a body describing a curve in free space, -and therefore, like that, to be explained by a force -acting upon the body; the Cartesian denies that the -planets do move in free space. They are, he maintains, -immersed in a plenum. It is only when it -appears that comets pass through this plenum in all<span class="pagenum" id="Page_194">194</span> -directions with no impediment, and that no possible -form and motion of its whirlpools can explain the forces -and motions which are observed in the solar system, -that he is compelled to allow the Newtonian's classification -of events of the <i>same kind</i>.</p> - -<p>Thus it does not appear that this Rule of Newton -can be interpreted in any distinct and positive manner, -otherwise than as enjoining that, in the task of induction, -we employ clear ideas, rigorous reasoning, and -close and fair comparison of the results of the hypothesis -with the facts. These are, no doubt, important -and fundamental conditions of a just induction; but -in this injunction we find no peculiar or technical -criterion by which we may satisfy ourselves that we -are right, or detect our errors. Still, of such general -prudential rules, none can be more wise than one -which thus, in the task of connecting facts by means -of ideas, recommends that the ideas be clear, the facts, -correct, and the chain of reasoning which connects -them, without a flaw.</p> - - -<p><a id="XVIII14"></a>14. <i>Of the Third Rule.</i>—The Third Rule, that -"qualities which are observed without exception be -held to be universal," as I have already said, seems to -be intended to authorize the assertion of gravitation -as a universal attribute of matter. We formerly stated, -in treating of Mechanical Ideas<a name="FNanchor_221" id="FNanchor_221"></a><a href="#Footnote_221" class="fnanchor">[221]</a>, that this application -of such a Rule appears to be a mode of reasoning far -from conclusive. The assertion of the universality of -any property of bodies must be grounded upon the -reason of the case, and not upon any arbitrary maxim. -Is it intended by this Rule to prohibit any further examination -how far gravity is an original property of -matter, and how far it may be resolved into the result -of other agencies? We know perfectly well that this -was not Newton's intention; since the cause of gravity -was a point which he proposed to himself as a subject -of inquiry. It would certainly be very unphilosophical -to pretend, by this Rule of Philosophizing, to prejudge -the question of such hypotheses as that of Mosotti,<span class="pagenum" id="Page_195">195</span> -That gravity is the excess of the electrical attraction -over electrical repulsion, and yet to adopt this hypothesis, -would be to suppose electrical forces more -truly universal than gravity; for according to the -hypothesis, gravity, being the inequality of the attraction -and repulsion, is only an accidental and partial -relation of these forces. Nor would it be allowable to -urge this Rule as a reason of assuming that double -stars are attracted to each other by a force varying -according to the inverse square of the distance; without -examining, as Herschel and others have done, the -orbits which they really describe. But if the Rule -is not available in such cases, what is its real value and -authority? and in what cases are they exemplified?</p> - - -<p><a id="XVIII15"></a>15. In a former work<a name="FNanchor_222" id="FNanchor_222"></a><a href="#Footnote_222" class="fnanchor">[222]</a>, it was shown that the -fundamental laws of motion, and the properties of -matter which these involve, are, after a full consideration -of the subject, unavoidably assumed as universally -true. It was further shown, that although our knowledge -of these laws and properties be gathered from experience, -we are strongly impelled, (some philosophers -think, authorized,) to look upon these as not only universally, -but necessarily true. It was also stated, that -the law of gravitation, though its universality may be -deemed probable, does not apparently involve the same -necessity as the fundamental laws of motion. But it -was pointed out that these are some of the most -abstruse and difficult questions of the whole of philosophy; -involving the profound, perhaps insoluble, -problem of the identity or diversity of Ideas and -Things. It cannot, therefore, be deemed philosophical -to cut these Gordian knots by peremptory maxims, -which encourage us to decide without rendering a -reason. Moreover, it appears clear that the reason -which is rendered for this Rule by the Newtonians is -quite untenable; namely, that we know extension, -hardness, and inertia, to be universal qualities of bodies -by experience alone, and that we have the same<span class="pagenum" id="Page_196">196</span> -evidence of experience for the universality of gravitation. -We have already observed that we cannot, with -any propriety, say that we <i>find</i> by experience all bodies -are extended. This could not be a just assertion, -unless we conceive the possibility of our finding the -contrary. But who can conceive our finding by experience -some bodies which are not extended? It -appears, then, that the reason given for the Third -Rule of Newton involves a mistake respecting the -nature and authority of experience. And the Rule -itself cannot be applied without attempting to decide, -by the casual limits of observation, questions which -necessarily depend upon the relations of ideas.</p> - - -<p><a id="XVIII16"></a>16. <i>Of the Fourth Rule.</i>—Newton's Fourth Rule -is, that "Propositions collected from phenomena by -induction, shall be held to be true, notwithstanding -contrary hypotheses; but shall be liable to be rendered -more accurate, or to have their exceptions pointed out, -by additional study of phenomena." This Rule contains -little more than a general assertion of the authority -of induction, accompanied by Newton's usual -protest against hypotheses.</p> - -<p>The really valuable part of the Fourth Rule is that -which implies that a constant verification, and, if necessary, -rectification, of truths discovered by induction, -should go on in the scientific world. Even when the -law is, or appears to be, most certainly exact and universal, -it should be constantly exhibited to us afresh in -the form of experience and observation. This is necessary, -in order to discover exceptions and modifications -if such exist: and if the law be rigorously true, the -contemplation of it, as exemplified in the world of -phenomena, will best give us that clear apprehension -of its bearings which may lead us to see the ground of -its truth.</p> - -<p>The concluding clause of this Fourth Rule appears, -at first, to imply that all inductive propositions are to -be considered as merely provisional and limited, and -never secure from exception. But to judge thus would -be to underrate the stability and generality of scientific -truths; for what man of science can suppose that we<span class="pagenum" id="Page_197">197</span> -shall hereafter discover exceptions to the universal -gravitation of all parts of the solar system? And it -is plain that the author did not intend the restriction -to be applied so rigorously; for in the Third Rule, -as we have just seen, he authorizes us to infer universal -properties of matter from observation, and carries -the liberty of inductive inference to its full -extent. The Third Rule appears to encourage us to -assert a law to be universal, even in cases in which -it has not been tried; the Fourth Rule seems to warn -us that the law may be inaccurate, even in cases in -which it has been tried. Nor is either of these suggestions -erroneous; but both the universality and the -rigorous accuracy of our laws are proved by reference -to Ideas rather than to Experience; a truth, which, -perhaps, the philosophers of Newton's time were somewhat -disposed to overlook.</p> - - -<p><a id="XVIII17"></a>17. The disposition to ascribe all our knowledge to -Experience, appears in Newton and the Newtonians -by other indications; for instance, it is seen in their -extreme dislike to the ancient expressions by which -the principles and causes of phenomena were described, -as the <i>occult causes</i> of the Schoolmen, and the <i>forms</i> -of the Aristotelians, which had been adopted by Bacon. -Newton says<a name="FNanchor_223" id="FNanchor_223"></a><a href="#Footnote_223" class="fnanchor">[223]</a>, that the particles of matter not only -possess inertia, but also active principles, as gravity, -fermentation, cohesion; he adds, "These principles I -consider not as Occult Qualities, supposed to result -from the Specific Forms of things, but as General -Laws of Nature, by which the things themselves are -formed: their truth appearing to us by phenomena, -though their causes be not yet discovered. For these -are manifest qualities, and their causes only are occult. -And the Aristotelians gave the name of <i>occult qualities</i>, -not to manifest qualities, but to such qualities only as -they supposed to lie hid in bodies, and to the unknown -causes of manifest effects: such as would be the causes -of gravity, and of magnetick and electrick attractions,<span class="pagenum" id="Page_198">198</span> -and of fermentations, if we should suppose that these -forces or actions arose from qualities unknown to us, -and incapable of being discovered and made manifest. -Such occult qualities put a stop to the improvement of -Natural Philosophy, and therefore of late years have -been rejected. To tell us that every species of things -is endowed with an occult specific quality by which it -acts and produces manifest effects, is to tell us nothing: -but to derive two or three general principles of -motion from phenomena, and afterwards to tell us how -the properties and actions of all corporeal things follow -from these manifest principles, would be a great -step in philosophy, though the causes of those principles -were not yet discovered: and therefore I scruple -not to propose the principles of motion above maintained, -they being of very general extent, and leave -their causes to be found out."</p> - - -<p><a id="XVIII18"></a>18. All that is here said is highly philosophical and -valuable; but we may observe that the investigation of -<i>specific forms</i> in the sense in which some writers had -used the phrase, was by no means a frivolous or unmeaning -object of inquiry. Bacon and others had used -<i>form</i> as equivalent to <i>law</i><a name="FNanchor_224" id="FNanchor_224"></a><a href="#Footnote_224" class="fnanchor">[224]</a>. If we could ascertain -that arrangement of the particles of a crystal from -which its external crystalline form and other properties -arise, this arrangement would be the <i>internal form</i> -of the crystal. If the undulatory theory be true, the -<i>form</i> of light is transverse vibrations: if the emission -theory be maintained, the <i>form</i> of light is particles -moving in straight lines, and deflected by various -forces. Both the terms, <i>form</i> and <i>law</i>, imply an ideal -connexion of sensible phenomena; form supposes mat<span class="pagenum" id="Page_199">199</span>ter -which is moulded to the form; law supposes objects -which are governed by the law. The former term -refers more precisely to existences, the latter to occurrences. -The latter term is now the more familiar, and -is, perhaps, the better metaphor: but the former also -contains the essential antithesis which belongs to the -subject, and might be used in expressing the same conclusions.</p> - -<p>But occult causes, employed in the way in which -Newton describes, had certainly been very prejudicial -to the progress of knowledge, by stopping inquiry with -a mere word. The absurdity of such pretended explanations -had not escaped ridicule. The pretended physician -in the comedy gives an example of an occult -cause or virtue.</p> - -<div class="poetry-container"><div class="poetry"><div class="stanza"> - <div class="verse indent4">Mihi demandatur</div> - <div class="verse indent4">A doctissimo Doctore</div> - <div class="verse indent2"><i>Quare</i> Opium facit dormire:</div> - <div class="verse indent4">Et ego respondeo,</div> - <div class="verse indent4"><i>Quia</i> est in eo</div> - <div class="verse indent4"><i>Virtus dormitiva</i>,</div> - <div class="verse">Cujus natura est sensus assoupire.</div> -</div></div></div> - - -<p><a id="XVIII19"></a>19. But the most valuable part of the view presented -to us in the quotation just given from Newton is -the distinct separation, already noticed as peculiarly -brought into prominence by him, of the determination -of the <i>laws</i> of phenomena, and the investigation of -their <i>causes</i>. The maxim, that the former inquiry -must precede the latter, and that if the general laws -of facts be discovered, the result is highly valuable, -although the causes remain unknown, is extremely -important; and had not, I think, ever been so strongly -and clearly stated, till Newton both repeatedly promulgated -the precept, and added to it the weight of -the most striking examples.</p> - -<p>We have seen that Newton, along with views the -most just and important concerning the nature and -methods of science, had something of the tendency, -prevalent in his time, to suspect or reject, at least -speculatively, all elements of knowledge except observation. -This tendency was, however, in him so<span class="pagenum" id="Page_200">200</span> -corrected and restrained by his own wonderful sagacity -and mathematical habits, that it scarcely led to any -opinion which we might not safely adopt. But we -must now consider the cases in which this tendency -operated in a more unbalanced manner, and led to the -assertion of doctrines which, if consistently followed, -would destroy the very foundations of all general and -certain knowledge.</p> - - - -<hr class="chap" /> - -<p><span class="pagenum" id="Page_201">201</span></p> - - -</div><div class="chapter"> -<h2><a name="CHAPTER_XIX" id="CHAPTER_XIX"></a>CHAPTER XIX.<br /> - -<span class="smcap medium">Locke and his French Followers.</span></h2> - - -<p><a id="XIX1"></a> -<span class="dropcap"><span class="dsmall">1.</span> I</span>N the constant opposition and struggle of the -schools of philosophy, which consider our Senses -and our Ideas respectively, as the principal sources of -our knowledge, we have seen that at the period of -which we now treat, the tendency was to exalt the -external and disparage the internal element. The disposition -to ascribe our knowledge to observation alone, -had already, in Bacon's time, led him to dwell to a -disproportionate degree upon that half of his subject; -and had tinged Newton's expressions, though it had -not biassed his practice. But this partiality soon assumed -a more prominent shape, becoming extreme in -Locke, and extravagant in those who professed to -follow him.</p> - -<p>Indeed Locke appears to owe his popularity and -influence as a popular writer mainly to his being one -of the first to express, in a plain and unhesitating -manner, opinions which had for some time been ripening -in the minds of a large portion of the cultivated -public. Hobbes had already promulgated the main -doctrines which Locke afterwards urged, on the subject -of the origin and nature of our knowledge: but -in him these doctrines were combined with offensive -opinions on points of morals, government, and religion, -so that their access to general favour was impeded: -and it was to Locke that they were indebted for the -extensive influence which they soon after obtained. -Locke owed this authority mainly to the intellectual -circumstances of the time. Although a writer of -great merit, he by no means possesses such metaphysical -acuteness or such philosophical largeness of view,<span class="pagenum" id="Page_202">202</span> -or such a charm of writing, as must necessarily give -him the high place he has held in the literature of -Europe. But he came at a period when the reign of -Ideas was tottering to its fall. All the most active -and ambitious spirits had gone over to the new opinions, -and were prepared to follow the fortunes of the Philosophy -of Experiment, then in the most prosperous -and brilliant condition, and full of still brighter promise. -There were, indeed, a few learned and thoughtful -men who still remained faithful to the empire of -Ideas; partly, it may be, from a too fond attachment -to ancient systems; but partly, also, because they knew -that there were subjects of vast importance, in which -experience did not form the whole foundation of our -knowledge. They knew, too, that many of the plausible -tenets of the new philosophy were revivals of -fallacies which had been discussed and refuted in ancient -times. But the advocates of mere experience -came on with a vast store of weighty truth among -their artillery, and with the energy which the advance -usually bestows. The ideal system of philosophy could, -for the present, make no effectual resistance; Locke, -by putting himself at the head of the assault, became -the hero of his day: and his name has been used as -the watchword of those who adhere to the philosophy -of the senses up to our own times.</p> - - -<p><a id="XIX2"></a>2. Locke himself did not assert the exclusive authority -of the senses in the extreme unmitigated -manner in which some who call themselves his disciples -have done. But this is the common lot of the -leaders of revolutions, for they are usually bound by -some ties of affection and habit to the previous state -of things, and would not destroy all traces of that -condition: while their followers attend, not to their -inconsistent wishes, but to the meaning of the revolution -itself; and carry out, to their genuine and complete -results, the principles which won the victory, -and which have been brought out more sharp from -the conflict. Thus Locke himself does not assert that -all our ideas are derived from Sensation, but from -Sensation <i>and Reflection</i>. But it was easily seen that,<span class="pagenum" id="Page_203">203</span> -in this assertion, two very heterogeneous elements -were conjoined: that while to pronounce Sensation -the origin of ideas, is a clear decided tenet, the acceptance -or rejection of which determines the general -character of our philosophy; to make the same declaration -concerning Reflection, is in the highest degree -vague and ambiguous; since reflection may either be -resolved into a mere modification of sensation, as was -done by one school, or may mean all that the opposite -school opposes to sensation, under the name of Ideas. -Hence the clear and strong impression which fastened -upon men's minds, and which does in fact represent -all the systematic and consistent part of Locke's philosophy, -was, that in it all our ideas are represented -as derived from Sensation.</p> - - -<p><a id="XIX3"></a>3. We need not spend much time in pointing out -the inconsistencies into which Locke fell; as all must -fall into inconsistencies who recognize no source of -knowledge except the senses. Thus he maintains that -our Idea of Space is derived from the senses of sight -and touch; our Idea of Solidity from the touch alone. -Our Notion of Substance is an unknown support of -unknown qualities, and is illustrated by the Indian -fable of the tortoise which supports the elephant, which -supports the world. Our Notion of Power or Cause -is in like manner got from the senses. And yet, -though these ideas are thus mere fragments of our -experience, Locke does not hesitate to ascribe to them -necessity and universality when they occur in propositions. -Thus he maintains the necessary truth of -geometrical properties: he asserts that the resistance -arising from solidity is absolutely insurmountable<a name="FNanchor_225" id="FNanchor_225"></a><a href="#Footnote_225" class="fnanchor">[225]</a>; he -conceives that nothing short of Omnipotence can -annihilate a particle of matter<a name="FNanchor_226" id="FNanchor_226"></a><a href="#Footnote_226" class="fnanchor">[226]</a>; and he has no misgivings -in arguing upon the axiom that Every thing -must have a cause. He does not perceive that, upon -his own account of the origin of our knowledge, we -can have no right to make any of these assertions. If<span class="pagenum" id="Page_204">204</span> -our knowledge of the truths which concern the external -world were wholly derived from experience, all -that we could venture to say would be,—that geometrical -properties of figures are true <i>as far as we have -tried them</i>;—that we have seen <i>no example</i> of a solid -body being reduced to occupy less space by pressure, -or of a material substance annihilated by natural -means;—and that <i>wherever we have examined</i>, we have -found that every change has had a cause. Experience -can never entitle us to declare that what she has not -seen is impossible; still less, that things which she can -not see are certain. Locke himself intended to throw -no doubt upon the certainty of either human or divine -knowledge; but his principles, when men discarded -the temper in which he applied them, and the checks -to their misapplication which he conceived that he -had provided, easily led to a very comprehensive skepticism. -His doctrines tended to dislodge from their -true bases the most indisputable parts of knowledge; -as, for example, pure and mixed mathematics. It may -well be supposed, therefore, that they shook the foundations -of many other parts of knowledge in the minds -of common thinkers.</p> - -<p>It was not long before these consequences of the -overthrow of ideas showed themselves in the speculative -world. I have already in a previous work<a name="FNanchor_227" id="FNanchor_227"></a><a href="#Footnote_227" class="fnanchor">[227]</a> -mentioned Hume's skeptical inferences from Locke's -maxim, that we have no ideas except those which -we acquire by experience; and the doctrines set up -in opposition to this by the metaphysicians of Germany. -I might trace the progress of the sensational -opinions in Britain till the reaction took place here -also: but they were so much more clearly and decidedly -followed out in France, that I shall pursue -their history in that country.</p> - - -<p><a id="XIX4"></a>4. <i>The French Followers of Locke, Condillac, &c.</i>—Most -of the French writers who adopted Locke's leading -doctrines, rejected the "Reflection," which formed<span class="pagenum" id="Page_205">205</span> -an anomalous part of his philosophy, and declared that -Sensation alone was the source of ideas. Among these -writers, Condillac was the most distinguished. He -expressed the leading tenet of their school in a clear -and pointed manner by saying that "All ideas are -transformed sensations." We have already considered -this phrase<a name="FNanchor_228" id="FNanchor_228"></a><a href="#Footnote_228" class="fnanchor">[228]</a>, and need not here dwell upon it.</p> - -<p>Opinions such as these tend to annihilate, as we -have seen, one of the two co-ordinate elements of our -knowledge. Yet they were far from being so prejudicial -to the progress of science, or even of the philosophy -of science, as might have been anticipated. One -reason of this was, that they were practically corrected, -especially among the cultivators of Natural Philosophy, -by the study of mathematics; for that study did really -supply all that was requisite on the ideal side of science, -so far as the ideas of space, time, and number, -were concerned, and partly also with regard to the idea -of cause and some others. And the methods of discovery, -though the philosophy of them made no material -advance, were practically employed with so much activity, -and in so many various subjects, that a certain -kind of prudence and skill in this employment was -very widely diffused.</p> - - -<p><a id="XIX5"></a>5. <i>Importance of Language.</i>—In one respect this -school of metaphysicians rendered a very valuable service -to the philosophy of science. They brought into -prominent notice the great importance of <i>words</i> and -<i>terms</i> in the formation and progress of knowledge, and -pointed out that the office of language is not only to -convey and preserve our thoughts, but to perform the -analysis in which reasoning consists. They were led -to this train of speculation, in a great measure, by -taking pure mathematical science as their standard -example of substantial knowledge. Condillac, rejecting, -as we have said, almost all those ideas on which -universal and demonstrable truths must be based, -was still not at all disposed to question the reality of<span class="pagenum" id="Page_206">206</span> -human knowledge; but was, on the contrary, a zealous -admirer of the evidence and connexion which appear -in those sciences which have the ideas of space and -number for their foundation, especially the latter. He -looked for the grounds of the certainty and reality of -the knowledge which these sciences contain; and found -them, as he conceived, in the nature of the <i>language</i> -which they employ. The <i>Signs</i> which are used in -arithmetic and algebra enable us to keep steadily in -view the identity of the same quantity under all the -forms which, by composition and decomposition, it -may be made to assume; and these Signs also not -only express the operations which are performed, but -suggest the extension of the operations according to -analogy. Algebra, according to him, is only a very -perfect language; and language answers its purpose of -leading us to truth, by possessing the characteristics of -algebra. Words are the symbols of certain groups of -impressions or facts; they are so selected and applied -as to exhibit the analogies which prevail among these -facts; and these analogies are the truths of which our -knowledge consists. "Every language is an analytical -method; every analytical method is a language<a name="FNanchor_229" id="FNanchor_229"></a><a href="#Footnote_229" class="fnanchor">[229]</a>;" -these were the truths "alike new and simple," as he -held, which he conceived that he had demonstrated. -"The art of speaking, the art of writing, the art of -reasoning, the art of thinking, are only, at bottom, one -and the same art<a name="FNanchor_230" id="FNanchor_230"></a><a href="#Footnote_230" class="fnanchor">[230]</a>." Each of these operations consists -in a succession of analytical operations; and words are -the marks by which we are able to fix our minds upon -the steps of this analysis.</p> - - -<p><a id="XIX6"></a>6. The analysis of our impressions and notions -does in reality lead to truth, not only in virtue of the -identity of the whole with its parts, as Condillac held, -but also in virtue of certain Ideas which govern the -synthesis of our sensations, and which contain the -elements of universal truths, as we have all along endeavoured -to show. But although Condillac overlooked -or rejected this doctrine, the importance of words, as<span class="pagenum" id="Page_207">207</span> -marking the successive steps of this synthesis and -analysis, is not less than he represented it to be. Every -truth, once established by induction from facts, when -it is become familiar under a brief and precise form -of expression, becomes itself a fact; and is capable of -being employed, along with other facts of a like kind, -as the materials of fresh inductions. In this successive -process, the term, like the cord of a fagot, both binds -together the facts which it includes, and makes it possible -to manage the assemblage as a single thing. On -occasion of most discoveries in science, the selection of -a technical term is an essential part of the proceeding. -In the <i>History of Science</i>, we have had numerous opportunities -of remarking this; and the List of technical -terms given as an Index to that work, refers us, by -almost every word, to one such occasion. And these -terms, which thus have had so large a share in the -formation of science, and which constitute its language, -do also offer the means of analyzing its truths, each -into its constituent truths; and these into facts more -special, till the original foundations of our most general -propositions are clearly exhibited. The relations -of general and particular truths are most evidently -represented by the Inductive Tables given in Book II. -of the <i>Novum Organon Renovatum</i>. But each step -in each of these Tables has its proper form of expression, -familiar among the cultivators of science; -and the analysis which our Tables display, is commonly -performed in men's minds, when it becomes -necessary, by fixing the attention successively upon a -series of words, not upon the lines of a Table. Language -offers to the mind such a scale or ladder as the -Table offers to the eye; and since such Tables present -to us, as we have said, the Logic of Induction, that is, -the formal conditions of the soundness of our reasoning -from facts, we may with propriety say that a just analysis -of the meaning of words is an essential portion of -Inductive Logic.</p> - -<p>In saying this, we must not forget that a decomposition -of general truths into ideas, as well as into -facts, belongs to our philosophy; but the point we<span class="pagenum" id="Page_208">208</span> -have here to remark, is the essential importance of -words to the latter of these processes. And this point -had not ever had its due weight assigned to it till the -time of Condillac and other followers of Locke, who -pursued their speculations in the spirit I have just -described. The doctrine of the importance of terms is -the most considerable addition to the philosophy of -science which has been made since the time of Bacon<a name="FNanchor_231" id="FNanchor_231"></a><a href="#Footnote_231" class="fnanchor">[231]</a>.</p> - - -<p><a id="XIX7"></a>7. <i>The French Encyclopedists.</i>—The French <i>Encyclopédie</i>, -published in 1751, of which Diderot and Dalembert -were the editors, may be considered as representing -the leading characters of European philosophy -during the greater part of the eighteenth century. The -writers in this work belong for the most part to the -school of Locke and Condillac; and we may make a -few remarks upon them, in order to bring into view -one or two points in addition to what we have already -said of that school. The <i>Discours Préliminaire</i>, written -by Dalembert, is celebrated as containing a view of -the origin of our knowledge, and the connexion and -classification of the sciences.</p> - -<p>A tendency of the speculations of the Encyclopedists, -as of the School of Locke in general, is to reject -all ideal principles of connexion among facts, as something -which experience, the only source of true knowledge, -does not give. Hence all certain knowledge -consists only in the recognition of the same thing under -different aspects, or different forms of expression. -Axioms are not the result of an original relation of -ideas, but of the use, or it may be the abuse<a name="FNanchor_232" id="FNanchor_232"></a><a href="#Footnote_232" class="fnanchor">[232]</a>, of words. -In like manner, the propositions of Geometry are a -series of modifications,—of distortions, so to speak,—of -one original truth; much as if the proposition were -stated in the successive forms of expression presented -by a language which was constantly growing more and<span class="pagenum" id="Page_209">209</span> -more artificial. Several of the sciences which rest -upon physical principles, that is, (says the writer,) -truths of experience or simple hypotheses, have only -an experimental or hypothetical certainty. Impenetrability -added to the idea of extent is a mystery in -addition: the nature of motion is a riddle for philosophers: -the metaphysical principle of the laws of percussion -is equally concealed from them. The more -profoundly they study the idea of matter and of the -properties which represent it, the more obscure this -idea becomes; the more completely does it escape -them.</p> - - -<p><a id="XIX8"></a>8. This is a very common style of reflection, even -down to our own times. I have endeavoured to show -that concerning the Fundamental Ideas of space, of -force and resistance, of substance, external quality, -and the like, we know enough to make these Ideas the -grounds of certain and universal truths;—enough to -supply us with axioms from which we can demonstratively -reason. If men wish for any other knowledge -of the nature of matter than that which ideas, and -facts conformable to ideas, give them, undoubtedly -their desire will be frustrated, and they will be left in -a mysterious vacancy; for it does not appear how such -knowledge as they ask for could be knowledge at all. -But in reality, this complaint of our ignorance of the -real nature of things proceeds from the rejection of -ideas, and the assumption of the senses alone as the -ground of knowledge. "Observation and calculation -are the only sources of truth:" this is the motto of -the school of which we now speak. And its import -amounts to this:—that they reject all ideas except the -idea of number, and recognize the modifications which -parts undergo by addition and subtraction as the only -modes in which true propositions are generated. The -laws of nature are assemblages of facts: the truths of -science are assertions of the identity of things which -are the same. "By the avowal of almost all philosophers," -says a writer of this school<a name="FNanchor_233" id="FNanchor_233"></a><a href="#Footnote_233" class="fnanchor">[233]</a>, "the most sublime<span class="pagenum" id="Page_210">210</span> -truths, when once simplified and reduced to their lowest -terms, are converted into facts, and thenceforth -present to the mind only this proposition; the white is -white, the black is black."</p> - -<p>These statements are true in what they positively -assert, but they involve error in the denial which by -implication they convey. It is true that observation -and demonstration are the only sources of scientific -truth; but then, demonstration may be founded on -other grounds besides the elementary properties of -number. It is true that the theory of gravitation is -but the assertion of a general fact; but this is so, not -because a sound theory does not involve ideas, but because -our apprehension of a fact does.</p> - - -<p><a id="XIX9"></a>9. Another characteristic indication of the temper -of the Encyclopedists and of the age to which they -belong, is the importance by them assigned to those -practical <i>Arts</i> which minister to man's comfort and -convenience. Not only, in the body of the Encyclopedia, -are the Mechanical Arts placed side by side -with the Sciences, and treated at great length; but in -the Preliminary Discourse, the preference assigned to -the liberal over the mechanical Arts is treated as a -prejudice<a name="FNanchor_234" id="FNanchor_234"></a><a href="#Footnote_234" class="fnanchor">[234]</a>, and the value of science is spoken of as -measured by its utility. "The discovery of the Mariner's -Compass is not less advantageous to the human -race than the explanation of its properties would be to -physics.—Why should we not esteem those to whom -we owe the fusee and the escapement of watches as -much as the inventors of Algebra?" And in the classification -of sciences which accompanies the Discourse, -the labours of artisans of all kinds have a place.</p> - -<p>This classification of the various branches of science -contained in the Dissertation is often spoken of. It -has for its basis the classification proposed by Bacon, -in which the parts of human knowledge are arranged -according to the faculties of the mind in which they -originate; and these faculties are taken, both by Bacon -and by Dalembert, as Memory, Reason, and Imagi<span class="pagenum" id="Page_211">211</span>nation. -The insufficiency of Bacon's arrangement as a -scientific classification is so glaring, that the adoption -of it, with only superficial modifications, at the period -of the Encyclopedia, is a remarkable proof of the want -of original thought and real philosophy at the time of -which we speak.</p> - - -<p><a id="XIX10"></a>10. We need not trace further the opinion which -derives all our knowledge from the senses in its application -to the philosophy of Science. Its declared aim -is to reduce all knowledge to the knowledge of Facts; -and it rejects all inquiries which involve the Idea of -Cause, and similar Ideas, describing them as "metaphysical," -or in some other damnatory way. It professes, -indeed, to discard all Ideas; but, as we have -long ago seen, some Ideas or other are inevitably included -even in the simplest Facts. Accordingly the -speculations of this school are compelled to retain the -relations of Position, Succession, Number and Resemblance, -which are rigorously ideal relations. The philosophy -of Sensation, in order to be consistent, ought -to reject these Ideas along with the rest, and to deny -altogether the possibility of general knowledge.</p> - -<p>When the opinions of the Sensational School had -gone to an extreme length, a Reaction naturally began -to take place in men's minds. Such have been the -alternations of opinion, from the earliest ages of human -speculation. Man may perhaps have existed in an -original condition in which he was only aware of the -impressions of Sense; but his first attempts to analyse -his perceptions brought under his notice Ideas as a -separate element, essential to the existence of knowledge. -Ideas were thenceforth almost the sole subject -of the study of philosophers; of Plato and his disciples, -professedly; of Aristotle, and still more of the -followers and commentators of Aristotle, practically. -And this continued till the time of Galileo, when the -authority of the Senses again began to be asserted; -for it was shown by the great discoveries which were -then made, that the Senses had at least some share in -the promotion of knowledge. As discoveries more -numerous and more striking were supplied by Obser<span class="pagenum" id="Page_212">212</span>vation, -the world gradually passed over to the opinion -that the share which had been ascribed to Ideas in the -formation of real knowledge was altogether a delusion, -and that Sensation alone was true. But when this -was asserted as a general doctrine, both its manifest -falsity and its alarming consequences roused men's -minds, and made them recoil from the extreme point -to which they were approaching. Philosophy again -oscillated back towards Ideas; and over a great part of -Europe, in the clearest and most comprehensive minds, -this regression from the dogmas of the Sensational -School is at present the prevailing movement. We -shall conclude our review by noticing a few indications -of this state of things.</p> - - - -<hr class="chap" /> - -<p><span class="pagenum" id="Page_213">213</span></p> - - -</div><div class="chapter"> -<h2><a name="CHAPTER_XX" id="CHAPTER_XX"></a>CHAPTER XX.<br /> - -<span class="smcap medium">The Reaction against the Sensational School.</span></h2> - - -<p><a id="XX1"></a> -<span class="dropcap"><span class="dsmall">1.</span> W</span>HEN Locke's <i>Essay</i> appeared, it was easily -seen that its tendency was to urge, in a much -more rigorous sense than had previously been usual, -the ancient maxim of Aristotle, adopted by the schoolmen -of the middle ages, that "nothing exists in the -intellect but what has entered by the senses." Leibnitz -expressed in a pointed manner the limitation with -which this doctrine had always been understood. "Nihil -est in intellectu quod non prius fuerit in sensu;—<i>nempe</i>," -he added, "<i>nisi intellectus ipse</i>." To this it -has been objected<a name="FNanchor_235" id="FNanchor_235"></a><a href="#Footnote_235" class="fnanchor">[235]</a>, that we cannot say that the intellect -is <i>in</i> the intellect. But this remark is obviously -frivolous; for the faculties of the understanding -(which are what the argument against the Sensational -School requires us to reserve) may be said to be <i>in</i> the -understanding, with as much justice as we may assert -there are <i>in</i> it the impressions derived from sense. -And when we take account of these faculties, and -of the Ideas to which, by their operation, we necessarily -subordinate our apprehension of phenomena, we -are led to a refutation of the philosophy which makes -phenomena, unconnected by Ideas, the source of all -knowledge. The succeeding opponents of the Lockian -school insisted upon and developed in various ways -this remark of Leibnitz, or some equivalent view.</p> - - -<p><a id="XX2"></a>2. It was by inquiries into the foundations of -Morals that English philosophers were led to question -the truth of Locke's theory. Dr. Price, in his <i>Review<span class="pagenum" id="Page_214">214</span> -of the Principal Questions in Morals</i>, first published -in 1757, maintained that we cannot with propriety -assert all our ideas to be derived from sensation and -reflection. He pointed out, very steadily, the other -source. "The power, I assert, that <i>understands</i>, or -the faculty within us that discerns <i>truth</i>, and that -compares all the objects of thought and <i>judges</i> of them, -is a spring of new ideas<a name="FNanchor_236" id="FNanchor_236"></a><a href="#Footnote_236" class="fnanchor">[236]</a>." And he exhibits the antithesis -in various forms. "Were not <i>sense</i> and <i>knowledge</i> -entirely different, we should rest satisfied with sensible -impressions, such as light, colours and sounds, and inquire -no further about them, at least when the impressions -are strong and vigorous: whereas, on the -contrary, we necessarily desire some further acquaintance -with them, and can never be satisfied till we have -subjected them to the survey of reason. Sense presents -<i>particular</i> forms to the mind, but cannot rise to any -<i>general</i> ideas. It is the intellect that examines and -compares the presented forms, that rises above individuals -to universal and abstract ideas; and thus looks -downward upon objects, takes in at one view an infinity -of particulars, and is capable of discovering -general truths. Sense sees only the outside of things, -reason acquaints itself with their natures. Sensation -is only a mode of feeling in the mind; but knowledge -implies an active and vital energy in the mind<a name="FNanchor_237" id="FNanchor_237"></a><a href="#Footnote_237" class="fnanchor">[237]</a>."</p> - - -<p><a id="XX3"></a>3. The necessity of refuting Hume's inferences from -the mere sensation system led other writers to limit, in -various ways, their assent to Locke. Especially was -this the case with a number of intelligent metaphysicians -in Scotland, as Reid, Beattie, Dugald Stewart, -and Thomas Brown. Thus Reid asserts<a name="FNanchor_238" id="FNanchor_238"></a><a href="#Footnote_238" class="fnanchor">[238]</a>, "that the -account which Mr. Locke himself gives of the Idea of -Power cannot be reconciled to his favourite doctrine, -that all our simple ideas have their origin from sensation -or reflection." Reid remarks, that our memory -and our reasoning power come in for a share in the<span class="pagenum" id="Page_215">215</span> -origin of this idea: and in speaking of reasoning, he -obviously assumes the axiom that every event must -have a cause. By succeeding writers of this school, -the assumption of the fundamental principles, to which -our nature in such cases irresistibly directs us, is more -clearly pointed out. Thus Stewart defends the form -of expression used by Price<a name="FNanchor_239" id="FNanchor_239"></a><a href="#Footnote_239" class="fnanchor">[239]</a>: "A variety of intuitive -judgments might be mentioned, involving simple ideas, -which it is impossible to trace to any origin but to the -power which enables us to form these judgments. Thus -it is surely an intuitive truth that the sensations of -which I am conscious, and all those I remember, belong -to one and the same being, which I call <i>myself</i>. -Here is an intuitive judgment involving the simple -idea of <i>Identity</i>. In like manner, the changes which -I perceive in the universe impress me with a conviction -that some cause must have operated to produce -them. Here is an intuitive judgment involving the -simple Idea of <i>Causation</i>. When we consider the -adjacent angles made by a straight line standing upon -another, and perceive that their sum is equal to two -right angles, the judgment we form involves a simple -idea of <i>Equality</i>. To say, therefore, that the Reason -or the Understanding is a source of new ideas, is not -so exceptionable a mode of speaking as has been sometimes -supposed. According to Locke, <i>Sense</i> furnishes -our ideas, and Reason perceives their agreements and -disagreements. But the truth is, that these agreements -and disagreements are in many instances, simple -ideas, of which no analysis can be given; and of -which the origin must therefore be referred to Reason, -according to Locke's own doctrine." This view, according -to which the Reason or Understanding is the -source of certain simple ideas, such as Identity, Causation, -Equality, which ideas are necessarily involved -in the intuitive judgments which we form, when we -recognize fundamental truths of science, approaches -very near in effect to the doctrine which in several works -I have presented, of Fundamental Ideas belonging to<span class="pagenum" id="Page_216">216</span> -each science, and manifesting themselves in the axioms -of the science. It may be observed, however, that by -attempting to enumerate these ideas and axioms, so as -to lay the foundations of the whole body of physical -science, and by endeavouring, as far as possible, to -simplify and connect each group of such Ideas, I -have at least given a more systematic form to this -doctrine. I have, moreover, traced it into many -consequences to which it necessarily leads, but which -do not appear to have been contemplated by the metaphysicians -of the Scotch school. But I gladly acknowledge -my obligations to the writers of that school; -and I trust that in the near agreement of my views -on such points with theirs, there is ground for believing -the system of philosophy which I have presented, -to be that to which the minds of thoughtful men, -who have meditated on such subjects, are generally -tending.</p> - - -<p><a id="XX4"></a>4. As a further instance that such a tendency is -at work, I may make a quotation from an eminent -English philosophical writer of another school. "If -you will be at the pains," says Archbishop Whately<a name="FNanchor_240" id="FNanchor_240"></a><a href="#Footnote_240" class="fnanchor">[240]</a>, -"carefully to analyze the simplest description you hear -of any transaction or state of things, you will find that -the process which almost invariably takes place is, in -logical language, this: that each individual <i>has in his -mind</i> certain major premises or principles relative to -the subject in question;—that observation of what -actually presents itself to the senses, supplies minor -premises; and that the statement given (and which is -reported as a thing experienced) consists, in fact, of -the <i>conclusions</i> drawn from the combinations of these -premises." The major premises here spoken of are -the Fundamental Ideas, and the Axioms and Propositions -to which they lead; and whatever is regarded -as a fact of observation is necessarily a conclusion in -which these propositions are assumed; for these contain, -as we have said, the conditions of our experience.<span class="pagenum" id="Page_217">217</span> -Our experience conforms to these axioms and their -consequences, whether or not the connexion be stated -in a logical manner, by means of premises and a conclusion.</p> - - -<p><a id="XX5"></a>5. The same persuasion is also suggested by the -course which the study of metaphysics has taken of -late years in France. In that country, as we have -seen, the Sensational System, which was considered as -the necessary consequence of the revolution begun by -Locke, obtained a more complete ascendancy than it -did in England; and in that country too, the reaction, -among metaphysical and moral writers, when its time -came, was more decided and rapid than it was among -Locke's own countrymen. It would appear that M. -Laromiguière was one of the first to give expression to -this feeling, of the necessity of a modification of the -sensational philosophy. He began by professing himself -the disciple of Condillac, even while he was almost -unconsciously subverting the fundamental principles -of that writer. And thus, as M. Cousin justly observes<a name="FNanchor_241" id="FNanchor_241"></a><a href="#Footnote_241" class="fnanchor">[241]</a>, -his opinions had the more powerful effect from -being presented, not as thwarting and contradicting, -but as sharing and following out the spirit of his age. -M. Laromiguière's work, entitled <i>Essai sur les Facultés -de l'Ame</i>, consists of lectures given to the Faculty -of Letters of the Academy of Paris, in the years 1811, -1812 and 1813. In the views which these lectures -present, there is much which the author has in common -with Condillac. But he is led by his investigation -to assert<a name="FNanchor_242" id="FNanchor_242"></a><a href="#Footnote_242" class="fnanchor">[242]</a>, that it is not true that sensation is the -sole fundamental element of our thoughts and our understanding. -<i>Attention</i> also is requisite: and here we -have an element of quite another kind. For sensation -is passive; attention is active. Attention does not -spring out of sensation; the passive principle is not -the reason of the active principle. Activity and passivity -are two facts entirely different. Nor can this -activity be defined or derived; being, as the author<span class="pagenum" id="Page_218">218</span> -says, a fundamental idea. The distinction is manifest -by its own nature; and we may find evidence of it in -the very forms of language. To <i>look</i> is more than to -<i>see</i>; to <i>hearken</i> is more than to <i>hear</i>. The French -language marks this distinction with respect to other -senses also. "On <i>voit</i>, et l'on <i>regarde</i>; on <i>entend</i>, et -l'on <i>écoute</i>; on <i>sent</i>, et l'on <i>flaire</i>; on <i>goûte</i>, et l'on -<i>savoure</i>." And thus the mere sensation, or capacity -of feeling, is only the occasion on which the attention -is exercised; while the attention is the foundation of -all the operations of the understanding.</p> - -<p>The reader of my works will have seen how much -I have insisted upon the activity of the mind, -as the necessary basis of all knowledge. In all observation -and experience, the mind is active, and -by its activity apprehends all sensations in subordination -to its own ideas; and thus it becomes capable -of collecting knowledge from phenomena, since -ideas involve general relations and connexions, which -sensations of themselves cannot involve. And thus -we see that, in this respect also, our philosophy -stands at that point to which the speculations of the -most reflecting men have of late constantly been -verging.</p> - - -<p><a id="XX6"></a>6. M. Cousin himself, from whom we have quoted -the above account of Laromiguière, shares in this tendency, -and has argued very energetically and successfully -against the doctrines of the Sensational School. -He has made it his office once more to bring into -notice among his countrymen, the doctrine of ideas as -the sources of knowledge; and has revived the study -of Plato, who may still be considered as one of the -great leaders of the ideal school. But the larger -portion of M. Cousin's works refers to questions -out of the reach of our present review, and it would -be unsuitable to dwell longer upon them in this -place.</p> - - -<p><a id="XX7"></a>7. We turn to speculations more closely connected -with our present subject. M. Ampère, a French man -of science, well entitled by his extensive knowledge, -and large and profound views, to deal with the philo<span class="pagenum" id="Page_219">219</span>sophy -of the sciences, published in 1834, his <i>Essai sur -la Philosophie des Sciences, ou Exposition analytique -d'une Classification Naturelle de toutes les Connaissances -Humaines</i>. In this remarkable work we see strong -evidence of the progress of the reaction against the -system which derives our knowledge from sensation -only. The author starts from a maxim, that in classing -the sciences, we must not only regard the nature -of the objects about which each science is concerned, -but also the point of view under which it considers -them: that is, the <i>ideas</i> which each science involves. -M. Ampère also gives briefly his views of the intellectual -constitution of man; a subject on which he -had long and sedulously employed his thoughts; and -these views are far from belonging to the Sensational -School. Human thought, he says, is composed of phenomena -and of conceptions. Phenomena are external, -or <i>sensitive</i>; and internal, or <i>active</i>. Conceptions are -of four kinds; <i>primitive</i>, as space and motion, duration -and cause; <i>objective</i>, as our idea of matter and substance; -<i>onomatic</i>, or those which we associate with -the general terms which language presents to us; and -<i>explicative</i>, by which we ascend to causes after a comparative -study of phenomena. He teaches further, -that in deriving ideas from sensation, the mind is not -passive; but exerts an action which, when voluntary, -is called <i>attention</i>, but when it is, as it often is, involuntary, -may be termed <i>reaction</i>.</p> - -<p>I shall not dwell upon the examination of these -opinions<a name="FNanchor_243" id="FNanchor_243"></a><a href="#Footnote_243" class="fnanchor">[243]</a>; but I may remark, that both in the recognition -of conceptions as an original and essential element -of the mind, and in giving a prominent place to -the active function of the mind, in the origin of our -knowledge, this view approaches to that which I have -presented in preceding works; although undoubtedly -with considerable differences.</p> - - -<p><a id="XX8"></a>8. The classification of the sciences which M.<span class="pagenum" id="Page_220">220</span> -Ampère proposes, is founded upon a consideration of -the sciences themselves; and is, the author conceives, -in accordance with the conditions of natural classifications, -as exhibited in Botany and other sciences. It -is of a more symmetrical kind, and exhibits more steps -of subordination, than that to which I have been led; -it includes also practical Art as well as theoretical Science; -and it is extended to moral and political as well -as physical Sciences. It will not be necessary for me -here to examine it in detail: but I may remark, that -it is throughout a <i>dichotomous</i> division, each higher -member being subdivided into two lower ones, and so -on. In this way, M. Ampère obtains sciences of the -First Order, each of which is divided into two sciences -of the Second, and four of the Third Order. Thus -Mechanics is divided into <i>Cinematics</i>, <i>Statics</i>, <i>Dynamics</i>, -and <i>Molecular Mechanics</i>; Physics is divided -into <i>Experimental Physics</i>, <i>Chemistry</i>, <i>Stereometry</i>, and -<i>Atomology</i>; Geology is divided into <i>Physical Geography</i>, -<i>Mineralogy</i>, <i>Geonomy</i>, and <i>Theory of the Earth</i>. -Without here criticizing these divisions or their principle, -I may observe that <i>Cinematics</i>, the doctrine of -motion without reference to the force which produces -it, is a portion of knowledge which our investigation -has led us also to see the necessity of erecting into -a separate science; and which we have termed <i>Pure -Mechanism</i>. Of the divisions of Geology, <i>Physical -Geography</i>, especially as explained by M. Ampère, is -certainly a part of the subject, both important and -tolerably distinct from the rest. <i>Geonomy</i> contains -what we have termed in the History, <i>Descriptive Geology</i>;—the -exhibition of the facts separate from the -inquiry into their causes; while our <i>Physical Geology</i> -agrees with M. Ampère's <i>Theory of the Earth</i>. <i>Mineralogy</i> -appears to be placed by him in a different place -from that which it occupies in our scheme: but in -fact, he uses the term for a different science; he -applies it to the classification not of <i>simple minerals</i>, -but of <i>rocks</i>, which is a science auxiliary to geology, -and which has sometimes been called <i>Petralogy</i>. What -we have termed <i>Mineralogy</i>, M. Ampère unites with<span class="pagenum" id="Page_221">221</span> -<i>Chemistry</i>. "It belongs," he says<a name="FNanchor_244" id="FNanchor_244"></a><a href="#Footnote_244" class="fnanchor">[244]</a>, "to Chemistry, -and not to Mineralogy, to inquire how many atoms of -silicium and of oxygen compose silica; to tell us that -its primitive form is a rhombohedron of certain angles, -that it is called <i>quartz</i>, &c.; leaving, on one hand, to -Molecular Geometry the task of explaining the different -secondary forms which may result from the primitive -form; and on the other hand, leaving to Mineralogy -the office of describing the different varieties of -quartz, and the rocks in which they occur, according -as the quartz is crystallized, transparent, coloured, -amorphous, solid, or in sand." But we may remark, -that by adopting this arrangement, we separate from -Mineralogy almost all the knowledge, and absolutely -all the general knowledge, which books professing to -treat of that science have usually contained. The -consideration of Mineralogical Classifications, which, -as may be seen in the <i>History of Science</i>, is so curious -and instructive, is forced into the domain of Chemistry, -although many of the persons who figure in it were -not at all properly chemists. And we lose, in this -way, the advantage of that peculiar office which, in -our arrangement, Mineralogy fills; of forming a rigorous -transition from the sciences of classification to -those which consider the mathematical properties of -bodies; and connecting the external characters and -the internal constitution of bodies by means of a system -of important general truths. I conceive, therefore, -that our disposition of this science, and our mode of -applying the name, are far more convenient than those -of M. Ampère.</p> - - -<p><a id="XX9"></a>9. We have seen the reaction against the pure sensational -doctrines operating very powerfully in England -and in France. But it was in Germany that these -doctrines were most decidedly rejected; and systems -in extreme opposition to these put forth with confidence, -and received with applause. Of the authors -who gave this impulse to opinions in that country, Kant<span class="pagenum" id="Page_222">222</span> -was the first, and by far the most important. I have -in the <i>History of Ideas</i> (b. iii. c. 3), endeavoured to explain -how he was aroused, by the skepticism of Hume, -to examine wherein the fallacy lay which appeared to -invalidate all reasonings from effect to cause; and how -this inquiry terminated in a conviction that the foundations -of our reasonings on this and similar points were -to be sought in the mind, and not in the phenomena;—in -the <i>subject</i>, and not in the <i>object</i>. The revolution -in the customary mode of contemplating human knowledge -which Kant's opinions involved, was most complete. -He himself, with no small justice, compares<a name="FNanchor_245" id="FNanchor_245"></a><a href="#Footnote_245" class="fnanchor">[245]</a> -it with the change produced by Copernicus's theory -of the solar system. "Hitherto," he says, "men have -assumed that all our knowledge must be regulated -by the objects of it; yet all attempts to make out -anything concerning objects <i>à priori</i> by means of our -conceptions," (as for instance their geometrical properties) -"must, on this foundation, be unavailing. Let -us then try whether we cannot make out something -more in the problems of metaphysics, by assuming -that objects must be regulated by our knowledge, -since this agrees better with that supposition, which -we are prompted to make, that we can know something -of them <i>à priori</i>. This thought is like that of -Copernicus, who, when he found that nothing was to -be made of the phenomena of the heavens so long -as everything was supposed to turn about the spectator, -tried whether the matter might not be better -explained if he made the spectator turn, and left the -stars at rest. We may make the same essay in metaphysics, -as to what concerns our intuitive knowledge -respecting objects. If our apprehension of objects -must be regulated by the properties of the objects, I -cannot comprehend how we can possibly know anything -about them <i>à priori</i>. But if the object, as apprehended -by us, be regulated by the constitution of -our faculties of apprehension, I can readily conceive<span class="pagenum" id="Page_223">223</span> -this possibility." From this he infers that our experience -must be regulated by our conceptions.</p> - - -<p><a id="XX10"></a>10. This view of the nature of knowledge soon -superseded entirely the doctrines of the Sensational -School among the metaphysicians of Germany. These -philosophers did not gradually modify and reject the -dogmas of Locke and Condillac, as was done in England -and France<a name="FNanchor_246" id="FNanchor_246"></a><a href="#Footnote_246" class="fnanchor">[246]</a>; nor did they endeavour to ascertain -the extent of the empire of Ideas by a careful survey -of its several provinces, as we have been doing in -this series of works. The German metaphysicians -saw at once that Ideas and Things, the Subjective -and the Objective elements of our knowledge, were, -by Kant's system, brought into opposition and correlation, -as equally real and equally indispensable. -Seeing this, they rushed at once to the highest -and most difficult problem of philosophy,—to determine -what this correlation is;—to discover how Ideas -and Things are at the same time opposite and identical;—how -the world, while it is distinct from and -independent of us, is yet, as an object of our knowledge, -governed by the conditions of our thoughts. -The attempts to solve this problem, taken in the widest -sense, including the forms which it assumes in Morals, -Politics, the Arts, and Religion, as well as in the -Material Sciences, have, since that time, occupied the -most profound speculators of Germany; and have given -rise to a number of systems, which, rapidly succeeding -each other, have, each in its day, been looked upon -as a complete solution of the problem. To trace the -characters of these various systems, does not belong -to the business of the present chapter: my task is -ended when I have shown, as I have now done, how -the progress of thought in the philosophical world, -followed from the earliest up to the present time, has<span class="pagenum" id="Page_224">224</span> -led to that recognition of the co-existence and joint -necessity of the two opposite elements of our knowledge; -and when I have pointed out processes adapted -to the extension of our knowledge, which a true view -of its nature has suggested or may suggest.</p> - -<p>The latter portion of this task occupies the Third -Book of the <i>Novum Organon Renovatum</i>. With regard -to the recent succession of German systems of philosophy, -I shall add something in a subsequent chapter: -and I shall also venture to trace further than I have -yet done, the bearing of the philosophy of science -upon the theological view of the universe and the -moral and religious condition of man.</p> - - - -<hr class="chap" /> - -<p><span class="pagenum" id="Page_225">225</span></p> - - -</div><div class="chapter"> -<h2><a name="CHAPTER_XXI" id="CHAPTER_XXI"></a>CHAPTER XXI.<br /> - -<span class="smcap medium">Further Advance of the Sensational School.<br /> - -M. Auguste Comte.</span></h2> - - -<p class="drop-cap"><span class="smcap">I shall</span> now take the liberty of noticing the views -published by a contemporary writer; not that it -forms part of my design to offer any criticism upon -the writings of all those who have treated of those -subjects on which we are now employed; but because -we can more distinctly in this manner point out the -contrasts and ultimate tendencies of the several systems -of opinion which have come under our survey: -and since from among these systems we have endeavoured -to extract and secure the portion of truth -which remains in each, and to reject the rest, we are -led to point out the errors on which our attention is -thus fixed, in recent as well as older writers.</p> - -<p>M. Auguste Comte published in 1830 the first, and -in 1835 the second volume of his <i>Cours de Philosophie -Positive</i>; of which the aim is not much different from -that of the present work, since as he states (p. viii.) -such a title as the <i>Philosophy of the Sciences</i> would -describe a part of his object, and would be inappropriate -only by excluding that portion (not yet published) -which refers to speculations concerning social -relations.</p> - - -<p><a id="XXI1"></a>1. <i>M. Comte on Three States of Science.</i>—By employing -the term <i>Philosophie Positive</i>, he wishes to -distinguish the philosophy involved in the present -state of our sciences from the previous forms of human -knowledge. For according to him, each branch of -knowledge passes, in the course of man's history, -through three different states; it is first <i>theological</i>, -then <i>metaphysical</i>, then <i>positive</i>. By the latter term<span class="pagenum" id="Page_226">226</span> -he implies a state which includes nothing but general -representations of facts;—phenomena <i>arranged according</i> -to relations of succession and resemblance. This -"positive philosophy" rejects all inquiry after causes, -which inquiry he holds to be void of sense<a name="FNanchor_247" id="FNanchor_247"></a><a href="#Footnote_247" class="fnanchor">[247]</a> and inaccessible. -All such conceptions belong to the "metaphysical" -state of science which deals with abstract -forces, real entities, and the like. Still more completely -does he reject, as altogether antiquated and absurd, -the "theological" view of phenomena. Indeed he -conceives<a name="FNanchor_248" id="FNanchor_248"></a><a href="#Footnote_248" class="fnanchor">[248]</a> that any one's own consciousness of what -passes within himself is sufficient to convince him of -the truth of the law of the three phases through which -knowledge must pass. "Does not each of us," he -says, "in contemplating his own history, recollect -that he has been successively a <i>theologian</i> in his infancy, -a <i>metaphysician</i> in his youth, and a <i>physicist</i> in -his ripe age? This may easily be verified for all men -who are up to the level of their time."</p> - -<p>It is plain from such statements, and from the whole -course of his work, that M. Comte holds, in their most -rigorous form, the doctrines to which the speculations -of Locke and his successors led; and which tended, -as we have seen, to the exclusion of all ideas except -those of number and resemblance. As M. Comte -refuses to admit into his philosophy the fundamental -idea of Cause, he of course excludes most of the other -ideas, which are, as we endeavoured to show, the -foundations of science; such as the ideas of Media by -which secondary qualities are made known to us; the -ideas of Chemical Attraction, of Polar Forces, and -the like. He would reduce all science to the mere -expression of laws of phenomena, expressed in formulæ -of space, time, and number; and would condemn as -unmeaning, and as belonging to an obsolete state of -science, all endeavours to determine the causes of -phenomena, or even to refer them to any of the other -ideas just mentioned.</p> - -<p><span class="pagenum" id="Page_227">227</span></p> - - -<p><a id="XXI2"></a>2. <i>M. Comte rejects the Search of Causes.</i>—In -a previous work<a name="FNanchor_249" id="FNanchor_249"></a><a href="#Footnote_249" class="fnanchor">[249]</a> I have shown, I trust decisively, -that it is the genuine office of science to inquire -into the causes as well as the laws of phenomena;—that -such an inquiry cannot be avoided; and -that it has been the source of almost all the science -we possess. I need not here repeat the arguments -there urged; but I may make a remark or two upon -M. Comte's hypothesis, that all science is first "metaphysical" -and then "positive;" since it is in virtue -of this hypothesis that he rejects the investigation of -causes, as worthy only of the infancy of science. All -discussions concerning ideas, M. Comte would condemn -as "metaphysical," and would consider as mere preludes -to positive philosophy. Now I venture to assert, -on the contrary, that discussions concerning ideas, and -real discoveries, have in every science gone hand in -hand. There is no science in which the pretended -order of things can be pointed out. There is no science -in which the discoveries of the laws of phenomena, -when once begun, have been carried on independently -of discussions concerning ideas. There is no science -in which the expression of the laws of phenomena can -at this time dispense with ideas which have acquired -their place in science in virtue of metaphysical considerations. -There is no science in which the most -active disquisitions concerning ideas did not come -<i>after</i>, not <i>before</i>, the first discovery of laws of phenomena. -In Astronomy, the discovery of the phenomenal -laws of the epicyclical motions of the heavens -led to assumptions of the metaphysical principle of -equable circular motions: Kepler's discoveries would -never have been made but for his metaphysical notions. -These discoveries of the laws of phenomena did not -lead immediately to Newton's theory, <i>because</i> a century -of metaphysical discussions was requisite as a preparation. -Newton then discovered, not merely a law -of phenomena, but a <i>cause</i>; and <i>therefore</i> he was the<span class="pagenum" id="Page_228">228</span> -greatest of discoverers. The same is the case in Optics; -the ancients possessed some share of our knowledge -of facts; but meddled little with the metaphysical -reasonings of the subject. In modern times -when men began to inquire into the <i>nature</i> of light, -they soon extended their knowledge of its <i>laws</i>. When -this series of discoveries had come to a pause, a new -series of brilliant discoveries of laws of phenomena -went on, inseparably connected with a new series of -views of the nature and cause of light. In like manner, -the most modern discoveries in chemistry involve -indispensably the idea of polar forces. The metaphysics -(in M. Comte's sense) of each subject advances in -a parallel line with the knowledge of physical laws. -The Explication of Conceptions must go on, as we -have already shown, at the same rate as the Colligation -of Facts.</p> - -<p>M. Comte will say<a name="FNanchor_250" id="FNanchor_250"></a><a href="#Footnote_250" class="fnanchor">[250]</a> that Newton's discovery of -gravitation only consists in exhibiting the astronomical -phenomena of the universe as one single fact under -different points of view. But this <i>fact</i> involves the -idea of <i>force</i>, that is, of <i>cause</i>. And that this idea -is not a mere modification of the ideas of time and -space, we have shown: if it were so, how could it -lead to the axiom that attraction is mutual, an indispensable -part of the Newtonian theory? M. Comte -says<a name="FNanchor_251" id="FNanchor_251"></a><a href="#Footnote_251" class="fnanchor">[251]</a> that we do not know what attraction is, since we -can only define it by identical phrases: but this is just -as true of space, or time, or motion; and is in fact -exactly the characteristic of a fundamental idea. We -do not obtain such ideas from definitions, but we possess -them not the less truly because we cannot define -them.</p> - -<p>That M. Comte's hypothesis is historically false, is -obvious by such examples as I have mentioned. Metaphysical -discussions have been essential steps in the -progress of each science. If we arbitrarily reject all -these portions of scientific history as useless trifling,<span class="pagenum" id="Page_229">229</span> -belonging to the first rude attempts at knowledge, we -shall not only distort the progress of things, but pervert -the plainest facts. Of this we have an example -in M. Comte's account of Kepler's mechanical speculations. -We have seen, in the History of Physical -Astronomy, that Kepler's second law, (that the planets -describe areas about the sun proportional to the times,) -was proved by him, by means of calculations founded -on the observations of Tycho; but that the mechanical -reason of it was not assigned till a later period, -when it appeared as the first proposition of Newton's -<i>Principia</i>. It is plain from the writings of Kepler, -that it was impossible for him to show how this law -resulted from the forces which were in action; since -the forces which he considered were not those tending -to the centre, which really determine the property in -question, but forces exerted by the sun <i>in the direction -of the planet's motion</i>, without which forces Kepler -conceived that the motion could not go on. In short, -the state of mechanical science in Kepler's time was -such that no demonstration of the law could be given. -The terms in which such a demonstration must be -expressed had not at that time acquired a precise -significance; and it was in virtue of many subsequent -<i>metaphysical</i> discussions (as M. Comte would term -them) that these terms became capable of expressing -sound mechanical reasoning. Kepler did indeed pretend -to assign what he called a "physical proof" of -his law, depending upon this, that the sun's force is -less at greater distances; a condition which does not -at all influence the result. Thus Kepler's reason for -his law proves nothing but the confusion of thought in -which he was involved on such subjects. Yet M. Comte -assigns to Kepler the credit of having proved this law -by sound mechanical reasoning, as well as established -it as a matter of fact<a name="FNanchor_252" id="FNanchor_252"></a><a href="#Footnote_252" class="fnanchor">[252]</a>. "This discovery by Kepler,"<span class="pagenum" id="Page_230">230</span> -he adds, "is the more remarkable, inasmuch as it occurred -before the science of dynamics had really been -created by Galileo." We may remark that inasmuch -as M. Comte perceived this incongruity in the facts as -he stated them, it is the more remarkable that he did -not examine them more carefully.</p> - - -<p><a id="XXI3"></a>3. <i>Causes in Physics.</i>—The condemnation of the -inquiry into causes which is conveyed in M. Comte's -notion of the three stages of Science, he again expresses -more in detail, in stating<a name="FNanchor_253" id="FNanchor_253"></a><a href="#Footnote_253" class="fnanchor">[253]</a> what he calls his -<i>Fundamental theory of hypotheses</i>. This "theory" is, that -we may employ hypotheses in our natural philosophy, -but these hypotheses must always be such as admit of -a positive verification. We must have no suppositions -concerning the agents by which effects are produced. -All such suppositions have an anti-scientific character, -and can only impede the real progress of physics. -There can be no use in the ethers and imaginary fluids -to which some persons refer the phenomena of heat, -light, electricity and magnetism. And in agreement -with this doctrine, M. Comte in his account<a name="FNanchor_254" id="FNanchor_254"></a><a href="#Footnote_254" class="fnanchor">[254]</a> of the<span class="pagenum" id="Page_231">231</span> -Science of Optics, condemns, as utterly unphilosophical -and absurd, both the theory of emission and -that of undulation.</p> - -<p>To this we reply, that theory of one kind or other -is indispensable to the expression of the phenomena; -and that when the laws are expressed, and apparently -explained, by means of a theory, to forbid us to inquire -whether it be really true or false, is a pedantic -and capricious limitation of our knowledge, to which -the intellect of man neither can nor should submit. -If any one holds the adoption of one or other of these -theories to be indifferent, let him express the <i>laws of -phenomena</i> of diffraction in terms of the theory of -emission<a name="FNanchor_255" id="FNanchor_255"></a><a href="#Footnote_255" class="fnanchor">[255]</a>. If any one rejects the doctrine of undulation, -let him point out some other way of connecting -double refraction with polarization. And surely no -man of science will contend that the beautiful branch -of science which refers to that connexion is not a -portion of our positive knowledge.</p> - -<p>M. Comte's contempt for the speculations of the -undulationists seems to have prevented his acquainting -himself with their reasonings, and even with the laws -of phenomena on which they have reasoned, although -these form by far the most striking and beautiful -addition which Science has received in modern times. -He adduces, as an insuperable objection to the undulatory -theory, a difficulty which is fully removed by -calculation in every work on the subject:—the existence -of shadow<a name="FNanchor_256" id="FNanchor_256"></a><a href="#Footnote_256" class="fnanchor">[256]</a>. He barely mentions the subject of -diffraction, and Young's law of interferences;—speaks -of Fresnel as having applied this principle to the -phenomena of coloured rings, "on which the ingenious -labours of Newton left much to desire;" as if Fresnel's -labours on this subject had been the supplement of -those of Newton: and after regretting that "this -principle of interferences has not yet been distinctly<span class="pagenum" id="Page_232">232</span> -disentangled from chemical conceptions on the nature -of light," concludes his chapter. He does not even -mention the phenomena of dipolarization, of circular -and elliptical polarization, or of the optical properties -of crystals; discoveries of laws of phenomena quite as -remarkable as any which can be mentioned.</p> - -<p>M. Comte's favourite example of physical research -is Thermotics, and especially Fourier's researches with -regard to heat. It is shown<a name="FNanchor_257" id="FNanchor_257"></a><a href="#Footnote_257" class="fnanchor">[257]</a> in the History of Thermotics, -that the general phenomena of radiation required -the assumption of a fluid to express them; -as appears in the <i>theory of exchanges</i><a name="FNanchor_258" id="FNanchor_258"></a><a href="#Footnote_258" class="fnanchor">[258]</a>. And the explanation -of the principal laws of radiation, which -Fourier gives, depends upon the conception of material -molecular radiation. The <i>flux</i> of caloric, of which -Fourier speaks, cannot be conceived otherwise than as -implying a material flow. M. Comte apologizes<a name="FNanchor_259" id="FNanchor_259"></a><a href="#Footnote_259" class="fnanchor">[259]</a> for -this expression, as too figurative, and says that it -merely indicates a <i>fact</i>. But what is the flow of a -current of fluid except a fact? And is it not evident -that without such expressions, and the ideas corresponding -to them, Fourier could neither have conveyed -nor conceived his theory?</p> - -<p>In concluding this discussion it must be recollected, -that though it is a most narrow and untenable rule to -say that we will admit no agency of ethers and fluids -into philosophy; yet the reality of such agents is only -to be held in the way, and to the extent, which the -laws of phenomena indicate. It is not only allowable, -but inevitable to assume, as the vehicle of heat and -light, a medium possessing some of the properties of -more familiar kinds of matter. But the idea of such -a medium, which we possess, and on which we cannot -but reason, can be fully developed only by an assiduous -study of the cases in which it is applicable. It -may be, that as science advances, all our knowledge -may converge to one general and single aspect of the<span class="pagenum" id="Page_233">233</span> -universe. We abandon and reject this hope, if we -refuse to admit those ideas which must be our stepping-stones -in advancing to such a point: and we no -less frustrate such an expectation, if we allow ourselves -to imagine that from our present position we can stride -at once to the summit.</p> - - -<p><a id="XXI4"></a>4. <i>Causes in other Sciences.</i>—But if it is, in the -sciences just mentioned, impracticable to reduce our -knowledge to laws of phenomena alone, without referring -to causes, media, and other agencies; how much -more plainly is it impossible to confine our thoughts -to phenomena, and to laws of succession and resemblance, -in other sciences, as chemistry, physiology, and -geology? Who shall forbid us, or why should we be -forbidden, to inquire whether chemical and galvanic -forces are identical; whether irritability is a peculiar -vital power; whether geological causes have been uniform -or paroxysmal? To exclude such inquiries, would -be to secure ourselves from the poison of error by -abstaining from the banquet of truth:—it would be to -attempt to feed our minds with the meagre diet of -space and number, because we may find too delightful -a relish in such matters as cause and end, symmetry -and affinity, organization and development.</p> - -<p>Thus M. Comte's arrangement of the progress of -science as successively metaphysical and positive, is -contrary to history in fact, and contrary to sound philosophy -in principle. Nor is there any better foundation -for his statement that theological views are to be -found only in the rude infantine condition of human -knowledge, and vanish as science advances. Even in -material sciences this is not the case. We have shown -in the chapter on Final Causes, that physiologists have -been directed in their remarks by the conviction of a -purpose in every part of the structure of animals; and -that this idea, which had its rise <i>after</i> the first observations, -has gone on constantly gaining strength and -clearness, so that it is now the basis of a large portion -of the science. We have seen, too, in the Book on the -palætiological sciences, that the researches of that class -do by no means lead us to reject an origin of the series<span class="pagenum" id="Page_234">234</span> -of events, nor to suppose this origin to be included in -the series of natural laws. Science has not at all -shown any reason for denying either the creation or -the purpose of the universe.</p> - -<p>This is true of those aspects of the universe which -have become the subjects of rigorous science: but how -small a portion of the whole do they form! Especially -how minute a proportion does our knowledge bear to -our ignorance, if we admit into science, as M. Comte -advises, only the laws of phenomena! Even in the -best explored fields of science, how few such laws do -we know! Meteorology, climate, terrestrial magnetism, -the colours and other properties of bodies, the conditions -of musical and articulate sound, and a thousand -other facts of physics, are not defined by any -known laws. In physiology we may readily convince -ourselves how little we know of laws, since we can -hardly study one species without discovering some unguessed -property, or apply the microscope without -seeing some new structure in the best known organs. -And when we go on to social and moral and political -matters, we may well doubt whether any one single -rigorous rule of phenomena has ever been stated, although -on such subjects man's ideas have been busily -and eagerly working ever since his origin. What a -wanton and baseless assumption it would be, then, to -reject those suggestions of a Governor of the universe -which we derive from man's moral and spiritual nature, -and from the institutions of society, because we -fancy we see in the small field of our existing "positive -knowledge" a tendency to exclude "theological views!" -Because we can explain the motion of the stars by a -general Law which seems to imply no hyperphysical -agency, and can trace a few more limited laws in -other properties of matter, we are exhorted to reject -convictions irresistibly suggested to us by our bodies -and our souls, by history and antiquities, by conscience -and human law.</p> - - -<p><a id="XXI5"></a>5. <i>M. Comte's practical philosophy.</i>—It is not -merely as a speculative doctrine that M. Comte urges -the necessity of our thus following the guidance of<span class="pagenum" id="Page_235">235</span> -"positive philosophy." The fevered and revolutionary -condition of human society at present arises, according -to him<a name="FNanchor_260" id="FNanchor_260"></a><a href="#Footnote_260" class="fnanchor">[260]</a>, from the simultaneous employment of three -kinds of philosophy radically incompatible;—theological, -metaphysical, and positive philosophy. The -remedy for the evil is to reject the two former, and to -refer everything to that positive philosophy, of which -the destined triumph cannot be doubtful. In like -manner, our European education<a name="FNanchor_261" id="FNanchor_261"></a><a href="#Footnote_261" class="fnanchor">[261]</a>, still essentially -theological, metaphysical, and literary, must be replaced -by a <i>positive</i> education, suited to the spirit of -our epoch.</p> - -<p>With these practical consequences of M. Comte's -philosophy we are not here concerned: but the notice -of them may serve to show how entirely the rejection -of the theological view pervades his system; and how -closely this rejection is connected with the principles -which lead him also to reject the fundamental ideas of -the sciences as we have presented them.</p> - - -<p><a id="XXI6"></a>6. <i>M. Comte on Hypotheses.</i>—In the detail of -M. Comte's work, I do not find any peculiar or novel -remarks on the induction by which the sciences are -formed; except we may notice, as such, his permission -of hypotheses to the inquirer, already referred to. -"There can only be," he says<a name="FNanchor_262" id="FNanchor_262"></a><a href="#Footnote_262" class="fnanchor">[262]</a>, "two general modes -fitted to reveal to us, in a direct and entirely rational -manner, the true law of any phenomenon;—either the -immediate analysis of this phenomenon, or its exact -and evident relation to some more extended law, previously -established;—in a word, <i>induction</i>, or <i>deduction</i>. -But both these ways would certainly be insufficient, -even with regard to the simplest phenomenon, -in the eyes of any one who fully comprehends the -essential difficulties of the intimate study of nature, if -we did not often begin by anticipating the result, and -making a provisory supposition, at first essentially -conjectural, even with respect to some of the notions -which constitute the final object of inquiry. Hence<span class="pagenum" id="Page_236">236</span> -the introduction, which is strictly indispensable, of -hypotheses in natural philosophy." We have already -seen that the "permissio intellectus" had been noticed -as a requisite step in discovery, as long before as the -time of Bacon.</p> - - -<p><a id="XXI7"></a>7. <i>M. Comte's Classification of Sciences.</i>—I do not -think it necessary to examine in detail M. Comte's -views of the philosophy of the different sciences; but -it may illustrate the object of the present work, to -make a remark upon his attempt to establish a distinction -between physical and chemical science. This distinction -he makes to consist in three points<a name="FNanchor_263" id="FNanchor_263"></a><a href="#Footnote_263" class="fnanchor">[263]</a>;—that -Physics considers general and Chemistry special properties;—that -Physics considers masses and Chemistry -molecules;—that in Physics the mode of arrangement -of the molecules remains constant, while in Chemistry -this arrangement is necessarily altered. M. Comte -however allows that these lines of distinction are vague -and insecure; for, among many others, magnetism, a -special property, belongs to physics, and breaks down -his first criterion; and molecular attractions are a constant -subject of speculation in physics, so that the -second distinction cannot be insisted on. To which -we may add that the greater portion of chemistry does -not attend at all to the arrangement of the molecules, -so that the third character is quite erroneous. The -real distinction of these branches of science is, as we -have seen, the fundamental ideas which they employ. -Physics deals with relations of space, time, and number, -media, and scales of qualities, according to intensity -and other differences; while chemistry has for its -subject elements and attractions as shown in composition; -and polarity, though in different senses, belongs -to both. The failure of this attempt of M. Comte at distinguishing -these provinces of science by their objects, -may be looked upon as an illustration of the impossibility -of establishing a philosophy of the sciences on -any other ground than the ideas which they involve.</p> - -<p><span class="pagenum" id="Page_237">237</span></p> - -<p>We have thus traced to its extreme point, so far as -the nature of science is concerned, one of those two -antagonistic opinions, of which the struggle began in -the outset of philosophy, and has continued during the -whole of her progress;—namely, the opinions which -respectively make our sensations and our ideas the -origin of our knowledge. The former, if it be consistent -with itself, must consider all knowledge of causes -as impossible, since no sensation can give us the idea -of cause. And when this opinion is applied to science, -it reduces it to the mere investigation of laws of phenomena, -according to relations of space, time, and -number. I purposely abstain, as far as possible, from -the consideration of the other consequences, not strictly -belonging to the physical sciences, which were drawn -from the doctrine that all our ideas are only transformed -sensations. The materialism, the atheism, the -sensualist morality, the anarchical polity, which some -of the disciples of the Sensational School erected upon -the fundamental dogmas of their sect, do not belong to -our present subject, and are matters too weighty to be -treated of as mere accessories.</p> - -<hr class="tb" /> - -<p>The above Remarks were written before I had seen -the third volume of M. Comte's work, or the subsequent -volumes. But I do not find, in anything which -those volumes contain, any ground for altering what I -have written. Indeed they are occupied altogether -with subjects which do not come within the field of my -present speculations.</p> - - - -<hr class="chap" /> - -<p><span class="pagenum" id="Page_238">238</span></p> - - -</div><div class="chapter"> -<h2><a name="CHAPTER_XXII" id="CHAPTER_XXII"></a>CHAPTER XXII.<br /> - -<span class="smcap medium">Mr. Mill's Logic<a name="FNanchor_264" id="FNanchor_264"></a><a href="#Footnote_264" class="fnanchor">[264]</a>.</span></h2> - - -<p class="drop-cap"><span class="smcap">The</span> <i>History of the Inductive Sciences</i> was published -in 1837, and the <i>Philosophy of the Inductive -Sciences</i> in 1840. In 1843 Mr. Mill published his -<i>System of Logic</i>, in which he states that without the -aid derived from the facts and ideas in my volumes, -the corresponding portion of his own would most probably -not have been written, and quotes parts of what -I have said with commendation. He also, however, -dissents from me on several important and fundamental -points, and argues against what I have said -thereon. I conceive that it may tend to bring into a -clearer light the doctrines which I have tried to establish, -and the truth of them, if I discuss some of the -differences between us, which I shall proceed to do<a name="FNanchor_265" id="FNanchor_265"></a><a href="#Footnote_265" class="fnanchor">[265]</a>.</p> - -<p>Mr. Mill's work has had, for a work of its abstruse -character, a circulation so extensive, and admirers so -numerous and so fervent, that it needs no commendation -of mine. But if my main concern at present had -not been with the points in which Mr. Mill <i>differs</i> -from me, I should have had great pleasure in pointing -out passages, of which there are many, in which Mr. -Mill appears to me to have been very happy in promoting -or in expressing philosophical truth.</p> - -<p>There is one portion of his work indeed which -tends to give it an interest of a wider kind than be<span class="pagenum" id="Page_239">239</span>longs -to that merely scientific truth to which I purposely -and resolutely confined my speculations in the -works to which I have referred. Mr. Mill has introduced -into his work a direct and extensive consideration -of the modes of dealing with moral and political -as well as physical questions; and I have no doubt -that this part of his book has, for many of his readers, -a more lively interest than any other. Such a comprehensive -scheme seems to give to doctrines respecting -science a value and a purpose which they cannot -have, so long as they are restricted to mere material -sciences. I still retain the opinion, however, upon -which I formerly acted, that the philosophy of science -is to be extracted from the portions of science which -are universally allowed to be most certainly established, -and that those are the physical sciences. I am -very far from saying, or thinking, that there is no -such thing as Moral and Political Science, or that no -method can be suggested for its promotion; but I -think that by attempting at present to include the -Moral Sciences in the same formulæ with the Physical, -we open far more controversies than we close; -and that in the moral as in the physical sciences, the -first step towards showing how truth is to be discovered, -is to study some portion of it which is assented -to so as to be beyond controversy.</p> - - -<p>I. <a id="XXII1"></a><i>What is Induction?</i>—1. Confining myself, then, -to the material sciences, I shall proceed to offer my -remarks on Induction with especial reference to Mr. -Mill's work. And in order that we may, as I have -said, proceed as intelligibly as possible, let us begin -by considering what we mean by <i>Induction</i>, as a mode -of obtaining truth; and let us note whether there is -any difference between Mr. Mill and me on this subject.</p> - -<p>"For the purposes of the present inquiry," Mr. Mill -says (i. 347<a name="FNanchor_266" id="FNanchor_266"></a><a href="#Footnote_266" class="fnanchor">[266]</a>), "Induction may be defined the opera<span class="pagenum" id="Page_240">240</span>tion -of discovering and forming general propositions:" -meaning, as appears by the context, the discovery of -them from particular facts. He elsewhere (i. 370) -terms it "generalization from experience:" and again -he speaks of it with greater precision as the inference -of a more general proposition from less general ones.</p> - -<p>2. Now to these definitions and descriptions I -assent as far as they go; though, as I shall have to -remark, they appear to me to leave unnoticed a feature -which is very important, and which occurs in all -cases of Induction, so far as we are concerned with it. -Science, then, consists of general propositions, inferred -from particular facts, or from less general propositions, -by Induction; and it is our object to discern the nature -and laws of <i>Induction</i> in this sense. That the -propositions are general, or are more general than the -facts from which they are inferred, is an indispensable -part of the notion of Induction, and is essential to any -discussion of the process, as the mode of arriving at -Science, that is, at a body of general truths.</p> - -<p>3. I am obliged therefore to dissent from Mr. Mill -when he includes, in his notion of Induction, the process -by which we arrive <i>at individual facts</i> from other -facts <i>of the same order of particularity</i>.</p> - -<p>Such inference is, at any rate, not Induction <i>alone</i>; -if it be Induction at all, it is Induction applied to an -example.</p> - -<p>For instance, it is a general law, obtained by Induction -from particular facts, that a body falling vertically -downwards from rest, describes spaces proportional -to the squares of the times. But that a particular -body will fall through 16 feet in one second -and 64 feet in two seconds, is not an induction simply, -it is a result obtained by applying the inductive law -to a particular case.</p> - -<p>But further, such a process is often not induction -<i>at all</i>. That a ball striking another ball directly will -communicate to it as much momentum as the striking -ball itself loses, is a law established by induction: but -if, from habit or practical skill, I make one billiard-ball -strike another, so as to produce the velocity which<span class="pagenum" id="Page_241">241</span> -I wish, without knowing or thinking of the general -law, the term <i>Induction</i> cannot then be rightly applied. -If I <i>know the law</i> and act upon it, I have in -my mind both the general induction and its particular -application. But if I act by the ordinary billiard-player's -skill, without thinking of momentum or law, -there is no Induction in the case.</p> - -<p>4. This distinction becomes of importance, in reference -to Mr. Mill's doctrine, because he has extended -his use of the term <i>Induction</i>, not only to the cases in -which the general induction is consciously applied to -a particular instance; but to the cases in which the -particular instance is dealt with by means of experience, -in that rude sense in which <i>experience</i> can be -asserted of brutes; and in which, of course, we can in -no way imagine that the law is possessed or understood, -as a general proposition. He has thus, as I -conceive, overlooked the broad and essential difference -between speculative knowledge and practical action; -and has introduced cases which are quite foreign to -the idea of science, alongside with cases from which -we may hope to obtain some views of the nature of -science and the processes by which it must be formed.</p> - -<p>5. Thus (ii. 232) he says, "This inference of one -particular fact from another is a case of induction. -It is of this sort of induction that brutes are capable." -And to the same purpose he had previously said (i. -251), "He [the burnt child who shuns the fire] is not -generalizing: he is inferring a particular from particulars. -In the same way also, brutes reason ... not -only the burnt child, but the burnt dog, dreads the -fire."</p> - -<p>6. This confusion, (for such it seems to me,) of -knowledge with practical tendencies, is expressed more -in detail in other places. Thus he says (i. 118), "I -cannot dig the ground unless I have an idea of the -ground and of a spade, and of all the other things I -am operating upon."</p> - -<p>7. This appears to me to be a use of words which -can only tend to confuse our idea of knowledge by obliterating -all that is distinctive in <i>human</i> knowledge.<span class="pagenum" id="Page_242">242</span> -It seems to me quite false to say that I cannot dig the -ground, unless I have an idea of the ground and of my -spade. Are we to say that we cannot <i>walk</i> the ground, -unless we have an idea of the ground, and of our feet, -and of our shoes, and of the muscles of our legs? Are -we to say that a mole cannot dig the ground, unless -he has an idea of the ground and of the snout and -paws with which he digs it? Are we to say that a -pholas cannot perforate a rock, unless he have an idea -of the rock, and of the acid with which he corrodes it?</p> - -<p>8. This appears to me, as I have said, to be a line -of speculation which can lead to nothing but confusion. -The knowledge concerning which I wish to inquire is -<i>human</i> knowledge. And in order that I may have -any chance of success in the inquiry, I find it necessary -to single out that kind of knowledge which is -especially and distinctively human. Hence, I pass by, -in this part of my investigation, all the <i>knowledge</i>, if -it is to be so called, which man has in no other way -than brutes have it;—all that merely shows itself in -action. For though action may be modified by habit, -and habit by experience, in animals as well as in men, -such experience, so long as it retains that merely practical -form, is no part of the materials of science. -Knowledge in a <i>general</i> form, is alone knowledge for -that purpose; and to <i>that</i>, therefore, I must confine -my attention; at least till I have made some progress -in ascertaining its nature and laws, and am thus prepared -to compare such knowledge,—<i>human knowledge</i> -properly so called,—with mere animal tendencies to -action; or even with practical skill which does not -include, as for the most part practical skill does not -include, speculative knowledge.</p> - -<p>9. And thus, I accept Mr. Mill's definition of Induction -only in its first and largest form; and reject, -as useless and mischievous for our purposes, his extension -of the term to the practical influence which experience -of one fact exercises upon a creature dealing -with similar facts. Such influence cannot be resolved -into <i>ideas</i> and <i>induction</i>, without, as I conceive, making -all our subsequent investigation vague and hete<span class="pagenum" id="Page_243">243</span>rogeneous, -indefinite and inconclusive. If we must -speak of animals as <i>learning</i> from experience, we may -at least abstain from applying to them terms which -imply that they learn, in the same way in which men -learn astronomy from the stars, and chemistry from -the effects of mixture and heat. And the same may -be said of the language which is to be used concerning -what <i>men</i> learn, when their <i>learning</i> merely shows -itself in action, and does not exist as a general thought. -<i>Induction</i> must not be applied to such cases. <i>Induction</i> -must be confined to cases where we have in our -minds general propositions, in order that the sciences, -which are our most instructive examples of the -process we have to consider, may be, in any definite -and proper sense, <i>Inductive</i> Sciences.</p> - -<p>10. Perhaps some persons may be inclined to say -that this difference of opinion, as to the extent of -meaning which is to be given to the term <i>Induction</i>, -is a question merely of words; a matter of definition -only. This is a mode in which men in our time often -seem inclined to dispose of philosophical questions; -thus evading the task of forming an opinion upon such -questions, while they retain the air of looking at the -subject from a more comprehensive point of view. -But as I have elsewhere said, such questions of definition -are never questions of definition merely. A proposition -is always implied along with the definition; -and the truth of the proposition depends upon the -settlement of the definition. This is the case in the -present instance. We are speaking of <i>Induction</i>, and -we mean that kind of Induction by which the sciences -now existing among men have been constructed. On -this account it is, that we cannot include, in the meaning -of the term, mere practical tendencies or practical -habits; for science is not constructed of these. No -accumulation of these would make up any of the acknowledged -sciences. The elements of such sciences -are something of a kind different from practical habits. -The elements of such sciences are principles which we -<i>know</i>; truths which can be contemplated as being -<i>true</i>. Practical habits, practical skill, instincts and<span class="pagenum" id="Page_244">244</span> -the like, appear in action, and in action only. Such -endowments or acquirements show themselves when -the occasion for action arrives, and then, show themselves -in the act; without being put, or being capable -of being put, in the form of truths contemplated by the -intellect. But the elements and materials of Science -are necessary truths contemplated by the intellect. It -is by consisting of such elements and such materials, -that Science <i>is</i> Science. Hence a use of the term <i>Induction</i> -which requires us to obliterate this distinction, -must make it impossible for us to arrive at any consistent -and intelligible view of the nature of Science, -and of the mental process by which Sciences come into -being. We must, for the purpose which Mr. Mill and -I have in common, retain his larger and more philosophical -definition of Induction,—that it is the inference -of a more general proposition from less general -ones.</p> - -<p>11. Perhaps, again, some persons may say, that -practical skill and practical experience <i>lead</i> to science, -and may therefore be included in the term <i>Induction</i>, -which describes the formation of science. But to this -we reply, that these things lead to science as occasions -only, and do not form part of science; and that science -begins then only when we look at the facts in a -general point of view. This distinction is essential to -the philosophy of science. The rope-dancer may, by -his performances, suggest, to himself or to others, properties -of the center of gravity; but this is so, because -man has a tendency to speculate and to think of general -truths, as well as a tendency to dance on a rope on -special occasions, and to acquire skill in such dancing -by practice. The rope-dancer does not dance by Induction, -any more than the dancing dog does. To -apply the terms Science and Induction to such cases, -carries us into the regions of metaphor; as when we -call birds of passage "wise meteorologists," or the bee -"a natural chemist, who turns the flower-dust into -honey." This is very well in poetry: but for our purposes -we must avoid recognizing these cases as really -belonging to the sciences of meteorology and chemis<span class="pagenum" id="Page_245">245</span>try,—as -really cases of Induction. Induction for us -is general propositions, <i>contemplated as such</i>, derived -from particulars.</p> - -<p>Science may result <i>from</i> experience and observation -<i>by</i> Induction; but Induction is not therefore the same -thing as experience and observation. Induction is -experience or observation <i>consciously</i> looked at in a -<i>general</i> form. This consciousness and generality are -necessary parts of that knowledge which is science. -And accordingly, on the other hand, science cannot -result from mere Instinct, as distinguished from Reason; -because Instinct by its nature is not conscious -and general, but operates blindly and unconsciously in -particular cases, the actor not seeing or thinking of -the rule which he obeys.</p> - -<p>12. A little further on I shall endeavour to show -that not only a general <i>thought</i>, but a general <i>word</i> or -phrase is a requisite element in Induction. This doctrine, -of course, still more decidedly excludes the case -of animals, and of mere practical knowledge in man. -A burnt child dreads the fire; but reason must be -unfolded, before the child learns to understand the -words "fire will hurt you." The burnt dog never -thus learns to understand words. And this difference -points to an entirely different state of thought in the -two cases: or rather, to a difference between a state of -rational thought on the one hand, and of mere practical -instinct on the other.</p> - -<p>13. Besides this difference of speculative thought -and practical instinct which thus are, as appears to me, -confounded in Mr. Mill's philosophy, in such a way as -tends to destroy all coherent views of human knowledge, -there is another set of cases to which Mr. Mill -applies the term <i>Induction</i>, and to which it appears to -me to be altogether inapplicable. He employs it to -describe the mode in which superstitious men, in ignorant -ages, were led to the opinion that striking natural -events presaged or accompanied calamities. Thus -he says (i. 389), "The opinion so long prevalent that -a comet or any other unusual appearance in the -heavenly regions was the precursor of calamities to<span class="pagenum" id="Page_246">246</span> -mankind, or at least to those who witnessed it; the belief -in the oracles of Delphi and Dodona; the reliance -on astrology, or on the weather-prophecies in almanacs; -were doubtless inductions supposed to be grounded on -experience;" and he speaks of these insufficient inductions -being extinguished by the stronger inductions -subsequently obtained by scientific inquiry. And in -like manner, he says in another place (i. 367), "Let us -now compare different predictions: the first, that -eclipses will occur whenever one planet or satellite is -so situated as to cast its shadow upon another: the -second, that they will occur whenever some great -calamity is impending over mankind."</p> - -<p>14. Now I cannot see how anything but confusion -can arise from applying the term <i>Induction</i> to superstitious -fancies like those here mentioned. They are -not imperfect truths, but entire falsehoods. Of that, -Mr. Mill and I are agreed: how then can they exemplify -the progress towards truth? They were not -collected from the facts by seeking a law of their -occurrence; but were suggested by an imagination of -the anger of superior powers shown by such deviations -from the ordinary course of nature. If we are to speak -of <i>inductions</i> to any purpose, they must be such inductions -as represent the facts, in some degree at least. -It is not meant, I presume, that these opinions are in -any degree true: to what purpose then are they adduced? -If I were to hold that my dreams predict or -conform to the motions of the stars or of the clouds, -would this be an induction? It would be so, as much -one as those here so denominated: yet what but confusion -could arise from classing it among scientific -truths? Mr. Mill himself has explained (ii. 389) the way -in which such delusions as the prophecies of almanac-makers, -and the like, obtain credence; namely, by the -greater effect which the positive instances produce on -ordinary minds in comparison with the negative, when -the rule has once taken possession of their thoughts. -And this being, as he says, the recognized explanation -of such cases, why should we not leave them to their -due place, and not confound and perplex the whole of<span class="pagenum" id="Page_247">247</span> -our investigation by elevating them to the rank of -"inductions"? The very condemnation of such opinions -is that they are not at all inductive. When we have -made any progress in our investigation of the nature -of science, to attempt to drive us back to the wearisome -discussion of such elementary points as these, is -to make progress hopeless.</p> - - -<p>II. <a id="XXII2"></a><i>Induction or Description?</i>—15. In the cases -hitherto noticed, Mr. Mill extends the term <i>Induction</i>, -as I think, too widely, and applies it to cases to which -it is not rightly applicable. I have now to notice a -case of an opposite kind, in which he does not apply it -where I do, and condemns me for using it in such -a case. I had spoken of Kepler's discovery of the -Law, that the planets move round the sun in ellipses, -as an example of Induction. The separate facts of any -planet (Mars, for instance,) being in certain places at -certain times, are all included in the general proposition -which Kepler discovered, that Mars describes an -ellipse of a certain form and position. This appears to -me a very simple but a very distinct example of the -operation of discovering general propositions; general, -that is, with reference to particular facts; which operation -Mr. Mill, as well as myself, says is Induction. But -Mr. Mill denies this operation in this case to be Induction -at all (i. 357). I should not have been prepared -for this denial by the previous parts of Mr. Mill's book, -for he had said just before (i. 350), "such facts as the -magnitudes of the bodies of the solar system, their -distances from each other, the figure of the earth and -its rotation ... are proved indirectly, by the aid of inductions -founded on other facts which we can more -easily reach." If the figure of the earth and its rotation -are proved by Induction, it seems very strange, -and is to me quite incomprehensible, how the figure of -the earth's orbit and its revolution (and of course, of -the figure of Mars's orbit and his revolution in like -manner,) are not also proved by Induction. No, says -Mr. Mill, Kepler, in putting together a number of -places of the planet into one figure, only performed an -act of <i>description</i>. "This descriptive operation," he<span class="pagenum" id="Page_248">248</span> -adds (i. 359), "Mr. Whewell, by an aptly chosen expression, -has termed Colligation of Facts." He goes -on to commend my observations concerning this process, -but says that, according to the old and received -meaning of the term, it is not Induction at all.</p> - -<p>16. Now I have already shown that Mr. Mill himself, -a few pages earlier, had applied the term <i>Induction</i> -to cases undistinguishable from this in any essential -circumstance. And even in this case, he allows that -Kepler did really perform an act of Induction (i. 358), -"namely, in concluding that, because the observed -places of Mars were correctly represented by points in -an imaginary ellipse, therefore Mars would continue to -revolve in that same ellipse; and even in concluding -that the position of the planet during the time which -had intervened between the two observations must -have coincided with the intermediate points of the -curve." Of course, in Kepler's Induction, of which I -speak, I include all this; all this is included in speaking -of the <i>orbit</i> of Mars: a continuous line, a periodical -motion, are implied in the term <i>orbit</i>. I am unable to -see what would remain of Kepler's discovery, if we -take from it these conditions. It would not only not -be an induction, but it would not be a description, for -it would not recognize that Mars moved in an orbit. -Are particular positions to be conceived as points in a -curve, without thinking of the intermediate positions -as belonging to the same curve? If so, there is no law -at all, and the facts are not bound together by any -intelligible tie.</p> - -<p>In another place (ii. 209) Mr. Mill returns to his -distinction of Description and Induction; but without -throwing any additional light upon it, so far as I can -see.</p> - -<p>17. The only meaning which I can discover in this -attempted distinction of Description and Induction is, -that when particular facts are bound together by their -relation in <i>space</i>, Mr. Mill calls the discovery of the -connexion <i>Description</i>, but when they are connected -by other general relations, as time, cause and the like, -Mr. Mill terms the discovery of the connexion <i>Induc<span class="pagenum" id="Page_249">249</span>tion</i>. -And this way of making a distinction, would -fall in with the doctrine of other parts of Mr. Mill's -book, in which he ascribes very peculiar attributes to -space and its relations, in comparison with other Ideas, -(as I should call them). But I cannot see any ground -for this distinction, of connexion according to space -and other connexions of facts.</p> - -<p>To stand upon such a distinction, appears to me to -be the way to miss the general laws of the formation -of science. For example: The ancients discovered -that the planets revolved in recurring periods, and -thus connected the observations of their motions according -to the Idea of <i>Time</i>. Kepler discovered that -they revolved in ellipses, and thus connected the observations -according to the Idea of <i>Space</i>. Newton -discovered that they revolved in virtue of the Sun's -attraction, and thus connected the motions according -to the Idea of <i>Force</i>. The first and third of these discoveries -are recognized on all hands as processes of -Induction. Why is the second to be called by a different -name? or what but confusion and perplexity -can arise from refusing to class it with the other two? -It is, you say, Description. But such Description is a -kind of Induction, and must be spoken of as Induction, -if we are to speak of Induction as the process by which -Science is formed: for the three steps are all, the -second in the same sense as the first and third, in -co-ordination with them, steps in the formation of -astronomical science.</p> - -<p>18. But, says Mr. Mill (i. 363), "it is a fact surely -that the planet does describe an ellipse, and a fact -which we could see if we had adequate visual organs -and a suitable position." To this I should reply: "Let -it be so; and it is a fact, surely, that the planet does -move periodically: it is a fact, surely, that the planet -is attracted by the sun. Still, therefore, the asserted -distinction fails to find a ground." Perhaps Mr. Mill -would remind us that the elliptical form of the orbit is -a fact which we could see if we had adequate visual -organs and a suitable position: but that force is a -thing which we cannot see. But this distinction also<span class="pagenum" id="Page_250">250</span> -will not bear handling. Can we not see a tree blown -down by a storm, or a rock blown up by gunpowder? -Do we not here see force:—see it, that is, by its effects, -the only way in which we need to see it in the case -of a planet, for the purposes of our argument? Are -not such operations of force, Facts which may be -the objects of sense? and is not the operation of the -sun's Force a Fact of the same kind, just as much as -the elliptical form of orbit which results from the -action? If the latter be "surely a Fact," the former -is a Fact no less surely.</p> - -<p>19. In truth, as I have repeatedly had occasion to -remark, all attempts to frame an argument by the -exclusive or emphatic appropriation of the term <i>Fact</i> -to particular cases, are necessarily illusory and inconclusive. -There is no definite and stable distinction -between Facts and Theories; Facts and Laws; Facts -and Inductions. Inductions, Laws, Theories, which -are true, <i>are</i> Facts. Facts involve Inductions. It is -a fact that the moon is attracted by the earth, just as -much as it is a Fact that an apple falls from a tree. -That the former fact is collected by a more distinct -and conscious Induction, does not make it the less -a Fact. That the orbit of Mars is a Fact—a true -Description of the path—does not make it the less -a case of Induction.</p> - -<p>20. There is another argument which Mr. Mill -employs in order to show that there is a difference -between mere colligation which is description, and induction -in the more proper sense of the term. He -notices with commendation a remark which I had -made (i. 364), that at different stages of the progress -of science the facts had been successfully connected by -means of very different conceptions, while yet the later -conceptions have not contradicted, but included, so far -as they were true, the earlier: thus the ancient Greek -representation of the motions of the planets by means -of epicycles and eccentrics, was to a certain degree of -accuracy true, and is not negatived, though superseded, -by the modern representation of the planets as describing -ellipses round the sun. And he then reasons that<span class="pagenum" id="Page_251">251</span> -this, which is thus true of Descriptions, cannot be true -of Inductions. He says (i. 367), "Different descriptions -therefore may be all true: but surely not different -explanations." He then notices the various explanations -of the motions of the planets—the ancient doctrine -that they are moved by an inherent virtue; the -Cartesian doctrine that they are moved by impulse and -by vortices; the Newtonian doctrine that they are -governed by a central force; and he adds, "Can it be -said of these, as was said of the different descriptions, -that they are all true as far as they go? Is it not -true that one only can be true in any degree, and that -the other two must be altogether false?"</p> - -<p>21. And to this questioning, the history of science -compels me to reply very distinctly and positively, in -the way which Mr. Mill appears to think extravagant -and absurd. I am obliged to say, Undoubtedly, -all these explanations <i>may</i> be true and consistent with -each other, and would be so if each had been followed -out so as to show in what manner it could be made -consistent with the facts. And this was, in reality, -in a great measure done<a name="FNanchor_267" id="FNanchor_267"></a><a href="#Footnote_267" class="fnanchor">[267]</a>. The doctrine that the -heavenly bodies were moved by vortices was successively -modified, so that it came to coincide in its -results with the doctrine of an inverse-quadratic centripetal -force, as I have remarked in the <i>History</i><a name="FNanchor_268" id="FNanchor_268"></a><a href="#Footnote_268" class="fnanchor">[268]</a>. When -this point was reached, the vortex was merely a -machinery, well or ill devised, for producing such a -centripetal force, and therefore did not contradict the -doctrine of a centripetal force. Newton himself does -not appear to have been averse to explaining gravity -by impulse. So little is it true that if the one theory be -true the other must be false. The attempt to explain -gravity by the impulse of streams of particles flowing -through the universe in all directions, which I have mentioned -in the <i>Philosophy</i><a name="FNanchor_269" id="FNanchor_269"></a><a href="#Footnote_269" class="fnanchor">[269]</a> so far from being incon<span class="pagenum" id="Page_252">252</span>sistent -with the Newtonian theory, that it is founded -entirely upon it. And even with regard to the doctrine, -that the heavenly bodies move by an inherent virtue; -if this doctrine had been maintained in any such way -that it was brought to agree with the facts, the inherent -virtue must have had its laws determined; and -then, it would have been found that the virtue had a -reference to the central body; and so, the "inherent -virtue" must have coincided in its effect with the -Newtonian force; and then, the two explanations -would agree, except so far as the word "inherent" -was concerned. And if such a part of an earlier theory -as this word <i>inherent</i> indicates, is found to be untenable, -it is of course rejected in the transition to later -and more exact theories, in Inductions of this kind, -as well as in what Mr. Mill calls Descriptions. There -is therefore still no validity discoverable in the distinction -which Mr. Mill attempts to draw between -"descriptions" like Kepler's law of elliptical orbits, -and other examples of induction.</p> - -<p>22. When Mr. Mill goes on to compare what he -calls different predictions—the first, the true explanation -of eclipses by the shadows which the planets and -satellites cast upon one another, and the other, the -belief that they will occur whenever some great calamity -is impending over mankind, I must reply, as I -have stated already, (Art. 17), that to class such superstitions -as the last with cases of Induction, appears to -me to confound all use of words, and to prevent, as -far as it goes, all profitable exercise of thought. What -possible advantage can result from comparing (as if -they were alike) the relation of two descriptions of a -phenomenon, each to a certain extent true, and therefore -both consistent, with the relation of a scientific -truth to a false and baseless superstition?</p> - -<p>23. But I may make another remark on this -example, so strangely introduced. If, under the influence -of fear and superstition, men may make such -mistakes with regard to laws of nature, as to imagine -that eclipses portend calamities, are they quite secure -from mistakes in <i>description</i>? Do not the very per<span class="pagenum" id="Page_253">253</span>sons -who tell us how eclipses predict disasters, also -describe to us fiery swords seen in the air, and armies -fighting in the sky? So that even in this extreme case, -at the very limit of the rational exercise of human -powers, there is nothing to distinguish Description -from Induction.</p> - -<p>I shall now leave the reader to judge whether this -feature in the history of science,—that several views -which appear at first quite different are yet all true,—which -Mr. Mill calls a curious and interesting remark -of mine, and which he allows to be "strikingly true" -of the Inductions which he calls <i>Descriptions</i>, (i. 364) -is, as he says, "unequivocally false" of other Inductions. -And I shall confide in having general assent -with me, when I continue to speak of Kepler's <i>Induction</i> -of the elliptical orbits.</p> - -<p>I now proceed to another remark.</p> - - -<p>III. <a id="XXII3"></a><i>In Discovery a new Conception is introduced.</i>—</p> - -<p>24. There is a difference between Mr. Mill and me -in our view of the essential elements of this Induction -of Kepler, which affects all other cases of Induction, -and which is, I think, the most extensive and important -of the differences between us. I must therefore -venture to dwell upon it a little in detail.</p> - -<p>I conceive that Kepler, in discovering the law of -Mars's motion, and in asserting that the planet moved -in an ellipse, did this;—he bound together particular -observations of separate places of Mars by the notion, -or, as I have called it, the <i>conception</i>, of an <i>ellipse</i>, -which was supplied by his own mind. Other persons, -and he too, before he made this discovery, had present -to their minds the facts of such separate successive positions -of the planet; but could not bind them together -rightly, because they did not apply to them this conception -of an <i>ellipse</i>. To supply this conception, required -a special preparation, and a special activity in -the mind of the discoverer. He, and others before -him, tried other ways of connecting the special facts, -none of which fully succeeded. To discover such a -connexion, the mind must be conversant with certain -relations of space, and with certain kinds of figures.<span class="pagenum" id="Page_254">254</span> -To discover the right figure was a matter requiring -research, invention, resource. To hit upon the right -conception is a difficult step; and when this step is -once made, the facts assume a different aspect from -what they had before: that done, they are seen in a -new point of view; and the catching this point of -view, is a special mental operation, requiring special -endowments and habits of thought. Before this, the -facts are seen as detached, separate, lawless; afterwards, -they are seen as connected, simple, regular; as -parts of one general fact, and thereby possessing innumerable -new relations before unseen. Kepler, then, -I say, bound together the facts by superinducing upon -them the <i>conception</i> of an <i>ellipse</i>; and this was an -essential element in his Induction.</p> - -<p>25. And there is the same essential element in -all Inductive discoveries. In all cases, facts, before -detached and lawless, are bound together by a new -thought. They are reduced to law, by being seen in -a new point of view. To catch this new point of -view, is an act of the mind, springing from its previous -preparation and habits. The facts, in other -discoveries, are brought together according to other -relations, or, as I have called them, <i>Ideas</i>;—the -Ideas of Time, of Force, of Number, of Resemblance, -of Elementary Composition, of Polarity, and the like. -But in all cases, the mind performs the operation by -an apprehension of some such relations; by singling -out the one true relation; by combining the apprehension -of the true relation with the facts; by applying to -them the Conception of such a relation.</p> - -<p>26. In previous writings, I have not only stated -this view generally, but I have followed it into detail, -exemplifying it in the greater part of the History -of the principal Inductive Sciences in succession. I -have pointed out what are the Conceptions which have -been introduced in every prominent discovery in those -sciences; and have noted to which of the above Ideas, -or of the like Ideas, each belongs. The performance -of this task is the office of the greater part of my -<i>Philosophy of the Inductive Sciences</i>. For that work<span class="pagenum" id="Page_255">255</span> -is, in reality, no less historical than the <i>History</i> which -preceded it. The <i>History of the Inductive Sciences</i> is -the history of the discoveries, mainly so far as concerns -the <i>Facts</i> which were brought together to form -sciences. The <i>Philosophy</i> is, in the first ten Books, -the history of the <i>Ideas</i> and <i>Conceptions</i>, by means of -which the facts were connected, so as to give rise to -scientific truths. It would be easy for me to give a -long list of the Ideas and Conceptions thus brought -into view, but I may refer any reader who wishes to -see such a list, to the Tables of Contents of the <i>History</i>, -and of the first ten Books of the <i>Philosophy</i>.</p> - -<p>27. That these Ideas and Conceptions are really -distinct elements of the scientific truths thus obtained, -I conceive to be proved beyond doubt, not only by -considering that the discoveries never were made, nor -could be made, till the right Conception was obtained, -and by seeing how difficult it often was to obtain this -element; but also, by seeing that the Idea and the -Conception itself, as distinct from the Facts, was, in -almost every science, the subject of long and obstinate -controversies;—controversies which turned upon the -possible relations of Ideas, much more than upon the -actual relations of Facts. The first ten Books of the -<i>Philosophy</i> to which I have referred, contain the history -of a great number of these controversies. These -controversies make up a large portion of the history -of each science; a portion quite as important as the -study of the facts; and a portion, at every stage of -the science, quite as essential to the progress of truth. -Men, in seeking and obtaining scientific knowledge, -have always shown that they found the formation of -right conceptions in their own minds to be an essential -part of the process.</p> - -<p>28. Moreover, the presence of a Conception of the -mind as a special element of the inductive process, -and as the tie by which the particular facts are bound -together, is further indicated, by there being some -special new <i>term</i> or <i>phrase</i> introduced in every induction; -or at least some term or phrase thenceforth -steadily applied to the facts, which had not been<span class="pagenum" id="Page_256">256</span> -applied to them before; as when Kepler asserted that -Mars moved round the sun in an <i>elliptical orbit</i>, or -when Newton asserted that the planets <i>gravitate</i> towards -the sun; these new terms, <i>elliptical orbit</i>, and -<i>gravitate</i>, mark the new conceptions on which the -inductions depend. I have in the <i>Philosophy</i><a name="FNanchor_270" id="FNanchor_270"></a><a href="#Footnote_270" class="fnanchor">[270]</a> further -illustrated this application of "technical terms," that -is, fixed and settled terms, in every inductive discovery; -and have spoken of their use in enabling men -to proceed from each such discovery to other discoveries -more general. But I notice these terms here, -for the purpose of showing the existence of a conception -in the discoverer's mind, corresponding to the -term thus introduced; which conception, the term is -intended to convey to the minds of those to whom the -discovery is communicated.</p> - -<p>29. But this element of discovery,—right conceptions -supplied by the mind in order to bind the facts -together,—Mr. Mill denies to be an element at all. He -says, of Kepler's discovery of the elliptical orbit (i. -363), "It superadded nothing to the particular facts -which it served to bind together;" yet he adds, "except -indeed the knowledge that a resemblance existed -between the planetary orbit and other ellipses;" that -is, except the knowledge that it <i>was</i> an ellipse;—precisely -the circumstance in which the discovery consisted. -Kepler, he says, "asserted as a fact that the -planet moved in an ellipse. But this fact, which -Kepler did not add to, but found in the motion of -the planet ... was the very fact, the separate parts of -which had been separately observed; it was the sum -of the different observations."</p> - -<p>30. That the fact of the elliptical motion was not -merely the <i>sum</i> of the different observations, is plain -from this, that other persons, and Kepler himself before -his discovery, did not find it by adding together -the observations. The fact of the elliptical orbit was -not the sum of the observations <i>merely</i>; it was the<span class="pagenum" id="Page_257">257</span> -sum of the observations, <i>seen under a new point of -view</i>, which point of view Kepler's mind supplied. -Kepler found it in the facts, because it was there, no -doubt, for one reason; but also, for another, because -he had, in his mind, those relations of thought which -enabled him to find it. We may illustrate this by a -familiar analogy. We too find the law in Kepler's -book; but if we did not understand Latin, we should -not find it there. We must learn Latin in order to -find the law in the book. In like manner, a discoverer -must know the language of science, as well as -look at the book of nature, in order to find scientific -truth. All the discussions and controversies respecting -Ideas and Conceptions of which I have spoken, -may be looked upon as discussions and controversies -respecting the grammar of the language in which nature -speaks to the scientific mind. Man is the <i>Interpreter</i> -of Nature; not the Spectator merely, but the -Interpreter. The study of the language, as well as -the mere sight of the characters, is requisite in order -that we may read the inscriptions which are written -on the face of the world. And this study of the language -of nature, that is, of the necessary coherencies -and derivations of the relations of phenomena, is to be -pursued by examining Ideas, as well as mere phenomena;—by -tracing the formation of Conceptions, as -well as the accumulation of Facts. And this is what -I have tried to do in the books already referred to.</p> - -<p>31. Mr. Mill has not noticed, in any considerable -degree, what I have said of the formation of the Conceptions -which enter into the various sciences; but he -has, in general terms, denied that the Conception is -anything different from the facts themselves. "If," -he says (i. 301), "the facts are rightly classed under -the conceptions, it is because there is in the facts -themselves, something of which the conception is a -copy." But it is a copy which cannot be made by a -person without peculiar endowments; just as a person -cannot copy an ill-written inscription, so as to -make it convey sense, unless he understand the language. -"Conceptions," Mr. Mill says (ii. 217), "do not<span class="pagenum" id="Page_258">258</span> -develope themselves from within, but are impressed -from without." But what comes from without is not -enough: they must have both origins, or they cannot -make knowledge. "The conception," he says again -(ii. 221), "is not furnished <i>by</i> the mind till it has -been furnished <i>to</i> the mind." But it is furnished to -the mind by its own activity, operating according to -its own laws. No doubt, the conception may be -formed, and in cases of discovery, must be formed, by -the suggestion and excitement which the facts themselves -produce; and must be so moulded as to agree -with the facts. But this does not make it superfluous -to examine, out of what <i>materials</i> such conceptions are -formed, and <i>how</i> they are capable of being moulded so -as to express laws of nature; especially, when we see -how large a share this part of discovery—the examination -how our ideas can be modified so as to agree with -nature,—holds, in the history of science.</p> - -<p>32. I have already (Art. 28) given, as evidence -that the conception enters as an element in every induction, -the constant introduction in such cases, of a -new fixed term or phrase. Mr. Mill (ii. 282) notices -this introduction of a new phrase in such cases as -important, though he does not appear willing to allow -that it is necessary. Yet the necessity of the conception -at least, appears to result from the considerations -which he puts forward. "What darkness," he says, -"would have been spread over geometrical demonstration, -if wherever the word <i>circle</i> is used, the definition -of a circle was inserted instead of it." "If we want -to make a particular combination of ideas permanent -in the mind, there is nothing which clenches it like a -name specially devoted to express it." In my view, -the new conception is the <i>nail</i> which connects the -previous notions, and the name, as Mr. Mill says, -<i>clenches</i> the junction.</p> - -<p>33. I have above (Art. 30) referred to the difficulty -of getting hold of the right conception, as a -proof that induction is not a mere juxtaposition of -facts. Mr. Mill does not dispute that it is often difficult -to hit upon the right conception. He says (i. 360),<span class="pagenum" id="Page_259">259</span> -"that a conception of the mind is introduced, is indeed -most certain, and Mr. Whewell has rightly stated -elsewhere, that to hit upon the right conception is -often a far more difficult, and more meritorious achievement, -than to prove its applicability when obtained. -But," he adds, "a conception implies and corresponds -to something conceived; and although the conception -itself is not in the facts, but in our mind, it must be a -conception of something which really is in the facts." -But to this I reply, that its being really in the facts, -does not help us at all towards knowledge, if we cannot -see it there. As the poet says,</p> - -<div class="poetry-container"><div class="poetry"><div class="stanza"> - <div class="verse">It is the mind that sees: the outward eyes</div> - <div class="verse">Present the object, but the mind descries.</div> -</div></div></div> - -<p>And this is true of the sight which produces knowledge, -as well as of the sight which produces pleasure -and pain, which is referred to in the Tale.</p> - -<p>34. Mr. Mill puts his view, as opposed to mine, in -various ways, but, as will easily be understood, the -answers which I have to offer are in all cases nearly -to the same effect. Thus, he says (ii. 216), "the tardy -development of several of the physical sciences, for -example, of Optics, Electricity, Magnetism, and the -higher generalizations of Chemistry, Mr. Whewell -ascribes to the fact that mankind had not yet possessed -themselves of the idea of Polarity, that is, of -opposite properties in opposite directions. But what -was there to suggest such an idea, until by a separate -examination of several of these different branches of -knowledge it was shown that the facts of each of them -did present, in some instances at least, the curious -phenomena of opposite properties in opposite directions?" -But on this I observe, that these facts did -not, nor do yet, present this conception to ordinary -minds. The opposition of properties, and even the -opposition of directions, which are thus apprehended -by profound cultivators of science, are of an abstruse -and recondite kind; and to conceive any one kind of -polarity in its proper generality, is a process which -few persons hitherto appear to have mastered; still -less, have men in general come to conceive of them all<span class="pagenum" id="Page_260">260</span> -as modifications of a general notion of Polarity. The -description which I have given of Polarity in general, -"opposite properties in opposite directions," is of itself -a very imperfect account of the manner in which corresponding -antitheses are involved in the portions of -science into which Polar relations enter. In excuse -of its imperfection, I may say, that I believe it is the -first attempt to define Polarity in general; but yet, -the conception of Polarity has certainly been strongly -and effectively present in the minds of many of the -sagacious men who have discovered and unravelled -polar phenomena. They attempted to convey this -conception, each in his own subject, sometimes by -various and peculiar expressions, sometimes by imaginary -mechanism by which the antithetical results were -produced; their mode of expressing themselves being -often defective or imperfect, often containing what -was superfluous; and their meaning was commonly -very imperfectly apprehended by most of their hearers -and readers. But still, the conception was there, gradually -working itself into clearness and distinctness, -and in the mean time, directing their experiments, and -forming an essential element of their discoveries. So -far would it be from a sufficient statement of the case -to say, that they conceived polarity because they saw -it;—that they saw it as soon as it came into view;—and -that they described it as they saw it.</p> - -<p>35. The way in which such conceptions acquire -clearness and distinctness is often by means of Discussions -of Definitions. To define well a thought which -already enters into trains of discovery, is often a difficult -matter. The business of such definition is a part -of the business of discovery. These, and other remarks -connected with these, which I had made in the -<i>Philosophy</i>, Mr. Mill has quoted and adopted (ii. 242). -They appear to me to point very distinctly to the doctrine -to which he refuses his assent,—that there is a -special process in the mind, in addition to the mere -observation of facts, which is necessary at every step -in the progress of knowledge. The Conception must -be <i>formed</i> before it can be <i>defined</i>. The Definition<span class="pagenum" id="Page_261">261</span> -gives the last stamp of distinctness to the Conception; -and enables us to express, in a compact and lucid -form, the new scientific propositions into which the -new Conception enters.</p> - -<p>36. Since Mr. Mill assents to so much of what has -been said in the <i>Philosophy</i>, with regard to the process -of scientific discovery, how, it may be asked, would he -express these doctrines so as to exclude that which he -thinks erroneous? If he objects to our saying that -when we obtain a new inductive truth, we connect -phenomena by applying to them a new Conception -which fits them, in what terms would he describe the -process? If he will not agree to say, that in order to -discover the law of the facts, we must find an appropriate -Conception, what language would he use instead -of this? This is a natural question; and the answer -cannot fail to throw light on the relation in which his -views and mine stand to each other.</p> - -<p>Mr. Mill would say, I believe, that when we obtain -a new inductive law of facts, we find something in -which the facts <i>resemble each other</i>; and that the business -of making such discoveries is the business of discovering -such resemblances. Thus, he says (of me,) -(ii. 211), "his Colligation of Facts by means of appropriate -Conceptions, is but the ordinary process of finding -by a comparison of phenomena, in what consists -their agreement or resemblance." And the Methods -of experimental Inquiry which he gives (i. 450, &c.), -proceed upon the supposition that the business of discovery -may be thus more properly described.</p> - -<p>37. There is no doubt that when we discover a law -of nature by induction, we find some point in which -all the particular facts agree. All the orbits of the -planets agree in being ellipses, as Kepler discovered; -all falling bodies agree in being acted on by a uniform -force, as Galileo discovered; all refracted rays agree in -having the sines of incidence and refraction in a constant -ratio, as Snell discovered; all the bodies in the -universe agree in attracting each other, as Newton -discovered; all chemical compounds agree in being -constituted of elements in definite proportions, as<span class="pagenum" id="Page_262">262</span> -Dalton discovered. But it appears to me a most scanty, -vague, and incomplete account of these steps in science, -to say that the authors of them discovered something -in which the facts in each case agreed. The -point in which the cases agree, is of the most diverse -kind in the different cases—in some, a relation of -space, in others, the action of a force, in others, the -mode of composition of a substance;—and the point -of agreement, visible to the discoverer alone, does not -come even into his sight, till after the facts have been -connected by thoughts of his own, and regarded in -points of view in which he, by his mental acts, places -them. It would seem to me not much more inappropriate -to say, that an officer, who disciplines his men -till they move together at the word of command, does -so by finding something in which they agree. If the -power of consentaneous motion did not exist in the individuals, -he could not create it: but that power being -there, he finds it and uses it. Of course I am aware -that the parallel of the two cases is not exact; but in -the one case, as in the other, that in which the particular -things are found to agree, is something formed -in the mind of him who brings the agreement into -view.</p> - - -<p>IV. <a id="XXII4"></a><i>Mr. Mill's Four Methods of Inquiry.</i>—38. Mr. -Mill has not only thus described the business of scientific -discovery; he has also given rules for it, founded -on this description. It may be expected that we -should bestow some attention upon the methods of -inquiry which he thus proposes. I presume that they -are regarded by his admirers as among the most valuable -parts of his book; as certainly they cannot fail to -be, if they describe methods of scientific inquiry in -such a manner as to be of use to the inquirer.</p> - -<p>Mr. Mill enjoins four methods of experimental inquiry, -which he calls <i>the Method of Agreement</i>, <i>the -Method of Difference</i>, <i>the Method of Residues</i>, and <i>the -Method of Concomitant Variations</i><a name="FNanchor_271" id="FNanchor_271"></a><a href="#Footnote_271" class="fnanchor">[271]</a>. They are all<span class="pagenum" id="Page_263">263</span> -described by formulæ of this kind:—Let there be, -in the observed facts, combinations of antecedents, -<i>ABC</i>, <i>BC</i>, <i>ADE</i>, &c. and combinations of corresponding -consequents, <i>abc</i>, <i>bc</i>, <i>ade</i>, &c.; and let the -object of inquiry be, the consequence of some cause <i>A</i>, -or the cause of some consequence <i>a</i>. The Method of -Agreement teaches us, that when we find by experiment -such facts as <i>abc</i> the consequent of <i>ABC</i>, and -<i>ade</i> the consequent of <i>ADE</i>, then <i>a</i> is the consequent -of <i>A</i>. The Method of Difference teaches us that -when we find such facts as <i>abc</i> the consequent of <i>ABC</i>, -and <i>bc</i> the consequent of <i>BC</i>, then <i>a</i> is the consequent -of <i>A</i>. The Method of Residues teaches us, that if <i>abc</i> -be the consequent of <i>ABC</i>, and if we have already ascertained -that the effect of <i>A</i> is <i>a</i>, and the effect of <i>B</i> -is <i>b</i>, then we may infer that the effect of <i>C</i> is <i>c</i>. The -Method of Concomitant Variations teaches us, that if -a phenomenon <i>a</i> varies according as another phenomenon -<i>A</i> varies, there is some connexion of causation -direct or indirect, between <i>A</i> and <i>a</i>.</p> - -<p>39. Upon these methods, the obvious thing to remark -is, that they take for granted the very thing -which is most difficult to discover, the reduction of the -phenomena to formulæ such as are here presented to -us. When we have any set of complex facts offered to -us; for instance, those which were offered in the cases -of discovery which I have mentioned,—the facts of the -planetary paths, of falling bodies, of refracted rays, of -cosmical motions, of chemical analysis; and when, in -any of these cases, we would discover the law of nature -which governs them, or, if any one chooses so to -term it, the feature in which all the cases agree, where -are we to look for our <i>A</i>, <i>B</i>, <i>C</i> and <i>a</i>, <i>b</i>, <i>c</i>? Nature -does not present to us the cases in this form; and how -are we to reduce them to this form? You say, <i>when</i> -we find the combination of <i>ABC</i> with <i>abc</i> and <i>ABD</i> -with <i>abd</i>, then we may draw our inference. Granted: -but when and where are we to find such combinations? -Even now that the discoveries are made, who will -point out to us what are the <i>A</i>, <i>B</i>, <i>C</i> and <i>a</i>, <i>b</i>, <i>c</i> elements -of the cases which have just been enumerated?<span class="pagenum" id="Page_264">264</span> -Who will tell us which of the methods of inquiry -those historically real and successful inquiries exemplify? -Who will carry these formulæ through the -history of the sciences, as they have really grown up; -and show us that these four methods have been operative -in their formation; or that any light is thrown -upon the steps of their progress by reference to these -formulæ?</p> - -<p>40. Mr. Mill's four methods have a great resemblance -to Bacon's "Prerogatives of Instances;" for -example, the Method of Agreement to the <i>Instantiæ -Ostensivæ</i>; the Method of Differences to the <i>Instantiæ -Absentiæ in Proximo</i>, and the <i>Instantiæ Crucis</i>; the -Method of Concomitant Variations to the <i>Instantiæ -Migrantes</i>. And with regard to the value of such -methods, I believe all study of science will convince -us more and more of the wisdom of the remarks which -Sir John Herschel has made upon them<a name="FNanchor_272" id="FNanchor_272"></a><a href="#Footnote_272" class="fnanchor">[272]</a>.</p> - -<p>"It has always appeared to us, we must confess, -that the help which the classification of instances -under their different titles of prerogative, affords to -inductions, however just such classification may be in -itself, is yet more apparent than real. The force of -the instance must be felt in the mind before it can be -referred to its place in the system; and before it can -be either referred or appreciated it must be known; -and when it <i>is</i> appreciated, we are ready enough to -weave our web of induction, without greatly troubling -ourselves whence it derives the weight we acknowledge -it to have in our decisions.... No doubt such instances -as these are highly instructive; but the difficulty -in physics is to find such, not to perceive their -force when found."</p> - - -<p>V. <a id="XXII5"></a><i>His Examples.</i>—41. If Mr. Mill's four methods -had been applied by him in his book to a large body -of conspicuous and undoubted examples of discovery, -well selected and well analysed, extending along the -whole history of science, we should have been better<span class="pagenum" id="Page_265">265</span> -able to estimate the value of these methods. Mr. Mill -has certainly offered a number of examples of his -methods; but I hope I may say, without offence, that -they appear to me to be wanting in the conditions -which I have mentioned. As I have to justify myself -for rejecting Mr. Mill's criticism of doctrines which I -have put forward, and examples which I have adduced, -I may, I trust, be allowed to offer some critical remarks -in return, bearing upon the examples which he -has given, in order to illustrate his doctrines and -precepts.</p> - -<p>42. The first remark which I have to make is, -that a large proportion of his examples (i. 480, &c.) -is taken from one favourite author; who, however -great his merit may be, is too recent a writer to have -had his discoveries confirmed by the corresponding -investigations and searching criticisms of other labourers -in the same field, and placed in their proper -and permanent relation to established truths; these -alleged discoveries being, at the same time, principally -such as deal with the most complex and slippery portions -of science, the laws of vital action. Thus Mr. -Mill has adduced, as examples of discoveries, Prof. -Liebig's doctrine—that death is produced by certain -metallic poisons through their forming indecomposable -compounds; that the effect of respiration upon the -blood consists in the conversion of peroxide of iron -into protoxide—that the antiseptic power of salt arises -from its attraction for moisture—that chemical action -is contagious; and others. Now supposing that we -have no doubt of the truth of these discoveries, we -must still observe that they cannot wisely be cited, -in order to exemplify the nature of the progress -of knowledge, till they have been verified by other -chemists, and worked into their places in the general -scheme of chemistry; especially, since it is tolerably -certain that in the process of verification, they will -be modified and more precisely defined. Nor can I -think it judicious to take so large a proportion of our -examples from a region of science in which, of all -parts of our material knowledge, the conceptions both of<span class="pagenum" id="Page_266">266</span> -ordinary persons, and even of men of science themselves, -are most loose and obscure, and the genuine principles -most contested; which is the case in physiology. It -would be easy, I think, to point out the vague and -indeterminate character of many of the expressions in -which the above examples are propounded, as well as -their doubtful position in the scale of chemical generalization; -but I have said enough to show why I -cannot give much weight to these, as cardinal examples -of the method of discovery; and therefore I shall -not examine in detail how far they support Mr. Mill's -methods of inquiry.</p> - -<p>43. Mr. Liebig supplies the first and the majority -of Mr. Mill's examples in chapter IX. of his Book on -Induction. The second is an example for which Mr. -Mill states himself to be indebted to Mr. Alexander -Bain; the law established being this, that (i. 487) -electricity cannot exist in one body without the simultaneous -excitement of the opposite electricity in some -neighbouring body, which Mr. Mill also confirms by -reference to Mr. Faraday's experiments on voltaic -wires.</p> - -<p>I confess I am quite at a loss to understand what -there is in the doctrine here ascribed to Mr. Bain -which was not known to the electricians who, from -the time of Franklin, explained the phenomena of the -Leyden vial. I may observe also that the mention of -an "electrified atmosphere" implies a hypothesis long -obsolete. The essential point in all those explanations -was, that each electricity produced by induction the -opposite electricity in neighbouring bodies, as I have -tried to make apparent in the <i>History</i><a name="FNanchor_273" id="FNanchor_273"></a><a href="#Footnote_273" class="fnanchor">[273]</a>. Faraday has, -more recently, illustrated this universal co-existence of -opposite electricities with his usual felicity.</p> - -<p>But the conjunction of this fact with voltaic phenomena, -implies a non-recognition of some of the simplest -doctrines of the subject. "Since," it is said (i. 488), -"common or machine electricity, and voltaic electricity<span class="pagenum" id="Page_267">267</span> -may be considered for the present purpose to be identical, -Faraday wished to know, &c." I think Mr. -Faraday would be much astonished to learn that he -considered electricity in equilibrium, and electricity in -the form of a voltaic current, to be, for any purpose, -identical. Nor do I conceive that he would assent to -the expression in the next page, that "from the nature -of a voltaic charge, the two opposite currents necessary -to the existence of each other are both accommodated -in one wire." Mr. Faraday has, as it appears to me, -studiously avoided assenting to this hypothesis.</p> - -<p>44. The next example is the one already so copiously -dwelt upon by Sir John Herschel, Dr. Wells's -researches on the production of Dew. I have already -said<a name="FNanchor_274" id="FNanchor_274"></a><a href="#Footnote_274" class="fnanchor">[274]</a> that "this investigation, although it has sometimes -been praised as an original discovery, was in fact -only resolving the phenomenon into principles already -discovered namely, the doctrine of a <i>constituent temperature</i> -of vapour, the different conducting power of -different bodies, and the like. And this agrees in -substance with what Mr. Mill says (i. 497); that the -discovery, when made, was corroborated by deduction -from the known laws of aqueous vapour, of conduction, -and the like. Dr. Wells's researches on Dew -tended much in this country to draw attention to the -general principles of Atmology; and we may see, in -this and in other examples which Mr. Mill adduces, -that the explanation of special phenomena by means -of general principles, already established, has, for common -minds, a greater charm, and is more complacently -dwelt on, than the discovery of the general principles -themselves.</p> - -<p>45. The next example, (i. 502) is given in order to -illustrate the Method of Residues, and is the discovery -by M. Arago that a disk of copper affects the vibrations -of the magnetic needle. But this apparently detached -fact affords little instruction compared with the -singularly sagacious researches by which Mr. Faraday<span class="pagenum" id="Page_268">268</span> -discovered the cause of this effect to reside in the -voltaic currents which the motion of the magnetic -needle developed in the copper. I have spoken of this -discovery in the <i>History</i><a name="FNanchor_275" id="FNanchor_275"></a><a href="#Footnote_275" class="fnanchor">[275]</a>. Mr. Mill however is -quoting Sir John Herschel in thus illustrating the -Method of Residues. He rightly gives the Perturbations -of the Planets and Satellites as better examples -of the method<a name="FNanchor_276" id="FNanchor_276"></a><a href="#Footnote_276" class="fnanchor">[276]</a>.</p> - -<p>46. In the next chapter (c. x.) Mr. Mill speaks of -Plurality of causes and of the Intermixture of effects, -and gives examples of such cases. He here teaches -(i. 517) that chemical synthesis and analysis, (as when -oxygen and hydrogen compose water, and when water -is resolved into oxygen and hydrogen,) is properly -<i>transformation</i>, but that because we find that the -weight of the compound is equal to the sum of the -weights of the elements, we take up the notion of -chemical <i>composition</i>. I have endeavoured to show<a name="FNanchor_277" id="FNanchor_277"></a><a href="#Footnote_277" class="fnanchor">[277]</a> -that the maxim, that the sum of the weights of the -elements is equal to the weight of the compound, was, -historically, not <i>proved</i> from experiment, but <i>assumed</i> -in the reasonings upon experiments.</p> - -<p>47. I have now made my remarks upon nearly all -the examples which Mr. Mill gives of scientific inquiry, -so far as they consist of knowledge which has -really been obtained. I may mention, as points which -appear to me to interfere with the value of Mr. Mill's -references to examples, expressions which I cannot -reconcile with just conceptions of scientific truth; as -when he says (i. 523), "some other force which <i>impinges -on</i> the first force;" and very frequently indeed, -of the "tangential <i>force</i>," as co-ordinate with the centripetal -force.</p> - -<p>When he speaks (ii. 20, Note) of "the doctrine now -universally received that the earth is a great natural -magnet with two poles," he does not recognize the -recent theory of Gauss, so remarkably coincident with<span class="pagenum" id="Page_269">269</span> -a vast body of facts<a name="FNanchor_278" id="FNanchor_278"></a><a href="#Footnote_278" class="fnanchor">[278]</a>. Indeed in his statement, he -rejects no less the earlier views proposed by Halley, -theorized by Euler, and confirmed by Hansteen, which -show that we are compelled to assume at least <i>four</i> -poles of terrestrial magnetism; which I had given an -account of in the first edition of the <i>History</i>.</p> - -<p>There are several other cases which he puts, in -which, the knowledge spoken of not having been yet -acquired, he tells us how he would set about acquiring -it; for instance, if the question were (i. 526) whether -mercury be a cure for a given disease; or whether the -brain be a voltaic pile (ii. 21); or whether the moon -be inhabited (ii. 100); or whether all crows are black -(ii. 124); I confess that I have no expectation of any -advantage to philosophy from discussions of this kind.</p> - -<p>48. I will add also, that I do not think any light -can be thrown upon scientific methods, at present, by -grouping along with such physical inquiries as I have -been speaking of, speculations concerning the human -mind, its qualities and operations. Thus he speaks -(i. 508) of human characters, as exemplifying the -effect of plurality of causes; of (i. 518) the phenomena -of our mental nature, which are analogous to chemical -rather than to dynamical phenomena; of (i. 518) the -reason why susceptible persons are imaginative; to -which I may add, the passage where he says (i. 444), -"let us take as an example of a phenomenon which -we have no means of fabricating artificially, a human -mind." These, and other like examples, occur in the -part of his work in which he is speaking of scientific -inquiry in general, not in the Book on the Logic of -the Moral Sciences; and are, I think, examples more -likely to lead us astray than to help our progress, in -discovering the laws of Scientific Inquiry, in the ordinary -sense of the term.</p> - - -<p>VI. <a id="XXII6"></a><i>Mr. Mill against Hypothesis.</i>—49. I will -now pass from Mr. Mill's methods, illustrated by such -examples as those which I have been considering, to<span class="pagenum" id="Page_270">270</span> -the views respecting the conditions of Scientific Induction -to which I have been led, by such a survey as -I could make, of the whole history of the principal -Inductive Sciences; and especially, to those views to -which Mr. Mill offers his objections<a name="FNanchor_279" id="FNanchor_279"></a><a href="#Footnote_279" class="fnanchor">[279]</a>.</p> - -<p>Mr. Mill thinks that I have been too favourable to -the employment of hypotheses, as means of discovering -scientific truth; and that I have countenanced a laxness -of method, in allowing hypotheses to be established, -merely in virtue of the accordance of their -results with the phenomena. I believe I should be -as cautious as Mr. Mill, in accepting mere hypothetical -explanations of phenomena, in any case in which -we had the phenomena, and their relations, placed -before both of us in an equally clear light. I have -not accepted the Undulatory theory of Heat, though -recommended by so many coincidences and analogies<a name="FNanchor_280" id="FNanchor_280"></a><a href="#Footnote_280" class="fnanchor">[280]</a>. -But I see some grave reasons for not giving any great -weight to Mr. Mill's admonitions;—reasons drawn<span class="pagenum" id="Page_271">271</span> -from the language which he uses on the subject, and -which appears to me inconsistent with the conditions -of the cases to which he applies it. Thus, when he -says (ii. 22) that the condition of a hypothesis accounting -for all the known phenomena is "often fulfilled -equally well by two conflicting hypotheses," I can -only say that I know of no such case in the history of -Science, where the phenomena are at all numerous -and complicated; and that if such a case were to occur, -one of the hypotheses might always be resolved -into the other. When he says, that "this evidence -(the agreement of the results of the hypothesis with -the phenomena) cannot be of the smallest value, because -we cannot have in the case of such an hypothesis -the assurance that if the hypothesis be false it -must lead to results at variance with the true facts," -we must reply, with due submission, that we have, in -the case spoken of, the most complete evidence of this; -for any change in the hypothesis would make it incapable -of accounting for the facts. When he says that -"if we give ourselves the license of inventing the -causes as well as their laws, a person of fertile imagination -might devise a hundred modes of accounting -for any given fact;" I reply, that the question is about -accounting for a large and complex series of facts, of -which the laws have been ascertained: and as a test -of Mr. Mill's assertion, I would propose as a challenge -to any person of fertile imagination to devise any <i>one</i> -other hypothesis to account for the perturbations of -the moon, or the coloured fringes of shadows, besides -the hypothesis by which they have actually been explained -with such curious completeness. This challenge -has been repeatedly offered, but never in any degree -accepted; and I entertain no apprehension that Mr. -Mill's supposition will ever be verified by such a performance.</p> - -<p>50. I see additional reason for mistrusting the -precision of Mr. Mill's views of that accordance of -phenomena with the results of a hypothesis, in several -others of the expressions which he uses (ii. 23). He -speaks of a hypothesis being a "<i>plausible</i> explanation<span class="pagenum" id="Page_272">272</span> -of all or most of the phenomena;" but the case which -we have to consider is where it gives an <i>exact</i> representation -of all the phenomena in which its results -can be traced. He speaks of its being certain that -the laws of the phenomena are "<i>in some measure -analogous</i>" to those given by the hypothesis; the case -to be dealt with being, that they are in every way -identical. He speaks of this analogy being certain, -from the fact that the hypothesis can be "for a moment -<i>tenable</i>;" as if any one had recommended a hypothesis -which is tenable only while a small part of the facts -are considered, when it is inconsistent with others -which a fuller examination of the case discloses. I -have nothing to say, and have said nothing, in favour -of hypotheses which are <i>not</i> tenable. He says there -are many such "<i>harmonies</i> running through the laws -of phenomena in other respects radically distinct;" -and he gives as an instance, the laws of light and -heat. I have never alleged such harmonies as grounds -of theory, unless they should amount to identities; -and if they should do this, I have no doubt that the -most sober thinkers will suppose the causes to be of -the same kind in the two harmonizing instances. If -chlorine, iodine and brome, or sulphur and phosphorus, -have, as Mr. Mill says, analogous properties, I should -call these substances <i>analogous</i>: but I can see no -temptation to frame an hypothesis that they are <i>identical</i> -(which he seems to fear), so long as Chemistry -proves them distinct. But any hypothesis of an analogy -in the constitution of these elements (suppose, for instance, -a resemblance in their atomic form or composition) -would seem to me to have a fair claim to trial; -and to be capable of being elevated from one degree -of probability to another by the number, variety, and -exactitude of the explanations of phenomena which it -should furnish.</p> - - -<p>VII. <a id="XXII7"></a><i>Against prediction of Facts.</i>—51. These expressions -of Mr. Mill have reference to a way in which -hypotheses may be corroborated, in estimating the -value of which, it appears that he and I differ. "It -seems to be thought," he says (ii. 23), "that an hypo<span class="pagenum" id="Page_273">273</span>thesis -of the sort in question is entitled to a more -favourable reception, if, besides accounting for the -facts previously known, it has led to the anticipation -and prediction of others which experience afterwards -verified." And he adds, "Such predictions and their -fulfilment are indeed well calculated to strike the -ignorant vulgar;" but it is strange, he says, that any -considerable stress should be laid upon such a coincidence -by scientific thinkers. However strange it may -seem to him, there is no doubt that the most scientific -thinkers, far more than the ignorant vulgar, have -allowed the coincidence of results predicted by theory -with fact afterwards observed, to produce the strongest -effects upon their conviction; and that all the best-established -theories have obtained their permanent -place in general acceptance in virtue of such coincidences, -more than of any other evidence. It was not -the ignorant vulgar alone, who were struck by the -return of Halley's comet, as an evidence of the Newtonian -theory. Nor was it the ignorant vulgar, who -were struck with those facts which did so much strike -men of science, as curiously felicitous proofs of the -undulatory theory of light,—the production of darkness -by two luminous rays interfering in a special -manner; the refraction of a single ray of light into -a conical pencil; and other complex yet precise results, -predicted by the theory and verified by experiment. -It must, one would think, strike all persons in proportion -to their thoughtfulness, that when Nature thus -does our bidding, she acknowledges that we have -learnt her true language. If we can predict new facts -which we have not seen, as well as explain those which -we have seen, it must be because our explanation is -not a mere formula of observed facts, but a truth of -a deeper kind. Mr. Mill says, "If the laws of the -propagation of light agree with those of the vibrations -of an elastic fluid in so many respects as is necessary -to make the hypothesis a plausible explanation of all -or most of the phenomena known at the time, it is -nothing strange that they should accord with each -other in one respect more." Nothing strange, if the<span class="pagenum" id="Page_274">274</span> -theory be true; but quite unaccountable, if it be not. -If I copy a long series of letters of which the last -half-dozen are concealed, and if I guess those aright, -as is found to be the case when they are afterwards -uncovered, this must be because I have made out the -import of the inscription. To say, that because I have -copied all that I could see, it is nothing strange that -I should guess those which I cannot see, would be -absurd, without supposing such a ground for guessing. -The notion that the discovery of the laws and causes -of phenomena is a loose haphazard sort of guessing, -which gives "plausible" explanations, accidental coincidences, -casual "harmonies," laws, "in some measure -analogous" to the true ones, suppositions "tenable" -for a time, appears to me to be a misapprehension of -the whole nature of science; as it certainly is inapplicable -to the case to which it is principally applied by -Mr. Mill.</p> - -<p>52. There is another kind of evidence of theories, -very closely approaching to the verification of untried -predictions, and to which, apparently, Mr. Mill does -not attach much importance, since he has borrowed -the term by which I have described it, <i>Consilience</i>, -but has applied it in a different manner (ii. 530, -563, 590). I have spoken, in the <i>Philosophy</i><a name="FNanchor_281" id="FNanchor_281"></a><a href="#Footnote_281" class="fnanchor">[281]</a>, of -the <i>Consilience of Inductions</i>, as one of the <i>Tests of -Hypotheses</i>, and have exemplified it by many instances; -for example, the theory of universal gravitation, obtained -by induction from the motions of the planets, -was found to explain also that peculiar motion of -the spheroidal earth which produces the Precession -of the Equinoxes. This, I have said, was a striking -and surprising coincidence which gave the theory a -stamp of truth beyond the power of ingenuity to -counterfeit. I may compare such occurrences to a -case of interpreting an unknown character, in which -two different inscriptions, deciphered by different -persons, had given the same alphabet. We should,<span class="pagenum" id="Page_275">275</span> -in such a case, believe with great confidence that the -alphabet was the true one; and I will add, that I -believe the history of science offers no example in -which a theory supported by such consiliences, had -been afterwards proved to be false.</p> - -<p>53. Mr. Mill accepts (ii. 21) a rule of M. Comte's, -that we may apply hypotheses, provided they are capable -of being afterwards verified as facts. I have a -much higher respect for Mr. Mill's opinion than for -M. Comte's<a name="FNanchor_282" id="FNanchor_282"></a><a href="#Footnote_282" class="fnanchor">[282]</a>; but I do not think that this rule will be -found of any value. It appears to me to be tainted -with the vice which I have already noted, of throwing -the whole burthen of explanation upon the unexplained -word <i>fact</i>—unexplained in any permanent -and definite opposition to theory. As I have said, -the Newtonian theory <i>is</i> a fact. Every true theory -is a fact. Nor does the distinction become more clear -by Mr. Mill's examples. "The vortices of Descartes -would have been," he says, "a perfectly legitimate -hypothesis, if it had been possible by any mode of -explanation which we could entertain the hope of -possessing, to bring the question whether such vortices -exist or not, within the reach of our observing faculties." -But this was possible, and was done. The free<span class="pagenum" id="Page_276">276</span> -passage of comets through the spaces in which these -vortices should have been, convinced men that these -vortices did not exist. In like manner Mr. Mill rejects -the hypothesis of a luminiferous ether, "because -it can neither be seen, heard, smelt, tasted, or touched." -It is a strange complaint to make of the vehicle of -light, that it cannot be heard, smelt, or tasted. Its -vibrations <i>can</i> be seen. The fringes of shadows for -instance, show its vibrations, just as the visible lines -of waves near the shore show the undulations of the -sea. Whether this can be touched, that is, whether -it resists motion, is hardly yet clear. I am far -from saying there are not difficulties on this point, -with regard to <i>all</i> theories which suppose a <i>medium</i>. -But there are no more difficulties of this kind in the -undulatory theory of light, than there are in Fourier's -theory of heat, which M. Comte adopts as a model of -scientific investigation; or in the theory of voltaic -<i>currents</i>, about which Mr. Mill appears to have no -doubt; or of electric <i>atmospheres</i>, which, though generally -obsolete, Mr. Mill appears to favour; for though -it had been said that we <i>feel</i> such atmospheres, no one -had said that they have the other attributes of matter.</p> - - -<p>VIII. <a id="XXII8"></a><i>Newton's Vera Causa.</i>—54. Mr. Mill conceives -(ii. 17) that his own rule concerning hypotheses -coincides with Newton's Rule, that the cause assumed -must be a <i>vera causa</i>. But he allows that "Mr. -Whewell ... has had little difficulty in showing that his -(Newton's) conception was neither precise nor consistent -with itself." He also allows that "Mr. Whewell -is clearly right in denying it to be necessary that -the cause assigned should be a cause already known; -else how could we ever become acquainted with new -causes?" These points being agreed upon, I think that -a little further consideration will lead to the conviction -that Newton's Rule of philosophizing will best become -a valuable guide, if we understand it as asserting that -when the explanation of two or more different kinds -of phenomena (as the revolutions of the planets, the -fall of a stone, and the precession of the equinoxes,) -lead us to <i>the same</i> cause, such a coincidence gives a<span class="pagenum" id="Page_277">277</span> -reality to the cause. We have, in fact, in such a case, -a Consilience of Inductions.</p> - -<p>55. When Mr. Mill condemns me (ii. 24) (using, -however, expressions of civility which I gladly acknowledge,) -for having recognized no mode of Induction -except that of trying hypothesis after hypothesis -until one is found which fits the phenomena, I must -beg to remind the readers of our works, that Mr. Mill -himself allows (i. 363) that the process of finding a -conception which binds together observed facts "is -tentative, that it consists of a succession of guesses, -many being rejected until one at last occurs fit to be -chosen." I must remind them also that I have given -a Section upon the <i>Tests of Hypotheses</i>, to which I -have just referred,—that I have given various methods -of Induction, as the <i>Method of Gradation</i>, the <i>Method -of Natural Classification</i>, the <i>Method of Curves</i>, the -<i>Method of Means</i>, the <i>Method of Least Squares</i>, the -<i>Method of Residues</i>: all which I have illustrated by -conspicuous examples from the History of Science; -besides which, I conceive that what I have said of the -Ideas belonging to each science, and of the construction -and explication of conceptions, will point out in -each case, in what region we are to look for the Inductive -Element in order to make new discoveries. -I have already ventured to say, elsewhere, that the -methods which I have given, are as definite and practical -as any others which have been proposed, with the -great additional advantage of being the methods by -which all great discoveries in science have really been -made.</p> - - -<p>IX. <a id="XXII9"></a><i>Successive Generalizations.</i>—56. There is one -feature in the construction of science which Mr. Mill -notices, but to which he does not ascribe, as I conceive, -its due importance: I mean, that process by which we -not only ascend from particular facts to a general law, -but when this is done, ascend from the first general -law to others more general; and so on, proceeding to -the highest point of generalization. This character of -the scientific process was first clearly pointed out by -Bacon, and is one of the most noticeable instances of<span class="pagenum" id="Page_278">278</span> -his philosophical sagacity. "There are," he says, "two -ways, and can be only two, of seeking and finding -truth. The one from sense and particulars, takes a -flight to the most general axioms, and from these -principles and their truth, settled once for all, invents -and judges of intermediate axioms. The other method -collects axioms from sense and particulars, ascending -<i>continuously and by degrees</i>, so that in the end it -arrives at the most general axioms:" meaning by -<i>axioms</i>, laws or principles. The structure of the -most complete sciences consists of several such steps,—<i>floors</i>, -as Bacon calls them, of successive generalization; -and thus this structure may be exhibited as -a kind of scientific pyramid. I have constructed this -pyramid in the case of the science of Astronomy<a name="FNanchor_283" id="FNanchor_283"></a><a href="#Footnote_283" class="fnanchor">[283]</a>: -and I am gratified to find that the illustrious Humboldt -approves of the design, and speaks of it as -executed with complete success<a name="FNanchor_284" id="FNanchor_284"></a><a href="#Footnote_284" class="fnanchor">[284]</a>. The capability of -being exhibited in this form of successive generalizations, -arising from particulars upward to some very -general law, is the condition of all tolerably perfect -sciences; and the steps of the successive generalizations -are commonly the most important events in the history -of the science.</p> - -<p>57. Mr. Mill does not reject this process of generalization; -but he gives it no conspicuous place, -making it only one of three modes of reducing a law -of causation into other laws. "There is," he says -(i. 555), "the <i>subsumption</i> of one law under another; ... -the gathering up of several laws into one more general -law which includes them all. He adds afterwards, -that the general law is the <i>sum</i> of the partial ones -(i. 557), an expression which appears to me inadequate, -for reasons which I have already stated. The general -law is not the mere sum of the particular laws. It is, -as I have already said, their amount <i>in a new point of<span class="pagenum" id="Page_279">279</span> -view</i>. A new conception is introduced; thus, Newton -did not merely add together the laws of the motions -of the moon and of the planets, and of the satellites, -and of the earth; he looked at them altogether as the -result of a universal force of mutual gravitation; and -therein consisted his generalization. And the like -might be pointed out in other cases.</p> - -<p>58. I am the more led to speak of Mr. Mill as not -having given due importance to this process of successive -generalization, by the way in which he speaks -in another place (ii. 525) of this doctrine of Bacon. -He conceives Bacon "to have been radically wrong -when he enunciates, as a universal rule, that induction -should proceed from the lowest to the middle principles, -and from those to the highest, never reversing -that order, and consequently, leaving no room for the -discovery of new principles by way of deduction<a name="FNanchor_285" id="FNanchor_285"></a><a href="#Footnote_285" class="fnanchor">[285]</a> at -all."</p> - -<p>59. I conceive that the Inductive Table of Astronomy, -to which I have already referred, shows that -in that science,—the most complete which has yet existed,—the -history of the science has gone on, as to its -general movement, in accordance with the view which -Bacon's sagacity enjoined. The successive generalizations, -<i>so far as they were true</i>, were made by successive -generations. I conceive also that the Inductive Table of -Optics shows the same thing; and this, without taking -for granted the truth of the Undulatory Theory; for -with regard to all the steps of the progress of the -science, lower than that highest one, there is, I conceive, -no controversy.</p> - -<p>60. Also, the Science of Mechanics, although Mr. -Mill more especially refers to it, as a case in which the<span class="pagenum" id="Page_280">280</span> -highest generalizations (for example the Laws of Motion) -were those earliest ascertained with any scientific -exactness, will, I think, on a more careful examination -of its history, be found remarkably to confirm Bacon's -view. For, in that science, we have, in the first place, -very conspicuous examples of the vice of the method -pursued by the ancients in flying to the highest generalizations -first; as when they made their false distinctions -of the laws of <i>natural</i> and <i>violent</i> motions, and of -<i>terrestrial</i> and <i>celestial</i> motions. Many erroneous laws -of motion were asserted through neglect of facts or -want of experiments. And when Galileo and his school -had in some measure succeeded in discovering some of -the true laws of the motions of terrestrial bodies, they -did not at once assert them as general: for they did -not at all apply those laws to the celestial motions. -As I have remarked, all Kepler's speculations respecting -the causes of the motions of the planets, went upon -the supposition that the First Law of terrestrial Motion -did not apply to celestial bodies; but that, on the contrary, -some continual force was requisite to keep up, -as well as to originate, the planetary motions. Nor -did Descartes, though he enunciated the Laws of -Motion with more generality than his predecessors, -(but not with exactness,) venture to trust the planets -to those laws; on the contrary, he invented his machinery -of Vortices in order to keep up the motions -of the heavenly bodies. Newton was the first who -extended the laws of terrestrial motion to the celestial -spaces; and in doing so, he used all the laws of the -celestial motions which had previously been discovered -by more limited inductions. To these instances, I may -add the gradual generalization of the Third Law of motion -by Huyghens, the Bernoullis, and Herman, which -I have described in the <i>History</i><a name="FNanchor_286" id="FNanchor_286"></a><a href="#Footnote_286" class="fnanchor">[286]</a> as preceding that -Period of Deduction, to which the succeeding narrative<a name="FNanchor_287" id="FNanchor_287"></a><a href="#Footnote_287" class="fnanchor">[287]</a> -is appropriated. In Mechanics, then, we have a cardinal -example of the historically gradual and successive<span class="pagenum" id="Page_281">281</span> -ascent of science from particulars to the most general -laws.</p> - -<p>61. The Science of Hydrostatics may appear to -offer a more favourable example of the ascent to the -most general laws, without going through the intermediate -particular laws; and it is true, with reference -to this science, as I have observed<a name="FNanchor_288" id="FNanchor_288"></a><a href="#Footnote_288" class="fnanchor">[288]</a>, that it does exhibit -the <i>peculiarity</i> of our possessing the most general -principles on which the phenomena depend, and from -which many cases of special facts are explained by -deduction; while other cases cannot be so explained, -from the want of principles intermediate between the -highest and the lowest. And I have assigned, as the -reason of this peculiarity, that the general principles -of the Mechanics of Fluids were not obtained with -reference to the science itself, but by extension from -the sister science of the Mechanics of Solids. The -two sciences are parts of the same Inductive Pyramid; -and having reached the summit of this Pyramid on -one side, we are tempted to descend on the other from -the highest generality to more narrow laws. Yet even -in this science, the best part of our knowledge is -mainly composed of inductive laws, obtained by inductive -examination of particular classes of facts. The -mere mathematical investigations of the laws of waves, -for instance, have not led to any results so valuable as -the experimental researches of Bremontier, Emy, the -Webers, and Mr. Scott Russell. And in like manner -in Acoustics, the Mechanics of Elastic Fluids<a name="FNanchor_289" id="FNanchor_289"></a><a href="#Footnote_289" class="fnanchor">[289]</a>, the -deductions of mathematicians made on general principles -have not done so much for our knowledge, as -the cases of vibrations of plates and pipes examined -experimentally by Chladni, Savart, Mr. Wheatstone -and Mr. Willis. We see therefore, even in these -sciences, no reason to slight the wisdom which exhorts -us to ascend from particulars to intermediate laws, -rather than to hope to deduce these latter better from -the more general laws obtained once for all.</p> - -<p><span class="pagenum" id="Page_282">282</span></p> - -<p>62. Mr. Mill himself indeed, notwithstanding that -he slights Bacon's injunction to seek knowledge by -proceeding from less general to more general laws, -has given a very good reason why this is commonly -necessary and wise. He says (ii. 526), "Before we -attempt to explain deductively, from more general laws, -any new class of phenomena, it is desirable to have -gone as far as is practicable in ascertaining the empirical -laws of these phenomena; so as to compare the -results of deduction, not with one individual instance -after another, but with general propositions expressive -of the points of agreement which have been found -among many instances. For," he adds with great -justice, "if Newton had been obliged to verify the -theory of gravitation, not by deducing from it Kepler's -laws, but by deducing all the observed planetary positions -which had served Kepler to establish those laws, -the Newtonian theory would probably never have -emerged from the state of an hypothesis." To which -we may add, that it is certain, from the history of the -subject, that in that case the hypothesis would never -have been framed at all.</p> - - -<p>X. <a id="XXII10"></a><i>Mr. Mill's Hope from Deduction.</i>—63. Mr. -Mill expresses a hope of the efficacy of Deduction, -rather than Induction, in promoting the future progress -of Science; which hope, so far as the physical -sciences are concerned, appears to me at variance with -all the lessons of the history of those sciences. He -says (i. 579), "that the advances henceforth to be -expected even in physical, and still more in mental and -social science, will be chiefly the result of deduction, -is evident from the general considerations already -adduced:" these considerations being, that the phenomena -to be considered are very complex, and are -the result of many known causes, of which we have -to disentangle the results.</p> - -<p>64. I cannot but take a very different view from -this. I think that any one, looking at the state of -physical science, will see that there are still a vast -mass of cases, in which we do not at all know the -causes, at least, in their full generality; and that the<span class="pagenum" id="Page_283">283</span> -knowledge of new causes, and the generalization of -the laws of those already known, can only be obtained -by new <i>inductive</i> discoveries. Except by new Inductions, -equal, in their efficacy for grouping together -phenomena in new points of view, to any which have -yet been performed in the history of science, how are -we to solve such questions as those which, in the -survey of what we already know, force themselves -upon our minds? Such as, to take only a few of -the most obvious examples—What is the nature of -the connexion of heat and light? How does heat -produce the expansion, liquefaction and vaporization -of bodies? What is the nature of the connexion -between the optical and the chemical properties of -light? What is the relation between optical, crystalline -and chemical polarity? What is the connexion -between the atomic constitution and the physical qualities -of bodies? What is the tenable definition of a -mineral species? What is the true relation of the -apparently different types of vegetable life (monocotyledons, -dicotyledons, and cryptogamous plants)? -What is the relation of the various types of animal -life (vertebrates, articulates, radiates, &c.)? What is -the number, and what are the distinctions of the Vital -Powers? What is the internal constitution of the -earth? These, and many other questions of equal -interest, no one, I suppose, expects to see solved by -deduction from principles already known. But we -can, in many of them, see good hope of progress by -a large use of induction; including, of course, copious -and careful experiments and observations.</p> - -<p>65. With such questions before us, as have now -been suggested, I can see nothing but a most mischievous -narrowing of the field and enfeebling of the spirit -of scientific exertion, in the doctrine that "Deduction -is the great scientific work of the present and of future -ages;" and that "A revolution is peaceably and progressively -effecting itself in philosophy the reverse of -that to which Bacon has attached his name." I trust, -on the contrary, that we have many new laws of -nature still to discover; and that our race is destined<span class="pagenum" id="Page_284">284</span> -to obtain a sight of wider truths than any we yet discern, -including, as cases, the general laws we now -know, and obtained from these known laws as they -must be, by Induction.</p> - -<p>66. I can see, however, reasons for the comparatively -greater favour with which Mr. Mill looks upon -Deduction, in the views to which he has mainly directed -his attention. The explanation of remarkable phenomena -by known laws of Nature, has, as I have already -said, a greater charm for many minds than the discovery -of the laws themselves. In the case of such -explanations, the problem proposed is more definite, -and the solution more obviously complete. For the -process of induction includes a mysterious step, by -which we pass from particulars to generals, of which -step the reason always seems to be inadequately rendered -by any words which we can use; and this step -to most minds is not demonstrative, as to few is it -given to perform it on a great scale. But the process -of explanation of facts by known laws is deductive, and -has at every step a force like that of demonstration, -producing a feeling peculiarly gratifying to the clear -intellects which are most capable of following the -process. We may often see instances in which this -admiration for deductive skill appears in an extravagant -measure; as when men compare Laplace with -Newton. Nor should I think it my business to argue -against such a preference, unless it were likely to leave -us too well satisfied with what we know already, to -chill our hope of scientific progress, and to prevent our -making any further strenuous efforts to ascend, higher -than we have yet done, the mountain-chain which -limits human knowledge.</p> - -<p>67. But there is another reason which, I conceive, -operates in leading Mr. Mill to look to Deduction as -the principal means of future progress in knowledge, -and which is a reason of considerable weight in the -subjects of research which, as I conceive, he mainly -has in view. In the study of our own minds and of -the laws which govern the history of society, I do not -think that it is very likely that we shall hereafter<span class="pagenum" id="Page_285">285</span> -arrive at any wider principles than those of which we -already possess some considerable knowledge; and this, -for a special reason; namely, that our knowledge in -such cases is not gathered by mere external observation -of a collection of external facts; but acquired by attention -to internal facts, our own emotions, thoughts, and -springs of action; facts are connected by ties existing -in our own consciousness, and not in mere observed -juxtaposition, succession, or similitude. How the -character, for instance, is influenced by various causes, -(an example to which Mr. Mill repeatedly refers, ii. -518, &c.), is an inquiry which may perhaps be best -conducted by considering what we know of the influence -of education and habit, government and occupation, -hope and fear, vanity and pride, and the like, -upon men's characters, and by tracing the various -effects of the intermixture of such influences. Yet -even here, there seems to be room for the discovery of -laws in the way of experimental inquiry: for instance, -what share race or family has in the formation of -character; a question which can hardly be solved to -any purpose in any other way than by collecting and -classing instances. And in the same way, many of -the principles which regulate the material wealth of -states, are obtained, if not exclusively, at least most -clearly and securely, by induction from large surveys -of facts. Still, however, I am quite ready to admit -that in Mental and Social Science, we are much less -likely than in Physical Science, to obtain new truths -by any process which can be distinctively termed <i>Induction</i>; -and that in those sciences, what may be called -<i>Deductions</i> from principles of thought and action of -which we are already conscious, or to which we assent -when they are felicitously picked out of our thoughts -and put into words, must have a large share; and I -may add, that this observation of Mr. Mill appears to -me to be important, and, in its present connexion, new.</p> - - -<p>XI. <a id="XXII11"></a><i>Fundamental opposition of our doctrines.</i>—68. -I have made nearly all the remarks which I -now think it of any consequence to make upon Mr. -Mill's <i>Logic</i>, so far as it bears upon the doctrines contained -in my <i>History</i> and <i>Philosophy</i>. And yet there<span class="pagenum" id="Page_286">286</span> -remains still untouched one great question, involving -probably the widest of all the differences between him -and me. I mean the question whether geometrical -axioms, (and, as similar in their evidence to these, <i>all</i> -axioms,) be truths derived from experience, or be necessary -truths in some deeper sense. This is one of the -fundamental questions of philosophy; and all persons -who take an interest in metaphysical discussions, know -that the two opposite opinions have been maintained -with great zeal in all ages of speculation. To me it -appears that there are <i>two</i> distinct elements in our -knowledge, Experience, without, and the Mind, within. -Mr. Mill derives all our knowledge from Experience -<i>alone</i>. In a question thus going to the root of all -knowledge, the opposite arguments must needs cut deep -on both sides. Mr. Mill cannot deny that our knowledge -of geometrical axioms and the like, <i>seems</i> to be -<i>necessary</i>. I cannot deny that our knowledge, axiomatic -as well as other, <i>never is</i> acquired <i>without experience</i>.</p> - -<p>69. Perhaps ordinary readers may despair of following -our reasonings, when they find that they can -only be made intelligible by supposing, on the one -hand, a person who thinks distinctly and yet has never -seen or felt any external object; and on the other -hand, a person who is transferred, as Mr. Mill supposes -(ii. 117), to "distant parts of the stellar regions where -the phenomena may be entirely unlike those with -which we are acquainted," and where even the axiom, -that every effect must have a cause, does not hold good. -Nor, in truth, do I think it necessary here to spend -many words on this subject. Probably, for those who -take an interest in this discussion, most of the arguments -on each side have already been put forwards with -sufficient repetition. I have, in an "Essay on the -Fundamental Antithesis of Philosophy," and in some -accompanying "Remarks," printed<a name="FNanchor_290" id="FNanchor_290"></a><a href="#Footnote_290" class="fnanchor">[290]</a> at the end of the -second edition of my <i>Philosophy</i>, given my reply to -what has been said on this subject, both by Mr. Mill, -and by the author of a very able critique on my <i>His<span class="pagenum" id="Page_287">287</span>tory</i> -and <i>Philosophy</i> which appeared in the <i>Quarterly -Review</i> in 1841: and I will not here attempt to revive -the general discussion.</p> - -<p>70. Perhaps I may be allowed to notice, that in -one part of Mr. Mill's work where this subject is -treated, there is the appearance of one of the parties -to the controversy pronouncing judgment in his own -cause. This indeed is a temptation which it is especially -difficult for an author to resist, who writes a -treatise upon <i>Fallacies</i>, the subject of Mr. Mill's fifth -Book. In such a treatise, the writer has an easy way -of disposing of adverse opinions by classing them as -"Fallacies," and putting them side by side with opinions -universally acknowledged to be false. In this way, -Mr. Mill has dealt with several points which are still, -as I conceive, matters of controversy (ii. 357, &c.).</p> - -<p>71. But undoubtedly, Mr. Mill has given his -argument against my opinions with great distinctness -in another place (i. 319). In order to show -that it is merely habitual association which gives -to an experimental truth the character of a necessary -truth, he quotes the case of the laws of motion, -which were really discovered from experiment, but are -now looked upon as the only conceivable laws; and -especially, what he conceives as "the <i>reductio ad absurdum</i> -of the theory of inconceivableness," an opinion -which I had ventured to throw out, that if we could -conceive the Composition of bodies distinctly, we might -be able to see that it is necessary that the modes of -their composition should be definite. I do not think -that readers in general will see anything absurd in -the opinion, that the laws of Mechanics, and even the -laws of the Chemical Composition of bodies, may depend -upon principles as necessary as the properties of -space and number; and that this necessity, though not -at all perceived by persons who have only the ordinary -obscure and confused notions on such subjects, may be -evident to a mind which has, by effort and discipline, -rendered its ideas of Mechanical Causation, Elementary -Composition and Difference of Kind, clear and precise. -It may easily be, I conceive, that while such necessary<span class="pagenum" id="Page_288">288</span> -principles are perceived to be necessary only by a few -minds of highly cultivated insight, such principles as -the axioms of Geometry and Arithmetic may be perceived -to be necessary by <i>all</i> minds which have any -habit of abstract thought at all: and I conceive also, -that though these axioms are brought into distinct -view by a certain degree of intellectual cultivation, -they may still be much better described as conditions -of experience, than as results of experience:—as laws -of the mind and of its activity, rather than as facts -impressed upon a mind merely passive.</p> - - -<p>XII. <a id="XXII12"></a><i>Absurdities in Mr. Mill's Logic.</i>—72. I -will not pursue the subject further: only, as the question -has arisen respecting the absurdities to which -each of the opposite doctrines leads, I will point out -opinions connected with this subject, which Mr. Mill -has stated in various parts of his book.</p> - -<p>He holds (i. 317) that it is merely from habit that -we are unable to conceive the <i>last point</i> of space or -the <i>last instant</i> of time. He holds (ii. 360) that it is -strange that any one should rely upon the <i>à priori</i> -evidence that space or extension is infinite, or that nothing -can be made of nothing. He holds (i. 304) that -the first law of <i>motion</i> is <i>rigorously true</i>, but that the -axioms respecting the <i>lever</i> are only <i>approximately</i> true. -He holds (ii. 110) that there may be sidereal firmaments -in which events succeed each other at random, -without obeying any laws of causation; although one -might suppose that even if space and cause are both to -have their limits, still they might terminate together: -and then, even on this bold supposition, we should no -<i>where</i> have a world in which events were <i>casual</i>. He -holds (ii. 111) that the axiom, that every event must -have a cause, is established by means of an "induction -by simple enumeration:" and in like manner, that -the principles of number and of geometry are proved -by this method of simple enumeration alone. He -ascribes the proof (i. 162) of the axiom, "things which -are equal to the same are equal to each other," to the -fact that this proposition has been perpetually <i>found</i> -true and never false. He holds (i. 338) that "In all<span class="pagenum" id="Page_289">289</span> -propositions concerning numbers, a condition is implied, -without which none of them would be true; and -that condition is an assumption which <i>may be false</i>. -<i>The condition is that</i> 1 = 1."</p> - -<p>73. Mr. Mill further holds (i. 309), that it is a -characteristic property of geometrical forms, that they -are capable of being painted in the imagination with a -distinctness equal to reality:—that our ideas of forms -exactly resemble our sensations: which, it is implied, -is not the case with regard to any other class of our -ideas;—that we thus may have mental pictures of all -possible combinations of lines and angles, which are -as fit subjects of geometrical experimentation as the -realities themselves. He says, that "we know that -the imaginary lines exactly resemble real ones;" and -that we obtain this knowledge respecting the characteristic -property of the idea of space by experience; though -it does not appear <i>how</i> we can compare our <i>ideas</i> with -the <i>realities</i>, since we know the realities only <i>by</i> our -ideas; or why this property of their resemblance should -be confined to <i>one class</i> of ideas alone.</p> - -<p>74. I have now made such remarks as appear to -me to be necessary, on the most important parts of -Mr. Mill's criticism of my <i>Philosophy</i>. I hope I have -avoided urging any thing in a contentious manner; as -I have certainly written with no desire of controversy, -but only with a view to offer to those who may be willing -to receive it, some explanation of portions of my -previous writings. I have already said, that if this -had not have been my especial object, I could with -pleasure have noted the passages of Mr. Mill's <i>Logic</i> -which I admire, rather than the points in which we -differ. I will in a very few words refer to some of -these points, as the most agreeable way of taking leave -of the dispute.</p> - -<p>I say then that Mr. Mill appears to me especially -instructive in his discussion of the nature of the proof -which is conveyed by the syllogism; and that his -doctrine, that the force of the syllogism consists in an -<i>inductive assertion, with an interpretation added to it</i>, -solves very happily the difficulties which baffle the<span class="pagenum" id="Page_290">290</span> -other theories of this subject. I think that this doctrine -of his is made still more instructive, by his excepting -from it the cases of Scriptural Theology and of Positive -Law (i. 260), as cases in which general propositions, -not particular facts, are our original data. I consider -also that the recognition of <i>Kinds</i> (i. 166) as classes in -which we have, not a finite but an <i>inexhaustible</i> body -of resemblances among individuals, and as groups -made by nature, not by mere definition, is very valuable, -as stopping the inroad to an endless train of false -philosophy. I conceive that he takes the right ground -in his answer to Hume's argument against miracles -(ii. 183): and I admire the acuteness with which he -has criticized Laplace's tenets on the Doctrine of -Chances, and the candour with which he has, in the -second edition, acknowledged oversights on this subject -made in the first. I think that much, I may -almost say all, which he says on the subject of Language, -is very philosophical; for instance, what he -says (ii. 238) of the way in which words acquire their -meaning in common use. I especially admire the acuteness -and force with which he has shown (ii. 255) how -moral principles expressed in words degenerate into -formulas, and yet how the formula cannot be rejected -without a moral loss. This "perpetual oscillation in -spiritual truths," as he happily terms it, has never, -I think, been noted in the same broad manner, and -is a subject of most instructive contemplation. And -though I have myself refrained from associating moral -and political with physical science in my study of the -subject, I see a great deal which is full of promise -for the future progress of moral and political knowledge -in Mr. Mill's sixth Book, "On the Logic of the -Moral and Political Sciences." Even his arrangement -of the various methods which have been or may be -followed in "the Social Science,"—"the Chemical or -Experimental Method," "the Geometrical or Abstract -Method," "the Physical or Concrete Deductive Method," -"the Inverse Deductive or Historical Method," -though in some degree fanciful and forced, abounds -with valuable suggestions; and his estimate of "the<span class="pagenum" id="Page_291">291</span> -interesting philosophy of the Bentham school," the -main example of "the geometrical method," is interesting -and philosophical. On some future occasion, -I may, perhaps, venture into the region of which Mr. -Mill has thus essayed to map the highways: for it -is from no despair either of the great progress to be -made in such truth as that here referred to, or of -the effect of philosophical method in arriving at such -truth, that I have, in what I have now written, confined -myself to the less captivating but more definite -part of the subject.</p> - - - -<hr class="chap" /> - -<p><span class="pagenum" id="Page_292">292</span></p> - - -</div><div class="chapter"> -<h2><a name="CHAPTER_XXIII" id="CHAPTER_XXIII"></a>CHAPTER XXIII.<br /> - -<span class="smcap medium">Political Economy as an Inductive Science.</span></h2> - - -<p><a id="XXIII1"></a>(<i>Moral Sciences.</i>)—1. <span class="smcap">Both</span> M. Comte and Mr. Mill, -in speaking of the methods of advancing science, aim, as -I have said, at the extension of their methods to moral -subjects, and aspire to suggest means for the augmentation -of our knowledge of ethical, political, and social -truths. I have not here ventured upon a like extension -of my conclusions, because I wished to confine my -views of the philosophy of discovery to the cases in -which all allow that solid and permanent discoveries -have been made. Moreover in the case of moral speculations, -we have to consider not only observed external -facts and the ideas by which they are colligated, -but also internal facts, in which the instrument of -observation is consciousness, and in which observations -and ideas are mingled together, and act and react in a -peculiar manner. It may therefore be doubted whether -the methods which have been effectual in the discovery -of physical theories will not require to be greatly modified, -or replaced by processes altogether different, -when we would make advances in ethical, political, or -social knowledge. In ethics, at least, it seems plain -that we must take our starting-point not without but -within us. Our mental powers, our affections, our reason, -and any other faculties which we have, must be the -basis of our convictions. And in this field of knowledge, -the very form of our highest propositions is different -from what it is in the physical sciences. In -Physics we examine what <i>is</i>, in a form more or less -general: in Ethics we seek to determine what <span class="smcap">OUGHT</span> -<i>to be</i>, as the highest rule, which is supreme over all<span class="pagenum" id="Page_293">293</span> -others. In this case we cannot expect the methods of -physical discovery to aid us.</p> - -<p>But others of the subjects which I have mentioned, -though strongly marked and influenced by this ethical -element, are still of a mixed character, and require -also observation of external facts of human, individual, -and social conduct, and generalizations derived from -such observations. The facts of political constitutions -and social relations in communities of men, and the -histories of such communities, afford large bodies of -materials for political and social science; and it seems -not at all unlikely that such science may be governed, -in its formation and progress, by laws like those which -govern the physical sciences, and may be steered clear -of errors and directed towards truths by an attention -to the forms which error and truth have assumed in -the most stable and certain sciences. The different -forms of society, and the principal motives which operate -upon men regarded in masses, may be classified -as facts; and though our consciousness of what we ourselves -are and the affections which we ourselves feel -are always at work in our interpretations of such facts, -yet the knowledge which we thus obtain may lead us -to bodies of knowledge which we may call <i>Sciences</i>, -and compare with the other sciences as to their form -and maxims.</p> - - -<p><a id="XXIII2"></a>(<i>Political Economy.</i>)—2. Among such bodies of -knowledge, I may notice as a specimen, the science of -<i>Political Economy</i>, and may compare it with other -sciences in the respects which have been referred to.</p> - -<p>M. Comte has given a few pages to the discussion of -this science of Political Economy<a name="FNanchor_291" id="FNanchor_291"></a><a href="#Footnote_291" class="fnanchor">[291]</a>; but what he has -said amounts only to a few vague remarks on Adam -Smith and Destutt de Tracy; his main object being, -it would seem, to introduce his usual formula, and to -condemn all that has hitherto been done (with which -there is no evidence that he is adequately acquainted) -as worthless, because it is "theological," "metaphysical," -"literary," and not "<i>positive</i>."</p> - -<p><span class="pagenum" id="Page_294">294</span></p> - -<p>Mr. Mill has much more distinctly characterized the -plan and form of Political Economy in his system<a name="FNanchor_292" id="FNanchor_292"></a><a href="#Footnote_292" class="fnanchor">[292]</a>. -He regards this science as that which deals with the -results which take place in human society in consequence -of the desire of wealth. He explains, however, -that it is only for the sake of convenience that one of -the motives which operate upon man is thus insulated -and treated as if it were the only one:—that there are -other principles, for instance, the principles on which -the progress of population depends, which co-operate -with the main principle, and materially modify its results: -and he gives reasons why this mode of simplifying -the study of social phenomena tends to promote -the progress of systematic knowledge.</p> - -<p>Instead of discussing these reasons, I will notice the -way in which the speculations of political economists -have exemplified tendencies to error, and corrections -of those tendencies, of the same nature as those -which we have already noticed in speaking of other -sciences.</p> - - -<p><a id="XXIII3"></a>(<i>Wages, Profits, and Rent.</i>)—3. We may regard as -one of the first important steps in this science, Adam -Smith's remark, that the value or price of any article -bought and sold consists of three elements, <i>Wages</i>, <i>Profits</i>, -and <i>Rent</i>. Some of the most important of subsequent -speculations were attempts to determine the laws of each -of these three elements. At first it might be supposed -that there ought to be added to them a fourth element, -<i>Materials</i>. But upon consideration it will be seen that -materials, as an element of price, resolves itself into -wages and rent; for all materials derive their value -from the labour which is bestowed upon them. The -iron of the ploughshare costs just what it costs to sink -the mine, dig up and smelt the iron. The wood of the -frame costs what it costs to cut down the tree, together -with the rent of the ground on which it grows.</p> - - -<p><a id="XXIII4"></a>(<i>Premature Generalizations.</i>)—4. But what determines -Wages?—The amount of persons seeking work,<span class="pagenum" id="Page_295">295</span> -that is, speaking loosely, the population; and the amount -of money which is devoted to the payment of wages. -And what determines the population? It was replied,—the -means of subsistence. And how does the population -tend to increase?—In a geometrical ratio. And -how does the subsistence tend to increase?—At most in -an arithmetical ratio. And hence it was inferred that -the population tends constantly to run beyond the -means of subsistence, and will be limited by a threatened -deficiency of these means. And the wages paid -must be such as to form this limit. And therefore the -wages paid will always be such as just to keep up the -population in its ordinary state of progress. Here -was one general proposition which was gathered from -summary observations of society.</p> - -<p>Again: as to Rent: Adam Smith had treated Rent -as if it were a monopoly price—the result of a monopoly -of the land by the landowners. But subsequent -writers acutely remarked that land is of various degrees -of fertility, and there is some land which barely -pays the cultivator, if cultivating it he pay no rent. -And rent can be afforded for other land only in so far -as it is better than this bad land. And thus, there -was obtained another general proposition; that the -Rent of good land was just equal to the excess of its -produce over the worst cultivable land.</p> - -<p>Now these two propositions are examples of a hasty -and premature generalization, like that from which -the sweeping physical systems of antiquity were derived. -They were examples of that process which -Francis Bacon calls <i>anticipation</i>; in which we leap at -once from a few facts to propositions of the highest -generality; and supposing these to be securely established, -proceed to draw a body of conclusions from -them, and thus frame a system.</p> - -<p>And what is the sounder and wiser mode of proceeding -in order to obtain a science of such things? -We must classify the facts which we observe, and take -care that we do not ascribe to the facts in our immediate -neighbourhood or specially under our notice, a -generality of prevalence which does not belong to<span class="pagenum" id="Page_296">296</span> -them. We must proceed by the ladder of Induction, -and be sure we have obtained the narrower generalizations, -before we aspire to the widest.</p> - - -<p><a id="XXIII5"></a>(<i>Correction of them by Induction. Rent.</i>)—5. For instance; -in the case of the latter of the above two propositions—that -Rent is the excess of the produce of -good soils over the worst—that is the case in England -and Scotland; but is it the case in other countries? -Let us see. Why is it the case in England? Because -if the rent demanded for good land were <i>more</i> than the -excess of the produce over bad land, the farmer would -prefer the bad land as more gainful. If the rent demanded -for good land were <i>less</i> than the excess, the -bad land would be abandoned by the farmer.</p> - -<p>But all this goes upon the supposition that the farmer -can remove from good land to bad, or from bad to -good, or apply his capital in some other way than -farming, according as it is more gainful. This is true -in England; but is it true all over the world?</p> - -<p>By no means. It is true in scarcely any other part -of the world. In almost every other part of the world -the cultivator is bound to the land, so that he cannot -remove himself and his capital from it; and cannot, -because he is not satisfied with his position upon it, -seek and find a position and a subsistence elsewhere. -On the contrary, he is bound by the laws and customs -of the country, by constitution, history and character, -so that he cannot, or can only with great difficulty, -change his plan and mode of life. And thus over -great part of the world the fundamental supposition on -which rests the above generalization respecting Rent is -altogether false.</p> - -<p>An able political economist<a name="FNanchor_293" id="FNanchor_293"></a><a href="#Footnote_293" class="fnanchor">[293]</a> has taken the step, -which as we have said, sound philosophy would have -prescribed: he has classified the states of society which -exist or have existed on the earth, as they bear on this -point, the amount of Rent. He has classified the -modes in which the produce is, in different countries<span class="pagenum" id="Page_297">297</span> -and different stages of society, divided between the -cultivator and the proprietor: and he finds that the natural -divisions are these:—<i>Serf Rents</i>, that is, labour -rents paid by the Cultivator to the Landowner, as in -Russia: <i>Métayer Rents</i>, where the produce is divided between -the Cultivator and the Landowner, as in Central -Europe: <i>Ryot Rents</i>, where a portion of the produce is -paid to the Sovereign as Landlord, as in India: <i>Cottier -Rents</i>, where a money-rent is paid by a Cultivator who -raises his own subsistence from the soil; and <i>Farmers' -Rents</i>, where a covenanted Rent is paid by a person -employing labourers. In this last case alone is it true -that the Rent is equal to the excess of good over bad -soils.</p> - -<p>The error of the conclusion, in this case, arises from -assuming the mobility of capital and labour in cases in -which it is not moveable: which is much as if mechanicians -had reasoned respecting rigid bodies, supposing -them to be fluid bodies.</p> - -<p>But the error of method was in not classifying the -facts of societies before jumping to a conclusion which -was to be applicable to all societies.</p> - - -<p><a id="XXIII6"></a>(<i>Wages.</i>)—6. And in like manner there is an error of -the same kind in the assertion of the other general -principles:—that wages are determined by the capital -which is forthcoming for the payment of wages; and -that population is determined in its progress by wages. -For there is a vast mass of population on the surface -of the earth which does not live upon wages: and -though in England the greater part of the people lives -upon wages, in the rest of the world the part that -does so is small. And in this case, as in the other, -we must class these facts as they exist in different -nations, before we can make assertions of any wide -generality.</p> - -<p>Mr. Jones<a name="FNanchor_294" id="FNanchor_294"></a><a href="#Footnote_294" class="fnanchor">[294]</a> classed the condition of labourers in different -countries in the same inductive manner in which -he classed the tenure of land. He pointed out that<span class="pagenum" id="Page_298">298</span> -there are three broad distinct classes of them: <i>Unhired -Labourers</i>, who cultivate the ground which they occupy, -and live on <i>self-produced wages</i>; <i>Paid Dependants</i>, -who are paid out of the <i>revenue</i> or income of -their employers, as the military retainers and domestic -artizans of feudal times in Europe, and the greater -part of the people of Asia at the present day; and -<i>Hired Labourers</i>, who are paid wages from <i>capital</i>.</p> - -<p>This last class, though taken as belonging to the -normal condition of society by many political economists, -is really the exceptional case, taking the world -at large; and no propositions concerning the structure -and relations of ranks in society can have any wide -generality which are founded on a consideration of -this case alone.</p> - - -<p><a id="XXIII7"></a>(<i>Population.</i>)—7. And again: with regard to the proposition -that the progress of population depends merely -on the rate of wages, a very little observation of different -communities, and of the same communities at -different times, will show that this is a very rash and -hasty generalization. When wages rise, whether or -not population shall undergo a corresponding increase -depends upon many other circumstances besides this -single fact of the increase of wages. The effect of a -rise of wages upon population is affected by the form -of the wages, the time occupied by the change, the -institutions of the society under consideration, and -other causes: and a due classification of the conditions -of the society according to these circumstances, is requisite -in order to obtain any general proposition concerning -the effect of a rise or fall of wages upon the -progress of the population.</p> - -<p>And thus those precepts of the philosophy of discovery -which we have repeated so often, which are so -simple, and which seem so obvious, have been neglected -or violated in the outset of Political Economy -as in so many other sciences:—namely, the precepts -that we must classify our facts before we generalize, -and seek for narrower generalizations and inductions -before we aim at the widest. If these maxims had -been obeyed, they would have saved the earlier specu<span class="pagenum" id="Page_299">299</span>lators -on this subject from some splendid errors; but, -on the other hand, it may be said, that if these earlier -speculators had not been thus bold, the science could -not so soon have assumed that large and striking form -which made it so attractive, and to which it probably -owes a large part of its progress.</p> - - - - -<hr class="chap" /> - -<p><span class="pagenum" id="Page_300">300</span></p> - - -</div><div class="chapter"> -<h2><a name="CHAPTER_XXIV" id="CHAPTER_XXIV"></a>CHAPTER XXIV.<br /> - -<span class="smcap medium">Modern German Philosophy<a name="FNanchor_295" id="FNanchor_295"></a><a href="#Footnote_295" class="fnanchor">[295]</a>.</span></h2> - - -<p class="center"><a id="XXIV1"></a>I. <i>Science is the Idealization of Facts.</i></p> - -<p>1. <span class="smcap">I have</span> spoken, a few chapters back, of the Reaction -against the doctrines of the Sensational School in -England and France. In Germany also there was a -Reaction against these doctrines;—but there, this movement -took a direction different from its direction in -other countries. Omitting many other names, Kant, -Fichte, Schelling and Hegel may be regarded as the -writers who mark, in a prominent manner, this Germanic -line of speculation. The problem of philosophy, -in the way in which they conceived it, may best be explained -by reference to that Fundamental Antithesis of -which I had occasion to speak in the <i>History of Scientific -Ideas</i><a name="FNanchor_296" id="FNanchor_296"></a><a href="#Footnote_296" class="fnanchor">[296]</a>. And in order to characterize the steps taken -by these modern German philosophers, I must return -to what I have said concerning the Fundamental -Antithesis.</p> - -<p>This Antithesis, as I have there remarked, is stated -in various ways:—as the Antithesis of Thoughts and -Things; of Ideas and Sensations; of Theory and Facts; -of Necessary Truth and Experience; of the Subjective -and Objective elements of our knowledge; and in other -phrases. I have further remarked that the elements -thus spoken of, though opposed, are inseparable. We -cannot have the one without the other. We cannot -have thoughts without thinking of Things: we cannot -have things before us without thinking of them.</p> - -<p><span class="pagenum" id="Page_301">301</span></p> - -<p>Further, it has been shown, I conceive, that our -knowledge derives from the former of these two elements, -namely our Ideas, its form and character of -knowledge; our ideas being the necessary <i>Forms</i> of -knowledge, while the <i>Matter</i> of our knowledge in each -case is supplied by the appropriate perception or outward -experience.</p> - -<p>Thus our Ideas of Space and Time are the necessary -Forms of our geometrical and arithmetical knowledge; -and no sensations or experience are needed as -the matter of such knowledge, except in so far as sensation -and experience are needed to evoke our Ideas in -any degree. And hence these sciences are sometimes -called <i>Formal</i> sciences. All other Sciences involve, -along with the experience and observation appropriate -to each, a development of the ideal conditions of knowledge -existing in our minds; and I have given the -history, both of this development of ideas and of the -matter derived from experience, in two former works, -the <i>History of Scientific Ideas</i>, and the <i>History of the -Inductive Sciences</i>. I have there traced this history -through the whole body of the physical sciences.</p> - -<p>But though Ideas and Perceptions are thus separate -elements in our philosophy, they cannot in fact be -distinguished and separated, but are different aspects -of the same thing. And the only way in which we can -approach to truth is by gradually and successively, in -one instance after another, advancing from the perception -to the idea; from the fact to the theory.</p> - -<p>2. I would now further observe, that in this progression -from fact to theory, we advance (when the -theory is complete and completely possessed by the -mind) from the apprehension of truths as <i>actual</i> to -the apprehension of them as <i>necessary</i>; and thus Facts -which were originally observed merely as Facts become -the consequences of theory, and are thus brought within -the domain of Ideas. That which was a part of the -objective world becomes also a part of the subjective -world; a necessary part of the thoughts of the theorist. -And in this way the progress of true theory is the -<i>Idealization of Facts</i>.</p> - -<p><span class="pagenum" id="Page_302">302</span></p> - -<p>Thus the Progress of Science consists in a perpetual -reduction of Facts to Ideas. Portions are perpetually -transferred from one side to another of the -Fundamental Antithesis: namely, from the Objective -to the Subjective side. The Centre or Fulcrum of the -Antithesis is shifted by every movement which is -made in the advance of science, and is shifted so that -the ideal side gains something from the real side.</p> - -<p>3. I will proceed to illustrate this Proposition a -little further. Necessary Truths belong to the Subjective, -Observed Facts to the Objective side of our -knowledge. Now in the progress of that exact -speculative knowledge which we call Science, Facts -which were at a previous period merely Observed -Facts, come to be known as Necessary Truths; and -the attempts at new advances in science generally -introduce the representation of known truths of fact, -as included in higher and wider truths, and therefore, -so far, necessary.</p> - -<p>We may exemplify this progress in the history -of the science of Mechanics. Thus the property of the -lever, the inverse proportion of the weights and arms, -was known as a fact before the time of Aristotle, and -known as no more; for he gives many fantastical and -inapplicable reasons for the fact. But in the writings -of Archimedes we find this fact brought within the -domain of necessary truth. It was there transferred -from the empirical to the ideal side of the Fundamental -Antithesis; and thus a progressive step was -made in science. In like manner, it was at first -taken by Galileo as a mere fact of experience, that in -a falling body, the velocity increases in proportion to -the time; but his followers have seen in this the -necessary effect of the uniform force of gravity. In -like manner, Kepler's empirical Laws were shown by -Newton to be necessary results of a central force -attracting inversely as the square of the distance. -And if it be still, even at present, doubtful whether -this is the <i>necessary</i> law of a central force, as some -philosophers have maintained that it is, we cannot -doubt that if now or hereafter, those philosophers<span class="pagenum" id="Page_303">303</span> -could establish their doctrine as certain, they would -make an important step in science, in addition to -those already made.</p> - -<p>And thus, such steps in science are made, whenever -empirical facts are discerned to be necessary laws; or, -if I may be allowed to use a briefer expression, whenever -<i>facts are idealized</i>.</p> - -<p>4. In order to show how widely this statement is -applicable, I will exemplify it in some of the other -sciences.</p> - -<p>In Chemistry, not to speak of earlier steps in -the science, which might be presented as instances of -the same general process, we may remark that the -analyses of various compounds into their elements, -according to the quantity of the elements, form a vast -multitude of facts, which were previously empirical -only, but which are reduced to a law, and therefore -to a certain kind of ideal necessity, by the discovery -of their being compounded according to definite and -multiple proportions. And again, this very law of -definite proportions, which may at first be taken as -a law given by experience only, it has been attempted -to make into a necessary truth, by asserting that -bodies must necessarily consist of atoms, and atoms -must necessarily combine in definite small numbers. -And however doubtful this Atomic Theory may at -present be, it will not be questioned that any chemical -philosopher who could establish it, or any other -Theory which would produce an equivalent change -in the aspect of the science, would make a great -scientific advance. And thus, in this Science also, -the Progress of Science consists in the transfer of -facts from the empirical to the necessary side of -the antithesis; or, as it was before expressed, in the -idealization of facts.</p> - -<p>5. We may illustrate the same process in the -Natural History Sciences. The discovery of the -principle of Morphology in plants was the reduction -of a vast mass of Facts to an <i>Idea</i>; as Schiller said -to Göthe when he explained the discovery; although -the latter, cherishing a horror of the term <i>Idea</i>,<span class="pagenum" id="Page_304">304</span> -which perhaps is quite as common in England as in -Germany, was extremely vexed at being told that he -possessed such furniture in his mind. The applications -of this Principle to special cases, for instance, to -Euphorbia by Brown, to Reseda by Lindley, have -been attempts to idealize the facts of these special -cases.</p> - -<p>6. We may apply the same view to steps in -Science which are still under discussion;—the question -being, whether an advance has really been made in -science or not. For instance, in Astronomy, the -Nebular Hypothesis has been propounded, as an -explanation of many of the observed phenomena of -the Universe. If this Hypothesis could be conceived -ever to be established as a true Theory, this must be -done by its taking into itself, as necessary parts of -the whole Idea, many Facts which have already been -observed; such as the various form of nebulæ;—many -Facts which it must require a long course of years to -observe, such as the changes of nebulæ from one form -to another;—and many facts which, so far as we can -at present judge, are utterly at variance with the Idea, -such as the motions of satellites, the relations of the -material elements of planets, the existence of vegetable -and animal life upon their surfaces. But if all these -Facts, when fully studied, should appear to be included -in the general Idea of Nebular Condensation -according to the Laws of Nature, the Facts so -idealized would undoubtedly constitute a very remarkable -advance in science. But then, we are to recollect -that we are not to suppose that the Facts will agree -with the Idea, merely because the Idea, considered by -itself, and without carefully attending to the Facts, is -a large and striking Idea. And we are also to recollect -that the Facts may be compared with another -Idea, no less large and striking; and that if we take -into our account, (as, in forming an Idea of the Course -of the Universe, we must do,) not only vegetable and -animal, but also <i>human</i> life, this other Idea appears -likely to take into it a far larger portion of the known -Facts, than the Idea of the Nebular Hypothesis.<span class="pagenum" id="Page_305">305</span> -The other Idea which I speak of is the Idea of Man -as the principal Object in the Creation; to whose -sustenance and development the other parts of the -Universe are subservient as means to an end; and -although, in our attempts to include all known Facts -in this Idea, we again meet with many difficulties, -and find many trains of Facts which have no apparent -congruity with the Idea; yet we may say that, -taking into account the Facts of man's intellectual -and moral condition, and his history, as well as -the mere Facts of the material world, the difficulties -and apparent incongruities are far less -when we attempt to idealize the Facts by reference -to this Idea, of Man as the End of Creation, than according -to the other Idea, of the World as the -result of Nebular Condensation, without any conceivable -End or Purpose. I am now, of course, merely -comparing these two views of the Universe, as supposed -steps in science, according to the general notion -which I have just been endeavouring to explain, that -a step in science is some Idealization of Facts.</p> - -<p>7. Perhaps it will be objected, that what I have -said of the Idealization of Facts, as the manner in -which the progress of science goes on, amounts to -no more than the usual expressions, that the progress -of science consists in reducing Facts to Theories. -And to this I reply, that the advantage at which I -aim, by the expression which I have used, is this, to -remind the reader, that Fact and Theory, in every -subject, are not marked by separate and prominent -features of difference, but only by their present -opposition, which is a transient relation. They are -related to each other no otherwise than as the poles -of the fundamental antithesis: the point which -separates those poles shifts with every advance of -science; and then, what was Theory becomes Fact. -As I have already said elsewhere, a true Theory is a -Fact; a Fact is a familiar Theory. If we bear this -in mind, we express the view on which I am now -insisting when we say that the progress of science -consists in reducing Facts to Theories. But I think<span class="pagenum" id="Page_306">306</span> -that speaking of <i>Ideas</i> as opposed to Facts, we express -more pointedly the original Antithesis, and the -subsequent identification of the Facts with the Idea. -The expression appears to be simple and apt, when -we say, for instance, that the Facts of Geography are -identified with the Idea of globular Earth; the Facts -of Planetary Astronomy with the Idea of the Heliocentric -system; and ultimately, with the Idea of Universal -Gravitation.</p> - -<p>8. We may further remark, that though by successive -steps in science, successive Facts are reduced -to Ideas, this process can never be complete. However -the point may shift which separates the two -poles, the two poles will always remain. However, -far the ideal element may extend, there will always -be something beyond it. However far the phenomena -may be idealized, there will always remain some -which are not idealized, and which are mere phenomena. -This also is implied by making our expressions -refer to the fundamental antithesis: for because the -antithesis <i>is</i> fundamental, its two elements will -always be present; the objective as well as the -subjective. And thus, in the contemplation of the -universe, however much we understand, there must -always be something which we do not understand; -however far we may trace necessary truths, there -must always be things which are to our apprehension -arbitrary: however far we may extend the sphere of -our internal world, in which we feel power and see -light, it must always be surrounded by our external -world, in which we see no light, and only feel resistance. -Our subjective being is inclosed in an objective -shell, which, though it seems to yield to our efforts, -continues entire and impenetrable beyond our reach, -and even enlarges in its extent while it appears to -give up to us a portion of its substance.</p> - - -<p class="center"><a id="XXIV2"></a>II. <i>Successive German Philosophies.</i></p> - -<p>9. The doctrine of the Fundamental Antithesis -of two elements of which the union is involved in all<span class="pagenum" id="Page_307">307</span> -knowledge, and of which the separation is the task of -all philosophy, affords us a special and distinct mode -of criticizing the philosophies which have succeeded -each other in the world; and we may apply it to the -German Philosophies of which we have spoken.</p> - -<p>The doctrine of the Fundamental Antithesis is briefly -this:</p> - -<p><i>That in every act of knowledge (1) there are two -opposite elements which we may call Ideas and Perceptions; -but of which the opposition appears in various -other antitheses; as Thoughts and Things, Theories -and Facts, Necessary Truths and Experiential Truths; -and the like: (2) that our knowledge derives from the -former of these elements, namely our Ideas, its form -and character as knowledge, our Ideas of space and -time being the necessary forms, for instance, of our -geometrical and arithmetical knowledge; (3) and in -like manner, all our other knowledge involving a -development of the ideal conditions of knowledge existing -in our minds: (4) but that though ideas and perceptions -are thus separate elements in our philosophy, -they cannot, in fact, be distinguished and separated, -but are different aspects of the same thing; (5) that the -only way in which we can approach to truth is by -gradually and successively, in one instance after -another, advancing from the perception to the idea; -from the fact to the theory; from the apprehension of -truths as actual to the apprehension of them as necessary. -(6) This successive and various progress from fact to -theory constitutes the history of science; (7) and this -progress, though always leading us nearer to that -central unity of which both the idea and the fact are -emanations, can never lead us to that point, nor to any -measurable proximity to it, or definite comprehension -of its place and nature.</i></p> - -<p>10. Now the doctrine being thus stated, successive -sentences of the statement contain successive steps of -German philosophy, as it has appeared in the series of -celebrated authors whom I have named.</p> - -<p>Ideas, and Perceptions or Sensations, being regarded -as the two elements of our knowledge, Locke, or at<span class="pagenum" id="Page_308">308</span> -least the successors of Locke, had rejected the former -element, Ideas, and professed to resolve all our knowledge -into Sensation. After this philosophy had prevailed -for a time, Kant exposed, to the entire conviction -of the great body of German speculators, the untenable -nature of this account of our knowledge. He taught -(one of the first sentences of the above statement) -that (2) <i>Our knowledge derives from our Ideas its form -and character as knowledge; our Ideas of space and -time being, for instance, the necessary forms of our geometrical -and arithmetical knowledge</i>. Fichte carried -still further this view of our knowledge, as derived -from our Ideas, or from its nature as knowledge; and -held that (3) <i>all our knowledge is a development of the -ideal conditions of knowledge existing in our minds</i> -(one of our next following sentences). But when the -ideal element of our knowledge was thus exclusively -dwelt upon, it was soon seen that this ideal system -no more gave a complete explanation of the real nature -of knowledge, than the old sensational doctrine had -done. Both elements, Ideas and Sensations, must be -taken into account. And this was attempted by -Schelling, who, in his earlier works, taught (as we -have also stated above) that (4) <i>Ideas and Facts are -different aspects of the same thing</i>:—this thing, the -central basis of truth in which both elements are involved -and identified, being, in Schelling's language, -the <i>Absolute</i>, while each of the separate elements is -subjected to <i>conditions</i> arising from their union. But -this Absolute, being a point inaccessible to us, and -inconceivable by us, as <i>our</i> philosophy teaches (as -above), cannot to any purpose be made the basis of -our philosophy: and accordingly this <i>Philosophy of -the Absolute</i> has not been more permanent than its -predecessors. Yet the philosophy of Hegel, which -still has a wide and powerful sway in Germany, is, -in the main, a development of the same principle as -that of Schelling;—the identity of the idea and the -fact; and Hegel's <i>Identity-System</i>, is rather a more -methodical and technical exposition of Schelling's -Philosophy of the Absolute than a new system. But<span class="pagenum" id="Page_309">309</span> -Hegel traces the manifestation of the identity of the -idea and fact in the <i>progress</i> of human knowledge; -and thus in some measure approaches to our doctrine -(above stated), that (5) <i>the way in which we approach -to truth is by gradually and successively, in one instance -after another</i>, that is, <i>historically, advancing from the -perception to the idea, from the fact to the theory</i>: while -at the same time Hegel has not carried out this view -in any comprehensive or complete manner, so as to -show that (6) <i>this process constitutes the history of -science</i>: and as with Schelling, his system shows an -entire want of the conviction (above expressed as -part of our doctrine), (7) that <i>we can never, in our -speculations reach or approach to the central unity -of which both idea and fact are emanations</i>.</p> - -<p>11. This view of the relation of the Sensational -School, of the Schools of Kant, Fichte, Schelling, and -Hegel, and of the fundamental defects of all, may be -further illustrated. It will, of course, be understood -that our illustration is given only as a slight and imperfect -sketch of these philosophies; but their relation -may perhaps become more apparent by the very brevity -with which it is stated; and the object of the present -chapter is not the detailed criticism of systems, but -this very relation of systems to each other.</p> - -<p>The actual and the ideal, the external and the internal -elements of knowledge, were called by the -Germans the <i>objective</i> and the <i>subjective</i> elements respectively. -The forms of knowledge and especially -space and time, were pronounced by Kant to be -essentially <i>subjective</i>; and this view of the nature -of knowledge, more fully unfolded and extended to -all knowledge, became the <i>subjective ideality</i> of Fichte. -But the subjective and the objective are, as we -have said, in their ultimate and supreme form, one; -and hence we are told of the <i>subjective-objective</i>, a -phrase which has also been employed by Mr. -Coleridge. Fichte had spoken of the subjective element -as the <i>Me</i>, (das Ich); and of the objective -element as the <i>Not-me</i>, (das Nicht-Ich); and has -deduced the <i>Not-me</i> from the <i>Me</i>. Schelling, on the<span class="pagenum" id="Page_310">310</span> -contrary, laboured with great subtlety to deduce -the <i>Me</i> from the <i>Absolute</i> which includes both. And -this Absolute, or Subjective-objective, is spoken of by -Schelling as unfolding itself into endless other antitheses. -It was held that from the assumption of such -a principle might be deduced and explained the oppositions -which, in the contemplation of nature, present -themselves at every step, as leading points of general -philosophy:—for example, the opposition of matter as -<i>passive</i> and <i>active</i>, as <i>dead</i> and <i>organized</i>, as <i>unconscious</i> -or <i>conscious</i>; the opposition of <i>individual</i> and -<i>species</i>, of <i>will</i> and <i>moral rule</i>. And this antithetical -development was carried further by Hegel, who taught -that the Absolute Idea developes itself so as to assume -qualities, limitations, and seeming oppositions, and -then completes the cycle of its development by returning -into unity.</p> - -<p>12. That there is, in the history of Science, much -which easily lends itself to such a formula, the views -which I have endeavoured to expound, show and exemplify -in detail. But yet the attempts to carry this -view into detail by conjecture—by a sort of divination—with -little or no attention to the historical progress -and actual condition of knowledge, (and such are those -which have been made by the philosophers whom I -have mentioned,) have led to arbitrary and baseless -views of almost every branch of knowledge. Such -oppositions and differences as are found to exist in -nature, are assumed as the representatives of the -elements of necessary antitheses, in a manner in which -scientific truth and inductive reasoning are altogether -slighted. Thus, this peculiar and necessary antithetical -character is assumed to be displayed in -attraction and repulsion, in centripetal and centrifugal -forces, in a supposed positive and negative electricity, -in a supposed positive and negative magnetism; in -still more doubtful positive and negative elements of -light and heat; in the different elements of the atmosphere, -which are, quite groundlessly, assumed to have a -peculiar antithetical character: in animal and vegetable -life: in the two sexes; in gravity and light.<span class="pagenum" id="Page_311">311</span> -These and many others, are given by Schelling, as -instances of the radical opposition of forces and elements -which necessarily pervades all nature. I conceive -that the heterogeneous and erroneous principles -involved in these views of the material world show us -how unsafe and misleading is the philosophical assumption -on which they rest. And the Triads of -Hegel, consisting of Thesis, Antithesis, and Union, are -still more at variance with all sound science. Thus -we are told that matter and motion are determined as -<i>inertia</i>, <i>impulsion</i>, <i>fall</i>; that Absolute Mechanics determines -itself as <i>centripetal force</i>, <i>centrifugal force</i>, -<i>universal gravitation</i>. Light, it is taught, is a secondary -determination of matter. Light is the most -intimate element of nature, and might be called <i>the -Me</i> of nature: it is limited by what we may call -negative light, which is darkness.</p> - -<p>13. In these rash and blind attempts to construct -physical science <i>à priori</i>, we may see how imperfect -the Hegelian doctrines are as a complete philosophy. -In the views of moral and political subjects the results -of such a scheme are naturally less obviously absurd, -and may often be for a moment striking and attractive, -as is usually the case with attempts to reduce -history to a formula. Thus we are told that <i>the -State</i> appears under the following determinations:—first -as one, substantial, self-included: next, varied, individual, -active, disengaging itself from the substantial and -motionless unity: next, as two principles, altogether -distinct, and placed front to front in a marked and -active opposition: then, arising out of the ruins of the -preceding, the idea appears afresh, one, identical, -harmonious. And the East, Greece, Rome, Germany, -are declared to be the historical forms of these successive -determinations. Whatever amount of real historical -colour there may be for this representation, it -will hardly, I think, be accepted as evidence of a profound -political philosophy; but on such parts of the -subject I shall not here dwell.</p> - -<p>14. I may observe that in the series of philosophical -systems now described, the two elements of the<span class="pagenum" id="Page_312">312</span> -Fundamental Antithesis are alternately dwelt upon -in an exaggerated degree, and then confounded. The -Sensational School could see in human knowledge -nothing but facts: Kant and Fichte fixed their attention -almost entirely upon ideas: Schelling and Hegel -assume the identity of the two, (a point we never can -reach,) as the origin of their philosophy. The external -world in Locke's school was all in all. In the -speculations of Kant this external world became a dim -and unknown region. Things were acknowledged to -be <i>something</i> in themselves, but <i>what</i>, the philosopher -could not tell. Besides the <i>phænomenon</i> which we -see, Kant acknowledged a <i>noumenon</i> which we think -of; but this assumption, for such it is, exercises no -influence upon his philosophy.</p> - -<p>15. We may for the sake of illustration imagine to -ourselves each system of philosophy as a Drama in -which <i>Things</i> are the <i>Dramatis Personæ</i> and the <i>Idea</i> -which governs the system is the <i>Plot</i> of the drama. -In Kant's Drama, Things in themselves are merely a -kind of 'Mute Personages,' κωφὰ πρόσωπα, which stand -on the stage to be pointed at and talked about, but -which do not tell us anything, or enter into the action -of the piece. Fichte carries this further, and if we go -on with the same illustration, we may say that he makes -the whole drama into a kind of Monologue; in which -the author tells the story, and merely names the -persons who appear. If we would still carry on the -image, we may say that Schelling, going upon the principle -that the whole of the drama is merely a progress -to the Denouement, which denouement contains the -result of all the preceding scenes and events, starts -with the last scene of the piece; and bringing all the -characters on the stage in their final attitudes, would -elicit the story from this. While the true mode of -proceeding is, to follow the drama Scene by Scene, -learning as much as we can of the Action and the -Characters, but knowing that we shall not be allowed -to see the Denouement, and that to do so is probably -not the lot of our species on earth. So far as any -philosopher has thus followed the historical progress of<span class="pagenum" id="Page_313">313</span> -the grand spectacle offered to the eyes of speculative -man, in which the Phenomena of Nature are the -Scenes, and the Theory of them the Plot, he has taken -the course by which knowledge really has made its advances. -But those who have partially done this, have -often, like Hegel, assumed that they had divined the -whole course and end of the story, and have thus -criticised the scenes and the characters in a spirit -quite at variance with that by which any real insight -into the import of the representation can be obtained.</p> - -<p>If it be asked which position we can assign, in this -dramatic illustration, to those who hold that all our -knowledge is derived from facts only, and who reject -the supposition of ideas; we may say that they look -on with a belief that the drama has <i>no</i> plot, and that -these scenes are improvised without connexion or purpose.</p> - -<p>16. I will only offer one more illustration of the -relative position of these successive philosophies. Kant -compares the change which he introduced into philosophy -to the change which Copernicus introduced into -astronomical theory. When Copernicus found that -nothing could be made of the phenomena of the heavens -so long as everything was made to turn round -the spectator, he tried whether the matter might not -be better explained if he made the spectator turn, and -left the stars at rest. So Kant conceives that our -experience is regulated by our own faculties, as the -phenomena of the heavens are regulated by our own -motions. But accepting and carrying out this illustration, -we may say that Kant, in explaining the phenomena -of the heavens by means of the motions of the -earth, has almost forgotten that the planets have their -own proper motions, and has given us a system which -hardly explains anything besides broadest appearances, -such as the annual and daily motions of the sun; and -that Fichte appears as if he wished to deduce all the -motions of the planets, as well as of the sun, from the -conditions of the spectator;—while Schelling goes to -the origin of the system, like Descartes, and is not -content to show how the bodies move, without also<span class="pagenum" id="Page_314">314</span> -proving that from some assumed original condition, -all the movements and relations of the system must -necessarily be what they are. It may be that a theory -which explains how the planets, with their orbits and -accompaniments, have come into being, may offer itself -to bold speculators, like those who have framed and -produced the nebular hypothesis. But I need not -remind my readers either how precarious such a -hypothesis is; or, that if it be capable of being considered -probable, its proofs must gradually dawn upon -us, step by step, age after age: and that a system of -doctrine which assumes such a scheme as a certain -and fundamental truth, and deduces the whole of -astronomy from it, must needs be arbitrary, and liable -to the gravest error at every step. Such a precarious -and premature philosophy, at best, is that of Schelling -and Hegel; especially as applied to those sciences in -which, by the past progress of all sure knowledge, we -are taught what the real cause and progress of knowledge -is: while at the same time we may allow that all -these forms of philosophy, since they do recognize the -condition and motion of the spectator, as a necessary -element in the explanation of the phenomena, are a -large advance upon the Ptolemaic scheme—the view of -those who appeal to phenomena alone as the source of -our knowledge, and say that the sun, the moon, and the -planets move as we see them move, and that all further -theory is imaginary and fantastical.</p> - - - -<hr class="chap" /> - -<p><span class="pagenum" id="Page_315">315</span></p> - - -</div><div class="chapter"> -<h2><a name="CHAPTER_XXV" id="CHAPTER_XXV"></a>CHAPTER XXV.<br /> - -<span class="smcap medium">The Fundamental Antithesis as it exists in the -Moral World.</span></h2> - - -<p> -<span class="dropcap"><span class="dsmall">1.</span> W</span>E HAVE hitherto spoken of the Fundamental -Antithesis as the ground of our speculations -concerning the material world, at least mainly. We -have indeed been led by the physical sciences, and especially -by Biology, to the borders of Psychology. We -have had to consider not only the mechanical effects of -muscular contraction, but the sensations which the -nerves receive and convey:—the way in which sensations -become perceptions; the way in which perceptions -determine actions. In this manner we have been led -to the subject of volition or will<a name="FNanchor_297" id="FNanchor_297"></a><a href="#Footnote_297" class="fnanchor">[297]</a>, and this brings us -to a new field of speculation, the moral nature of man; -and this moral nature is a matter not only of speculative -but of practical interest. On this subject I shall -make only a few brief remarks.</p> - -<p>2. Even in the most purely speculative view, the -moral aspect of man's nature differs from the aspect of -the material universe, in this respect, that in the -moral world, external events are governed in some -measure by the human will. When we speculate -concerning the laws of material nature, we suppose -that the phenomena of nature follow a course and -order which we may perhaps, in some measure, discover -and understand, but which we cannot change -or control. But when we consider man as an agent, -we suppose him able to determine some at least of -the events of the external world; and thus, able to -determine the actions of other men, and to lay down<span class="pagenum" id="Page_316">316</span> -laws for them. He cannot alter the properties of -fire and metals, stones and fluids, air and light; but he -can use fire and steel so as to compel other men's actions; -stone-walls and ocean-shores so as to control other -men's motions; gold and gems so as to have a hold on -other men's desires; articulate sounds and intelligible -symbols so as to direct other men's thoughts and move -their will. There is an external world of Facts; and -in this, the Facts are such as he makes them by his -Acts.</p> - -<p>3. But besides this, there is also, standing over -against this external world of Facts, an internal world -of Ideas. The Moral Acts without are the results of -Moral Ideas within. Men have an Idea of Justice, for -instance, according to which they are led to external -acts, as to use force, to make a promise, to perform a -contract, as individuals; or to make war and peace, to -enact laws and to execute them, as a nation.</p> - -<p>4. Some such internal moral Idea necessarily exists, -along with all properly human actions. Man feels -not only pain and anger, but indignation and the sentiment -of wrong, which feelings imply a moral idea of -right and wrong. Again, what he thinks of as wrong, -he tries to prevent; what he deems right, he attempts -to realize. The Idea gives a character to the Act; -the Act embodies the Idea. In the moral world as in -the natural world, the Antithesis is universal and inseparable. -It is an Antithesis of inseparable elements. -In human action, there is ever involved the Idea of -what is right, and the external Act in which this idea -is in some measure embodied.</p> - -<p>5. But the moral Ideas, such as that of Justice, -of Rightness, and the like, are always embodied incompletely -in the world of external action. Although -men's actions are to a great extent governed by the -Ideas of Justice, Rightness and the like; (for it must -be recollected that we include in their actions, laws, -and the enforcement of laws;) yet there is a large -portion of human actions which is not governed by such -ideas: (actions which result from mere desire, and -violations of law). There is a perpetual Antithesis of<span class="pagenum" id="Page_317">317</span> -Ideas and Facts, which is the fundamental basis of -moral as of natural philosophy. In the former as in -the latter subject, besides what is ideal, there is an -Actual which the ideal does not include. This Actual -is the region in which the results of mere desire, of -caprice, of apparent accident, are found. It is the -region of history, as opposed to justice; it is the -region of what <i>is</i>, as distinct from what <i>ought</i> to be.</p> - -<p>6. Now what I especially wish here to remark, is -this;—that the progress of man as a moral being consists -in a constant extension of the Idea into the region -of Facts. This progress consists in making human -actions conform more and more to the moral Ideas of -Justice, Rightness, and the like; including in human -actions, as we have said, Laws, the enforcement of -Laws, and other collective acts of bodies of men. The -History of Man <i>as</i> Man consists in this extension of -moral Ideas into the region of Facts. It is not that -the actual history of what men do has always consisted -in such an extension of moral Ideas; for there has -ever been, in the actual doings of men, a large portion -of facts which had no moral character; acts of desire, -deeds of violence, transgressions of acknowledged law, -and the like. But such events are not a part of the -genuine progress of humanity. They do not belong to -the history of man as man, but to the history of man -as brute. On the other hand, there are events which -belong to the history of man as man, events which -belong to the genuine progress of humanity; such as -the establishment of just laws; their enforcement; -their improvement by introducing into them a fuller -measure of moral Ideas. By such means there is a -constant progress of man as a moral being. By this -<i>realization of moral Ideas</i> there is a constant progress -of Humanity.</p> - -<p>7. I have made this reflection, because it appears -to me to bring into view an analogy between the Progress -of Science and the Progress of Man, or of Humanity, -in the sense in which I have used the term. -In both these lines of Progress, Facts are more and -more identified with Ideas. In both, there is a funda<span class="pagenum" id="Page_318">318</span>mental -Antithesis of Ideas and Facts, and progress -consists in a constant advance of the point which -separates the two elements of this Antithesis. In -both, Facts are constantly won over to the domain of -Ideas. But still, there is a difference in the two cases; -for in the one case the Facts are beyond our control. -We cannot make them other than they are; and all -that we can do, if we can do that, is to shape our Ideas -so that they shall coincide with the Facts, and still -have the manifest connexion which belongs to them as -Ideas. In the other case, the Facts are, to a certain -extent, in our power. They are what we make them, -for they are what we do. In this case, the Facts ought -to come towards the Ideas, rather than the Ideas -towards the Facts. As we called the former process -the Idealization of Facts, we may call this the Realization -of Ideas; and the analogy which I have here -wished to bring into view may be expressed by saying, -that the Progress of Physical Science consists in a -constant successive Idealization of Physical Facts; and -the Progress of man's Moral Being is a constant successive -Realization of Moral Ideas.</p> - -<p>8. Thus the necessary co-existence of an objective -and a subjective element belongs not only to human -knowledge, as was before explained, but also to human -action. The objective and the subjective element are -inseparable in this case as in the other. We have always -the Fact of Positive Law, along with the Idea of -Absolute Justice; the Facts of Gain or Loss, along -with the Idea of Rights. The Idea of Justice is inseparable -from historical facts, for justice gives to each -his own, and history determines what that is. We -cannot even conceive justice without society, or society -without law, and thus in the moral and in the natural -world the fundamental antithesis is inseparable, even -in thought. The two elements must always subsist; for -however far the moral ideas be realized in the world, -there will always remain much in the world which is -not conformable to moral ideas, even if it were only -through its necessary dependence on an unmoral and -immoral past. As in the physical world so in the<span class="pagenum" id="Page_319">319</span> -moral, however much the ideal sphere expands, it is -surrounded by a region which is not conformable to -the idea, although in one case the expansion takes -place by educing ideas out of facts, in the other, by -producing facts from ideas.</p> - -<p>I shall hereafter venture to pursue further this -train of speculation, but at present I shall make some -remarks on writers who may be regarded as the successors -amongst ourselves of these German schools of -Philosophy.</p> - - - - -<hr class="chap" /> - -<p><span class="pagenum" id="Page_320">320</span></p> - - -</div><div class="chapter"> -<h2><a name="CHAPTER_XXVI" id="CHAPTER_XXVI"></a>CHAPTER XXVI.<br /> - -<span class="smcap medium">Of the "Philosophy of the Infinite."</span></h2> - - -<p class="drop-cap"><span class="smcap">In</span> the last Chapter but one I stated that Schelling -propounded a Philosophy of the Absolute, the Absolute -being the original basis of truth in which the two -opposite elements, Ideas and Facts, are identified, and -that Hegel also founded his philosophy on the Identity -of these two elements. These German philosophies -appear to me, as I have ventured to intimate, of small -or no value in their bearing on the history of actual -science. I have in the history of the sciences noted -instances in which these writers seem to me to misconceive -altogether the nature and meaning of the facts of -scientific history; as where<a name="FNanchor_298" id="FNanchor_298"></a><a href="#Footnote_298" class="fnanchor">[298]</a> Schelling condemns Newton's -Opticks as a fabric of fallacies: and where<a name="FNanchor_299" id="FNanchor_299"></a><a href="#Footnote_299" class="fnanchor">[299]</a> Hegel -says that the glory due to Kepler has been unjustly -transferred to Newton. As it appears to me important -that English philosophers should form a just estimate -of Hegel's capacity of judging and pronouncing on this -subject, I will print in the Appendix a special discussion -of what he has said respecting Newton's discovery -of the law of gravitation.</p> - -<p>Recently attempts have been made to explain to -English readers these systems of German philosophy, -and in these attempts there are some points which may -deserve our notice as to their bearing on the philosophy -of science. I find some difficulty in discussing these -attempts, for they deal much with phrases which appear -to me to offer no grasp to man's power of reason. -What, for instance, is the <i>Absolute</i>, which occupies a<span class="pagenum" id="Page_321">321</span> -prominent place in these expositions? It is, as I have -stated, in Schelling, the central basis of truth in which -things and thoughts are united and identified. To attempt -to reason about such an "Absolute" appears to -me to be an entire misapprehension of the power of reason. -Again; one of the most eminent of the expositors -has spoken of each system of this kind as a <i>Philosophy -of the Unconditioned</i><a name="FNanchor_300" id="FNanchor_300"></a><a href="#Footnote_300" class="fnanchor">[300]</a>. But what, we must ask, is the -<i>Unconditioned</i>? That which is subject to no conditions, -is subject to no conditions which distinguish it -from any thing else, and so, cannot be a matter of -thought. But again; this <i>Absolute</i> or <i>Unconditioned</i> is -(if I rightly understand) said to be described also by -various other names; <i>unity</i>, <i>identity</i>, <i>substance</i>, <i>absolute -cause</i>, the <i>infinite</i>, <i>pure thought</i>, &c. As each of these -terms expresses some condition on which the name fixes -our thoughts, I cannot understand why they should any -of them be called the <i>Unconditioned</i>; and as they express -very different thoughts, I cannot understand why -they should be called by the same name. From speculations -starting from such a point, I can expect nothing -but confusion and perplexity; nor can I find that anything -else has come of them. They appear to me more -barren, and more certain to be barren, of any results -which have any place in our real knowledge, than the -most barren speculations of the schoolmen of the middle -ages: which indeed they much resemble in all their -features—their acuteness, their learning, their ambitious -aim, and their actual failure.</p> - -<p>2. But leaving the Absolute and the Unconditioned, -as notions which cannot be dealt with by our reason -without being something entirely different from their -definitions, we may turn for a moment to another notion -which is combined with them by the expositors of -whom I speak, and which has some bearing upon our -positive science, because it enters into the reasonings of -mathematics: I mean the notion of <i>Infinite</i>. Some of -those who hold that we can know nothing concerning<span class="pagenum" id="Page_322">322</span> -the Absolute and the Unconditioned, (which they -pretend to prove, though concerning such words I do -not conceive that anything can be true or false,) hold -also that the Infinite is in the same condition;—that -we can know nothing concerning what is Infinite;—therefore, -I presume, nothing concerning infinite space, -infinite time, infinite number, or infinite degrees.</p> - -<p>To disprove this doctrine, it might be sufficient to -point out that there is a vast mass of mathematical -science which includes the notion of infinites, and -leads to a great body of propositions concerning Infinites. -The whole of the infinitesimal calculus depends -upon conceiving finite magnitudes divided into an infinite -number of parts: these parts are infinitely small, -and of these parts there are other infinitesimal parts -infinitely smaller still, and so on, as far as we please -to go. And even those methods which shun the term -<i>infinite</i>, as Newton's method of Ultimate Ratios, the -method of Indivisibles, and the method of Exhaustions -of the ancient geometers, do really involve the notion -of infinite; for they imply a process continued without -limit.</p> - -<p>3. But perhaps it will be more useful to point out -the fallacies of the pretended proofs that we can know -nothing concerning Infinity and infinite things.</p> - -<p>The argument offered is, that of infinity we have no -notion but the negation of a limit, and that from this -negative notion no positive result can be deduced.</p> - -<p>But to this I reply: It is not at all true that our -notion of what is infinite is merely that it is <i>that</i> which -has no limit. We must ask further that <i>what</i>? that -space? that time? that number?—And if that space, -that what kind of space? That line? that surface? -that solid space?—And if that line, that line bounded -at one end, or not? If that surface, that surface -bounded on one, or on two, or on three sides? or on -none? However any of these questions are answered, -we may still have an infinite space. Till they are -answered, we can assert nothing about the space; not -because we can assert nothing about infinites; but -because we are not told what <i>kind</i> of infinite we are -talking of.</p> - -<p><span class="pagenum" id="Page_323">323</span></p> - -<p>In reality the definition of an Infinite Quantity is -not negative merely, but contains a positive part as -well. We assume a quantity of a certain kind which -may be augmented by carrying onward its limits in -one or more directions: this is a finite quantity of a -given kind. We <i>then</i>—when we have thus positively -determined the kind of the quantity—suppose the -limit in one or more directions to be annihilated, and -thus we have an infinite quantity. But in this infinite -quantity there remain the positive properties from -which we began, as well as the negative property, -the negation of a limit; and the positive properties -joined with the negative property may and do supply -grounds of reasoning respecting the infinite quantity.</p> - -<p>4. This is lore so elementary to mathematicians -that it appears almost puerile to dwell upon it; but this -seems to have been overlooked, in the proof that we can -have no knowledge concerning infinites. In such proof -it is assumed as quite evident, that all infinites are -equal. Yet, as we have seen, infinites may differ infinitely -among themselves, both in quantity and in kind. -A German writer is quoted<a name="FNanchor_301" id="FNanchor_301"></a><a href="#Footnote_301" class="fnanchor">[301]</a> for an "ingenious" proof -of this kind. In his writings, the opponent is supposed -to urge that a line <i>BAC</i> may be made infinite by -carrying the extremity <i>C</i> infinitely to the right, and -again infinite by carrying the extremity <i>B</i> infinitely to -the left; and thus the line infinitely extended both -ways would be double of the line infinite on one side -only. The supposed reply to this is, that it cannot be -so, because one infinite is equal to another: and moreover -that what is bounded at one end <i>A</i>, cannot be -infinite: both which assumptions are without the -smallest ground. That one infinite quantity may be -double of another, is just as clear and certain as that -one finite quantity may. For instance, if one leaf of -the book which the reader has before him were produced -infinitely upwards it would be an infinite space, -though bounded at the bottom and at both sides. If<span class="pagenum" id="Page_324">324</span> -the other leaf were in like manner produced infinitely -upwards it would in like manner be infinite; and the -two together, though each infinite, would be double of -either of them.</p> - -<p>5. As I have said, infinite quantities are conceived -by conceiving finite quantities increased by the transfer -of a certain limit, and then by negativing this limit -altogether. And thus an infinite number is conceived -by assuming the series 1, 2, 3, 4, and so on, up -to a limit, and then removing this limit altogether. -And this shows the baselessness of another argument -quoted from Werenfels. The opponent asks, Are there -in the infinite line an infinite number of feet? Then -in the double line there must be twice as many; and -thus the former infinite number did not contain all the -(possible) unities; (numerus infinitus non omnes habet -unitates, sed præter eum concipi possunt totidem unitates, -quibus ille careat, eique possunt addi). To which -I reply, that the definition of an infinite number is not -that it contains all possible unities: but this—that -the progress of numeration being begun according to -a certain law, goes on without limit. And accordingly -it is easy to conceive how one infinite number may be -larger than another infinite number, in any proportion. -If, for instance, we take, instead of the progression of -the natural numbers 1, 2, 3, 4, &c. and the progression of -the square numbers 1, 4, 9, 16, &c. any term of the -latter series will be greater than the corresponding term -of the other series in a ratio constantly increasing, and -the infinite term of the one, infinitely greater than the -corresponding infinite term of the other.</p> - -<p>6. In the same manner we form a conception of infinite -time, by supposing time to begin now, and to go -on, after the nature of time, without limit; or by going -back in thought from the present to a past time, and -by continuing this retrogression without limit. And -thus we have time infinite <i>a parte ante</i> and <i>a parte -post</i>, as the phrase used to run; and time infinite both -ways includes both, and is the most complete notion of -eternity.</p> - -<p>7. Perhaps those who thus maintain that we cannot<span class="pagenum" id="Page_325">325</span> -conceive anything infinite, mean that we cannot form -to ourselves a definite image of anything infinite. And -this of course is true. We cannot form to ourselves an -image of anything of which one of the characteristics -is that it is, in a certain way, unlimited. But this impossibility -does not prevent our reasoning about infinite -quantities; combining as elements of our reasoning, the -absence of a limit with other positive characters.</p> - -<p>8. One of the consequences which is drawn by the -assertors of the doctrine that we cannot know anything -about Infinity, is that we cannot obtain from -science any knowledge concerning God: And I have -been the more desirous to show the absence of proof of -this doctrine, because I conceive that science <i>does</i> give -us some knowledge, though it be very little, of the -nature of God: as I shall endeavour to show hereafter.</p> - -<p>For instance, I conceive that when we say that God -is an <i>eternal</i> Being, this phraseology is not empty -and unmeaning. It has been used by the wisest and -most thoughtful men in all ages, and, as I conceive, -may be used with undiminished, or with increased -propriety, after all the light which science and philosophy -have thrown upon such declarations. The -reader of Newton will recollect how emphatically he -uses this expression along with others of a cognate -character<a name="FNanchor_302" id="FNanchor_302"></a><a href="#Footnote_302" class="fnanchor">[302]</a>: "God is eternal and infinite, ... that is, He -endures from eternity to eternity, and is present from -infinity to infinity.... He is not eternity and infinity, -but eternal and infinite. He is not duration and space, -but He endures and is present. He endures always, -and is present everywhere, and by existing always and -everywhere He constitutes duration and space." We -shall see shortly that the view to which we are led may -be very fitly expressed by this language.</p> - -<p>But I will first notice some other aspects of this -philosophy.</p> - - - - -<hr class="chap" /> - -<p><span class="pagenum" id="Page_326">326</span></p> - - -</div><div class="chapter"> -<h2><a name="CHAPTER_XXVII" id="CHAPTER_XXVII"></a>CHAPTER XXVII.<br /> - -<span class="smcap medium">Sir William Hamilton on Inertia and Weight.</span></h2> - - -<p class="drop-cap"><span class="smcap">In</span> a preceding chapter I have spoken of Sir William -Hamilton as the expositor, to English readers, of -modern German systems, and especially of the so-called -"Philosophy of the Unconditioned." But the same -writer is also noticeable as a continuator of the speculations -of English and Scottish philosophers concerning -primary and secondary qualities; and these speculations -bear so far upon the philosophy of science that it -is proper to notice them here.</p> - - -<p><a id="XXVII1"></a>1. In our survey of the sciences, we have spoken of -a class which we have termed the Secondary Mechanical -Sciences; these being the sciences which explain -certain sensible phenomena, as sound, light, and heat, -by means of a medium interposed between external -bodies and our organs of sense. In these cases, we -ascribe to bodies certain qualities: we call them resonant, -bright, red or green, hot or cold. But in the -sciences which relate to these subjects, we explain these -qualities by the figure, size and motions of the parts -of the medium which intervenes between the object -and the ear, eye, or other sensible organ. And those -former qualities, sound, warmth and colour, are called -<i>secondary qualities</i> of the bodies; while the latter, -figure, size and motion, are called the <i>primary qualities</i> -of body.</p> - - -<p><a id="XXVII2"></a>2. This distinction, in its substance, is of great antiquity. -The atomic theory which was set up at an -early period of Greek philosophy was an attempt to -account for the secondary qualities of bodies by means -of their primary qualities. And this is really the -scientific ground of the distinction. <i>Those</i> are primary<span class="pagenum" id="Page_327">327</span> -qualities or attributes of body by means of which we, -in a scientific view, explain and derive their other -qualities. But the explanation of the sensible qualities -of bodies by means of their operation through a -medium has till now been very defective, and is so -still. We have to a certain extent theories of Sound, -Light and Heat, which reduce these qualities to scales -and standards, and in some measure account mechanically -for their differences and gradations. But we have -as yet no similar theory of Smells and Tastes. Still, -we do not doubt that fragrance and flavour are perceived -by means of an aerial medium in which odours -float, and a fluid medium in which sapid matters are -dissolved. And the special odour and flavour which -are thus perceived must depend upon the size, figure, -motion, number, &c. of the particles thus conveyed to -the organs of taste and smell: that is, <i>those</i> secondary -qualities, as well as the others, must depend upon the -primary qualities of the parts of the medium.</p> - - -<p><a id="XXVII3"></a>3. In this way the distinction of primary and secondary -qualities is definite and precise. But when men -attempt to draw the distinction by guess, without any -scientific principle, the separation of the two classes is -vague and various. I have, in the <i>History of Scientific -Ideas</i><a name="FNanchor_303" id="FNanchor_303"></a><a href="#Footnote_303" class="fnanchor">[303]</a>, pointed out some of the variations which are -to be found on this subject in the writings of philosophers. -Sir William Hamilton<a name="FNanchor_304" id="FNanchor_304"></a><a href="#Footnote_304" class="fnanchor">[304]</a> has given an account -of many more which he has compared and analysed -with great acuteness. He has shown how this distinction -is treated, among others, by the ancient atomists, -Leucippus and Democritus, by Aristotle, Galen, Galileo, -Descartes, Boyle, Malebranche, Locke, Reid, -Stewart, Royer-Collard. He then proceeds to give -his own view; which is, that we may most properly -divide the qualities of bodies into <i>three</i> classes, which -he calls <i>Primary</i>, <i>Secundo-primary</i>, and <i>Secondary</i>. -The former he enumerates as 1, Extension; 2, Divisibility; -3, Size; 4, Density or Rarity; 5, Figure;<span class="pagenum" id="Page_328">328</span> -6, Incompressibility absolute; 7, Mobility; 8, Situation. -The Secundo-primary are Gravity, Cohesion, -Inertia, Repulsion. The Secondary are those commonly -so called, Colour, Sound, Flavour, Savour, and -Tactical Sensation; to which he says may be added -the muscular and cutaneous sensation which accompany -the perception of the Secundo-primary qualities. -"Such, though less directly the result of foreign -causes, are Titillation, Sneezing, Horripilation, Shuddering, -the feeling of what is called Setting-the-teeth-on-edge, -&c."</p> - -<p>The Secundo-primary qualities Sir William Hamilton -traces in further detail. He explains that with -reference to Gravity, bodies are <i>heavy</i> or <i>light</i>. With -reference to Cohesion, there are many coordinate pairs, -of which he enumerates these:—<i>hard</i> and <i>soft</i>; <i>firm</i> -and <i>fluid</i>,—the fluid being subdivided into <i>thick</i> and -<i>thin</i>; <i>viscid</i> and <i>friable</i>; <i>tough</i> and <i>brittle</i>; <i>rigid</i> and -<i>flexible</i>; <i>fissile</i> and <i>infissile</i>; <i>ductile</i> and <i>inductile</i>; <i>retractile</i> -and <i>irretractile</i>; <i>rough</i> and <i>smooth</i>; <i>slippery</i> and -<i>tenacious</i>. With reference to Repulsion he gives these -qualities:—<i>compressible</i> and <i>incompressible</i>; <i>elastic</i> and -<i>inelastic</i>. And with reference to Inertia he mentions -only <i>moveable</i> and <i>immoveable</i>.</p> - -<p>I do not see what advantage is gained to philosophy -by such an enumeration of qualities as this, which, -after all, does not pretend to completeness; nor do I -see anything either precise or fundamental in such -distinctions as that of elasticity, a mode of cohesion, -and elasticity, a mode of repulsion. But a question in -which our philosophy is really concerned is how far -any of these qualities are <i>universal</i> qualities of matter. -Sir W. Hamilton holds that they are none of them -necessary qualities of matter, and therefore of course -not universal, and argues this point at some length. -With regard to one of his Secundo-primary qualities, -I will make some remarks.</p> - - -<p><a id="XXVII4"></a>4. <i>Inertia.</i>—In discussing the Ideas which enter into -the Mechanical Sciences<a name="FNanchor_305" id="FNanchor_305"></a><a href="#Footnote_305" class="fnanchor">[305]</a>, I have stated that the Idea<span class="pagenum" id="Page_329">329</span> -of Force and Resistance to Force, that is, of <i>Force</i> and -<i>Matter</i>, are the necessary foundations of those sciences. -Force cannot act without matter to act on; Matter -cannot exist without Force to keep its parts together -and to keep it in its place. But Force acting upon -matter may either be Force producing rest, or Force -producing motion. If we consider Force producing -motion, the motion produced, that is, the velocity -produced, must depend upon the quantity of matter -moved. It cannot be that the same power, acting in -the same way, shall produce the same velocity by -pushing a small pebble and a large rock. If this were -so, we could have no science on such matters. It -must needs be that the same force produces a smaller -velocity in the larger body; and this according to -some measure of its largeness. The measure of the -degree in which the body thus resists this communication -of motion is <i>inertia</i>. And the inertia is necessarily -supposed to be proportional to the quantity of -matter, because it is by this inertia that this existence -and quantity of the matter is measured. If therefore -any Science concerning Force and Matter is to exist, -matter must have inertia, and the inertia must be -proportional to the quantity of matter.</p> - - -<p><a id="XXVII5"></a>5. Sir W. Hamilton, in opposition to this, says, -that we can conceive a body occupying space, and yet -without attraction or repulsion for another body, and -wholly indifferent to this or that position, in space, -to motion and to rest. He infers thence that inertia -is not a necessary quality of bodies.</p> - -<p>To this I reply, that even if we can conceive such -bodies, (which in fact man, living in a world of matter -cannot conceive,) at any rate we cannot conceive any -<i>science</i> about such bodies. If bodies were indifferent -to motion and rest, Forces could not be measured by -their effects; nor could be measured or known in any -way. Such bodies might float about like clouds, visible -to the eye, but intangible, and governed by no laws -of motion. But if we have any science about bodies, -they must be tangible, and governed by laws of motion. -Not, then, from any observed properties of<span class="pagenum" id="Page_330">330</span> -bodies, but from the possibility of any science about -bodies, does it follow that all bodies have inertia.</p> - - -<p><a id="XXVII6"></a>6. <i>Gravity.</i>—Reasoning of the same kind may be -employed about weight. We can conceive, it is urged, -matter without weight. But I reply, we cannot conceive -a <i>science</i> which deals with matter that has no -weight:—a science, I mean, which deals with the quantity -of matter of bodies, as arising from the sum of their -elements. For the quantity of matter of bodies is and -must be measured by those sensible properties of matter -which undergo quantitative addition, subtraction -and division, as the matter is added, subtracted, and -divided. The quantity of matter cannot be known -in any other way. But this mode of measuring the -quantity of matter, in order to be true at all, must be -universally true. If it were only partially true—if -some kinds of matter had weight and others had not—the -limits of the mode of measuring matter by weight -would be arbitrary: and therefore the whole procedure -would be arbitrary, and as a mode of obtaining philosophical -truth, altogether futile. But we suppose -truth respecting the composition of bodies to be attainable; -therefore we must suppose the rule, which is -the necessary basis of such truth, to be itself true.</p> - -<p>Sir W. Hamilton has replied to these arguments, -but, as I conceive, without affecting the force of them. -I will repeat here the answer which I have already -given<a name="FNanchor_306" id="FNanchor_306"></a><a href="#Footnote_306" class="fnanchor">[306]</a>, and will reprint in the Appendix the Memoir -by which his objections were occasioned.</p> - -<p>He says, (1), that our reasoning assumes that we -must necessarily have it in our power to ascertain the -Quantity of Matter; whereas this may be a problem -out of the reach of human determination.</p> - -<p>To this I reply, that my reasoning <i>does</i> assume that -there is a science, or sciences, which make assertions -concerning the Quantity of Matter: Mechanics and -Chemistry are such sciences. My assertion is, that to -make such sciences possible, Quantity of Matter must<span class="pagenum" id="Page_331">331</span> -be proportional to Weight. If my opponent deny that -Mechanics and Chemistry can exist as science, he may -invalidate my proof; but not otherwise.</p> - -<p>(2) He says that there are two conceivable ways of -estimating the Quantity of Matter: by the Space occupied, -and by the Weight or Inertia; and that I assume -the second measure gratuitously.</p> - -<p>To which I reply, that the most elementary steps in -Mechanics and in Chemistry contradict the notion that -the Quantity of Matter is proportionate to the Space. -They proceed necessarily on a distinction between -Space and Matter:—between mere Extension and material -Substance.</p> - -<p>(3) He allows that we cannot make the Extension of -a body the measure of the Quantity of Matter, because, -he says, we do not know if "the compressing force" is -such as to produce "the closest compression." That is, -he assumes a compressing force, assumes a "closest compression," -assumes a peculiar (and very improbable) -atomic hypothesis; and all this, to supply a reason why -we are not to believe the first simple principle of -Mechanics and Chemistry.</p> - -<p>(4) He speaks of "a series of apparent fluids (as Light -or its vehicle, the Calorific, the Electro-galvanic, and -Magnetic agents) which we can neither denude of their -character of substance, nor clothe with the attribute of -weight."</p> - -<p>To which my reply is, that precisely because I cannot -"clothe" these agents with the attribute of Weight, I -<i>do</i> "denude them of the character of Substance." They -are not substances, but agencies. These Imponderable -Agents are not properly called "Imponderable Fluids." -This I conceive that I have proved; and the proof is -not shaken by denying the conclusion without showing -any defect in the reasoning.</p> - -<p>(5) Finally, my critic speaks about "a logical canon," -and about "a criterion of truth, subjectively necessary -and objectively certain;" which matters I shall not -waste the reader's time by discussing.</p> - - - - -<hr class="chap" /> - -<p><span class="pagenum" id="Page_332">332</span></p> - - -</div><div class="chapter"> -<h2><a name="CHAPTER_XXVIII" id="CHAPTER_XXVIII"></a>CHAPTER XXVIII.<br /> - -<span class="smcap medium">Influence of German Systems of Philosophy in -Britain.</span></h2> - - -<p class="drop-cap"><span class="smcap">The</span> philosophy of Kant, as I have already said, -involved a definite doctrine on the subject of the -Fundamental Antithesis, and a correction of some of the -errors of Locke and his successors. It was not however -at first favourably received among British philosophers, -and those who accepted it were judged somewhat capriciously -and captiously. I will say a word on these -points<a name="FNanchor_307" id="FNanchor_307"></a><a href="#Footnote_307" class="fnanchor">[307]</a>.</p> - -<p><a id="XXVIII1"></a>1. (<i>Stewart</i>)—Dugald Stewart, in his <i>Dissertation -on the Progress of the Moral Sciences</i>, repeatedly mentions -Kant's speculations, and always unfavourably. -In Note I to Part I. of the Dissertation he says, "In -our own times, Kant and his followers seem to have -thought that they had thrown a strong light on the -nature of <i>space</i> and also of <i>time</i>, when they introduced -the word <i>form</i> (<i>form of the intellect</i>) as a common -term applicable to both. Is not this to revert to the -scholastic folly of verbal generalization?" And in -Part II. he gives a long and laborious criticism of a -portion of Kant's speculations; of which the spirit -may be collected from his describing them as resulting -in "the metaphysical <i>conundrum</i>, that the human mind -(considered as a <i>noumenon</i> and not as a <i>phenomenon</i>) -neither exists in space nor time." And after mentioning -Meiners and Herder along with Kant, he adds,<span class="pagenum" id="Page_333">333</span> -"I am ashamed to say that in Great Britain the only -one of these names which has been much talked of -is Kant." And again in Note EE, he translates some -portion of the German philosopher, adding, that to the -expressions so employed he can attach no meaning.</p> - -<p>Stewart, in his criticism of Kant's doctrines, remarks -that, in asserting that the human mind possesses, -in its own ideas, an element of necessary and -universal truth, not derived from experience, Kant had -been anticipated by Price, by Cudworth, and even by -Plato; to whose <i>Theætetus</i> both Price and Cudworth -refer, as containing views similar to their own. And -undoubtedly this doctrine of ideas, as indispensable -sources of necessary truths, was promulgated and supported -by weighty arguments in the <i>Theætetus</i>; and -has ever since been held by many philosophers, in -opposition to the contrary doctrine, also extensively -held, that all truth is derived from experience. But, -in pointing out this circumstance as diminishing the -importance of Kant's speculations, Stewart did not -sufficiently consider that doctrines, fundamentally the -same, may discharge a very different office at different -periods of the history of philosophy. Plato's Dialogues -did not destroy, nor even diminish, the value of -Cudworth's "Immutable Morality." Notwithstanding -Cudworth's publications, Price's doctrines came out a -little afterwards with the air and with the effect of -novelties. Cudworth's assertion of ideas did not prevent -the rise of Hume's skepticism; and it was Hume's -skepticism which gave occasion to Kant's new assertion -of necessary and universal truth, and to his examination -into the grounds of the possibility and reality of -such truth. To maintain such doctrine <i>after</i> the appearance -of intermediate speculations, and with reference -to them, was very different from maintaining it before; -and this is the merit which Kant's admirers claim for -him. Nor can it be denied that his writings produced -an immense effect upon the mode of treating such -questions in Germany; and have had, even in this -country, an influence far beyond what Mr. Stewart -would have deemed their due.</p> - -<p><span class="pagenum" id="Page_334">334</span></p> - - -<p><a id="XXVIII2"></a>2. (<i>Mr. G. H. Lewes.</i>)—But as injustice has thus -been done to Kant by confounding his case with that of -his predecessors of like opinions, so on the other hand, -injustice has also been done, both to him and those -who have followed him in the assertion of ideas, by -confounding <i>their</i> case with his. This injustice seems -to me to be committed by a writer on the History of -Philosophy, who has given an account of the successive -schools of philosophy up to our own time;—has assigned -to Kant an important and prominent place -in the recent history of metaphysics;—but has still -maintained that Kant's philosophy, and indeed every -philosophy, is and must be a failure. In order to -prove this thesis, the author naturally has to examine -Kant's doctrines and the reasons assigned for them, -and to point out what he conceives to be the fallacy of -these arguments. This accordingly he professes to do; -but as soon as he has entered upon the argument, he -substitutes, as his opponent, for the philosopher of -Königsberg, a writer of our own time and country, -who does not profess himself a Kantian, who has been -repeatedly accused, with whatever justice, of misrepresenting -what he has borrowed from Kant, and whose -main views are, in the opinion of the writer himself, -very different from Kant's. Mr. Lewes<a name="FNanchor_308" id="FNanchor_308"></a><a href="#Footnote_308" class="fnanchor">[308]</a>, in the chapter -entitled "Examination of Kant's Fundamental -Principles," after a preliminary statement of the points -he intends to consider, says "Now to the question. -As Kant confessedly was led to his own system -by the speculations of Hume," and so on; and forthwith -he introduces the name of <i>Dr. Whewell</i> as the -writer whose views he has to criticize, without stating -how he connects him with Kant, and goes on arguing -against <i>him</i> for a dozen pages to the end of the Chapter.</p> - -<p><span class="pagenum" id="Page_335">335</span></p> - - -<p><a id="XXVIII3"></a>3. It is true, however, that I had adopted some of -Kant's views, or at least some of his arguments. The -chapters<a name="FNanchor_309" id="FNanchor_309"></a><a href="#Footnote_309" class="fnanchor">[309]</a> on the Ideas of Space and Time in the <i>Philosophy -of the Inductive Sciences</i>, were almost literal -translations of chapters in the <i>Kritik der Reinen Vernunft</i>. -Yet the author was charged by a reviewer at -the time, with explaining these doctrines "in a manner -incompatible with the clear views of Emanuel Kant." -It appeared to be assumed by the English admirers -of the Kantian philosophy, that Kant's views were -true and clear in Germany, but became untenable -when adopted in England.</p> - - -<p><a id="XXVIII4"></a>4. (<i>Mr. Mansel</i>)—But the most important of my -critics on this ground is Mr. Mansel, who has revived -the censure of my speculations as not doing justice to -the Kantian philosophy. "It is much to be regretted," -he says<a name="FNanchor_310" id="FNanchor_310"></a><a href="#Footnote_310" class="fnanchor">[310]</a>, "that Dr. Whewell, who has made good use -of Kantian principles in many parts of his <i>Philosophy -of the Inductive Sciences</i>," has not more accurately observed -Kant's distinction between the necessary laws -under which all men think, and the contingent laws -under which certain men think of certain things. And -further on Mr. Mansel, after giving great praise to the -general spirit of the <i>Philosophy of the Inductive Sciences</i>, -says, "It is to be regretted that the accuracy of -his theory has been in so many instances vitiated by a -stumble at the threshold of the Critical Philosophy." -Mr. Mansel is, indeed, by much the most zealous -English Kantian whose writings I have seen;—among -those, I mean, who have brought original powers of -philosophical thought to bear upon such subjects; and -have not been, as some have been, enslaved by an -admiration of German systems, just as bigotted as the -contempt of them which others feel. And as Mr.<span class="pagenum" id="Page_336">336</span> -Mansel has stated distinctly some of the points in -which he conceives that I have erred in deviating -from the doctrines of Kant, I should wish to make a -few remarks on those points.</p> - -<p><a id="XXVIII5"></a>5. Kant considers that Space and Time are conditions -of perception, and hence sources of necessary -and universal truth. Dr. Whewell agrees with Kant -in placing in the mind certain sources of necessary -truth; he calls these Fundamental Ideas, and reckons, -besides Space and Time, others, as Cause, Likeness, -Substance, and several more. Mr. Mill, the most -recent and able expounder of the opposite doctrine, -derives all truths from Observation, and denies that -there is such a separate source of truth as Ideas. Mr. -Mansel does not agree either with Mr. Mill or Dr. -Whewell; he adheres to the original Kantian thesis, -that Space and Time are sources of necessary truths, -but denies the office to the other Fundamental Ideas -of Dr. Whewell. In reading what has been said by -Mr. Mill, Mr. Mansel, and other critics, on the subject -of what I have called <i>Fundamental Ideas</i>, I am led to -perceive that I have expressed myself incautiously, -with regard to the identity of character between the -first two of these Fundamental Ideas, namely, Space -and Time, and the others, as Force, Composition, and -the like. And I am desirous of explaining, to those -who take an interest in these speculations, how far I -claim for the other Fundamental Ideas the same character -and attributes as for Space and Time.</p> - -<p><a id="XXVIII6"></a>6. The special and characteristic property of all -the Fundamental Ideas is what I have already mentioned, -that they are the mental sources of necessary -and universal scientific truths. I call them <i>Ideas</i>, -as being something not derived from sensation, but -governing sensation, and consequently giving form to -our experience;—<i>Fundamental</i>, as being the foundation -of knowledge, or at least of Science. And the -way in which those Ideas become the foundations of -Science is, that when they are clearly and distinctly -entertained in the mind, they give rise to inevitable -convictions or intuitions, which may be expressed as<span class="pagenum" id="Page_337">337</span> -<i>Axioms</i>; and these Axioms are the foundations of -Sciences respective of each Idea. The Idea of Space, -when clearly possessed, gives rise to geometrical Axioms, -and is thus the foundation of the Science of Geometry. -The Idea of Mechanical Force, (a modification -of the Idea of Cause,) when clearly developed in the -mind, gives birth to Axioms which are the foundation -of the Science of Mechanics. The Idea of Substance -gives rise to the Axiom which is universally accepted,—that -we cannot, by any process, (for instance, by -chemical processes,) create or destroy matter, but can -only combine and separate elements;—and thus gives -rise to the Science of Chemistry.</p> - - -<p><a id="XXVIII7"></a>7. Now it may be observed, that in giving this -account of the foundation of Science, I lay stress on -the condition that the Ideas must be <i>clearly and distinctly -possessed</i>. The Idea of Space must be quite -clear in the mind, or else the Axioms of Geometry -will not be seen to be true: there will be no <i>intuition</i> -of their truth; and for a mind in such a state, there -can be no Science of Geometry. A man may have a -confused and perplexed, or a vacant and inert state of -mind, in which it is not clearly apparent to him, that -two straight lines cannot inclose a space. But this is -not a frequent case. The Idea of Space is much more -commonly clear in the minds of men than the other -Ideas on which science depends, as Force, or Substance. -It is much more common to find minds in -which these latter Ideas are not so clear and distinct -as to make the Axioms of Mechanics or of Chemistry -self-evident. Indeed the examples of a state of mind -in which the Ideas of Force or of Substance are so -clear as to be made the basis of science, are comparatively -few. They are the examples of minds scientifically -cultivated, at least to some extent. Hence, -though the Axioms of Mechanics or of Chemistry may -be, in their own nature, as evident as those of Geometry, -they are not evident to so many persons, nor -at so early a period of intellectual or scientific culture. -And this being the case, it is not surprising that some -persons should doubt whether these Axioms are evident<span class="pagenum" id="Page_338">338</span> -at all;—should think that it is an error to assert -that there exist, in such sciences as Mechanics or -Chemistry, Fundamental Ideas, fit to be classed with -Space, as being, like it, the origin of Axioms.</p> - -<p>In speaking of all the Fundamental Ideas as being -alike the source of Axioms when clearly possessed, -without dwelling sufficiently upon the amount of -mental discipline which is requisite to give the mind -this clear possession of most of them; and in not -keeping before the reader the different degrees of evidence -which, in most minds, the Axioms of different -sciences naturally have, I have, as I have said, given -occasion to my readers to misunderstand me. I will -point out one or two passages which show that this -misunderstanding has occurred, and will try to remove -it.</p> - -<p><a id="XXVIII8"></a>8. The character of axiomatic truths seen by intuition -is, that they are not only seen to be true, but -to be necessary;—that the contrary of them is not -only false, but inconceivable. But this inconceivableness -depends entirely upon the clearness of the Ideas -which the axioms involve. So long as those Ideas -are vague and indistinct, the contrary of an Axiom -may be assented to, though it cannot be distinctly -conceived. It may be assented to, not because it is -possible, but because <i>we</i> do not see clearly what <i>is</i> -possible. To a person who is only beginning to think -geometrically, there may appear nothing absurd in the -assertion, that two straight lines may inclose a space. -And in the same manner, to a person who is only -beginning to think of mechanical truths, it may not -appear to be absurd, that in mechanical processes, Reaction -should be greater or less than Action; and so, -again, to a person who has not thought steadily about -Substance, it may not appear inconceivable, that by -chemical operations, we should generate new matter, -or destroy matter which already exists.</p> - -<p>Here then we have a difficulty:—the test of Axioms -is that the contrary of them is inconceivable; and yet -persons, till they have in some measure studied the -subject, do not see this inconceivableness. Hence our<span class="pagenum" id="Page_339">339</span> -Axioms must be evident only to a small number of -thinkers; and seem not to deserve the name of self-evident -or necessary truths.</p> - -<p>This difficulty has been strongly urged by Mr. Mill, -as supporting his view, that all knowledge of truth -is derived from experience. And in order that the -opposite doctrine, which I have advocated, may not -labour under any disadvantages which really do not -belong to it, I must explain, that I do not by any -means assert that those truths which I regard as -necessary, are all equally evident to common thinkers, -or evident to persons in all stages of intellectual development. -I may even say, that some of those truths -which I regard as necessary, and the necessity of which -I believe the human mind to be capable of seeing, by -due preparation and thought, are still such, that this -amount of preparation and thought is rare and peculiar; -and I will willingly grant, that to attain to and -preserve such a clearness and subtlety of mind as this -intuition requires, is a task of no ordinary difficulty -and labour.</p> - -<p><a id="XXVIII9"></a>9. This doctrine,—that some truths may be seen -by intuition, but yet that the intuition of them may -be a rare and difficult attainment,—I have not, it -would seem, conveyed with sufficient clearness to obviate -misapprehension. Mr. Mill has noticed a passage -of my <i>Philosophy</i> on this subject, which he has -understood in a sense different from that which I intended. -Speaking of the two Principles of Chemical -Science,—that combinations are definite in kind, and -in quantity,—I had tried to elevate myself to the -point of view in which these Principles are seen, not -only to be true, but to be necessary. I was aware -that even the profoundest chemists had not ventured -to do this; yet it appeared to me that there were considerations -which seemed to show that any other rule -would imply that the world was a world on which the -human mind could not employ itself in scientific speculation -at all. These considerations I ventured to -put forwards, not as views which could at present be -generally accepted, but as views to which chemical<span class="pagenum" id="Page_340">340</span> -philosophy appeared to me to tend. Mr. Mill, not -unnaturally, I must admit, supposed me to mean that -the two Principles of Chemistry just stated, are self-evident, -in the same way and in the same degree as -the Axioms of Geometry are so. I afterwards explained -that what I meant to do was, to throw out an -opinion, that <i>if</i> we could conceive the composition of -bodies <i>distinctly</i>, we might be able to see that it is -necessary that the modes of this composition should -be definite. This Mr. Mill does not object to<a name="FNanchor_311" id="FNanchor_311"></a><a href="#Footnote_311" class="fnanchor">[311]</a>: but -he calls it a great attenuation of my former opinion; -which he understood to be that we, (that is, men in -general,) already see, or may see, or ought to see, this -necessity. Such a general apprehension of the necessity -of definite chemical composition I certainly never -reckoned upon; and even in my own mind, the -thought of such a necessity was rather an anticipation -of what the intuitions of philosophical chemists in -another generation would be, than an assertion of what -they now are or ought to be; much less did I expect -that persons, neither chemists nor philosophers, would -already, or perhaps ever, see that a proposition, so -recently discovered to be true, is not only true, but -necessary.</p> - -<p><a id="XXVIII10"></a>10. Of the bearing of this view on the question at -issue between Mr. Mill and me, I may hereafter speak; -but I will now notice other persons who have misunderstood -me in the same way.</p> - -<p>An able writer in the <i>Edinburgh Review</i><a name="FNanchor_312" id="FNanchor_312"></a><a href="#Footnote_312" class="fnanchor">[312]</a> has, in -like manner, said, "Dr. Whewell seems to us to have -gone much too far in reducing to necessary truths -what assuredly the generality of mankind will not feel -to be so." It is a fact which I do not at all contest, -that the <i>generality of mankind</i> will not feel the Axioms -of Chemistry, or even of Mechanics, to be necessary -truths. But I had said, not that the generality of -mankind would feel this necessity, but (in a passage -just before quoted by the Reviewer) that the mind<span class="pagenum" id="Page_341">341</span> -under certain circumstances <i>attains a point of view</i> -from which it can pronounce mechanical (and other) -fundamental truths to be necessary in their nature, -though disclosed to us by experience and observation.</p> - -<p>Both the Edinburgh Reviewer and Mr. Mansel appear -to hold a distinction between the fundamental -truths of Geometry, and those of the other subjects -which I have classed with them. The latter says, -that perhaps metaphysicians may hereafter establish -the existence of other subjective conditions of intuitions -(or, as I should call them, Fundamental Ideas,) -besides Space and Time, but that in asserting such to -exist in the science of Mechanics, I certainly go too -far: and he gives as an instance my Essay,—"Demonstration -that all matter is heavy." I certainly did -not expect that the Principles asserted in that Essay -would be assented to as readily or as generally as the -Axioms of Geometry; but I conceive that I have -there proved that Chemical Science, using the balance -as one of its implements, cannot admit "imponderable -bodies" among its elements. This impossibility will, -I think, not only be found to exist in fact, but seen -to exist necessarily, by chemists, in proportion as -they advance towards general propositions of Chemical -Science in which the so-called "imponderable fluids" -enter. But even if I be right in this opinion, to how -few will this necessity be made apparent, and how -slowly will the intuition spread! I am as well aware -as my critics, that the necessity will probably never be -apparent to ordinary thinkers.</p> - - -<p><a id="XXVIII11"></a>11. Though Mr. Mansel does not acknowledge any -subjective conditions of intuition besides Space and -Time, he does recognize other <i>kinds of necessity</i>, which -I should equally refer to Fundamental Ideas; because -they are, no less than Space and Time, the foundations -of universal and necessary truths in science. Such -are<a name="FNanchor_313" id="FNanchor_313"></a><a href="#Footnote_313" class="fnanchor">[313]</a> the Principle of Substance;—All Qualities exist -in some subject: and the Principle of Causality;—<span class="pagenum" id="Page_342">342</span> -Every Event has its Cause. To these Principles he -ascribes a "metaphysical necessity," the nature and -grounds of which he analyses with great acuteness. -But what I have to observe is, that whatever <i>differences</i> -may be pointed out between the <i>grounds</i> of the -necessity, in this case of <i>metaphysical</i> necessity, and in -that which Mr. Mansel calls <i>mathematical</i> necessity -which belongs to the Conditions or Ideas of Space -and of Time; still, it is not the less true that the -Ideas of Substance and of Cause, <i>do</i> afford a foundation -for necessary truths, and that on these truths are -built Sciences. That every Change must have a Cause, -with the corresponding Axioms,—that the Cause is -known by the Effect, and Measured by it,—is the -basis of the Science of Mechanics. That there is a -Substance to which qualities belong, with the corresponding -Axiom,—that we cannot create or destroy -Substance, though we may alter Qualities by combining -and separating Substances,—is the basis of the -Science of Chemistry. And that this doctrine of the -Indestructibility of Substance is a primary axiomatic -truth, is certain; both because it has been universally -taken for granted by men seeking for general truths; -and because it is not and cannot be proved by experience<a name="FNanchor_314" id="FNanchor_314"></a><a href="#Footnote_314" class="fnanchor">[314]</a>. -So that I have here, even according to Mr. -Mansel's own statement, other grounds besides Space -and Time, for necessary truths in Science.</p> - -<p><a id="XXVIII12"></a>12. Besides mathematical and metaphysical necessity, -Mr. Mansel recognizes also a <i>logical necessity</i>. I will -not pretend to say that this kind of necessity is exactly -represented by any of those Fundamental Ideas -which are the basis of Science; but yet I think it will -be found that this logical necessity mainly operates -through the attribution of Names to things; and that -a large portion of its cogency arises from these maxims,—that -names must be so imposed that General Propositions -shall be possible,—and so that Reasoning -shall be possible. Now these maxims are really the<span class="pagenum" id="Page_343">343</span> -basis of Natural History, and are so stated in the <i>Philosophy -of the Inductive Sciences</i>. The former maxim -is the principle of all Classification; and though we -have no syllogisms in Natural History, the apparatus -of <i>genus</i>, <i>species</i>, <i>differentia</i>, and the like, which was -introduced in the analysis of syllogistic reasoning, is -really more constantly applied in Natural History -than in any other science.</p> - -<p><a id="XXVIII13"></a>13. Besides the different kinds of necessity which -Mr. Mansel thus acknowledges, I do not see why he -should not, on his own principles, recognize others; as -indeed he appears to me to do. He acknowledges, I -think, the distinction of Primary and Secondary qualities; -and this must involve him in the doctrine that -Secondary Qualities are necessarily perceived by means -of a <i>Medium</i>. Again: he would, I think, acknowledge -that in organized bodies, the parts exist for a -<i>Purpose</i>; and Purpose is an Idea which cannot be inferred -by reasoning from facts, without being possessed -and applied as an Idea. So that there would, I conceive, -exist, in his philosophy, all the grounds of necessary -truth which I have termed Fundamental Ideas; -only that he would further subdivide, classify, and analyse, -the kinds and grounds of this necessity.</p> - -<p>In this he would do well; and some of his distinctions -and analyses of this kind are, in my judgment, -very instructive. But I do not see what objection -there can be to my putting together all these kinds of -necessity, when my purpose requires it; and, inasmuch -as they all are the bases of Science, I may call them -by a general name; for instance, Grounds of Scientific -Necessity; and these are precisely what I mean by -<i>Fundamental Ideas</i>.</p> - -<p>That some steady thought, and even some progress -in the construction of Science, is needed in order to -see the necessity of the Axioms thus introduced, is -true, and is repeatedly asserted and illustrated in the -History of the Sciences. The necessity of such Axioms -is seen, but it is not seen at first. It becomes clearer -and clearer to each person, and clear to one person -after another, as the human mind dwells more and<span class="pagenum" id="Page_344">344</span> -more steadily on the several subjects of speculation. -<i>There are scientific truths which are seen by intuition, -but this intuition is progressive.</i> This is the remark -which I wish to make in answer to those of my critics -who have objected that truths which I have propounded -as Axioms, are not evident to all.</p> - - -<p><a id="XXVIII14"></a>14. That the Axioms of Science are not evident <i>to -all</i>, is true enough, and too true. Take the Axiom of -Substance:—that we may change the condition of a -substance in various ways, but cannot destroy it. This -has been assumed as evident by philosophers in all -ages; but if we ask an ordinary person whether a body -can be destroyed by fire, or diminished, will he unhesitatingly -reply, that it cannot? It requires some -thought to say<a name="FNanchor_315" id="FNanchor_315"></a><a href="#Footnote_315" class="fnanchor">[315]</a>, as the philosopher said, that the -weight of the smoke is to be found by subtracting the -weight of the ashes from that of the fuel; nay, even -when this is said, it appears, at first, rather an epigram -than a scientific truth. Yet it is by thinking only, not -by an experiment, that, from a happy guess it becomes -a scientific truth. And the thought is the basis, not -the result, of experimental truths; for which reason I -ascribe it to a Fundamental Idea. And so, such truths -are the genuine growth of the human mind; not innate, -as if they needed not to grow; still less, dead -twigs plucked from experience and stuck in from without; -not universal, as if they grew up everywhere; -but not the less, under favourable circumstances, the -genuine growth of the scientific intellect.</p> - -<p><a id="XXVIII15"></a>15. Not only do I hold that the Axioms, on which -the truths of science rest, grow from guesses into Axioms -in various ways, and often gradually, and at different -periods in different minds, and partially, even -in the end; but I conceive that this may be shown by -the history of science, as having really happened, with -regard to all the most conspicuous of such principles. -The scientific insight which enabled discoverers to -achieve their exploits, implied that they were among<span class="pagenum" id="Page_345">345</span> -the first to acquire an intuitive conviction of the Axioms -of their Science: the controversies which form so -large a portion of the history of science, arise from the -struggles between the clear-sighted and the dimsighted, -between those who were forwards and those who were -backwards in the progress of ideas; and these controversies -have very often ended in diffusing generally a -clearness of thought, on the controverted subject, which -at first, the few only, or perhaps not even they, possessed. -The History of Science consists of the History -of Ideas, as well as of the History of Experience and -Observation. The latter portion of the subject formed -the principal matter of my <i>History</i> of the Inductive -Sciences; the former occupied a large portion of the -<i>Philosophy</i> of the Inductive Sciences<a name="FNanchor_316" id="FNanchor_316"></a><a href="#Footnote_316" class="fnanchor">[316]</a>; which, I may -perhaps be allowed to explain, is, for the most part, a -Historical Work no less than the other; and was written -in a great measure, at the same time, and from the -same survey of the works of scientific writers.</p> - -<p><a id="XXVIII16"></a>16. I am aware that the explanation which I have -given, may naturally provoke the opponents of the -doctrine of scientific necessity to repeat their ordinary -fundamental objections, in a form adapted to the expressions -which I have used. They may say, the fact -that these so-called Axioms thus become evident only -during the progress of experience, proves that they are -derived from experience: they may, in reply to our -image, say, that truths are stuck into the mind by experience, -as seeds are stuck into the ground; and that -to maintain that they can grow under any other conditions, -is to hold the doctrine of spontaneous generation, -which is equally untenable in the intellectual and -in the physical world. I shall not however here resume -the general discussion; but shall only say briefly -in reply, that Axioms,—for instance, this Axiom, that -<i>material substances cannot be created or annihilated by -any process which we can apply</i>,—though it becomes -evident in the progress of experience, cannot be derived<span class="pagenum" id="Page_346">346</span> -from experience; for it is a proposition which never -has nor can be proved by experience; but which, -nevertheless, has been always assumed by men, seeking -for general truths, as necessarily true, and as controlling -and correcting all possible experience. And with -regard to the image of vegetable development, I may -say, that as such development implies both inherent -forms in the living seed, and nutritive powers in earth -and air; so the development of our scientific ideas implies -both a formative power, and materials acted on; -and that, though the analogy must be very defective, -we conceive that we best follow it by placing the formative -power in the living mind, and in the external -world the materials acted on: while the doctrine that -all truth is derived from experience only, appears to -reject altogether one of these elements, or to assert the -two to be one.</p> - - - - -<hr class="chap" /> - -<p><span class="pagenum" id="Page_347">347</span></p> - - -</div><div class="chapter"> -<h2><a name="CHAPTER_XXIX" id="CHAPTER_XXIX"></a>CHAPTER XXIX.<br /> - -<span class="smcap medium">Necessary Truth is progressive.<br /> - - -Objections considered.</span></h2> - -<p class="drop-cap"><span class="smcap">The</span> doctrine that necessary truth is progressive -is a doctrine very important in its bearing upon -the nature of the human mind; and, as I conceive, in -its theological bearing also. But it is a doctrine to -which objections are likely to be made from various -quarters, and I will consider some of these objections.</p> - -<p>1. Necessary truths, it will be said, cannot increase -in number. New ones cannot be added to the -old ones. For necessary truths are those of which the -necessity is plain and evident to all mankind—to the -common sense of man; such as the axioms of geometry. -But that which is evident to all mankind -must be evident from the first: that which is plain to -the common sense of man cannot require scientific discovery: -that which is necessarily true cannot require -accumulated proof.</p> - -<p>To this I reply, that necessary truths require for -their apprehension a certain growth and development -of the human mind. Though it is seen that they are -necessarily true, this is seen only by those who think -steadily and clearly, and to think steadily and clearly -on any kind of subject, requires time and attention;—requires -mental culture. This may be seen even in -the case of the axioms of geometry. These axioms -are self-evident: but to <i>whom</i> are they self-evident? -Not to uncultured savages, or young children; or persons -of loose vague habits of thought. To see the -truth and necessity of geometrical axioms, we need -geometrical culture.</p> - -<p>Therefore that any axioms are not evident without -patient thought and continued study of the subject, -does not disprove their necessity. Principles may be<span class="pagenum" id="Page_348">348</span> -axiomatic and necessary, although they require time, -and the progress of thought and of knowledge, to bring -them to light. And axioms may be thus gradually -brought to light by the progress of knowledge.</p> - -<p>Nor is it difficult to give examples of such axioms, -other than geometrical. There is an axiom which has -obtained currency among thoughtful men from the -time that man began to speculate about himself and -the universe:—<i>E nihilo nil fit</i>: Nothing can be made -of nothing. No material substance can be produced -or destroyed by natural causes, though its form and -consistence may be changed indefinitely. Is not this -an axiom? a necessary truth? Yet it is not evident -to all men at first, and without mental culture. At -first and before habits of steady and consistent thought -are formed, men think familiarly of the creation and -destruction of matter. Only when the mind has -received some philosophical culture does it see the -truth and necessity of the axiom of substance, and <i>then</i> -it does see it.</p> - -<p>And the axioms on which the science of mechanics -rests, that the cause is measured by the effects, that -reaction is equal and opposite to action, and the like,—are -not these evident to a mind cultivated by steady -thought on such subjects? and do they not require -such culture of the mind in order to see them? Are -they not obscure or uncertain to those who are not so -cultured, that is to common thinkers: to the general -bulk of mankind? Thus then it requires the discipline -of the science of mechanics to enable the mind to see -the axioms of that science.</p> - -<p>And does not this go further, as science and the -careful study of the grounds of science go further? To -a person well disciplined in mechanical reasoning it -has become, not a conclusion, but a principle, that in -mechanical action what is gained in power is lost in -time: or that in any change, the force gained is equal -to the force lost, so that new force cannot be generated, -any more than new matter, by natural changes. Is this -an axiom? a necessary fundamental truth? It appears -so to at least one great thinker and discoverer now<span class="pagenum" id="Page_349">349</span> -alive among us. If it do not appear so to us, or not -in the same sense, may not this be because we have -not yet reached his point of view? May not the conviction -which is now his alone become hereafter the -conviction of the philosophical world? And whatever -the case may be in this instance, have there not been -examples of this progress? Did not Galileo and the -disciples of Galileo reduce several mechanical principles -to the character of necessary truths, after they -had by experiment and reasoning discovered them to -be actually true? And have we not in these cases so -many proofs that necessary truth is progressive, along -with the progress of knowledge?</p> - -<p>2. But, it will be said, the necessary character -claimed for such truths is an illusion. The propositions -so brought into view are really established -by observation: by the study of external facts: and -it is only the effect of habit and familiarity which -makes men of science, when they well know them -to be true, think them to be necessarily true. They -are really the results of experience, as their history -shows; and therefore cannot be necessary and <i>à priori</i> -truths.</p> - -<p>To which I reply: Such principles as I have mentioned,—that -material substance cannot be produced -or destroyed—that the cause is measured by the effect—that -reaction is equal and opposite to action: are -not the results of experience, nor can be. No experience -can prove them; they are necessarily assumed as -the interpretation of experience. They were not proved -in the course of scientific investigations, but brought -to light as such investigations showed their necessity. -They are not the results, but the conditions of experimental -sciences. If the Axiom of Substance were not -true, and were not assumed, we could not have such a -science as Chemistry, that is, we could have no knowledge -at all respecting the changes of form of substances. -If the Axioms of Mechanics were not true and were -not assumed, we could have no science of Mechanics, -that is, no knowledge of the laws of force acting on -matter. It is not any special <i>results</i> of the science<span class="pagenum" id="Page_350">350</span> -in such cases; but the <i>existence</i>, the <i>possibility</i>, of -any science, which establishes the necessity of these -axioms. They are not the consequences of knowledge, -acquired from without, but the internal condition of -our being able to know. And when we are to <i>know</i> -concerning any new subject contained in the universe, -it is not inconceivable nor strange that there should -be new conditions of our knowledge.</p> - -<p>It is not inconceivable or strange, therefore, that as -new sciences are formed, new axioms, the foundations -of such sciences, should come into view. As the light -of clear and definite knowledge is kindled in successive -chambers of the universe, it may disclose, not -only the aspect of those new apartments, but also -the form and structure of the lamp which man is thus -allowed to carry from point to point, and to transmit -from hand to hand. And though the space illumined -to man's vision may always be small in comparison -with the immeasurable abyss of darkness by which it -is surrounded, and though the light may be dim and -feeble, as well as partial; this need not make us doubt -that, so far as we can by the aid of this lamp, we see -truly: so far as we discern the necessary laws of the -universe, the laws are true, and their truth is rooted -in that in which the being of the universe is rooted.</p> - -<p>And, to dwell for a moment longer on this image, -we may also conceive that all that this lamp—the -intellect of man cultivated by science,—does, by the -light which it gives, is this—that it dispels a darkness -which is dark for man alone, and discloses to -him some things in some measure as all things lie in -clear and perfect light before the eye of God. To -the Divine Mind all the laws of the universe are -plain and clear in all their multiplicity, extent and -depth. The human mind is capable of seeing some -of these laws, though only a few; to some extent, -though but a little way; to some depth, though never to -the bottom. But the Human Mind, can, in the course -of ages and generations, by the long exercise of thought, -successfully employed in augmenting knowledge, improve -its powers of vision; and may thus come to see<span class="pagenum" id="Page_351">351</span> -more laws than at first, to trace their extent more -largely, to understand them more thoroughly; and -thus the inward intellectual light of man may become -broader and broader from age to age, though ever -narrow when compared with completeness.</p> - -<p>3. Is it strange to any one that inward light, as -well as outward knowledge, should thus increase in -the course of man's earthly career? that as knowledge -extends, the foundations of knowledge should expand? -that as man goes on discovering new truths, he should -also discover something concerning the conditions of -truth? Is it wonderful that as science is progressive -the philosophy of science also should be progressive? -that as we know more of everything else, we should -also come to know more of our powers of knowing?</p> - -<p>This does not seem to have been supposed by philosophers -in general; or rather, they have assumed that -they could come to know more about the powers of -knowing by thinking about them, even without taking -into account the light thrown upon the nature of -knowledge by the progress of knowledge. From Plato -downwards, through Aristotle, through the Schoolmen, -to Descartes, to Locke, to Kant, Schelling and Hegel, -philosophers have been perpetually endeavouring to -explore the nature, the foundations, the consequences -of our knowledge. But since Plato, scarcely one of -them has ever proceeded as if new light were thrown -upon knowledge by new knowledge. They have, -many or all of them, attempted to establish fundamental -truths, some of them new fundamental truths, -about the human mind and the nature and conditions -of its knowledge. These attempts show that they do -not deny or doubt that there may be such new fundamental -truths. Such new fundamental truths respecting -the human mind and respecting knowledge -must be, in many cases at least, (as it will be seen -that they <i>are</i>, on examining the systems proposed -by the philosophers just mentioned,) seen by their own -light to be true. They are <i>new axioms</i> in philosophy. -These philosophers therefore, or their disciples, cannot -consistently blame us for holding the possibility of -new axioms being introduced into philosophy from age<span class="pagenum" id="Page_352">352</span> -to age, as there arise philosophers more and more -clear-sighted.</p> - -<p>4. But though <i>they</i> have no ground for rejecting -<i>our</i> new axioms merely because they are new, <i>we</i> may -have good ground for doubting the value of <i>their</i> new -axioms, that is, of the foundations of their systems; -because they are new truths about knowledge gathered -by merely exploring the old fields of knowledge. We -found our hopes of obtaining a larger view of the -constitution of the human mind than the early philosophers -had, on this:—that we obtain our view by -studying the operation of the human mind <i>since their -time</i>; its progress in acquiring a large stock of uncontested -truths and in obtaining a wide and real knowledge -of the universe. Here are new materials which -the ancients had not; and which may therefore justify -the hope that we may build our philosophy higher than -the ancients did. But modern philosophers who use -only the same materials as the ancient philosophers -used, have not the same grounds for hope which we -have. If they borrow all their examples and illustrations -of man's knowledge of the universe, from the condition -of the universe as existing in Space and Time, -that is, from the geometrical condition of the universe, -they may fail to obtain the light which might be -obtained if they considered that the universe is also -subject to conditions of <i>Substance</i>, of <i>Cause</i> and <i>Effect</i>, -of <i>Force</i> and <i>Matter</i>: is filled with <i>Kinds</i> of things, -in whose structure we assume <i>Design</i> and <i>Ends</i>; and -so on; and if they reflected that these conditions or -<i>Ideas</i> are not mere vague notions, but the bases of -sciences which all thoughtful persons allow to be certain -and real.</p> - -<p>It is then, as I have said, from taking advantage of -the progressive character which physical science, in the -history of man, has been found to possess, that I hope -to learn more of the nature and prospects of the human -mind and soul, than those can learn who still take -their stand on the old limited ground of man's knowledge. -The knowledge of Geometry by the Greeks -was the starting-point of their sound philosophy. It -showed that something might be certainly known, and<span class="pagenum" id="Page_353">353</span> -it showed, in some degree, how it was known. It -thus refuted the skepticism which was destroying philosophy, -and offered specimens of solid truth for the -philosopher to analyse. But the Greeks tried to go -beyond geometry in their knowledge of the universe. -They tried to construct a science of Astronomy—of -Harmonics—of Optics—of Mechanics. In the two -former subjects, they succeeded to a very considerable -extent. The question then arose, What was the philosophical -import of these new sciences? What light did -they throw on the nature of the universe, on the nature -of knowledge, on the nature of the human mind? These -questions Plato attempted to answer. He said that -the lesson of these new sciences is this:—that the -universe is framed upon the <i>Divine Ideas</i>; that man -can to a certain extent obtain sight of these Ideas; and -that when he does this, he <i>knows</i> concerning the universe. -And again, he also put the matter otherwise: -there is an <i>Intelligible World</i>, of which the Visible and -Sensible world is only a dim image. <i>Science</i> consists -in understanding the Intelligible World, which man is -to a certain extent able to do, by the nature of his -understanding. This was Plato's philosophy, founded -upon the progress which human knowledge had made -up to his time. Since his time, knowledge, that is -science, has made a large additional progress. What -is the philosophical lesson to be derived from this progress, -and from the new provinces thus added to -human knowledge? This is a question which I have -tried to answer. I am not aware that any one since -Plato has taken this line of speculation;—I mean, has -tried to spell out the lesson of philosophy which is -taught us, not by one specimen, or a few only, of the -knowledge respecting the universe which man has -acquired; but by including in his survey all the provinces -of human knowledge, and the whole history of -each. At any rate, whatever any one else may have -done in this way, it seems to me that new inferences -remain to be drawn, of the nature of those which Plato -drew: and those I here attempt to deduce and to -illustrate.</p> - -<hr class="chap" /> - -<p><span class="pagenum" id="Page_354">354</span></p> - - - - -</div><div class="chapter"> -<h2><a name="CHAPTER_XXX" id="CHAPTER_XXX"></a>CHAPTER XXX.<br /> - -<span class="smcap medium">The Theological Bearing of the Philosophy of -Discovery.</span></h2> - - -<p class="drop-cap"><span class="smcap">That</span> necessary truth is progressive;—that science -is the idealization of facts, and that this process -goes on from age to age, and advances with the advance -of scientific discovery;—these are doctrines -which I have endeavoured to establish and to elucidate. -If these doctrines are true, they are so important -that I may be excused should I return to them again -and again, and trace their consequences in various directions. -Especially I would examine the bearing of -these doctrines upon our religious philosophy. I have -hitherto abstained in a great measure from discussing -religious doctrines; but such a reserve carried too far -must deprive our philosophy of all completeness. No -philosophy of science can be complete which is not -also a philosophy of the universe; and no philosophy -of the universe can satisfy thoughtful men, which does -not include a reference to the power by which the universe -came to be what it is. Supposing, then, such a -reference to be admitted, let us see what aspect our -doctrines give to it.</p> - - -<p><a id="XXX1"></a>1. (<i>How can there be necessary truths concerning -the actual universe?</i>)—In looking at the bearing of our -doctrine on the philosophy of the universe, we are met -by a difficulty, which is indeed, only a former difficulty -under a new aspect. When we are come to the conclusion -that science consists of facts idealized, we are -led to ask, How this can be? <i>How can</i> facts be idealized? -How can that which is a fact of external observation -become a result of internal thought? How can -that which was known <i>à posteriori</i> become known <i>à<span class="pagenum" id="Page_355">355</span> -priori</i>? How can the world of things be identified -with the world of thoughts? How can we discover a -necessary connexion among mere phenomena?</p> - -<p>Or to put the matter otherwise: How is it that the -deductions of the intellect are verified in the world of -sense? How is it that the truths of science obtained -<i>à priori</i> are exemplified in the general rules of facts -observed <i>à posteriori</i>? How is it that facts, in science, -always do correspond to our ideas?</p> - -<p>I have propounded this paradox in various forms, -because I wish it to be seen that it is, at first sight, a -real, not merely a verbal contradiction, or at least a -difficulty. If we can discover the solution of this difficulty -in any one form, probably we can transpose -the answer so as to suit the other forms of the -question.</p> - -<p><a id="XXX2"></a>2. Suppose the case to be as I have stated it; that in -some sciences at least, laws which were at first facts of -observation come to be seen as necessary truths; and -let us see to what this amounts in the several sciences.</p> - -<p>It amounts to this: the truths of Geometry, such as -we discern them by the exercise of our own thoughts, -are always verified in the world of observation. The -laws of space, derived from our Ideas, are universally -true in the external world.</p> - -<p>In the same way, as to number: the laws or truths -respecting number, which are deduced from our Idea of -Number, are universally true in the external world.</p> - -<p>In the same way, as to the science which deals -with matter and force: the truths of which I have -spoken as derived from Ideas:—that action is equal to -reaction; and that causes are measured by their effects;—are -universally verified in all the laws of phenomena -of the external world, which are disclosed by the -science of Mechanics.</p> - -<p>In the same way with regard to the composition and -resolution of bodies into their elements; the truths -derived from our Idea of Matter:—that no composition -or resolution can increase or diminish the quantity of -matter in the world, and that the properties of compounds -are determined by their composition;—are<span class="pagenum" id="Page_356">356</span> -truths derived from Ideas of quantity of matter, and of -composition and resolution; but these truths are universally -verified when we come to the facts of Chemistry.</p> - -<p>In the same way it is a truth flowing from the Ideas -of the Kinds of things, (as the possible subject of general -propositions expressed in language,) that the kinds of -things must be definite; and this law is verified whenever -we express general propositions in general terms: -for instance, when we distinguish species in Mineralogy.</p> - -<p><a id="XXX3"></a>3. This last example may appear to most readers -doubtful. I have purposely pursued the enumeration -till I came to a doubtful example, because it is, and I -conceive always will be, impossible to extend this general -view to <i>all</i> the Sciences. On the contrary, this doctrine -applies at present to only a very few of the sciences, -even in the eyes of those who hold the existence -of ideal truths. The doctrine extends at present to a -few only of the sciences, even if it extend to one or -two besides those which have been mentioned—Geometry, -Mechanics, Chemistry, Mineralogy: and though -it may hereafter appear that Ideal Truths are possible -and attainable for a few other sciences, yet the laws -disclosed by sciences which cannot be reduced to ideal -elements will, I conceive, always very far outnumber -those which can be so reduced. The great body of our -scientific knowledge will always be knowledge obtained -by mere observation, not knowledge obtained by the -use of theories alone.</p> - -<p><a id="XXX4"></a>4. The survey of the history and philosophy of the -Sciences which we have attempted in previous works -enables us to offer a sort of estimate of the relative -portions of science which have and which have not -thus been idealized. For the Aphorisms<a name="FNanchor_317" id="FNanchor_317"></a><a href="#Footnote_317" class="fnanchor">[317]</a> which we -have collected from that survey, contain Axioms which -may be regarded as the Ideal portions of the various -sciences; and the inspection of that series of aphorisms -will show us to how such a portion of science, any<span class="pagenum" id="Page_357">357</span>thing -of this axiomatic or ideal character can he applied. -These Axioms are the Axioms of Geometry -(Aphorism XXVI); of Arithmetic (XXXVI); of -Causation (XLVII); of a medium for the sensation of -secondary qualities (LVIII), and their measure (LXIX); -of Polarity (LXXII); of Chemical Affinity (LXXVI); -of Substance (LXXVII); of Atoms (LXXIX).</p> - -<p>Have we any axioms in the sciences which succeed -these in our survey, as Botany, Zoology, Biology, Palæontology?</p> - -<p>There is the Axiom of Symmetry (LXXX); of Kind, -(already in some measure spoken of, (LXXXIII)); of -Final Cause (CV); of First Cause (CXVI).</p> - - -<p><a id="XXX5"></a>5. (<i>Small extent of necessary truth.</i>)—It is easily -seen how small a portion of each of these latter sciences -is included in these axioms: while, with regard to the -sciences first mentioned, the Axioms include, in a manner, -the whole of the science. The science is only -the consequence of the Axioms. The whole science of -Mechanics is only the development of the Axioms concerning -action and reaction, and concerning cause and -its measures, which I have mentioned as a part of our -Ideal knowledge.</p> - -<p>In fact, beginning from Geometry and Arithmetic, -and going through the sciences of Mechanics, of Secondary -Qualities, and of Chemistry, onwards to the sciences -which deal with Organized Beings, we find that -our ideal truths occupy a smaller and smaller share of -the sciences in succession, and that the vast variety of -facts and phenomena which nature offers to us, is less -and less subject to any rules or principles which we -can perceive to be necessary.</p> - -<p>But still, that there are principles,—necessary principles, -which prevail universally even in these higher -parts of the natural sciences,—appears on a careful consideration -of the axioms which I have mentioned:—that -in symmetrical natural bodies the similar parts are -similarly affected;—that every event must have a cause;—that -there must be a First Cause, and the like.</p> - -<p><a id="XXX6"></a>6. It being established, then, that in the progress -of science, facts are idealized—that <i>à posteriori</i> truths<span class="pagenum" id="Page_358">358</span> -become <i>à priori</i> truths;—that the world of things is -identified with the world of thoughts to a certain extent;—to -an extent which grows larger as we see into -the world of things more clearly; the question recurs -which I have already asked: How can this be?</p> - -<p>How can it be that the world without us is thus in -some respects identical with the world within us?—that -is our question.</p> - - -<p><a id="XXX7"></a>7. (<i>How did things come to be as they are?</i>)—It -would seem that we may make a step in the solution -of this question, if we can answer this other: How -did the world without us and the world within us come -to be what they are?</p> - -<p>To this question, two very different answers are returned -by those who do and those who do not believe -in a Supreme Mind or Intelligence, as the cause and -foundation of the world.</p> - -<p>Those who do not believe that the world has for its -cause and foundation a Supreme Intelligence, or who -do not connect their philosophy with this belief, would -reply to our inquiry, that the reason why man's -thoughts and ideas agree with the world is, that they -are borrowed from the world; and that the persuasion -that these Ideas and truths derived from them have -any origin except the world without us, is an illusion.</p> - -<p>On this view I shall not now dwell; for I wish to -trace out the consequences of the opposite view, that -there exists a Supreme Mind, which is the cause and -foundation of the universe. Those who hold this, and -who also hold that the human mind can become possessed -of necessary truths, if they are asked how it is -that these necessary truths are universally verified in -the material world, will reply, that it is so because the -Supreme Creative-Mind has made it so to be:—that the -truths which exist or can be generated in man's mind -agree with the laws of the universe, because He who -has made and sustains man and the universe has -caused them to agree:—that our Ideas correspond to -the Facts of the world, and the Facts to our Ideas, -because our Ideas are given us by the same power<span class="pagenum" id="Page_359">359</span> -which made the world, and given so that these can -and must agree with the world so made.</p> - - -<p><a id="XXX8"></a>8. (<i>View of the Theist</i>).—This, in its general form, -would be the answer of the <i>theist</i>, (so we may call -him who believes in a Supreme Intelligent Cause of -the world and of man,) to the questions which we -have propounded—the perplexity or paradox which -we have tried to bring into view. But we must endeavour -to trace this view—this answer—more into -detail.</p> - -<p>If a Supreme Intelligence be the cause of the world -and of the Laws which prevail among its phenomena, -these Laws must exist as Acts of that Intelligence—as -Laws caused by the thoughts of the Supreme Mind—as -Ideas in the Mind of God. And then the question -would be, How we are to conceive these thoughts, -these Ideas, to be at the same time Divine and human:—to -be at the same time Ideas in the Divine Mind, -and necessary truths in the human mind; and this is -the question which I would now inquire into.</p> - - -<p><a id="XXX9"></a>9. (<i>Is this Platonism?</i>)—To the terms in which the -inquiry is now propounded it may be objected that I -am taking for granted the Platonic doctrine, that the -world is constituted according to the Ideas of the -Divine Mind. It may be said that this doctrine is -connected with gross extravagancies of speculation -and fiction, and has long been obsolete among sound -philosophers.</p> - -<p>To which I reply, that if such doctrines have been -pushed into extravagancies, with <i>them</i> I have nothing -to do, nor have I any disposition or wish to revive -them. But I do not conceive the doctrine, to the extent -to which I have stated it, to be at all obsolete:—that -the Cause and Foundation of the Universe is a -Divine Mind: and from that doctrine it necessarily -follows, that the laws of the Universe are in the Ideas -of the Divine Mind.</p> - -<p>I would then, as I have said, examine the consequences -of this doctrine, in reference to the question -of which I have spoken. And in order to do this, it -may help us, if we consider separately the bearing of<span class="pagenum" id="Page_360">360</span> -this doctrine upon separate portions of our knowledge -of the universe;—separately its bearing upon the laws -which form the subject-matter of different sciences:—if -we take particular human Ideas, and consider what -the Divine Ideas must be with regard to each of them.</p> - -<p><a id="XXX10"></a>10. (<i>Idea of Space.</i>)—Let us take, in the first place, -the Idea of Space. Concerning this Idea we possess -necessary truths; namely, the Axioms of Geometry; -and, as necessarily resulting from them, the whole body -of Geometry. And our former inquiry, as narrowed -within the limits of this Idea, will be, How is it that -the truths of Geometry—<i>à priori</i> truths—are universally -verified in the observed phenomena of the universe? -And the theist's answer which we have given -will now assume this form:—This is so because the -Supreme Mind has constituted and constitutes the universe -according to the Idea of Space. The universe -conforms to the Idea of Space, and the Idea of Space -exists in the human mind;—is necessarily evoked and -awakened in the human mind existing in the universe. -And since the Idea of Space, which is a constituent of -the universe, is also a constituent of the human mind, -the consequences of this Idea in the universe and in -the human mind necessarily coincide; that is, the -<i>spacial</i> Laws of the universe necessarily coincide with -the <i>spacial</i> Science which man elaborates out of his -mind.</p> - -<p><a id="XXX11"></a>11. To this it may be objected, that we suppose the -Idea of Space in the Divine Mind (according to which -Idea, among others, the universe is constituted,) to be -identical with the Idea of Space in the human mind; -and this, it may be urged, is too limited and material a -notion of the Divine Mind to be accepted by a reverent -philosophy.</p> - -<p>I reply, that I suppose the Divine Idea of Space -and the human Idea of Space to coincide, <i>only so far</i> -as the human Idea goes; and that the Divine Idea -may easily have so much more luminousness and comprehensiveness -as Divine Ideas may be supposed to -have compared with human. Further, that this Idea -of Space, the first of the Ideas on which human science<span class="pagenum" id="Page_361">361</span> -is founded, is the most luminous and comprehensive of -such Ideas; and there are innumerable other Ideas, -the foundations of sciences more or less complete, which -are extremely obscure and limited in the human mind, -but which must be conceived to be perfectly clear and -unlimitedly comprehensive in the Divine Mind. And -thus, the distance between the human and the Divine -Mind, even as to the views which constitute the most -complete of the human sciences, is as great in our -view as in any other.</p> - -<p><a id="XXX12"></a>12. That the Idea of Space in the human mind, -though sufficiently clear and comprehensive to be the -source of necessary truths, is far too obscure and limited -to be regarded as identical with the Divine Idea, will be -plain to us, if we call to mind the perplexities which -the human mind falls into when it speculates concerning -space infinite. An Intelligence in which all these -perplexities should vanish by the light of the Idea -itself, would be infinitely elevated in clearness and -comprehensiveness of intellectual vision above human -intelligence, even though its Idea of Space should coincide -with the human Idea as far as the human Idea -goes.</p> - -<p>I do not shrink from saying, therefore, that the -Idea of Space which is a constituent of the human -mind existing in the universe is, as far as it goes, -identical with the Idea of Space which is a constituent -of the universe. And this I give as the answer to -the question, How it is that the necessary truths of -Geometry universally coincide with the relations of -the phenomena of the universe? And this doctrine, -it is to be remembered, carries us to the further doctrine, -that the Idea of Space in the human mind is, so -far as it goes, coincident with the Idea of Space in -the Divine Mind.</p> - - -<p><a id="XXX13"></a>13. (<i>Idea of Time.</i>)—What I have said of the Idea -of Space, may be repeated, for the most part, with regard -to the Idea of Time; except that the Idea of Time, as -such, does not give rise to a large collection of necessary -truths, such as the propositions of Geometry. -Some philosophers regard Number as a modification<span class="pagenum" id="Page_362">362</span> -or derivative of the Idea of Time. If we accept this -view, we have, in the Science of Arithmetic, a body of -necessary truths which flow from the Idea of Time. -But this doctrine, whichever way held, does not bear -much on the question with which we are now concerned. -That which we do hold is, that the Idea of -Time in the human mind is, so far as it goes, coincident -with the Idea of Time in the Divine Mind: -and that this is the reason why the events of the universe, -as contemplated by us, conform to necessary -laws of succession: while at the same time we must -suppose that all the perplexities in the Idea of Time -which embarrass the human mind—the perplexities, -for instance, which arise from contemplating a past -and a future eternity, are, in the Divine Mind, extinguished -in the Light of the Idea itself.</p> - -<p>Space and Time have, and have generally been regarded -as having, peculiar prerogatives in our speculations -concerning the constitution of the universe. -We see and perceive all things as subject to the laws -of Space and Time; or rather (for the term <i>Law</i> does -not here satisfy us), as being and happening <i>in</i> space -and <i>in</i> time: and probably most persons will have no -repugnance to the doctrine that the Divine Mind, as -well as the human, so regards them, and has so constituted -them and us that they <i>must</i> be so regarded. -Space and Time are human Ideas which include all -objects and events, and are the foundation of all human -Science. And we can conceive that Space and Time -are also Divine Ideas which the Divine Mind causes -to include all objects and events, and makes to be the -foundation of all existence. So far as these Ideas go, -our doctrine is not difficult or new.</p> - - -<p><a id="XXX14"></a>14. (<i>Ideas of Force and Matter.</i>)—But what are we -to say of the Ideas which come next in the survey of the -sciences, Force and Matter? These are human Ideas—the -foundations of several sciences—of the mechanical -sciences in particular. But are they the foundations -of necessary truths? Have we necessary truths -respecting Force and Matter? We have endeavoured -to prove that we have:—that certain fundamental pro<span class="pagenum" id="Page_363">363</span>positions -in the Science of Mechanics, although, historically -speaking, they were discovered by observation -and experience, are yet, philosophically speaking, -necessary propositions. And being such, the facts of -the universe must needs conform to these propositions; -and the reason why they do so, we hold, in this as in -the former case, to be, that these Ideas, Force and -Matter, are Ideas in the Divine Mind:—Ideas according -to which the universe is, by the Divine Cause, -constituted and established.</p> - -<p><a id="XXX15"></a>15. That Force and Matter are Ideas existing in -the Divine Mind, and coincident with the Idea of Force -and Matter in the human mind, as far as these go, -is a doctrine which is important in our view of the -universe in relation to its Cause and Foundation.</p> - -<p>These are very comprehensive and fundamental -Ideas, and there are certain universal relations among -external things which rest upon these Ideas. The two, -Force and Matter, are, in a certain way, the necessary -antithesis and opposite condition each of the other. -Force (that is Mechanical Force, Pressure or Impulse) -cannot act without matter to act upon. Matter (that -is Body) cannot exist without Force by which it is kept -in its place, by which its parts are held together, and -by which it excludes every other body from the place -which it occupies. We cannot conceive Force without -Matter, or Matter without Force; the two are, as -Action and Reaction, necessarily co-ordinate and coexistent. -In every part of the universe they must be -so. In every part of the universe, if there be material -objects, there must be Force; if there be Force, there -must be material objects.</p> - -<p>Our apprehension of this universal necessity arises -from our having the Ideas of Force and Matter which -are human Ideas. The actuality of this universal antithesis -arises from the Ideas of Force and Matter being -Ideas in the Divine Mind;—Ideas realized as a part of -the fundamental constitution of the universe.</p> - -<p>That Force and Matter are thus among the Ideas in -the Divine Mind, and that, with them, the Ideas of -Force and Matter in the human mind, regarded in their<span class="pagenum" id="Page_364">364</span> -most general form, agree so far as they go, is another -step in the doctrine which I am trying to unfold. -That the Ideas of Force and Matter in the Divine -Mind are such as to banish by their own light, innumerable -contradictions and perplexities which darken -these Ideas in the human mind, is to be supposed: and -thus the Divine Mind is infinitely luminous and comprehensive -compared with the human mind.</p> - - -<p><a id="XXX16"></a>16. (<i>Creation of Matter.</i>)—It may perhaps be urged, -as an objection to this doctrine, that it asserts Matter to -be a necessary constituent of the universe, and thus -involves the assertion of the eternity of Matter. But -in reality the doctrine asserts Matter to be eternal, -only in the way in which time and space are eternal. -Whether we hold that there was a creation before -which time and space did not exist,—with the poet -who says</p> - -<p> -Ere Time and Space <i>were</i> Time and Space were <i>not</i>,—<br /> -</p> - -<p>is not essential to our present inquiry. Certainly we -cannot conceive such a state, and therefore cannot -reason about it. We have no occasion here to speak -of Creation, nor have spoken of it. What I have said -is, that Space and Time, Force and Matter are universal -elements, principles, constituents, of the universe -as it is—and necessary Ideas of the human mind existing -in that universe. If there ever was a Creation -before which Matter did not exist, it was a Creation -before which Force did not exist. And in the universe -as it is, the two are necessarily co-existent in the human -thought because they are co-existent in the Divine -Thought which makes the world.</p> - -<p>We apply then to Force and Matter the doctrine—the -Platonic doctrine, if any one please so to call it,—that -the world is constituted according to the Ideas of -the Divine Mind, and that the human mind apprehends -the inward and most fundamental relations of -the universe by sharing in some measure of those same -Ideas.</p> - - -<p><a id="XXX17"></a>17. (<i>Platonic Ideas.</i>)—But do we go on with Plato -to extend this doctrine of Ideas to all the objects and<span class="pagenum" id="Page_365">365</span> -all the aspects of objects which constitute the material -universe? Do we say with Plato that there is not -only an Idea of a Triangle by conformity to which a -figure is a triangle, but an Idea of Gold, by conformity -to which a thing is gold, and Idea of a Table, by conformity -to which a thing is a table?</p> - -<p>We say none of these things. We say nothing -which at all approaches to them. We do not say that -there is an Idea of a Triangle, the archetype of all -triangles; we only say that man has an Idea of Space, -which is an Idea of a fundamental reality; and that -therefore from this Idea flow real and universal truths—about -triangles and other figures. Still less do we say -that we have an archetypal Idea of Gold, or of a Metal -in general, or of any of the kinds of objects which -exist in the world. Here we part company with Plato -altogether.</p> - -<p>But have we any Ideas at all with regard to objects -which we thus speak of as separable into Kinds? We -can have knowledge,—even exact and general knowledge, -that is, science—with regard to such things—with -regard to plants and metals—gold and iron. Do we -possess in our minds, with regard to those objects, any -Ideas, any universal principles, such as we possess with -regard to geometrical figures or mechanical actions? -And if so, are those human Ideas verified in the universe, -as the Ideas hitherto considered are? and do -they thus afford us further examples of Ideas in the -human mind which are also Ideas in the Divine Mind, -manifested in the constitution of the universe?</p> - - -<p><a id="XXX18"></a>18. (<i>Idea of Kinds.</i>)—We answer <i>Yes</i> to these questions, -on this ground:—the objects that exist in the -world, plants and metals, gold and iron, for example, -in order that they may be objects with regard to which -we can have any knowledge, must be objects of distinct -and definite thought. Plant must differ from metal, -gold from iron, in order that we may know anything -at all about any of these objects. The differences by -which such objects differ need not necessarily be expressed -by <i>definitions</i>, as the difference of a triangle -and a square are expressed; but there must manifestly<span class="pagenum" id="Page_366">366</span> -<i>be</i> fixed and definite differences, in order that we may -have any knowledge about them. These Kinds of -things must be so far distinct and definite, as to be -objects of distinct and definite thought. The <i>Kinds</i> of -natural objects must differ, and we must think of things -as of different Kinds, in order that we may know anything -about natural objects. Living in a world in -which we exercise our Intellect upon the natural objects -which surround us, we must regard them as -distinct from each other in Kind. We must have an -Idea of Kinds of natural objects.</p> - -<p><a id="XXX19"></a>19. The Idea of a Kind involves this principle: -That where the Kind differs the Properties may differ, -but so far as the Kind is the same the Properties contemplated -in framing the notion of each Kind are the -same. Gold cannot have the distinctive properties of -Iron without being Iron.</p> - -<p>In the case of human knowledge, each Kind is -marked by a <i>word</i>—a <i>name</i>; and the doctrine that -the notion of the Kind must be so applied that this -same Kind of object shall have the same properties, -has been otherwise expressed by saying that Names -must be so applied that general propositions may be -possible. We must so apply the name of Gold that we -may be able to say, gold has a specific gravity of a -certain amount and is ductile in a certain degree.</p> - -<p><a id="XXX20"></a>20. But this condition of the names of Kinds,—that -they must be such that general propositions about -these Kinds of objects shall be possible;—is it a necessary -result of the Idea of Kind? And if so, can the -Idea of Kind, thus implying the use of language, and -a condition depending on the use of language, be an -Idea in the Divine as well as in the human mind? -Can it be, in this respect, like the Ideas which we -have already considered, Space and Time, Force and -Matter?</p> - -<p>We cannot suppose that the Ideas which exist in -the Divine Mind imply, in the Supreme Intelligence, -the need of language, like human language. But -there is no incongruity in supposing that they imply -that which we take as the <i>condition</i> of such language<span class="pagenum" id="Page_367">367</span> -as we speak of, namely, distinct thought. There is -nothing incongruous in supposing that the Supreme -Intelligence regards the objects which exist in the -universe as distinct in Kind: and that the Idea of -Kind in the human mind agrees with the Idea of -Kind in the Divine Mind, as far as it goes. And as -we have seen, the Idea of Properties is correlative and -coexistent with the Idea of Kind, so that the one -changing, the other changes also. There is nothing -incongruous in supposing that the Divine Mind manifests -in the universe of which it is the Cause and -Foundation, these two, its co-ordinate Ideas: and that -the human mind sees that these two Ideas are co-ordinate -and coexistent, in virtue of its participating in -these Ideas of the Divine Mind. The universe is full -of things which man perceives do and must differ correspondingly -in kind and in properties; and this is so, -because the Ideas of various Kinds and various Properties -are part of the scheme of the universe in the -Divine Mind.</p> - -<p><a id="XXX21"></a>21. That the Ideas of Kinds and Properties as coordinate -and interdependent, though common, to a certain -extent, to the human and the Divine Mind, are -immeasurably more luminous, penetrating and comprehensive -in the Divine than in the human mind, is -abundantly evident. In fact, though man assents to -such axioms as these,—that the Properties of Things -depend upon their Kinds, and that the Kinds of -Things are determined by their Properties,—yet the -nature of connexion of Kinds and Properties is a matter -in which man's mind is all but wholly dark, and -on which the Divine Mind must be perfectly clear. -For in how few cases—if indeed in any one—can we -know what is the essence of any Kind;—what is the -real nature of the connexion between the character of -the Kind and its Properties! Yet on this point we must -suppose that the Divine Intellect, which is the foundation -of the world, is perfectly clear. Every Kind of -thing, every genus and species of object, appears to Him -in its essential character, and its properties follow as -necessary consequences. He sees the essences of things<span class="pagenum" id="Page_368">368</span> -through all time and through all space; while we, -slowly and painfully, by observation and experiment, -which we cannot idealize or can idealize only in the -most fragmentary manner, make out a few of the properties -of each Kind of thing. Our Science here is -but a drop in the ocean of that truth, which is known -to the Divine Mind but kept back from us; but still, -that we can know and do know anything, arises from -our taking hold of that principle, human as well as -Divine, that there are differences of Kinds of things, -and corresponding differences of their properties.</p> - - -<p><a id="XXX22"></a>22. (<i>Idea of Substance.</i>)—I shall not attempt to -enumerate all the Ideas which, being thus a part of the -foundation of Science in the human mind and of Existence -in the universe, are shown to be at the same -time Ideas in the Divine and in the human mind. But -there is one other of which the necessary and universal -application is so uncontested, that it may well serve -further to exemplify our doctrine. In all reasonings -concerning the composition and resolution of the elements -of bodies, it is assumed that the quantity of -matter cannot be increased or diminished by anything -which we can do to them. We have an Idea of <i>Substance</i>, -as something which may have its qualities -altered by our operations upon it, but cannot have its -quantity changed. And this Idea of Substance is universally -verified in the facts of observation and experiment. -Indeed it cannot fail to be so; for it regulates -and determines the way in which we interpret the facts -of observation and experiment. It authorized the philosopher -who was asked the weight of a column of -smoke to reply, "Subtract the weight of the ashes -from that of the fuel, and you have the weight of the -smoke:" for in virtue of that idea we assume that, in -combustion, or in any other operation, all the substance -which is subjected to the operation must exist -in the result in some form or other. Now why may -we reasonably make this assumption, and thus, as it -were, prescribe laws to the universe? Our reply is, -Because Substance is one of the Ideas according to -which the universe is constituted. The material things<span class="pagenum" id="Page_369">369</span> -which make up the universe are substance according -to this Idea. They are substance according to this -Idea in the Divine Mind, and they are substance according -to this Idea in the human mind, because the -human mind has this Idea, to a certain extent, in common -with the Divine Mind. In this, as in the other -cases, the Idea must be immeasurably more clear and -comprehensive in the Divine Mind than in the human. -The human Idea of substance is full of difficulty and -perplexity: as for instance; how a substance can assume -successively a solid, fluid and airy form; how two -substances can be combined so as entirely to penetrate -one another and have new qualities: and the like. -All these perplexities and difficulties we must suppose -to vanish in the Divine Idea of Substance. But still -there remains in the human, as in the Divine Idea, -the source and root of the universal truth, that though -substances may be combined or separated or changed -in form in the processes of nature or of art, no portion -of substance can come into being or cease to be.</p> - - -<p><a id="XXX23"></a>23. (<i>Idea of Final Cause.</i>)—There is yet one other -Idea which I shall mention, though it is one about which -difficulties have been raised, since the consideration of -such difficulties may be instructive: the Idea of a purpose, -or as it is often termed, a <i>Final Cause</i>, in organized -bodies. It has been held, and rightly<a name="FNanchor_318" id="FNanchor_318"></a><a href="#Footnote_318" class="fnanchor">[318]</a>, that the assumption -of a Final Cause of each part of animals and -plants is as inevitable as the assumption of an efficient -cause of every event. The maxim, that in organized -bodies nothing is <i>in vain</i>, is as necessarily true as the -maxim that nothing happens <i>by chance</i>. I have elsewhere<a name="FNanchor_319" id="FNanchor_319"></a><a href="#Footnote_319" class="fnanchor">[319]</a> -shown fully that this Idea is not deduced from -any special facts, but is assumed as a law governing all -facts in organic nature, directing the researches and interpreting -the observations of physiologists. I have also -remarked that it is not at variance with that other law, -that plants and that animals are constructed upon general -plans, of which plans, it may be, we do not see the<span class="pagenum" id="Page_370">370</span> -necessity, though we see how wide is their generality. -This Idea of a purpose,—of a Final Cause,—then, thus -supplied by our minds, is found to be applicable -throughout the organic world. It is in virtue of this -Idea that we conceive animals and plants as subject to -<i>disease</i>; for disease takes place when the parts do not -fully answer their <i>purpose</i>; when they do not do what -they <i>ought</i> to do. How is it then that we thus find -an Idea which is <i>supplied</i> by our own minds, but which -is <i>exemplified</i> in every part of the organic world? Here -perhaps the answer will be readily allowed. It is because -this Idea is an Idea of the Divine Mind. There -<i>is</i> a Final Cause in the constitution of these parts of -the universe, and therefore we can interpret them by -means of the Idea of Final Cause. We can <i>see</i> a purpose, -because there <i>is</i> a purpose. Is it too presumptuous -to suppose that we can thus enter into the Ends -and Purposes of the Divine Mind? We willingly -grant and declare that it would be presumptuous to -suppose that we can enter into them to any but a very -small degree. They doubtless go immeasurably beyond -our mode of understanding or conceiving them. But to -a certain extent we <i>can</i> go. We can go so far as to see -that they <i>are</i> Ends and Purposes. It is <i>not</i> a vain presumption -in us to suppose that we know that the eye -was made for seeing and the ear for hearing. In this -the most pious of men see nothing impious: the most -cautious philosophers see nothing rash. And that we -can see thus far into the designs of the Divine Mind, -arises, we hold, from this:—that we have an Idea of -Design and of Purpose which, so far as it is merely -<i>that</i>, is true; and so far, is Design and Purpose in the -same sense in the one case and in the other.</p> - -<p>I am very far from having exhausted the list of -Fundamental Ideas which the human mind possesses -and which have been made the foundations of Sciences. -Of all such Ideas, I might go on to remark, that they -are of universal validity and application in the region -of external Facts. In all the cases I might go on to -inquire, How is it that man's Ideas, developed in his -internal world, are found to coincide universally with<span class="pagenum" id="Page_371">371</span> -the laws of the external world? By what necessity, -on what ground does this happen? And in all cases -I should have had to reply, that this happens, and must -happen, because these Ideas of the human mind are -also Ideas of the Divine Mind according to which the -universe is constituted. Man has these thoughts, and -sees them verified in the universe, because God had -these thoughts and exemplifies them in the universe.</p> - - -<p><a id="XXX24"></a>24. (<i>Human immeasurably inferior to Divine</i>).—But -of all these Ideas, I should also have to remark, that -the way in which man possesses them is immeasurably -obscure and limited in comparison with the way in -which God must be supposed to possess them. These -human Ideas, though clear and real as far as they go, -in every case run into obscurity and perplexity, from -which the Ideas of the Divine Mind must be supposed -to be free. In every case, man, by following the train -of thought involved in each Idea, runs into confusion -and seeming contradictions. It may be that by thinking -more and more, and by more and more studying -the universe, he may remove some of this confusion -and solve some of these contradictions. But when he -has done in this way all that he can, an immeasurable -region of confusion and contradiction will still remain; -nor can he ever hope to advance very far, in dispelling -the darkness which hangs over the greater part of the -universe. His knowledge, his science, his Ideas, extend -only so far as he can keep his footing in the -shallow waters which lie on the shore of the vast -ocean of unfathomable truth.</p> - -<p><a id="XXX25"></a>25. But further, we have not, even so, exhausted -our estimate of the immeasurable distance between -the human mind and the Divine Mind:—very far from -it: we have only spoken of the smallest portion of the -region of truth,—that about which we have Sciences -and Scientific Ideas. In that region alone do we claim -for man the possession of Ideas the clearness of which -has in it something divine. But how narrow is the -province of Science compared with the whole domain -of human thought! We may enumerate the sciences -of which we have been speaking, and which involve<span class="pagenum" id="Page_372">372</span> -such Ideas as I have mentioned. How many are they? -Geometry, Arithmetic, Chemistry, Classification, Physiology. -To these we might have added a few others; -as the sciences which deal with Light, Heat, Polarities; -Geology and the other Palætiological Sciences; -and there our enumeration at present must stop. For -we can hardly as yet claim to have Sciences, in the -rigorous sense in which we use the term, about the -Vital Powers of man, his Mental Powers, his historical -attributes, as Language, Society, Arts, Law, and the -like. On these subjects few philosophers will pretend -to exhibit to us Ideas of universal validity, prevailing -through all the range of observation. Yet all these -things proceed according to Ideas in the Divine Mind -by which the universe, and by which man, is constituted. -In such provinces of knowledge, at least, we -have no difficulty in seeing or allowing how blind -man is with regard to their fundamental and constituent -principles; how weak his reason; how limited -his view. If on some of the plainest portions of possible -knowledge, man have Ideas which may be regarded -as coincident to a certain extent with those by which -the universe is really constituted; still on by far the -largest portion of the things which most concern him, -he has no knowledge but that which he derives from -experience, and which he cannot put in so general a -form as to have any pretensions to rest it upon a -foundation of connate Ideas.</p> - - -<p><a id="XXX26"></a>26. (<i>Science advances towards the Divine Ideas.</i>)—But -there is yet one remark tending somewhat in the -opposite direction, which I must make, as a part of -the view which I wish to present. Science, in the -rigorous sense of the term, involves, we have said, -Ideas which to a certain extent agree with the Ideas -of the Divine Mind. But science in that sense is progressive; -new sciences are formed and old sciences -extended. Hence it follows that the Ideas which man -has, and which agree with the Ideas of the Divine -Mind, may receive additions to their number from -time to time. This may seem a bold assertion; yet -this is what, with due restriction, we conceive to be<span class="pagenum" id="Page_373">373</span> -true. Such Ideas as we have spoken of receive additions, -in respect of their manifestation and development. -The Ideas, the germ of them at least, were in -the human mind before; but by the progress of scientific -thought they are unfolded into clearness and distinctness. -That this takes place with regard to scientific -Ideas, the history of science abundantly shows. -The Ideas of Space and Time indeed, were clear and -distinct from the first, and accordingly the Sciences of -Geometry and Arithmetic have existed from the earliest -times of man's intellectual history. But the Ideas -upon which the Science of Mechanics depends, having -been obscure in the ancient world, are become clear in -modern times. The Ideas of Composition and Resolution -have only in recent centuries become so clear -as to be the basis of a definite science. The Idea of -Substance indeed was always assumed, though vaguely -applied by the ancients; and the Idea of a Design or -End in vital structures is at least as old as Socrates. -But the Idea of Polarities was never put forth in a -distinct form till quite recently; and the Idea of Successive -Causation, as applied in Geology and in the -other Palætiological Sciences, was never scientifically -applied till modern times: and without attempting -to prove the point by enumeration, it will hardly be -doubted that many Scientific Ideas are clear and distinct -among modern men of science which were not so -in the ancient days.</p> - -<p>Now all such scientific Ideas are, as I have been -urging, points on which the human mind is a reflex of -the Divine Mind. And therefore in the progress of -science, we obtain, not indeed new points where the -human mind reflects the Divine, but new points where -this reflection is clear and luminous. We do not assert -that the progress of science can bring <i>into existence</i> -new elements of truth in the human mind, but it may -bring them <i>into view</i>. It cannot add to the characters -of Divine origin in the human mind, but it may add -to or unfold the <i>proofs</i> of such an origin. And this is -what we conceive it does. And though we do not conceive -that the Ideas which science thus brings into<span class="pagenum" id="Page_374">374</span> -view are the most important of man's thoughts in -other respects, yet they may, and we conceive do, supply -a proof of the Divine nature of the human mind, -which proof is of peculiar cogency. What other proofs -may be collected from other trains of human thought, -we shall hereafter consider.</p> - - -<p><a id="XXX27"></a>27. (<i>Recapitulation.</i>)—This, then, is the argument to -which we have been led by the survey of the sciences in -which we have been engaged:—That the human mind -can and does put forth, out of its natural stores, duly -unfolded, certain Ideas as the bases of scientific truths: -These Ideas are universally and constantly verified in -the universe: And the reason of this is, that they -agree with the Ideas of the Divine Mind according to -which the universe is constituted and sustained: The -human mind has thus in it an element of resemblance -to the Divine Mind: To a certain extent it looks -upon the universe as the Divine Mind does; and therefore -it is that it can see a portion of the truth: And -not only can the human mind thus see a portion of the -truth, as the Divine Mind sees it: but this portion, -though at present immeasurably small, and certain -to be always immeasurably small compared with the -whole extent of truth which with greater intellectual -powers, he might discern, nevertheless may increase -from age to age.</p> - -<p>This is then, I conceive, one of the results of the -progress of scientific discovery—the Theological Result -of the Philosophy of Discovery, as it may, I think, not -unfitly be called:—That by every step in such discovery -by which external facts assume the aspect of -necessary consequences of our Ideas, we obtain a fresh -proof of the Divine nature of the human mind: And -though these steps, however far we may go in this -path, can carry us only a very little way in the knowledge -of the universe, yet that such knowledge, so far -as we do obtain it, is Divine in its kind, and shows -that the human mind has something Divine in its -nature.</p> - -<p>The progress by which external facts assume the -aspect of necessary consequences of our Ideas, we have<span class="pagenum" id="Page_375">375</span> -termed the idealization of facts; and in this sense we -have said, that the progress of science consists in the -Idealization of Facts. But there is another way in -which the operation of man's mind may be considered—an -opposite view of the identification of Ideas with -Facts; which we must consider, in order to complete our -view of the bearing of the progress of human thought -upon the nature of man.</p> - - - - -<hr class="chap" /> - -<p><span class="pagenum" id="Page_376">376</span></p> - - -</div><div class="chapter"> -<h2><a name="CHAPTER_XXXI" id="CHAPTER_XXXI"></a>CHAPTER XXXI.<br /> - -<span class="smcap medium">Man's Knowledge of God.</span></h2> - - -<p><a id="XXXI1"></a> -<span class="dropcap"><span class="dsmall">1.</span> M</span>AN'S powers and means of knowledge are so -limited and imperfect that he can know <i>little</i> -concerning God. It is well that men in their theological -speculations should recollect that it is so, and -should pursue all such speculations in a modest and -humble spirit.</p> - -<p>But this humility and modesty defeat their own -ends, when they lead us to think that we can know -<i>nothing</i> concerning God: for to be modest and humble -in dealing with this subject, implies that we know <i>this</i>, -at least, that God is a proper object of modest and -humble thought.</p> - -<p><a id="XXXI2"></a>2. Some philosophers have been led, however, by -an examination of man's faculties and of the nature of -being, to the conclusion that man can know <i>nothing</i> -concerning God. But we may very reasonably doubt -the truth of this conclusion. We may ask, How can -we <i>know</i> that we <i>can</i> know nothing? If we can know -nothing, we cannot even know that.</p> - -<p>It is much more reasonable to begin with things -that we really do know, and to examine how far such -knowledge can carry us, respecting God, as well as -anything else. This is the course which we have been -following, and its results are very far from being -trifling or unimportant.</p> - -<p>In thus beginning from what we know, we start -from two points, on each of which we have, we conceive, -some real and sure knowledge:—namely, mathematical -and physical knowledge of the universe without -us; and a knowledge of our own moral and personal -nature within us.</p> - -<p><span class="pagenum" id="Page_377">377</span></p> - - -<p><a id="XXXI3"></a>3. (<i>From Nature we learn something of God.</i>)—In -pursuing the first line of thought, we are led to reason -thus. The universe is governed by certain Ideas: for -instance, everything which exists and happens in the -universe, exists and happens <span class="smcap">IN</span> <i>Space</i> and <i>Time</i>. Why -is this? It is, we conceive, because God has constituted -and constitutes the universe so that it may be -so; that is, because the Ideas of Space and of Time are -Ideas according to which God has established and upholds -the universe.</p> - -<p>But we may proceed further in this way, as we have -already said. The universe not only exists in space -and time, but it has in it substances—material substances: -or taking it collectively, Material <i>Substance</i>. -Can we know anything concerning this substance? -Yes: something we can know; for we know that material -substance cannot be brought into being or annihilated -by any natural process. We have then an Idea -of Substance which is a Law of the universe. How is -this?—We reply, that it is because our Idea of Substance -is an Idea on which God has established and -upholds the universe.</p> - -<p>Can we proceed further still? Can we discern any -other Ideas according to which the universe is constituted? -Yes: as we have already remarked, we can -discern several, though as we go on from one to another -they become gradually fainter in their light, less -cogent in their necessity. We can see that Force as -well as Material Substance is an Idea on which the -universe is constituted, and that <i>Force</i> and <i>Matter</i> are -a necessary and universal antithesis: we can see that -the Things which occupy the universe must be of definite -<i>Kinds</i>, in order that an intelligent mind may -occupy itself about them, and thus that the Idea of -Kind is a constitutive Idea of the universe. We can -see that some kinds of things have life, and our Idea -of Life is, that every part of a living thing is a means -to an End; and thus we recognize <i>End</i>, or Final -Cause, as an Idea which prevails throughout the universe, -and we recognize this Idea as an Idea according -to which God constitutes and upholds the universe.</p> - -<p><span class="pagenum" id="Page_378">378</span></p> - -<p>Since we know so much concerning the universe, -and since every Law of the universe which is a necessary -form of thought about the universe must -exist in the <i>Divine</i> Mind, in order that it may find -a place in <i>our</i> minds, how can we say that we can -know nothing concerning the Divine Mind?</p> - - -<p><a id="XXXI4"></a>4. (<i>Though but Little.</i>)—But on the other hand, we -easily see how little our knowledge is, compared with -what we do not know. Even the parts of our knowledge -which are the clearest are full of perplexities; -and of the Laws of the universe, including living -as well as lifeless things, how small a portion do we -know at all!</p> - -<p>Even the parts of our knowledge which are the clearest, -I say, are full of perplexities. Infinite Space and -an infinite Past, an infinite Future,—how helplessly -our reason struggles with these aspects of our Ideas! -And with regard to <i>Substance</i>, how did ingenerable and -indestructible substance come into being? And with -regard to <i>Matter</i>, how can passive Matter be endued -with living force? And with regard to <i>Kinds</i>, how -immeasurably beyond our power of knowing are their -numbers and their outward differences: still more their -internal differences and central essence! And with -regard to the <i>Design</i> which we see in the organs of -living things, though we can confidently say we see it, -how obscurely is it shown, and how much is our view -of it disturbed by other Laws and Analogies! And -the Life of things, the end to which such Design tends, -how full of impenetrable mysteries is it! or rather how -entirely a mass of mystery into which our powers of -knowledge strive in vain to penetrate!</p> - -<p>There is therefore no danger that by following this -train of thought we should elevate our view of man too -high, or bring down God in our thoughts to the likeness -of man. Even if we were to suppose the Idea of -the Divine Mind to be of the same kind as the Ideas -of the human mind, the very few Ideas of this kind, -which man possesses, compared with the whole range -of the universe, and the scanty length to which he can -follow each, make his knowledge so small and imper<span class="pagenum" id="Page_379">379</span>fect, -that he has abundant reason to be modest and -humble in his contemplations concerning the Intelligence -that knows all and constitutes all. He can, as -I have already said, wade but a few steps into the -margin of the boundless and unfathomable ocean of -truth.</p> - -<p><a id="XXXI5"></a>5. But the Ideas of the Divine Mind must necessarily -be different in kind, as well as in number and extent, -from the Ideas of the human mind, on this very account, -that they are complete and perfect. The Mind which -can conceive all the parts and laws of the universe in -all their mutual bearings, fundamental reasons, and -remote consequences, must be different in kind, as -well as in extent, from the mind which can only trace a -few of these parts, and see these laws in a few of their -aspects, and cannot sound the whole depth of any of -them. The Divine Mind differs from the human, in -the way in which we must needs suppose what is Divine -to differ from what is human.</p> - -<p><a id="XXXI6"></a>6. It has sometimes been said that the Divine Mind -differs from the human as the Infinite from the finite. -And this has been given as a reason why we cannot -know anything concerning God; for we cannot, it is -said, know <i>anything</i> concerning the Infinite. Our -conception of the Infinite being merely negative, (the -negation of a limit,) makes all knowledge about it impossible. -But this is not truly said. Our conception -of the Infinite is <i>not</i> merely negative. As I have -elsewhere remarked, our conception of the Infinite is -positive in this way:—that in order to form this conception, -we begin to follow a given Idea in a given -direction; and then, having thus begun, we suppose -that the progress of thought goes on in that direction -without limit. To arrive at our Idea of infinite space, -for example, we must determine what kind of space -we mean,—line, area or solid; and from what origin -we begin: and infinite space has different attributes -as we take different beginnings in this way.</p> - -<p>And so with regard to the kinds of infinity (for -there are many) which belong to the Divine Mind. -<i>We</i> have a few Ideas which represent the Laws of the<span class="pagenum" id="Page_380">380</span> -universe:—as Space, Time, Substance, Force, Matter, -Kind, End; of such Ideas the Divine Mind may have -an infinite number. These Ideas in the human mind -are limited in depth and clearness: in the Divine Mind -they must be infinitely clearer than the clearest human -Intuition; infinitely more profound than the profoundest -human thought. And in this way, and, as we shall -see, in other ways also, the Divine Mind infinitely -transcends the human mind when most fully instructed -and unfolded.</p> - -<p>In this way and in other ways also, I say. For we -have hitherto spoken of the human mind only as contemplating -the external world;—as discerning, to a certain -small extent, the laws of the universe. We have -spoken of the world of things without: we must now -speak of the world within us;—of the world of our -thoughts, our being, our moral and personal being.</p> - - -<p><a id="XXXI7"></a>7. (<i>From ourselves we learn something concerning -God.</i>)—We must speak of this: for this is, as I have -said, another starting point and another line in which -we may proceed from what we know, and see how far -our knowledge carries us, and how far it teaches us -anything concerning God.</p> - -<p>Looking at ourselves, we perceive that we have to -act, as well as to contemplate: we are practical as -well as speculative beings. And tracing the nature -and conditions of our actions, in the depths of our -thought we find that there is in the aspect of actions -a supreme and inevitable distinction of right and -wrong. We cannot help judging of our actions as -right and wrong. We acknowledge that there must -be such a judgment appropriate to them. We have -these Ideas of <i>right</i> and <i>wrong</i> as attributes of actions; -and thus we are <i>moral</i> beings.</p> - -<p><a id="XXXI8"></a>8. And again: the actions are <i>our</i> actions. <i>We</i> -act in this way or that. And <i>we</i> are not mere <i>things</i>, -which move and change as they are acted on, but which -do not themselves act, as man acts. I am not a Thing -but a <i>Person</i>; and the men with whom I act, who act -with me—act in various ways towards me, well or ill—are -also persons. Man is a personal being.</p> - -<p><span class="pagenum" id="Page_381">381</span></p> - -<p>The Ideas of right and wrong—the <i>moral</i> Ideas of -man—are then a part of the scheme of the universe to -which man belongs. Could they be this, if they were -not also a part of the nature of that Divine Mind -which constitutes the universe?—It would seem not: -the Moral Law of the universe must be a Law of the -Divine Mind, in order that it may be a Law felt and -discerned by man.</p> - - -<p><a id="XXXI9"></a>9. (<i>Objection answered.</i>)—But, it may be objected, -the Moral Law of the universe is a Law in a different -sense from the Laws of the universe of which we spoke -before—the mathematical and physical laws of the -universe. Those were laws according to which things -<i>are</i>, and events <i>occur</i>: but Moral Laws are Laws according -to which men <i>ought</i> to act, and according to -which actions <i>ought</i> to be. There is a difference, so -that we cannot reason from the human to the Divine -Mind in the same manner in this case as in the other.</p> - -<p>True: we cannot reason <i>in the same manner</i>. But -we can reason still more confidently. For the Law -directing what <i>ought to be</i> is the <i>Supreme Law</i>, and -the mind which constitutes the Supreme Law is the -<i>Supreme Mind</i>, that is, the Divine Mind.</p> - -<p><a id="XXXI10"></a>10. That the Moral Law is not verified among men -in fact, is not a ground for doubting that it is a Law -of the Divine Mind; but it is a ground for inquiring -what consequences the Divine Mind has annexed to -the violation of the Law; and in what manner the -supremacy of the Law will be established in the total -course of the history of the universe, including, it may -be, the history of other worlds than that in which we -now live.</p> - -<p>Considering how dimly and imperfectly we see what -consequences the Divine Governor has annexed to the -violation of the Moral Law, He who sees all these -consequences and has provided for the establishment -of His Law in the whole history of the human race, -must be supposed to be infinitely elevated above man -in wisdom;—more even in virtue of this aspect of His -nature, than in virtue of that which is derived from -the contemplation of the universe.</p> - -<p><span class="pagenum" id="Page_382">382</span></p> - - -<p><a id="XXXI11"></a>11. Man is a person; and his personality is his <i>highest</i> -attribute, or at least, that which makes all his highest -attributes possible. And the highest attribute which -belongs to the finite minds which exist in the universe -must exist also in the Infinite Mind which constitutes -the universe as it is. The Divine Mind must reside -in a <i>Divine Person</i>. And as man, by his personality, -acts in obedience to or in transgression of a moral -law, so God, by His Personality, acts in establishing -the Law and in securing its supremacy in the whole -history of the world.</p> - - -<p><a id="XXXI12"></a>12. (<i>Creation.</i>)—Acknowledging a Divine Mind -which is the foundation and support of the world as it -is, constituting and upholding its laws, it may be asked, -Does this view point to a beginning of the world? -Was there a time when the Divine Mind called into -being the world, before non-existent? Was there a -Creation of the world?</p> - -<p>I do not think that an answer to this question, -given either way, affects the argument which I have -been urging. The Laws of the Universe discoverable -by the human mind, are the Laws of the Divine -Mind, whether or not there was a time when these -Laws first came into operation, or first produced the -world which we see. The argument respecting the -nature of the Divine Mind is the same, whether or -not we suppose a Creation.</p> - -<p>But, in point of fact, every part of our knowledge -of the Universe does seem to point to a beginning. -Every part of the world has been, so far as we can -see, formed by natural causes out of something different -from what it now is. The Earth, with its lands -and seas, teeming with innumerable forms of living -things, has been produced from an earth formed of -other lands and seas, occupied with quite different -forms of life: and if we go far enough back, from an -earth in which there was no life. The stars which we -call <i>fixed</i> move and change; the nebulæ in their shape -show that they too are moving and changing. The -Earth was, some at least hold, produced by the condensation -of a nebula. The history of man, as well<span class="pagenum" id="Page_383">383</span> -as of others of its inhabitants, points to a beginning. -Languages, Arts, Governments, Histories, all seem to -have begun from a starting-point, however remote. -Indeed not only a beginning, but a beginning at no -remote period, appears to be indicated by most of the -sciences which carry us backwards in the world's history.</p> - -<p>But we must allow, on the other hand, that though -all such lines of research point <i>towards</i> a beginning, -none of them can be followed <i>up to</i> a beginning. All -the lines converge, but all melt away before they reach -the point of convergence. As I have elsewhere said<a name="FNanchor_320" id="FNanchor_320"></a><a href="#Footnote_320" class="fnanchor">[320]</a>, -in no science has man been able to arrive at a beginning -which is homogeneous with the known course of -events, though we can often go very far back, and -limit the hypotheses respecting the origin. We have, -in the impossibility of thus coming to any conclusion -by natural reason on the subject of creation, another -evidence of the infinitely limited nature of the human -mind, when compared with the Creative or Constitutive -Divine Mind.</p> - - -<p><a id="XXXI13"></a>13. (<i>End of the World.</i>)—But if our natural reason, -aided by all that science can teach, can tell us nothing -respecting the origin and beginning of this world, still -less can reason tell us anything with regard to the -<i>End</i> of this world. On this subject, the natural -sciences are even more barren of instruction than on -the subject of Creation. Yet we may say that as the -Constitution of the Universe, and its conformity to a -Collection of eternal and immutable Ideas as its elements, -are not inconsistent with the supposition of a -Beginning of the present course of the world, so neither -are they inconsistent with the supposition of an -End. Indeed it would not be at all impossible that -physical inquiries should present the prospect of an -End, even more clearly than they afford the retrospect -of a Beginning. If, for instance, it should be found -that the planets move in a resisting medium which<span class="pagenum" id="Page_384">384</span> -constantly retards their velocity, and must finally -make them fall in upon the central sun, there would -be an end of the earth as to its present state. We cannot -therefore, on the grounds of Science, deny either a -Beginning or an End of the present world.</p> - - -<p><a id="XXXI14"></a>14. But here another order of considerations comes -into play, namely, those derived from moral and theological -views of the world. On these we must, in conclusion, -say a few words.</p> - -<p>It is very plain that these considerations may lead -us to believe in a view of the Beginning, Middle, and -End of the history of the world, very different from -anything which the mere physical and natural sciences -can disclose to us. And these expressions to which I -have been led, the <i>Beginning</i>, the <i>Middle</i>, and the -<i>End</i> of the world's history according to theological -views, are full of suggestions of the highest interest. -But the interest which belongs to these suggestions is -of a solemn and peculiar kind; and the considerations -to which such suggestions point are better, I think, -kept apart from such speculations as those with which -I have been concerned in the present volume.</p> - - - - -<hr class="chap" /> - -<p><span class="pagenum" id="Page_385">385</span></p> - - -</div><div class="chapter"> -<h2><a name="CHAPTER_XXXII" id="CHAPTER_XXXII"></a>CHAPTER XXXII.<br /> - -<span class="smcap medium">Analogies of Physical and Religious Philosophy.</span></h2> - - -<p><a id="XXXII1"></a> -<span class="dropcap"><span class="dsmall">1.</span> A</span>NY assertion of analogy between physical and -religious philosophy will very properly be -looked upon with great jealousy as likely to be forced -and delusive; and it is only in its most general aspects -that a sound philosophy on the two subjects can offer -any points of resemblance. But in some of its general -conditions the discovery of truth in the one field of -knowledge and in the other may offer certain analogies, -as well as differences, which it may be instructive -to notice; and to some such aspects of our philosophy -I shall venture to refer.</p> - -<p>For the physical sciences—the sciences of observation -and speculation—the progress of our exact and -scientific knowledge, as I have repeatedly said, consists -in reducing the objects and events of the universe -to a conformity with Ideas which we have in our own -minds:—the Ideas, for instance, of Space, Force, Substance, -and the like. In this sense, the intellectual -progress of men consists in the Idealization of Facts.</p> - -<p><a id="XXXII2"></a>2. In moral subjects, on the other hand, where -man has not merely to observe and speculate, but also -to act;—where he does not passively leave the facts -and events of the world such as they are, but tries -actively to alter them and to improve the existing -state of things, his progress consists in doing this. He -makes a moral advance when he succeeds in doing -what he thus attempts:—when he really improves the -state of things with which he has to do by removing -evil and producing good:—when he makes the state -of things, namely, the relations between him and other -persons, his acts and their acts, conform more and<span class="pagenum" id="Page_386">386</span> -more to Ideas which he has in his own mind:—namely, -to the Ideas of Justice, Benevolence, and the -like. His moral progress thus consists in the realization -of Ideas.</p> - -<p>And thus we are led to the Aphorism, as we may -call it, that <i>Man's Intellectual Progress consists in the -Idealization of Facts, and his Moral Progress consists -in the Realization of Ideas</i>.</p> - - -<p><a id="XXXII3"></a>3. But further, though that progress of science -which consists in the idealization of facts may be -carried through several stages, and indeed, in the history -of science, has been carried through many stages, -yet it is, and always must be, a progress exceedingly -imperfect and incomplete, when compared with the -completeness to which its nature points. Only a few -sciences have made much progress; none are complete; -most have advanced only a step or two. In -none have we reduced all the Facts to Ideas. In -all or almost all the unreduced Facts are far more -numerous and extensive than those which have been -reduced. The general mass of the facts of the universe -are mere facts, unsubdued to the rule of science. -The Facts are not Idealized. The intellectual progress -is miserably scanty and imperfect, and would be -so, even if it were carried much further than it is -carried. How can we hope that it will ever approach -to completeness?</p> - -<p><a id="XXXII4"></a>4. And in like manner, the <i>moral</i> progress of man -is still more miserably scanty and incomplete. In -how small a degree has he in this sense realized his -Ideas! In how small a degree has he carried into -real effect, and embodied in the relations of society, in -his own acts and in those of others with whom he is -concerned, the Ideas of Justice and Benevolence and -the like! How far from a complete realization of such -moral Ideas are the acts of the best men, and the relations -of the best forms of society! How far from perfection -in these respects is man! and how certain it -is that he will always be very far from perfection! -Far below even such perfection as he can conceive, he -will always be in his acts and feelings. The moral<span class="pagenum" id="Page_387">387</span> -progress of man, of each man, and of each society, is, -as I have said, miserably scanty and incomplete; and -when regarded as the realization of his moral Ideas, -its scantiness and incompleteness become still more -manifest than before.</p> - -<p>Hence we are led to another Aphorism:—<i>that -man's progress in the realization of Moral Ideas, and -his progress in the Scientific idealization of Facts, are, -and always will be, exceedingly scanty and incomplete</i>.</p> - - -<p><a id="XXXII5"></a>5. But there is another aspect of Ideas, both physical -and moral, in which this scantiness and incompleteness -vanish. In the Divine Mind, all the physical -Ideas are entertained with complete fulness and -luminousness; and it is because they are so entertained -in the Divine Mind, and it is because the universe -is constituted and framed upon them, that we -find them verified in every part of the universe, whenever -we make our observation of facts and deduce -their laws.</p> - -<p>In like manner the Moral Ideas exist in the Divine -Mind in complete fulness and luminousness; and we -are naturally led to believe and expect that they must -be exemplified in the moral universe, as completely -and universally as the physical laws are exemplified in -the physical universe. Is this so? or under what conditions -can we conceive this to be?</p> - -<p><a id="XXXII6"></a>6. In answering this question, we must consider -how far the moral, still more even than the physical -Ideas of the Divine Mind, are elevated above our -human Ideas; but yet not so far as to have no resemblance -to our corresponding human Ideas; for if this -were so, we could not reason about them at all.</p> - -<p>In speaking of man's moral Ideas, Benevolence, -Justice, and the like, we speak of them as belonging -to man's <i>Soul</i>, rather than to his <i>Mind</i>, which we have -commonly spoken of as the seat of his physical Ideas. -A distinction is thus often made between the intellectual -and the moral faculties of man; but on this -distinction we here lay no stress. We may speak of -man's <i>Mind</i> and <i>Soul</i>, meaning that part of his being -in which are all his Ideas, intellectual and moral.</p> - -<p><span class="pagenum" id="Page_388">388</span></p> - -<p>And now let us consider the question which has -just been asked:—how we can conceive the Divine -Benevolence and Justice to be completely and universally -realized in the moral world, as the Ideas of -Space, Time, &c. are in the physical world?</p> - - -<p><a id="XXXII7"></a>7. Our Ideas of Benevolence, Justice, and of other -Virtues, may be elevated above their original narrowness, -and purified from their original coarseness, by moral -culture; as our Ideas of Force and Matter, of Substance -and Elements, and the like, may be made clear -and convincing by philosophical and scientific culture. -This appears, in some degree, in the history of moral -terms, as the progress of clearness and efficacy in the -Idea of the material sciences appears in the history of -the terms belonging to such sciences. Thus among -the Romans, while they confined their kindly affections -within their own class, a stranger was universally an -enemy; <i>peregrinus</i> was synonymous with <i>hostis</i>. But -at a later period, they regarded all <i>men</i> as having a -claim on their kindness; and he who felt and acted on -this claim was called <i>humane</i>. This meaning of the -word <i>humanity</i> shows the progress (in their Ideas at -least) of the virtue which the word <i>humanity</i> designates.</p> - -<p><a id="XXXII8"></a>8. And as man can thus rise to a point of view -where he sees that man is to be loved as man, so the -humane and loving man inevitably assumes that God -loves all men; and thus assumes that there is, or may -be, a love of man in man's heart, which represents and -resembles in kind, however remote in degree, the love -of God to man.</p> - -<p>But as in man's love of man there are very widely -different stages, rising from the narrow love of a savage -to his family or his tribe, to the widest and warmest -feelings of the most enlightened and loving universal -philanthropist;—so must we suppose that there are -stages immeasurably wider by which God's love of -man is more comprehensive and more tender than any -love of man for man. The religious philosopher will -fully assent to the expressions of this conviction delivered -by pious men in all ages. "The eternal God is<span class="pagenum" id="Page_389">389</span> -thy refuge, and beneath thee are the everlasting arms." -"When my father and my mother forsake me the Lord -taketh me up," is the expression of Divine Love, consistent -with philosophy as well as with revelation. But -as the Divine Love is more comprehensive and enduring -than any human love, so is it in an immeasurably greater -degree, more enlightened. It is not a love that seeks -merely the pleasure and gratification of its object; <i>that</i> -even an enlightened human love does not do. It seeks -the good of its objects; and such a good as is the greatest -good, to an Intelligence which can embrace all -cases, causes, and contingencies. To our limited understanding, -evil seems often to be inflicted, and the -good of a part seems inconsistent with the good of another -part. Our attempts to conceive a Supreme and -complete Good provided for all the creatures which -exist in the universe, baffle and perplex us, even more -than our attempts to conceive infinite space, infinite -time, and an infinite chain of causation. But as the -most careful attention which we can give to the Ideas -of Space, Time, and Causation convinces us that these -Ideas are perfectly clear and complete in the Divine -Mind, and that <i>our</i> perplexity and confusion on these -subjects arise only from the vast distance between the -Divine Mind and our human mind, so is it reasonable -to suppose the same to be the source of the confusion -which we experience when we attempt to determine -what most conduces to the good of our fellow-creatures; -and when, urged by love to them, we endeavour -to promote this good. We can do little of what Infinite -Love would do, yet are we not thereby dispensed -from seeking in some degree to imitate the working of -Divine Love. We can see but little of what Infinite -Intelligence sees, and this should be one source of confidence -and comfort, when we stumble upon perplexities -produced by the seeming mixture of good and evil -in the world.</p> - -<p><a id="XXXII9"></a>9. But when we ask the questions which have already -been stated: Whether this Infinite Divine Love is realized -in the world, and if so, How: I conceive that we -are irresistibly impelled to reply to the former question,<span class="pagenum" id="Page_390">390</span> -that it is: and we then turn to the latter. We are led -to assume that there is in God an Infinite Love of -man, a creature in a certain degree of a Divine nature. -We must, as a consequence of this, assume that the -Love of God to man, necessarily is, in the end, and on -the whole, completely and fully realized in the history -of the world. But what is the complete history of the -world! Is it that which consists in the lives of men such -as we see them between their birth and their death? If -the minds or souls of men are alive after the death of -the body, that future life, as well as this present life, -belongs to the history of the world;—to that providential -history, of which the totality, as we have said, -must be governed by Infinite Divine Love. And in -addition to all other reasons for believing that the -minds and souls of men do thus survive their present -life, is this:—that we thus can conceive, what otherwise -it is difficult or impossible to conceive, the operation -of Infinite Love in the whole of the history of -mankind. If there be a Future State in which men's -souls are still under the authority and direction of the -Divine Governor of the world, all that is here wanting -to complete the scheme of a perfect government of -Intelligent Love may thus be applied: all seeming and -partial evil may be absorbed and extinguished in an -ultimate and universal good.</p> - - -<p><a id="XXXII10"></a>10. The Idea of Justice as belonging to God suggests -to us some of the same kind of reflexions as -those which we have made respecting the Divine Love. -We believe God to be just: otherwise, as has been -said, He would not be God. And as we thus, from -the nature of our minds and souls, believe God to be -just, we must, in this belief, understand Justice according -to the Idea which we have of Justice; that is, -in some measure, according to the Idea of Justice, as -exemplified in human actions and feelings. It would -be absurd to combine the two propositions, that we -necessarily believe that God is just, and that by <i>just</i>, -we mean something entirely different from the common -meaning of the word.</p> - -<p>But though the Divine Idea of Justice must neces<span class="pagenum" id="Page_391">391</span>sarily, -in some measure, coincide with our Idea of -Justice, we must believe in this, as in other cases, that -the Divine Idea is immeasurably more profound, comprehensive, -and clear, than the human Idea. Even -the human Idea of Justice is susceptible of many and -large progressive steps, in the way of clearness, consistency, -and comprehensiveness. In the moral history -of man this Idea advances from the hard rigour of inflexible -written Law to the equitable estimation of the -real circumstances of each case; it advances also from -the narrow Law of a single community to a larger Law, -which includes and solves the conflicts of all such -Laws. Further, the administration of human Law is -always imperfect, often erroneous, in consequence of -man's imperfect knowledge of the facts of each case, -and still more, from his ignorance of the designs and -feelings of the actors. If the Judge could see into the -heart of the person accused, and could himself rise -higher and higher in judicial wisdom, he might exemplify -the Idea of Justice in a far higher degree than -has ever yet been done.</p> - -<p><a id="XXXII11"></a>11. But all such advance in the improvement of -human Justice must still be supposed to stop immeasurably -short of the Divine Justice, which must include -a perfect knowledge of all men's actions, and all -men's hearts and thoughts; and a universal application -of the wisest and most comprehensive Laws. And the -difference of the Divine and of the human Idea of -Justice may, like the differences of other Divine and -human Ideas, include the solution of all the perplexities -in which we find ourselves involved when we -would trace the Idea to all its consequences. The Divine -Idea is immeasurably elevated above the human -Idea; in the Divine Idea all inconsistency, defect, and -incompleteness vanish, and Justice includes in its administration -every man, without any admixture of injustice. -This is what we must conceive of the Divine -administration, since God is perfectly just.</p> - -<p><a id="XXXII12"></a>12. But here, as before, we have another conclusion -suggested to us. We are, by the considerations -just now spoken of, led to believe that, in the Divine<span class="pagenum" id="Page_392">392</span> -administration of the world is an administration of -perfect Justice;—that is, such is the Divine Administration -in the end and on the whole, taking into account -the whole of the providential history of the -world. But the course of the world, taking into account -only what happens to man in this present life, -is not, we may venture to say, a complete and entire -administration of justice. It often happens that injustice -is successful and triumphant, even in the end, -so far as the end is seen here. It happens that wrong -is done, and is not remedied or punished. It happens -that blameless and virtuous men are subjected to pain, -grief, violence, and oppression, and are not protected, -extricated, or avenged. In the affairs of this world, -the prevalence of injustice and wrong-doing is so apparent, -as to be a common subject of complaint: and -though the complaint may be exaggerated, and though -a calm and comprehensive view may often discern compensating -and remedial influences which are not visible -at first sight, still we cannot regard the lot of happiness -or misery which falls to each man in this world and -this life as apportioned according to a scheme of perfect -and universal justice, such as in our thoughts we -cannot but require the Divine administration to be.</p> - -<p><a id="XXXII13"></a>13. Here then we are again led to the same conviction -by regarding the Divine administration of the -world as the realization of the Divine Justice, to which -we were before led by regarding it as the realization -of the Divine Love. Since the Idea is not fully or -completely realized in man's life in this present world, -this present world cannot be the whole of the Divine -Administration. To complete the realization of the -Idea of Justice, as an element of the Divine Administration, -there must be a life of man after his life in -this present world. If man's mind and soul, the part -of him which is susceptible of happiness and misery, -survive this present life, and be still subject to the -Divine Administration, the Idea of Divine Justice -may still be completely realized, notwithstanding all -that here looks like injustice or defective justice; and -it belongs to the Idea of Justice to remedy and com<span class="pagenum" id="Page_393">393</span>pensate, -not to prevent wrong. And thus by this -supposition of a Future State of man's existence, we -are enabled to conceive that, in the whole of the Divine -Government of the universe, all seeming injustice -and wrong may be finally corrected and rectified, in an -ultimate and universal establishment of a reign of perfect -Righteousness.</p> - - -<p><a id="XXXII14"></a>14. Admitting the view thus presented, we may -again discern a remarkable analogy between what we -have called our <i>physical</i> Ideas (those of Space, Time, -Cause, Substance, and the like), and our <i>moral</i> Ideas, -(those of Benevolence, Justice, &c.). In both classes we -must suppose that our human Ideas represent, though -very incompletely and at an immeasurable distance, -the Divine Ideas. Even our physical Ideas, when pursued -to their consequences, are involved in a perplexity -and confusion from which the Divine Ideas are free. -Our Ideas of Benevolence and Justice are still more -full of imperfections and inconsistency, when we would -frame them into a complete scheme, and yet from such -imperfections and inconsistency we must suppose that -the Divine Benevolence and Justice are exempt. Our -physical Ideas we find in every case exactly exemplified -and realized in the universe, and we account for -this by considering that they are the Divine Ideas, on -which the universe is constituted. Our moral Ideas, -the Ideas of Benevolence and Justice in particular, -must also be realized in the universe, as a scheme of -Divine Government. But they are not realized in -the world as constituted of man living this present -life. The Divine Scheme of the world, therefore, extends -beyond this present life of man. If we could -include in our survey the future life as well as the -present life of man, and the future course of the Divine -Government, we should have a scheme of the -Moral Government of the universe, in which the Ideas -of Perfect Benevolence and Perfect Justice are as completely -and universally exemplified and realized, as the -Ideas of Space, Time, Cause, Substance, and the like, -are in the physical universe.</p> - - -<p><a id="XXXII15"></a>15. There is one other remark bearing upon this<span class="pagenum" id="Page_394">394</span> -analogy, which seems to deserve our attention. As I -have said in the last chapter, the scheme of the world, -as governed by our physical Ideas, seems to point to -a Beginning of the world, or at least of the present -course of the world: and if we suppose a Beginning, -our thoughts naturally turn to an End. But if our -physical Ideas point to a Beginning and suggest an -End, do our Ideas of Divine Benevolence and Justice -in any way lend themselves to this suggestion?—Perhaps -we might venture to say that in some degree -they do, even to the eye of a mere philosophical reason. -Perhaps our reason alone might suggest that there -is a progression in the human race, in various moral -attributes—in art, in civilization, and even in humanity -and in justice, which implies a beginning. And that -at any rate there is nothing inconsistent with our Idea -of the Divine Government in the supposition that the -history of this world has a Beginning, a Middle and -an End.</p> - -<p><a id="XXXII16"></a>16. If therefore there should be conveyed to us -by some channel especially appropriated to the communication -and development of moral and religious -Ideas, the knowledge that the world, as a scheme of -Divine Government, has <i>a Beginning</i>, <i>a Middle</i>, and -<i>an End</i>, of a Kind, or at least, invested with circumstances -quite different from any which our physical -Ideas can disclose to us, there would be, in such -a belief, nothing at all inconsistent with the analogies -which our philosophy—the philosophy of our Ideas -illustrated by the whole progress of science—has impressed -upon us. On the grounds of this philosophy, -we need find no difficulty in believing that as the -visible universe exhibits the operation of the Divine -Ideas of Space, Time, Cause, Substance, and the like, -and discloses to us traces of a Beginning of the present -mode of operation, so the moral universe exhibits -to us the operation of the Divine Benevolence and -Justice; and that these Divine attributes wrought in -a special and peculiar manner in the Beginning; interposed -in a peculiar and special manner in the Middle; -and will again act in a peculiar and special manner in<span class="pagenum" id="Page_395">395</span> -the End of the world. And thus the conditions of the -physical universe, and the Government of the Moral -world, are both, though in different ways, a part of the -work which God is carrying on from the Beginning of -things to the End—<i>opus quod Deus operator a principio -usque ad finem</i>.</p> - - -<p><a id="XXXII17"></a>17. We are led by such analogies as I have been -adducing to believe that the whole course of events in -which the minds and souls of men survive the present -life, and are hereafter subjected to the Divine government -in such a way as to complete all that is here deficient -in the world's history, is a scheme of perfect -Benevolence and Justice. Now, can we discern in -man's mind or soul itself any indication of a destiny -like this? Are there in us any powers and faculties -which seem as if they were destined to immortality? -If there be, we have in such faculties a strong confirmation -of that belief in the future life of man which has -already been suggested to us as necessary to render the -Divine government conceivable.</p> - - -<p><a id="XXXII18"></a>18. According to our philosophy there are powers -and faculties which do thus seem fitted to endure, and -not fitted to terminate and be extinguished. The Ideas -which we have in our minds—the physical Ideas, as -we have called them, according to which the universe -is constituted,—agree, as far as they go, with the Ideas -of the Divine Mind, seen in the constitution of the -universe. But these Divine Ideas are eternal and imperishable: -we therefore naturally conclude that the -human mind which includes such elements, is also -eternal and imperishable. Since the mind can take -hold of eternal truths, it must be itself eternal. Since -it is, to a certain extent, the image of God in its faculties, -it cannot ever cease to be the image of God. -When it has arrived at a stage in which it sees several -aspects of the universe in the same form in which they -present themselves to the Divine Mind, we cannot -suppose that the Author of the human mind will allow -it and all its intellectual light to be extinguished.</p> - -<p><a id="XXXII19"></a>19. And our conviction that this extinction of the -human mind cannot take place becomes stronger still,<span class="pagenum" id="Page_396">396</span> -when we consider that the mind, however imperfect -and scanty its discernment of truth may be, is still -capable of a vast, and even of an unlimited progress in -the pursuit and apprehension of truth. The mind is -capable of accepting and appropriating, through the -action of its own Ideas, every step in science which -has ever been made—every step which shall hereafter -be made. Can we suppose that this vast and boundless -capacity exists for a few years only, is unfolded -only into a few of its simplest consequences, and is -then consigned to annihilation? Can we suppose that -the wonderful powers which carry man on, generation -by generation, from the contemplation of one great -and striking truth to another, are buried with each -generation? May we not rather suppose that that -mind, which is capable of indefinite progression, is -allowed to exist in an infinite duration, during which -such progression may take place?</p> - -<p><a id="XXXII20"></a>20. I propose this argument as a ground of hope -and satisfactory reflexion to those who love to dwell on -the natural arguments for the Immortality of the Soul. -I do not attempt to follow it into detail. I know too -well how little such a cause can gain by obstinate and -complicated argumentation, to attempt to urge the -argument in that manner: and probably different persons, -among those who accept the argument as valid, -would give different answers to many questions of detail, -which naturally arise out of the acceptance of this -argument. I will not here attempt to solve, or even -to propound these questions. My main purpose in -offering these views and this argument at all, is to -give some satisfaction to those who would think it a -sad and blank result of this long survey of the nature -and progress of science in which we have been so long -engaged (through this series of works), that it should -in no way lead to a recognition of the Author of that -world about which our Science is, and to the high and -consolatory hopes which lift man beyond this world. -No survey of the universe can be at all satisfactory to -thoughtful men, which has not a theological bearing; -nor can any view of man's powers and means of know<span class="pagenum" id="Page_397">397</span>ing -be congenial to such men, which does not recognize -an infinite destination for the mind which has an infinite -capacity; an eternal being of the Faculty which -can take a steady hold of eternal being.</p> - - -<p><a id="XXXII21"></a>21. And as we may derive such a conviction from -our physical Ideas, so too may we no less from our -moral Ideas. Our minds apprehend Space and Time -and Force and the like, as Ideas which are not dependent -on the body; and hence we believe that our minds -shall not perish with our bodies. And in the same -manner our souls conceive pure Benevolence and perfect -Justice, which go beyond the conditions of this -mortal life; and hence we believe that our souls have -to do with a life beyond this mortal life.</p> - -<p>It is more difficult to speak of man's indefinite moral -progression even than of his indefinite intellectual -progression. Yet in every path of moral speculation -we have such a progression suggested to us. We may -begin, for instance, with the ordinary feelings and -affections of our daily nature:—Love, Hate, Scorn. -But when we would elevate the Soul in our imagination, -we ascend above these ordinary affections, and -take the repulsive and hostile ones as fitted only to -balance their own influences. And thus the poet, -speaking of a morally poetical nature, describes it:</p> - -<div class="poetry-container"> -<div class="poetry"> - <div class="stanza"> -<div class="verse">The Poet in a golden clime was born,</div> -<div class="verse indent2">With golden stars above.</div> -<div class="verse">He felt the hate <i>of</i> hate, the scorn <i>of</i> scorn,</div> -<div class="verse indent2">The love <i>of</i> love.</div> -</div></div></div> - -<p>But the loftier moralist can rise higher than this, and -can, and will, reject altogether Hate and Scorn from -his view of man's better nature. His description -would rather be—</p> - -<div class="poetry-container"> -<div class="poetry"> - <div class="stanza"> -<div class="verse">The good man in a loving clime was born,</div> -<div class="verse indent2">With loving stars above.</div> -<div class="verse">He felt sorrow for hate, pity for scorn,</div> -<div class="verse indent2">And love of love.</div> -</div></div></div> - -<p>He would, in his conception of such a character, -ascribe to it all the virtues which result from the<span class="pagenum" id="Page_398">398</span> -control and extinction of these repulsive and hostile -affections:—the virtues of magnanimity, forgivingness, -unselfishness, self-devotion, tenderness, sweetness. -And these we can conceive in a higher and higher -degree, in proportion as our own hearts become tender, -forgiving, pure and unselfish. And though in every -human stage of such a moral proficiency, we must -suppose that there is still some struggle with the remaining -vestiges of our unkind, unjust, angry and -selfish affections, we can see no limit to the extent to -which this struggle may be successful; no limit to the -degree in which these traces of the evil of our nature -may be worn out by an enduring practice and habit -of our better nature. And when we contemplate a -human character which has, through a long course of -years, and through many trials and conflicts, made -a large progress in this career of melioration, and is -still capable, if time be given, of further progress -towards moral perfection, is it not reasonable to suppose -that He who formed man capable of such progress, -and who, as we must needs believe, looks with -approval on such progress where made, will not allow -the progress to stop when it has gone on to the end of -man's short earthly life? Is it not rather reasonable -to suppose that the pure and elevated and all-embracing -affection, extinguishing all vices and including all virtues, -to which the good man thus tends, shall continue -to prevail in him as a permanent and ever-during condition, -in a life after this?</p> - -<p>But can man raise himself to such a stage of moral -progress, by his own efforts? Such a progress is an -approximation towards the perfection of moral Ideas, -and therefore an approximation towards the image of -God, in whom that perfection resides: is it not then -reasonable to suppose that man needs a Divine Influence -to enable him to reach this kind of moral -completeness? And is it not also reasonable to suppose -that, as he needs such aid, in order that the Idea -of his moral progress may be realized, so he will receive -such aid from the Divine Power which realizes the -Idea of Divine Love in the world; and to do so, must<span class="pagenum" id="Page_399">399</span> -realize it in those human souls which are most fitted -for such a purpose?</p> - -<p>But these questions remind me how difficult, and -indeed, how impossible it is to follow such trains of -reflexion by the light of philosophy alone. To answer -such questions, we need, not Religious Philosophy only, -but Religion: and as I do not here venture beyond -the domain of philosophy, I must, however abruptly, -conclude.</p> - - -<p class="center">THE END.</p> - -<hr class="chap" /> - -<p><span class="pagenum"><a name="Page_400" id="Page_400">[Pg 400]</a><br /><a name="Page_401" id="Page_401">[Pg 401]</a></span></p> - - - -<p><span class="pagenum"><a name="Page_402" id="Page_402">[Pg 402]</a><br /><a name="Page_403" id="Page_403">[Pg 403]</a></span></p> -</div><div class="chapter"> -<h2><a name="APPENDIX" id="APPENDIX"></a>APPENDIX.</h2> - - -<h3><span class="smcap"><a id="Appendix_A"></a>Appendix A.</span><br /> - -OF THE PLATONIC THEORY OF IDEAS.</h3> - -<p class="center">(<i>Cam. Phil. Soc.</i> Nov. 10, 1856.)</p> - - -<p class="drop-cap"><span class="smcap">Though</span> Plato has, in recent times, had many readers and admirers -among our English scholars, there has been an air of -unreality and inconsistency about the commendation which most of -these professed adherents have given to his doctrines. This appears -to be no captious criticism, for instance, when those who speak of -him as immeasurably superior in argument to his opponents, do not -venture to produce his arguments in a definite form as able to bear -the tug of modern controversy;—when they use his own Greek -phrases as essential to the exposition of his doctrines, and speak as -if these phrases could not be adequately rendered in English;—and -when they assent to those among the systems of philosophy of -modern times which are the most clearly opposed to the system of -Plato. It seems not unreasonable to require, on the contrary, that -if Plato is to supply a philosophy for us, it must be a philosophy -which can be expressed in our own language;—that his system, if -we hold it to be well founded, shall compel us to deny the opposite -systems, modern as well as ancient;—and that, so far as we hold -Plato's doctrines to be satisfactorily established, we should be able -to produce the arguments for them, and to refute the arguments -against them. These seem reasonable requirements of the adherents -of <i>any</i> philosophy, and therefore, of Plato's.</p> - -<p>I regard it as a fortunate circumstance, that we have recently -had presented to us an exposition of Plato's philosophy which does -conform to those reasonable conditions; and we may discuss this -exposition with the less reserve, since its accomplished author, -though belonging to this generation, is no longer alive. I refer to -the <i>Lectures</i> on the History of Ancient Philosophy, by the late -Professor Butler of Dublin. In these Lectures, we find an account -of the Platonic Philosophy which shows that the writer had considered -it as, what it is, an attempt to solve large problems, which in -all ages force themselves upon the notice of thoughtful men. In -Lectures VIII. and X., of the Second Series, especially, we have a<span class="pagenum" id="Page_404">404</span> -statement of the Platonic Theory of Ideas, which may be made a -convenient starting point for such remarks as I wish at present to -make. I will transcribe this account; omitting, as I do so, the -expressions which Professor Butler uses, in order to present the -theory, not as a dogmatical assertion, but as a view, at least not -extravagant. For this purpose, he says, of the successive portions -of the theory, that one is "not too absurd to be maintained;" that -another is "not very extravagant either;" that a third is "surely -allowable;" that a fourth presents "no incredible account" of the -subject; that a fifth is "no preposterous notion in substance, and no -unwarrantable form of phrase." Divested of these modest formulæ, -his account is as follows: [Vol. <span class="smcap">II.</span> p. 117.]</p> - -<p>"Man's soul is made to contain not merely a consistent scheme -of its own notions, but a direct apprehension of <i>real and eternal -laws beyond it</i>. These real and eternal laws are things <i>intelligible</i>, -and not things sensible.</p> - -<p>"These laws impressed upon creation by its Creator, and apprehended -by man, are something distinct equally from the Creator -and from man, and the whole mass of them may fairly be termed -the World of Things Intelligible.</p> - -<p>"Further, there are qualities in the supreme and ultimate Cause -of all, which are manifested in His creation, and not merely manifested, -but, in a manner—after being brought out of his super-essential -nature into the stage of being [which is] below him, but -next to him—are then by the causative act of creation deposited in -things, differencing them one from the other, so that the things -partake of them (μετέχουσι), communicate with them (κοινωνοῦσι).</p> - -<p>"The intelligence of man, excited to reflection by the impressions -of these objects thus (though themselves transitory) participant of -a divine quality, may rise to higher conceptions of the perfections -thus faintly exhibited; and inasmuch as these perfections are -unquestionably <i>real</i> existences, and <i>known</i> to be such in the very -act of contemplation,—this may be regarded as a direct intellectual -apperception of them,—a Union of the Reason with the Ideas in -that sphere of being which is common to both.</p> - -<p>"Finally, the Reason, in proportion as it learns to contemplate -the Perfect and Eternal, <i>desires</i> the enjoyment of such contemplations -in a more consummate degree, and cannot be fully satisfied, -except in the actual fruition of the Perfect itself.</p> - -<p>"These suppositions, taken together, constitute the Theory of -Ideas."</p> - -<p>In remarking upon the theory thus presented, I shall abstain -from any discussion of the theological part of it, as a subject which<span class="pagenum" id="Page_405">405</span> -would probably be considered as unsuited to the meetings of this -Society, even in its most purely philosophical form. But I conceive -that it will not be inconvenient, if it be not wearisome, to discuss -the Theory of Ideas as an attempt to explain the existence of real -knowledge; which Prof. Butler very rightly considers as the necessary -aim of this and cognate systems of philosophy<a name="FNanchor_321" id="FNanchor_321"></a><a href="#Footnote_321" class="fnanchor">[321]</a>.</p> - -<p>I conceive, then, that one of the primary objects of Plato's -Theory of Ideas is, to explain the existence of real knowledge, -that is, of demonstrated knowledge, such as the propositions of -geometry offer to us. In this view, the Theory of Ideas is one -attempt to solve a problem, much discussed in our times, What is -the ground of geometrical truth? I do not mean that this is the -whole object of the Theory, or the highest of its claims. As I have -said, I omit its theological bearings; and I am aware that there are -passages in the Platonic Dialogues, in which the Ideas which enter -into the apprehension and demonstration of geometrical truths are -spoken of as subordinate to Ideas which have a theological aspect. -But I have no doubt that one of the main motives to the construction -of the Theory of Ideas was, the desire of solving the Problem, -"How is it possible that man should apprehend necessary and -eternal truths?" That the truths are necessary, makes them eternal, -for they do not depend on time; and that they are eternal, -gives them at once a theological bearing.</p> - -<p>That Plato, in attempting to explain the nature and possibility of -real knowledge, had in his mind geometrical truths, as examples of -such knowledge is, I think, evident from the general purport of his -discourses on such subjects. The advance of Greek geometry into -a conspicuous position, at the time when the Heraclitean sect were -proving that nothing could be proved and nothing could be known, -naturally suggested mathematical truth as the refutation of the skepticism -of mere sensation. On the one side it was said, we can know -nothing except by our sensations; and that which we observe with -our senses is constantly changing; or at any rate, may change at any -moment. On the other hand it was said, we <i>do</i> know geometrical -truths, and as truly as we know them, that they cannot change. -Plato was quite alive to the lesson, and to the importance of this -kind of truths. In the <i>Meno</i> and in the <i>Phædo</i> he refers to them, -as illustrating the nature of the human mind: in the <i>Republic</i> and -the <i>Timæus</i> he again speaks of truths which far transcend anything<span class="pagenum" id="Page_406">406</span> -which the senses can teach, or even adequately exemplify. The -senses, he argues in the <i>Theætetus</i>, cannot give us the knowledge -which we have; the source of it must therefore be in the mind -itself; in the <i>Ideas</i> which it possesses. The impressions of sense -are constantly varying, and incapable of giving any certainty: but -the Ideas on which real truth depends are constant and invariable, -and the certainty which arises from these is firm and indestructible. -Ideas are the permanent, perfect objects, with which the mind -deals when it contemplates necessary and eternal truths. They -belong to a region superior to the material world, the world of -sense. They are the objects which make up the furniture of the -Intelligible World; with which the Reason deals, as the Senses -deal each with its appropriate Sensation.</p> - -<p>But, it will naturally be asked, what is the Relation of Ideas to -the Objects of Sense? Some connexion, or relation, it is plain, -there must be. The objects of sense can suggest, and can illustrate -real truths. Though these truths of geometry cannot be proved, -cannot even be exactly exemplified, by drawing diagrams, yet -diagrams are of use in helping ordinary minds to see the proof; -and to all minds, may represent and illustrate it. And though our -conclusions with regard to objects of sense may be insecure and -imperfect, they have some show of truth, and therefore some -resemblance to truth. What does this arise from? How is it explained, -if there is no truth except concerning Ideas?</p> - -<p>To this the Platonist replied, that the phenomena which present -themselves to the senses partake, in a certain manner, of Ideas, and -thus include so much of the nature of Ideas, that they include also -an element of Truth. The geometrical diagram of Triangles and -Squares which is drawn in the sand of the floor of the Gymnasium, -partakes of the nature of the true Ideal Triangles and Squares, so -that it presents an imitation and suggestion of the truths which are -true of them. The real triangles and squares are in the mind: -they are, as we have said, objects, not in the Visible, but in the -Intelligible World. But the Visible Triangles and Squares make -us call to mind the Intelligible; and thus the objects of sense -suggest, and, in a way, exemplify the eternal truths.</p> - -<p>This I conceive to be the simplest and directest ground of two -primary parts of the Theory of Ideas;—The Eternal Ideas constituting -an Intelligible World; and the Participation in these Ideas -ascribed to the objects of the world of sense. And it is plain that -so far, the Theory meets what, I conceive, was its primary purpose; -it answers the questions, How can we have certain knowledge, -though we cannot get it from Sense? and, How can we have<span class="pagenum" id="Page_407">407</span> -knowledge, at least apparent, though imperfect, about the world of -sense?</p> - -<p>But is this the ground on which Plato himself rests the truth of -his Theory of Ideas? As I have said, I have no doubt that these -were the questions which suggested the Theory; and it is perpetually -applied in such a manner as to show that it was held by Plato -in this sense. But his applications of the Theory refer very often -to another part of it;—to the Ideas, not of Triangles and Squares, -of space and its affections; but to the Ideas of Relations—as the -Relations of Like and Unlike, Greater and Less; or to things quite -different from the things of which geometry treats, for instance, to -Tables and Chairs, and other matters, with regard to which no -demonstration is possible, and no general truth (still less necessary -an eternal truth) capable of being asserted.</p> - -<p>I conceive that the Theory of Ideas, thus asserted and thus supported, -stands upon very much weaker ground than it does, when -it is asserted concerning the objects of thought about which necessary -and demonstrable truths are attainable. And in order to -devise arguments against <i>this</i> part of the Theory, and to trace -the contradictions to which it leads, we have no occasion to task -our own ingenuity. We find it done to our hands, not only in -Aristotle, the open opponent of the Theory of Ideas, but in works -which stand among the Platonic Dialogues themselves. And I wish -especially to point out some of the arguments against the Ideal -Theory, which are given in one of the most noted of the Platonic -Dialogues, the <i>Parmenides</i>.</p> - -<p>The <i>Parmenides</i> contains a narrative of a Dialogue held between -Parmenides and Zeno, the Eleatic Philosophers, on the one side, -and Socrates, along with several other persons, on the other. It -may be regarded as divided into two main portions; the first, in -which the Theory of Ideas is attacked by Parmenides, and defended -by Socrates; the second, in which Parmenides discusses, at length, -the Eleatic doctrine that <i>All things are One</i>. It is the former part, -the discussion of the Theory of Ideas, to which I especially wish to -direct attention at present: and in the first place, to that extension -of the Theory of Ideas, to things of which no general truth is -possible; such as I have mentioned, tables and chairs. Plato often -speaks of a Table, by way of example, as a thing of which there -must be an Idea, not taken from any special Table or assemblage -of Tables; but an Ideal Table, such that all Tables are Tables by -participating in the nature of this Idea. Now the question is, -whether there is any force, or indeed any sense, in this assumption; -and this question is discussed in the <i>Parmenides</i>. Socrates is there<span class="pagenum" id="Page_408">408</span> -represented as very confident in the existence of Ideas of the highest -and largest kind, the Just, the Fair, the Good, and the like. -Parmenides asks him how far he follows his theory. Is there, he -asks, an Idea of Man, which is distinct from us men? an Idea of -Fire? of Water? "In truth," replies Socrates, "I have often hesitated, -Parmenides, about these, whether we are to allow such -Ideas." When Plato had proceeded to teach that there is an Idea -of a Table, of course he could not reject such Ideas as Man, and -Fire, and Water. Parmenides, proceeding in the same line, pushes -him further still. "Do you doubt," says he, "whether there are -Ideas of things apparently worthless and vile? Is there an Idea of -a Hair? of Mud? of Filth?" Socrates has not the courage to -accept such an extension of the theory. He says, "By no means. -These are not Ideas. These are nothing more than just what we -see them. I have often been perplexed what to think on this subject. -But after standing to this a while, I have fled the thought, -for fear of falling into an unfathomable abyss of absurdities." On -this, Parmenides rebukes him for his want of consistency. "Ah -Socrates," he says, "you are yet young; and philosophy has not yet -taken possession of you as I think she will one day do--when you -will have learned to find nothing despicable in any of these things. -But now your youth inclines you to regard the opinions of men." -It is indeed plain, that if we are to assume an Idea of a Chair or a -Table, we can find no boundary line which will exclude Ideas of -everything for which we have a name, however worthless or offensive. -And this is an argument against the assumption of <i>such</i> -Ideas, which will convince most persons of the groundlessness of -the assumption:—the more so, as <i>for</i> the assumption of such Ideas, -it does not appear that Plato offers any argument whatever; nor -does this assumption solve any problem, or remove any difficulty<a name="FNanchor_322" id="FNanchor_322"></a><a href="#Footnote_322" class="fnanchor">[322]</a>. -Parmenides, then, had reason to say that consistency required -Socrates, if he assumed any such Ideas, to assume all. And I conceive -his reply to be to this effect; and to be thus a <i>reductio ad -absurdum</i> of the Theory of Ideas in this sense. According to the -opinions of those who see in the <i>Parmenides</i> an exposition of Platonic -doctrines, I believe that Parmenides is conceived in this -passage, to suggest to Socrates what is necessary for the completion -of the Theory of Ideas. But upon either supposition, I wish<span class="pagenum" id="Page_409">409</span> -especially to draw the attention of my readers to the position of -superiority in the Dialogue in which Parmenides is here placed -with regard to Socrates.</p> - -<p>Parmenides then proceeds to propound to Socrates difficulties -with regard to the Ideal Theory, in another of its aspects;—namely, -when it assumes Ideas of Relations of things; and here also, I wish -especially to have it considered how far the answers of Socrates to -these objections are really satisfactory and conclusive.</p> - -<p>"Tell me," says he (§ 10, Bekker), "You conceive that there are -certain Ideas, and that things partaking of these Ideas, are called -by the corresponding names;—an Idea of <i>Likeness</i>, things partaking -of which are called <i>Like</i>;—of <i>Greatness</i>, whence they are <i>Great</i>: -of <i>Beauty</i>, whence they are <i>Beautiful</i>?" Socrates assents, naturally: -this being the simple and universal statement of the Theory, -in this case. But then comes one of the real difficulties of the -Theory. Since the special things participate of the General Idea, -has each got the whole of the Idea, which is, of course, One; or -has each a part of the Idea? "For," says Parmenides, "can there -be any other way of participation than these two?" Socrates -replies by a similitude: "The Idea, though One, may be wholly in -each object, as the Day, one and the same, is wholly in each place." -The physical illustration, Parmenides damages by making it more -physical still. "You are ingenious, Socrates," he says, (§ 11) "in -making the same thing be in many places at the same time. If you -had a number of persons wrapped up in a sail or web, would you -say that each of them had the whole of it? Is not the case similar?" -Socrates cannot deny that it is. "But in this case, each person has -only a part of the whole; and thus your Ideas are partible." To -this, Socrates is represented as assenting in the briefest possible -phrase; and thus, here again, as I conceive, Parmenides retains his -superiority over Socrates in the Dialogue.</p> - -<p>There are many other arguments urged against the Ideal Theory -by Parmenides. The next is a consequence of this partibility of -Ideas, thus supposed to be proved, and is ingenious enough. It is this:</p> - -<p>"If the Idea of Greatness be distributed among things that are -Great, so that each has a part of it, each separate thing will be -Great in virtue of a part of Greatness which is less than Greatness -itself. Is not this absurd?" Socrates submissively allows that it is.</p> - -<p>And the same argument is applied in the case of the Idea of -Equality.</p> - -<p>"If each of several things have a part of the Idea of Equality, it -will be Equal to something, in virtue of something which is less -than Equality."</p> - -<p><span class="pagenum" id="Page_410">410</span></p> - -<p>And in the same way with regard to the Idea of Smallness.</p> - -<p>"If each thing be small by having a part of the Idea of Smallness, -Smallness itself will be greater than the small thing, since that is -a part of itself."</p> - -<p>These ingenious results of the partibility of Ideas remind us of -the ingenuity shown in the Greek geometry, especially the Fifth -Book of Euclid. They are represented as not resisted by Socrates -(§ 12): "In what way, Socrates, can things participate in Ideas, if -they cannot do so either integrally or partibly?" "By my troth," -says Socrates, "it does not seem easy to tell." Parmenides, who -completely takes the conduct of the Dialogue, then turns to another -part of the subject and propounds other arguments. "What do -you say to this?" he asks.</p> - -<p>"There is an Ideal Greatness, and there are many things, separate -from it, and Great by virtue of it. But now if you look at Greatness -and the Great things together, since they are all Great, they -must be Great in virtue of some higher Idea of Greatness which -includes both. And thus you have a Second Idea of Greatness; and -in like manner you will have a third, and so on indefinitely."</p> - -<p>This also, as an argument against the separate existence of Ideas, -Socrates is represented as unable to answer. He replies interrogatively:</p> - -<p>"Why, Parmenides, is not each of these Ideas a Thought, which, -by its nature, cannot exist in anything except in the Mind? In -that case your consequences would not follow."</p> - -<p>This is an answer which changes the course of the reasoning: but -still, not much to the advantage of the Ideal Theory. Parmenides -is still ready with very perplexing arguments. (§ 13.)</p> - -<p>"The Ideas, then," he says, "are Thoughts. They must be -Thoughts of something. They are Thoughts of something, then, -which exists in all the special things; some one thing which the -Thought perceives in all the special things; and this one Thought -thus involved in all, is the <i>Idea</i>. But then, if the special things, as -you say, participate in the Idea, they participate in the Thought; -and thus, all objects are made up of Thoughts, and all things think; -or else, there are thoughts in things which do not think."</p> - -<p>This argument drives Socrates from the position that Ideas are -Thoughts, and he moves to another, that they are Paradigms, -Exemplars of the qualities of things, to which the things themselves -are like, and their being thus like, is their participating in -the Idea. But here too, he has no better success. Parmenides -argues thus:</p> - -<p>"If the Object be like the Idea, the Idea must be like the<span class="pagenum" id="Page_411">411</span> -Object. And since the Object and the Idea are like, they must, -according to your doctrine, participate in the Idea of Likeness. -And thus you have one Idea participating in another Idea, and so -on in infinitum." Socrates is obliged to allow that this demolishes -the notion of objects partaking in their Ideas by likeness: and that -he must seek some other way. "You see then, O Socrates," says -Parmenides, "what difficulties follow, if any one asserts the independent -existence of Ideas!" Socrates allows that this is true. -"And yet," says Parmenides, "you do not half perceive the difficulties -which follow from this doctrine of Ideas." Socrates expresses -a wish to know to what Parmenides refers; and the aged sage -replies by explaining that if Ideas exist independently of us, we -can never know anything about them: and that even the Gods -could not know anything about man. This argument, though -somewhat obscure, is evidently stated with perfect earnestness, -and Socrates is represented as giving his assent to it. "And yet," -says Parmenides (end of § 18), "if any one gives up entirely the -doctrine of Ideas, how is any reasoning possible?"</p> - -<p>All the way through this discussion, Parmenides appears as vastly -superior to Socrates; as seeing completely the tendency of every -line of reasoning, while Socrates is driven blindly from one position -to another; and as kindly and graciously advising a young man -respecting the proper aims of his philosophical career; as well as -clearly pointing out the consequences of his assumptions. Nothing -can be more complete than the higher position assigned to Parmenides -in the Dialogue.</p> - -<p>This has not been overlooked by the Editors and Commentators -of Plato. To take for example one of the latest; in Steinhart's -Introduction to Hieronymus Müller's translation of <i>Parmenides</i> -(Leipzig, 1852), p. 261, he says: "It strikes us, at first, as strange, -that Plato here seems to come forward as the assailant of his own -doctrine of Ideas. For the difficulties which he makes Parmenides -propound against that doctrine are by no means sophistical or -superficial, but substantial and to the point. Moreover there is -among all these objections, which are partly derived from the -Megarics, scarce one which does not appear again in the penetrating -and comprehensive argumentations of Aristotle against the Platonic -Doctrine of Ideas."</p> - -<p>Of course, both this writer and other commentators on Plato -offer something as a solution of this difficulty. But though these -explanations are subtle and ingenious, they appear to leave no -satisfactory or permanent impression on the mind. I must avow -that, to me, they appear insufficient and empty; and I cannot help<span class="pagenum" id="Page_412">412</span> -believing that the solution is of a more simple and direct kind. It -may seem bold to maintain an opinion different from that of so -many eminent scholars; but I think that the solution which I offer, -will derive confirmation from a consideration of the whole Dialogue; -and therefore I shall venture to propound it in a distinct and -positive form. It is this:</p> - -<p>I conceive that the <i>Parmenides</i> is not a Platonic Dialogue at all; -but Antiplatonic, or more properly, <i>Eleatic</i>: written, not by -Plato, in order to explain and prove his Theory of Ideas, but by -some one, probably an admirer of Parmenides and Zeno, in order -to show how strong were his master's arguments against the -Platonists and how weak their objections to the Eleatic doctrine.</p> - -<p>I conceive that this view throws an especial light on every part -of the Dialogue, as a brief survey of it will show. Parmenides -and Zeno come to Athens to the Panathenaic festival: Parmenides -already an old man, with a silver head, dignified and benevolent in -his appearance, looking five and sixty years old: Zeno about forty, -tall and handsome. They are the guests of Pythodorus, outside -the Wall, in the Ceramicus; and there they are visited by Socrates -then young, and others who wish to hear the written discourses of -Zeno. These discourses are explanations of the philosophy of -Parmenides, which he had delivered in verse.</p> - -<p>Socrates is represented as showing, from the first, a disposition -to criticize Zeno's dissertation very closely; and without any prelude -or preparation, he applies the Doctrine of Ideas to refute the Eleatic -Doctrine that All Things are One. (§ 3.) When he had heard to -the end, he begged to have the first Proposition of the First Book -read again. And then, "How is it, O Zeno, that you say, That -if the Things which exist are Many, and not One, they must be at -the same time like and unlike? Is this your argument? Or do I -misunderstand you?" "No," says Zeno, "you understand quite -rightly." Socrates then turns to Parmenides, and says, somewhat -rudely, as it seems, "Zeno is a great friend of yours, Parmenides: -he shows his friendship not only in other ways, but also in what he -writes. For he says the same things which you say, though he -pretends that he does not. You say, in your poems, that All Things -are One, and give striking proofs: he says that existences are not -many, and he gives many and good proofs. You seem to soar above -us, but you do not really differ." Zeno takes this sally good-humouredly, -and tells him that he pursues the scent with the keenness -of a Laconian hound. "But," says he (§ 6), "there really is -less of ostentation in my writing than you think. My Essay was -merely written as a defence of Parmenides long ago, when I was<span class="pagenum" id="Page_413">413</span> -young; and is not a piece of display composed now that I am -older. And it was stolen from me by some one; so that I had no -choice about publishing it."</p> - -<p>Here we have, as I conceive, Socrates already represented as -placed in a disadvantageous position, by his abruptness, rude -allusions, and readiness to put bad interpretations on what is done. -For this, Zeno's gentle pleasantry is a rebuke. Socrates, however, -forthwith rushes into the argument; arguing, as I have said, for -his own Theory.</p> - -<p>"Tell me," he says, "do you not think there is an Idea of Likeness, -and an Idea of Unlikeness? And that everything partakes of -these Ideas? The things which partake of Unlikeness are unlike. -If all things partake of both Ideas, they are both like and unlike; -and where is the wonder? (§ 7.) If you could show that Likeness -itself was Unlikeness, it would be a prodigy; but if things which -partake of these opposites, have both the opposite qualities, it -appears to me, Zeno, to involve no absurdity.</p> - -<p>"So if Oneness itself were to be shown to be Maniness" (I hope -I may use this word, rather than <i>multiplicity</i>) "I should be surprised; -but if any one say that <i>I</i> am at the same time one and many, -where is the wonder? For I partake of maniness: my right side is -different from my left side, my upper from my under parts. But I -also partake of Oneness, for I am here One of us seven. So that -both are true. And so if any one say that stocks and stones, and -the like, are both one and many,—not saying that Oneness is -Maniness, nor Maniness Oneness, he says nothing wonderful: he -says what all will allow. (§ 8.) If then, as I said before, any one -should take separately the Ideas or Essence of Things, as Likeness -and Unlikeness, Maniness and Oneness, Rest and Motion, and the -like, and then should show that these can mix and separate again, -I should be wonderfully surprised, O Zeno: for I reckon that I -have tolerably well made myself master of these subjects<a name="FNanchor_323" id="FNanchor_323"></a><a href="#Footnote_323" class="fnanchor">[323]</a>. I -should be much more surprised if any one could show me this contradiction -involved in the Ideas themselves; in the object of the -Reason, as well as in Visible objects."</p> - -<p>It may be remarked that Socrates delivers all this argumentation -with the repetitions which it involves, and the vehemence of<span class="pagenum" id="Page_414">414</span> -its manner, without waiting for a reply to any of his interrogations; -instead of making every step the result of a concession of his -opponent, as is the case in the Dialogues where he is represented -as triumphant. Every reader of Plato will recollect also that in -those Dialogues, the triumph of temper on the part of Socrates is -represented as still more remarkable than the triumph of argument. -No vehemence or rudeness on the part of his adversaries prevents -his calmly following his reasoning; and he parries coarseness by -compliment. Now in this Dialogue, it is remarkable that this kind -of triumph is given to the adversaries of Socrates. "When Socrates -had thus delivered himself," says Pythodorus, the narrator of the -conversation, "we thought that Parmenides and Zeno would both -be angry. But it was not so. They bestowed entire attention -upon him, and often looked at each other, and smiled, as in -admiration of Socrates. And when he had ended, Parmenides -said: 'O Socrates, what an admirable person you are, for the -earnestness with which you reason! Tell me then, Do you then -believe the doctrine to which you have been referring;—that there -are certain Ideas, existing independent of Things; and that there -are, separate from the Ideas, Things which partake of them? -And do you think that there is an Idea of Likeness besides the -likeness which we have; and a Oneness and a Maniness, and the -like? And an Idea of the Right, and the Good, and the Fair, and -of other such qualities?'" Socrates says that he does hold this; -Parmenides then asks him, how far he carries this doctrine of -Ideas, and propounds to him the difficulties which I have already -stated; and when Socrates is unable to answer him, lets him off -in the kind but patronizing way which I have already described.</p> - -<p>To me, comparing this with the intellectual and moral attitude -of Socrates in the most dramatic of the other Platonic Dialogues, -it is inconceivable, that this representation of Socrates should be -Plato's. It is just what Zeno would have written, if he had -wished to bestow upon his master Parmenides the calm dignity and -irresistible argument which Plato assigns to Socrates. And this -character is kept up to the end of the Dialogue. When Socrates -(§ 19) has acknowledged that he is at loss which way to turn for -his philosophy, Parmenides undertakes, though with kind words, -to explain to him by what fundamental error in the course of his -speculative habits he has been misled. He says; "You try to -make a complete Theory of Ideas, before you have gone through -a proper intellectual discipline. The impulse which urges you to -such speculations is admirable—is divine. But you must exercise -yourself in reasoning which many think trifling, while you are yet<span class="pagenum" id="Page_415">415</span> -young; if you do not, the truth will elude your grasp." Socrates -asks submissively what is the course of such discipline: Parmenides -replies, "The course pointed out by Zeno, as you have heard." -And then, gives him some instructions in what manner he is to test -any proposed Theory. Socrates is frightened at the laboriousness -and obscurity of the process. He says, "You tell me, Parmenides, -of an overwhelming course of study; and I do not well comprehend -it. Give me an example of such an examination of a Theory." -"It is too great a labour," says he, "for one so old as I am." -"Well then, you, Zeno," says Socrates, "will you not give us such -an example?" Zeno answers, smiling, that they had better get it -from Parmenides himself; and joins in the petition of Socrates -to him, that he will instruct them. All the company unite in the -request. Parmenides compares himself to an aged racehorse, -brought to the course after long disuse, and trembling at the risk; -but finally consents. And as an example of a Theory to be -examined, takes his own Doctrine, that All Things are One, -carrying on the Dialogue thenceforth, not with Socrates, but with -Aristoteles (not the Stagirite, but afterwards one of the Thirty), -whom he chooses as a younger and more manageable respondent.</p> - -<p>The discussion of this Doctrine is of a very subtle kind, and -it would be difficult to make it intelligible to a modern reader. -Nor is it necessary for my purpose to attempt to do so. It is plain -that the discussion is intended seriously, as an example of true -philosophy; and each step of the process is represented as irresistible. -The Respondent has nothing to say but <i>Yes</i>; or <i>No</i>; <i>How -so</i>? <i>Certainly</i>; <i>It does appear</i>; <i>It does not appear</i>. The discussion -is carried to a much greater length than all the rest of the -Dialogue; and the result of the reasoning is summed up by Parmenides -thus: "If One exist, it is Nothing. Whether One exist -or do not exist, both It and Other Things both with regard to -Themselves and to Each other, All and Everyway are and are not, -appear and appear not." And this also is fully assented to; and -so the Dialogue ends.</p> - -<p>I shall not pretend to explain the Doctrines there examined -that One exists, or One does not exist, nor to trace their consequences. -But these were Formulæ, as familiar in the Eleatic -school, as Ideas in the Platonic; and were undoubtedly regarded -by the Megaric contemporaries of Plato as quite worthy of being -discussed, after the Theory of Ideas had been overthrown. This, -accordingly, appears to be the purport of the Dialogue; and it is -pursued, as we see, without any bitterness toward Socrates or his -disciples; but with a persuasion that they were poor philosophers, -conceited talkers, and weak disputants.</p> - -<p><span class="pagenum" id="Page_416">416</span></p> - -<p>The external circumstances of the Dialogue tend, I conceive, -to confirm this opinion, that it is not Plato's. The Dialogue -begins, as the <i>Republic</i> begins, with the mention of a Cephalus, -and two brothers, Glaucon and Adimantus. But this Cephalus -is not the old man of the Piræus, of whom we have so charming a -picture in the opening of the <i>Republic</i>. He is from Clazomenæ, -and tells us that his fellow-citizens are great lovers of philosophy; -a trait of their character which does not appear elsewhere. Even -the brothers Glaucon and Adimantus are not the two brothers -of Plato who conduct the Dialogue in the later books of the -<i>Republic</i>: so at least Ast argues, who holds the genuineness of the -Dialogue. This Glaucon and Adimantus are most wantonly introduced; -for the sole office they have, is to say that they have -a half-brother Antiphon, by a second marriage of their mother. -No such half-brother of Plato, and no such marriage of his mother, -are noticed in other remains of antiquity. Antiphon is represented -as having been the friend of Pythodorus, who was the host of -Parmenides and Zeno, as we have seen. And Antiphon, having -often heard from Pythodorus the account of the conversation of -his guests with Socrates, retained it in his memory, or in his -tablets, so as to be able to give the full report of it which we have -in the Dialogue <i>Parmenides</i><a name="FNanchor_324" id="FNanchor_324"></a><a href="#Footnote_324" class="fnanchor">[324]</a>. To me, all this looks like a clumsy -imitation of the Introductions to the Platonic Dialogues.</p> - -<p>I say nothing of the chronological difficulties which arise from -bringing Parmenides and Socrates together, though they are -considerable; for they have been explained more or less satisfactorily; -and certainly in the <i>Theætetus</i>, Socrates is represented as -saying that he when very young had seen Parmenides who was -very old<a name="FNanchor_325" id="FNanchor_325"></a><a href="#Footnote_325" class="fnanchor">[325]</a>. Athenæus, however<a name="FNanchor_326" id="FNanchor_326"></a><a href="#Footnote_326" class="fnanchor">[326]</a>, reckons this among Plato's -fictions. Schleiermacher gives up the identification and relation -of the persons mentioned in the Introduction as an unmanageable -story.</p> - -<p>I may add that I believe Cicero, who refers to so many of Plato's -Dialogues, nowhere refers to the <i>Parmenides</i>. Athenæus does -refer to it; and in doing so blames Plato for his coarse imputations -on Zeno and Parmenides. According to our view, these are -hostile attempts to ascribe rudeness to Socrates or to Plato. Stallbaum -acknowledges that Aristotle nowhere refers to this Dialogue.</p> -<hr class="chap" /> - -<p><span class="pagenum" id="Page_417">417</span></p> - - - -<h3><a name="Appendix_B" id="Appendix_B"></a><span class="smcap">Appendix B.</span><br /> - -ON PLATO'S SURVEY OF THE SCIENCES.</h3> - -<p class="center">(<i>Cam. Phil. Soc.</i> <span class="smcap">April 23, 1855.</span>)</p> - - -<p class="drop-cap"><span class="smcap">A survey</span> by Plato of the state of the Sciences, as existing in -his time, may be regarded as hardly less interesting than Francis -Bacon's Review of the condition of the Sciences of <i>his</i> time, contained -in the <i>Advancement of Learning</i>. Such a survey we have, in -the seventh book of Plato's <i>Republic</i>; and it will be instructive to -examine what the Sciences then were, and what Plato aspired to -have them become; aiding ourselves by the light afforded by the -subsequent history of Science.</p> - -<p>In the first place, it is interesting to note, in the two writers, -Plato and Bacon, the same deep conviction that the large and -profound philosophy which they recommended, had not, in their -judgment, been pursued in an adequate and worthy manner, by -those who had pursued it at all. The reader of Bacon will -recollect the passage in the <i>Novum Organon</i> (Lib. I. Aphorism 80) -where he speaks with indignation of the way in which philosophy -had been degraded and perverted, by being applied as a mere instrument -of utility or of early education: "So that the great -mother of the Sciences is thrust down with indignity to the offices -of a handmaid;—is made to minister to the labours of medicine or -mathematics; or again, to give the first preparatory tinge to the -immature minds of youth<a name="FNanchor_327" id="FNanchor_327"></a><a href="#Footnote_327" class="fnanchor">[327]</a>."</p> - -<p><span class="pagenum" id="Page_418">418</span></p> - -<p>In the like spirit, Plato says (<i>Rep.</i> <span class="smcap">VI.</span> § 11, Bekker's ed.):</p> - -<p>"Observe how boldly and fearlessly I set about my explanation of -my assertion that philosophers ought to rule the world. For I -begin by saying, that the State must begin to treat the study of -philosophy in a way opposite to that now practised. Now, those -who meddle at all with this study are put upon it when they are -children, between the lessons which they receive in the farm-yard -and in the shop<a name="FNanchor_328" id="FNanchor_328"></a><a href="#Footnote_328" class="fnanchor">[328]</a>; and as soon as they have been introduced to the -hardest part of the subject, are taken off from it, even those who -get the most of philosophy. By the hardest part, I mean, the -discussion of principles—Dialectic<a name="FNanchor_329" id="FNanchor_329"></a><a href="#Footnote_329" class="fnanchor">[329]</a>. And in their succeeding years, -if they are willing to listen to a few lectures of those who make -philosophy their business, they think they have done great things, -as if it were something foreign to the business of life. And as -they advance towards old age, with a very few exceptions, philosophy -in them is extinguished: extinguished far more completely than the -Heraclitean sun, for theirs is not lighted up again, as that is every -morning:" alluding to the opinion which was propounded, by way of -carrying the doctrine of the <i>unfixity</i> of sensible objects to an extreme; -that the Sun is extinguished every night and lighted again -in the morning. In opposition to this practice, Plato holds that -philosophy should be the especial employment of men's minds when -their bodily strength fails.</p> - -<p>What Plato means by <i>Dialectic</i>, which he, in the next Book, -calls the highest part of philosophy, and which is, I think, what he -here means by the hardest part of philosophy, I may hereafter -consider: but at present I wish to pass in review the Sciences -which he speaks of, as leading the way to that highest study. These -Sciences are Arithmetic, Plane Geometry, Solid Geometry, Astronomy -and Harmonics.</p> - -<p>The view in which Plato here regards the Sciences is, as the -instruments of that culture of the philosophical spirit which is to -make the philosopher the fit and natural ruler of the perfect State—the -Platonic Polity. It is held that to answer this purpose, the -mind must be instructed in something more stable than the knowledge -supplied by the senses;—a knowledge of objects which are -constantly changing, and which therefore can be no real permanent -Knowledge, but only Opinion. The real and permanent Knowledge -which we thus require is to be found in certain sciences, -which deal with <i>truths necessary and universal</i>, as we should now<span class="pagenum" id="Page_419">419</span> -describe them: and which therefore are, in Plato's language, a -knowledge of that which really <i>is</i><a name="FNanchor_330" id="FNanchor_330"></a><a href="#Footnote_330" class="fnanchor">[330]</a>.</p> - -<p>This is the object of the Sciences of which Plato speaks. And -hence, when he introduces Arithmetic, as the first of the Sciences which -are to be employed in this mental discipline, he adds (<span class="smcap">VII.</span> § 8) that -it must be not mere common Arithmetic, but a science which leads -to speculative truths<a name="FNanchor_331" id="FNanchor_331"></a><a href="#Footnote_331" class="fnanchor">[331]</a>, seen by Intuition<a name="FNanchor_332" id="FNanchor_332"></a><a href="#Footnote_332" class="fnanchor">[332]</a>; not an Arithmetic which -is studied for the sake of buying and selling, as among tradesmen -and shopkeepers, but for the sake of pure and real Science<a name="FNanchor_333" id="FNanchor_333"></a><a href="#Footnote_333" class="fnanchor">[333]</a>.</p> - -<p>I shall not dwell upon the details with which he illustrates this -view, but proceed to the other Sciences which he mentions.</p> - -<p>Geometry is then spoken of, as obviously the next Science in -order; and it is asserted that it really does answer the required -condition of drawing the mind from visible, mutable phenomena to -a permanent reality. Geometers indeed speak of their visible diagrams, -as if their problems were certain practical processes; to -erect a perpendicular; to construct a square: and the like. But -this language, though necessary, is really absurd. The figures are -mere aids to their reasonings. Their knowledge is really a knowledge -not of visible objects, but of permanent realities: and thus, -Geometry is one of the helps by which the mind may be drawn to -Truth; by which the philosophical spirit may be formed, which -looks upwards instead of downwards.</p> - -<p>Astronomy is suggested as the Science next in order, but Socrates, -the leader of the dialogue, remarks that there is an intermediate -Science first to be considered. Geometry treats of plane figures; -Astronomy treats of solids in motion, that is, of spheres in motion; -for the astronomy of Plato's time was mainly the doctrine of -the sphere. But before treating of solids in motion, we must -have a science which treats of solids simply. After taking space of -two dimensions, we must take space of three dimensions, length, -breadth and depth, as in cubes and the like<a name="FNanchor_334" id="FNanchor_334"></a><a href="#Footnote_334" class="fnanchor">[334]</a>. But such a Science, -it is remarked, has not yet been discovered. Plato "notes as<span class="pagenum" id="Page_420">420</span> -deficient" this branch of knowledge; to use the expression employed -by Bacon on the like occasions in his Review. Plato goes on to -say, that the cultivators of such a science have not received due encouragement; -and that though scorned and starved by the public, -and not recommended by any obvious utility, it has still made great -progress, in virtue of its own attractiveness.</p> - -<p>In fact, researches in Solid Geometry had been pursued with -great zeal by Plato and his friends, and with remarkable success. -The five Regular Solids, the Tetrahedron or Pyramid, Cube, Octahedron, -Dodecahedron and Icosahedron, had been discovered; and -the curious theorem, that of Regular Solids there can be just so -many, these and no others, was known. The doctrine of these -Solids was already applied in a way, fanciful and arbitrary, no -doubt, but ingenious and lively, to the theory of the Universe. In -the <i>Timæus</i>, the elements have these forms assigned to them respectively. -Earth has the Cube: Fire has the Pyramid: Water has -the Octahedron: Air has the Icosahedron: and the Dodecahedron -is the plan of the Universe itself. This application of the doctrine -of the Regular Solids shows that the knowledge of those figures -was already established; and that Plato had a right to speak of -Solid Geometry as a real and interesting Science. And that this -subject was so recondite and profound,—that these five Regular -Solids had so little application in the geometry which has a bearing -on man's ordinary thoughts and actions,—made it all the more -natural for Plato to suppose that these solids had a bearing on the -constitution of the Universe; and we shall find that such a belief -in later times found a ready acceptance in the minds of mathematicians -who followed in the Platonic line of speculation.</p> - -<p>Plato next proceeds to consider Astronomy; and here we have -an amusing touch of philosophical drama. Glaucon, the hearer and -pupil in the Dialogue, is desirous of showing that he has profited -by what his instructor had said about the real uses of Science. He -says Astronomy is a very good branch of education. It is such a -very useful science for seamen and husbandmen and the like. -Socrates says, with a smile, as we may suppose: "You are very -amusing with your zeal for utility. I suppose you are afraid of -being condemned by the good people of Athens for diffusing Useless -Knowledge." A little afterwards Glaucon tries to do better, -but still with no great success. He says, "You blamed me for -praising Astronomy awkwardly: but now I will follow your lead. -Astronomy is one of the sciences which you require, because it -makes men's minds look upwards, and study things above. Any one -can see that." "Well," says Socrates, "perhaps any one can see it<span class="pagenum" id="Page_421">421</span> -except me—I cannot see it." Glaucon is surprised, but Socrates -goes on: "Your notice of 'the study of things above' is certainly -a very magnificent one. You seem to think that if a man bends his -head back and looks at the ceiling he 'looks upwards' with his -mind as well as his eyes. You may be right and I may be wrong: -but I have no notion of any science which makes the <i>mind</i> look -upwards, except a science which is about the permanent and the -invisible. It makes no difference, as to that matter, whether a man -gapes and looks up or shuts his mouth and looks down. If a man -merely look up and stare at sensible objects, his mind does not look -upwards, even if he were to pursue his studies swimming on his back -in the sea."</p> - -<p>The Astronomy, then, which merely looks at phenomena does -not satisfy Plato. He wants something more. What is it? as -Glaucon very naturally asks.</p> - -<p>Plato then describes Astronomy as a real science (§ 11). "The -variegated adornments which appear in the sky, the visible luminaries, -we must judge to be the most beautiful and the most perfect -things of their kind: but since they are mere visible figures, we -must suppose them to be far inferior to the true objects; namely, -those spheres which, with their real proportions of quickness and -slowness, their real number, their real figures, revolve and carry -luminaries in their revolutions. These objects are to be apprehended -by reason and mental conception, not by vision." And he then -goes on to say that the varied figures which the skies present to the -eye are to be used as <i>diagrams</i> to assist the study of that higher -truth; just as if any one were to study geometry by means of beautiful -diagrams constructed by Dædalus or any other consummate -artist.</p> - -<p>Here then, Plato points to a kind of astronomical science which -goes beyond the mere arrangement of phenomena: an astronomy -which, it would seem, did not exist at the time when he wrote. It -is natural to inquire, whether we can determine more precisely -what kind of astronomical science he meant, and whether such -science has been brought into existence since his time.</p> - -<p>He gives us some further features of the philosophical astronomy -which he requires. "As you do not expect to find in the most -exquisite geometrical diagrams the true evidence of quantities being -equal, or double, or in any other relation: so the true astronomer -will not think that the proportion of the day to the month, or the -month to the year, and the like, are real and immutable things. -He will seek a deeper truth than these. We must treat Astronomy, -like Geometry, as a series of problems suggested by visible things.<span class="pagenum" id="Page_422">422</span> -We must apply the intelligent portion of our mind to the subject."</p> - -<p>Here we really come in view of a class of problems which astronomical -speculators at certain periods have proposed to themselves. -What is the real ground of the proportion of the day to the month, -and of the month to the year, I do not know that any writer of -great name has tried to determine: but to ask the reason of these -proportions, namely, that of the revolution of the earth on its axis, -of the moon in its orbit, and of the earth in its orbit, are questions -just of the same kind as to ask the reason of the proportion of -the revolutions of the planets in their orbits, and of the proportion -of the orbits themselves. Now who has attempted to assign such -reasons?</p> - -<p>Of course we shall answer, Kepler: not so much in the Laws of -the Planetary motions which bear his name, as in the Law which -at an earlier period he thought he had discovered, determining the -proportion of the distances of the several Planets from the Sun. -And, curiously enough, this solution of a problem which we may -conceive Plato to have had in his mind, Kepler gave by means of -the Five Regular Solids which Plato had brought into notice, and -had employed in his theory of the Universe given in the <i>Timæus</i>.</p> - -<p>Kepler's speculations on the subject just mentioned were given to -the world in the <i>Mysterium Cosmographicum</i> published in 1596. In -his Preface, he says "In the beginning of the year 1595 I brooded -with the whole energy of my mind on the subject of the Copernican -system. There were three things in particular of which I pertinaciously -sought the causes; why they are not other than they are: the -number, the size, and the motion of the orbits." We see how -strongly he had his mind impressed with the same thought which -Plato had so confidently uttered: that there must be some reason -for those proportions in the scheme of the Universe which appear -casual and vague. He was confident at this period that he had -solved two of the three questions which haunted him;—that he -could account for the number and the size of the planetary orbits. -His account was given in this way.—"The orbit of the Earth is a -circle; round the sphere to which this circle belongs describe a -dodecahedron; the sphere including this will give the orbit of -Mars. Round Mars inscribe a tetrahedron; the circle including -this will be the orbit of Jupiter. Describe a cube round Jupiter's -orbit; the circle including this will be the orbit of Saturn. Now -inscribe in the Earth's orbit an icosahedron: the circle inscribed in -it will be the orbit of Venus. Inscribe an octahedron in the orbit -of Venus; the circle inscribed in it will be Mercury's orbit. This is<span class="pagenum" id="Page_423">423</span> -the reason of the number of the planets;" and also of the magnitudes -of their orbits.</p> - -<p>These proportions were only approximations; and the Rule thus -asserted has been shown to be unfounded, by the discovery of new -Planets. This Law of Kepler has been repudiated by succeeding -Astronomers. So far, then, the Astronomy which Plato requires -as a part of true philosophy has not been brought into being. But -are we thence to conclude that the demand for such a kind of -Astronomy was a mere Platonic imagination?—was a mistake -which more recent and sounder views have corrected? We can -hardly venture to say that. For the questions which Kepler thus -asked, and which he answered by the assertion of this erroneous -Law, are questions of exactly the same kind as those which he asked -and answered by means of the true Laws which still fasten his -name upon one of the epochs of astronomical history. If he was -wrong in assigning reasons for the number and size of the planetary -orbits, he was right in assigning a reason for the proportion of the -motions. This he did in the <i>Harmonice Mundi</i>, published in 1619: -where he established that the squares of the periodic times of the -different Planets are as the cubes of their mean distances from the -central Sun. Of this discovery he speaks with a natural exultation, -which succeeding astronomers have thought well founded. He -says: "What I prophesied two and twenty years ago as soon as I -had discovered the five solids among the heavenly bodies; what I -firmly believed before I had seen the <i>Harmonics</i> of Ptolemy; what -I promised my friends in the title of this book (<i>On the perfect Harmony -of the celestial motions</i>), which I named before I was sure of -my discovery; what sixteen years ago I regarded as a thing to be -sought; that for which I joined Tycho Brahe, for which I settled in -Prague, for which I devoted the best part of my life to astronomical -contemplations; at length I have brought to light, and have recognized -its truth beyond my most sanguine expectations." (<i>Harm. -Mundi</i>, Lib. <span class="smcap">V.</span>)</p> - -<p>Thus the Platonic notion, of an Astronomy which deals with -doctrines of a more exact and determinate kind than the obvious -relations of phænomena, may be found to tend either to error or to -truth. Such aspirations point equally to the five regular solids -which Kepler imagined as determining the planetary orbits, and to -the Laws of Kepler in which Newton detected the effect of universal -gravitation. The realities which Plato looked for, as something -incomparably more real than the visible luminaries, are found, when -we find geometrical figures, epicycles and eccentrics, laws of motion<span class="pagenum" id="Page_424">424</span> -and laws of force, which explain the appearances. His Realities are -Theories which account for the Phenomena, Ideas which connect -the Facts.</p> - -<p>But, is Plato right in holding that such Realities as these are -<i>more real</i> than the Phenomena, and constitute an Astronomy of a -higher kind than that of mere Appearances? To this we shall, of -course, reply that Theories and Facts have each their reality, but -that these are realities of different kinds. Kepler's Laws are as real -as day and night; the force of gravity tending to the Sun is as real -as the Sun; but not more so. True Theories and Facts are equally -real, for true Theories <i>are</i> Facts, and Facts are familiar Theories. -Astronomy is, as Plato says, a series of Problems suggested by visible -Things; and the Thoughts in our own minds which bring the -solutions of these Problems, have a reality in the Things which suggest -them.</p> - -<p>But if we try, as Plato does, to separate and oppose to each other -the Astronomy of Appearances and the Astronomy of Theories, we -attempt that which is impossible. There are no Phenomena which -do not exhibit some Law; no Law can be conceived without Phenomena. -The heavens offer a series of Problems; but however many -of these Problems we solve, there remain still innumerable of them -unsolved; and these unsolved Problems have solutions, and are not -different in kind from those of which the extant solution is most -complete.</p> - -<p>Nor can we justly distinguish, with Plato, Astronomy into transient -appearances and permanent truths. The theories of Astronomy -are permanent, and are manifested in a series of changes: but -the change is perpetual just <i>because</i> the theory is permanent. The -perpetual change <i>is</i> the permanent theory. The perpetual changes -in the positions and movements of the planets, for instance, manifest -the permanent machinery: the machinery of cycles and epicycles, as -Plato would have said, and as Copernicus would have agreed; while -Kepler, with a profound admiration for both, would have asserted -that the motions might be represented by ellipses, more exactly, if -not more truly. The cycles and epicycles, or the ellipses, are as -real as space and time, <i>in</i> which the motions take place. But we -cannot justly say that space and time and motion are more real than -the bodies which move in space and time, or than the appearances -which these bodies present.</p> - -<p>Thus Plato, with his tendency to exalt Ideas above Facts,—to find -a Reality which is more real than Phenomena,—to take hold of a -permanent Truth which is more true than truths of observation,—<span class="pagenum" id="Page_425">425</span> -attempts what is impossible. He tries to separate the poles of the -Fundamental Antithesis, which, however antithetical, are inseparable.</p> - -<p>At the same time, we must recollect that this tendency to find a -Reality which is something beyond appearance, a permanence which -is involved in the changes, is the genuine spring of scientific discovery. -Such a tendency has been the cause of all the astronomical -science which we possess. It appeared in Plato himself, in Hipparchus, -in Ptolemy, in Copernicus, and most eminently in Kepler; and -in him perhaps in a manner more accordant with Plato's aspirations -when he found the five Regular Solids in the Universe, than when -he found there the Conic Sections which determine the form of the -planetary orbits. The pursuit of this tendency has been the source -of the mighty and successful labours of succeeding astronomers: and -the anticipations of Plato on this head were more true than he himself -could have conceived.</p> - -<p>When the above view of the nature of true astronomy has been -proposed, Glaucon says:</p> - -<p>"That would be a task much more laborious than the astronomy -now cultivated." Socrates replies: "I believe so: and such tasks -must be undertaken, if our researches are to be good for anything."</p> - -<p>After Astronomy, there comes under review another Science, -which is treated in the same manner. It is presented as one of the -Sciences which deal with real abstract truth; and which are therefore -suited to that development of the philosophic insight into -the highest truth, which is here Plato's main object. This Science -is <i>Harmonics</i>, the doctrine of the mathematical relations of musical -sounds. Perhaps it may be more difficult to explain to a general -audience, Plato's views on this than on the previous subjects: for -though Harmonics is still acknowledged as a Science including the -mathematical truths to which Plato here refers, these truths are less -generally known than those of geometry or astronomy. Pythagoras -is reported to have been the discoverer of the cardinal proposition in -this Mathematics of Music:—namely, that the musical notes which -the ear recognizes as having that definite and harmonious relation -which we call an <i>octave</i>, a <i>fifth</i>, a <i>fourth</i>, a <i>third</i>, have also, in some -way or other, the numerical relation of 2 to 1, 3 to 2, 4 to 3, 5 to 4. -I say "some way or other," because the statements of ancient writers -on this subject are physically inexact, but are right in the essential -point, that those simple numerical ratios are characteristic of -the most marked harmonic relations. The numerical ratios really -represent the rate of vibration of the air when those harmonics<span class="pagenum" id="Page_426">426</span> -are produced. This perhaps Plato did not know: but he knew -or assumed that those numerical ratios were cardinal truths in harmony: -and he conceived that the exactness of the ratios rested on -grounds deeper and more intellectual than any testimony which the -ear could give. This is the main point in his mode of applying the -subject, which will be best understood by translating (with some -abridgement) what he says. Socrates proceeds:</p> - -<p>(§ 11 near the end.) "Motion appears in many aspects. It -would take a very wise man to enumerate them all: but there are -two obvious kinds. One which appears in astronomy, (the revolutions -of the heavenly bodies,) and another which is the echo of that<a name="FNanchor_335" id="FNanchor_335"></a><a href="#Footnote_335" class="fnanchor">[335]</a>. -As the eyes are made for Astronomy, so are the ears made for the -motion which produces Harmony<a name="FNanchor_336" id="FNanchor_336"></a><a href="#Footnote_336" class="fnanchor">[336]</a>: and thus we have two sister -sciences, as the Pythagoreans teach, and we assent.</p> - -<p>(§ 12.) "To avoid unnecessary labour, let us first learn what -<i>they</i> can tell us, and see whether anything is to be added to it; -retaining our own view on such subjects: namely this:—that those -whose education we are to superintend—real philosophers—are -never to learn any imperfect truths:—anything which does not tend -to that point (exact and permanent truth) to which all our knowledge -ought to tend, as we said concerning astronomy. Now -those who cultivate music take a very different course from this. -You may see them taking immense pains in measuring musical notes -and intervals by the ear, as the astronomers measure the heavenly -motions by the eye.</p> - -<p>"Yes, says Glaucon, they apply their ears close to the instrument, -as if they could catch the note by getting near to it, and talk of -some kind of recurrences<a name="FNanchor_337" id="FNanchor_337"></a><a href="#Footnote_337" class="fnanchor">[337]</a>. Some say they can distinguish an -interval, and that this is the smallest possible interval, by which -others are to be measured; while others say that the two notes are -identical: both parties alike judging by the ear, not by the -intellect.</p> - -<p>"You mean, says Socrates, those fine musicians who torture their -notes, and screw their pegs, and pinch their strings, and speak of -the resulting sounds in grand terms of art. We will leave them, -and address our inquiries to our other teachers, the Pythagoreans."</p> - -<p>The expressions about the small interval in Glaucon's speech -appear to me to refer to a curious question, which we know was -discussed among the Greek mathematicians. If we take a keyed<span class="pagenum" id="Page_427">427</span> -instrument, and ascend from a key note by two <i>octaves</i> and a <i>third</i>, -(say from <i>A</i><sub>1</sub> to <i>C</i><sub>3</sub>) we arrive at the <i>same nominal note</i>, as if we -ascend four times by a <i>fifth</i> (<i>A</i><sub>1</sub> to <i>E</i><sub>1</sub>, <i>E</i><sub>1</sub> to <i>B</i><sub>2</sub>, <i>B</i><sub>2</sub> to <i>F</i><sub>2</sub>, <i>F</i><sub>2</sub> to <i>C</i><sub>3</sub>). -Hence one party might call this the <i>same</i> note. But if the Octaves, -Fifths, and Third be perfectly true intervals, the notes -arrived at in the two ways will not be really the same. (In the one -case, the note is ½ × ½ × ⅘; in the other ⅔ × ⅔ × ⅔ × ⅔; which are ⅕ -and 16/81, or in the ratio of 81 to 80). This small interval by which -the two notes really differ, the Greeks called a <i>Comma</i>, and it was -the smallest musical interval which they recognized. Plato disdains -to see anything important in this controversy; though the controversy -itself is really a curious proof of his doctrine, that there -is a mathematical truth in Harmony, higher than instrumental -exactness can reach. He goes on to say:</p> - -<p>"The musical teachers are defective in the same way as the -astronomical. They do indeed seek numbers in the harmonic notes, -which the ear perceives: but they do not ascend from them to the -Problem, What are harmonic numbers and what are not, and what -is the reason of each<a name="FNanchor_338" id="FNanchor_338"></a><a href="#Footnote_338" class="fnanchor">[338]</a>?" "That", says Glaucon, "would be a sublime -inquiry."</p> - -<p>Have we in Harmonics, as in Astronomy, anything in the succeeding -History of the Science which illustrates the tendency of Plato's -thoughts, and the value of such a tendency?</p> - -<p>It is plain that the tendency was of the same nature as that which -induced Kepler to call his work on Astronomy <i>Harmonice Mundi</i>; -and which led to many of the speculations of that work, in which -harmonical are mixed with geometrical doctrines. And if we are -disposed to judge severely of such speculations, as too fanciful for -sound philosophy, we may recollect that Newton himself seems to -have been willing to find an analogy between harmonic numbers -and the different coloured spaces in the spectrum.</p> - -<p>But I will say frankly, that I do not believe there really exists -any harmonical relation in either of these cases. Nor can the problem -proposed by Plato be considered as having been solved since his -time, any further than the recurrence of vibrations, when their ratios -are so simple, may be easily conceived as affecting the ear in a -peculiar manner. The imperfection of musical scales, which the -<i>comma</i> indicates, has not been removed; but we may say that, in -the case of this problem, as in the other ultimate Platonic problems, -the duplication of the cube and the quadrature of the circle, the<span class="pagenum" id="Page_428">428</span> -impossibility of a solution has been already established. The problem -of a perfect musical scale is impossible, because no power of 2 -can be equal to a power of 3; and if we further take the multiplier -5, of course it also cannot bring about an exact equality. This impossibility -of a perfect scale being recognized, the practical problem is -what is the system of <i>temperament</i> which will make the scale best -suited for musical purposes; and this problem has been very fully -discussed by modern writers.</p> - -<hr class="chap" /> - -<p><span class="pagenum" id="Page_429">429</span></p> - - - - -<h3><a name="Appendix_BB" id="Appendix_BB"></a><span class="smcap">Appendix BB.</span><br /> - -ON PLATO'S NOTION OF DIALECTIC.</h3> - -<p class="center">(<i>Cam. Phil. Soc.</i> <span class="smcap">May 7, 1855</span>.)</p> - - -<p class="drop-cap"><span class="smcap">The</span> survey of the sciences, arithmetic, plane geometry, solid -geometry, astronomy and harmonics—which is contained in the -seventh Book of the Republic (§ 6-12), and which has been discussed -in the preceding paper, represents them as instruments in -an education, of which the end is something much higher—as steps -in a progression which is to go further. "Do you not know," says -Socrates (§ 12), "that all this is merely a prelude to the strain -which we have to learn?" And what that strain is, he forthwith -proceeds to indicate. "That these sciences do not suffice, you -must be aware: for—those who are masters of such sciences—do -they seem to you to be good in dialectic? δεινοὶ διαλεκτικοὶ -εἷναι;"</p> - -<p>"In truth, says Glaucon, they are not, with very few exceptions, -so far as I have fallen in with them."</p> - -<p>"And yet, said I, if persons cannot give and receive a reason, -they cannot attain that knowledge which, as we have said, men -ought to have."</p> - -<p>Here it is evident that "to give and to receive a reason," is a -phrase employed as coinciding, in a general way at least, with being -"good in dialectic;" and accordingly, this is soon after asserted in -another form, the verb being now used instead of the adjective. -"It is dialectic discussion τὸ διαλέγεσθαι, which executes the -strain which we have been preparing." It is further said that it is -a progress to clear intellectual light, which corresponds to the progress -of bodily vision in proceeding from the darkened cave described -in the beginning of the Book to the light of day. This -progress, it is added, of course you call <i>Dialectic</i> διαλεκτικήν.</p> - -<p>Plato further says, that other sciences cannot properly be called -sciences. They begin from certain assumptions, and give us only -the consequences which follow from reasoning on such assumptions. -But these assumptions they cannot prove. To do so is not in the -province of each science. It belongs to a higher science: to the<span class="pagenum" id="Page_430">430</span> -science of Real Existences. You call the man Dialectical, who requires -a reason of the essence of each thing<a name="FNanchor_339" id="FNanchor_339"></a><a href="#Footnote_339" class="fnanchor">[339]</a>.</p> - -<p>And as Dialectic gives an account of other real existences, so -does it of that most important reality, the true guide of Life and of -Philosophy, the Real Good. He who cannot follow this through -all the windings of the battle of Life, knows nothing to any purpose. -And thus Dialectic is the pinnacle, the top stone of the -edifice of the sciences<a name="FNanchor_340" id="FNanchor_340"></a><a href="#Footnote_340" class="fnanchor">[340]</a>.</p> - -<p>Dialectic is here defined or described by Plato according to the -<i>subject</i> with which it treats, and the <i>object</i> with which it is to be -pursued: but in other parts of the Platonic Dialogues, Dialectic -appears rather to imply a certain <i>method</i> of investigation;—to describe -the <i>form</i> rather than the <i>matter</i> of discussion; and it will -perhaps be worth while to compare these different accounts of -Dialectic.</p> - -<p>(<i>Phædrus.</i>) One of the cardinal passages on this Point is in the -Phædrus, and may be briefly quoted. Phædrus, in the Dialogue -which bears his name, appears at first as an admirer of Lysias, a -celebrated writer of orations, the contemporary of Plato. In order -to expose this writer's style of composition as frigid and shallow, a -specimen of it is given, and Socrates not only criticises this, but -delivers, as rival compositions, two discourses on the same subject. -Of these discourses, given as the inspiration of the moment, the -first is animated and vigorous; the second goes still further, and -clothes its meaning in a gorgeous dress of poetical and mythical -images. Phædrus acknowledges that his favourite is outshone; -and Socrates then proceeds to point out that the real superiority of his -own discourse consists in its having a dialectical structure, beneath -its outward aspect of imagery and enthusiasm. He says: (§ 109, -Bekker. It is to be remembered that the subject of all the discourses -was <i>Love</i>, under certain supposed conditions.)</p> - -<p>"The rest of the performance may be taken as play: but there -were, in what was thus thrown out by a random impulse, two -features, of which, if any one could reduce the effect to an art, -it would be a very agreeable and useful task.</p> - -<p>"What are they? Phædrus asks.</p> - -<p>"In the first place, Socrates replies, the taking a connected view -of the scattered elements of a subject, so as to bring them into one<span class="pagenum" id="Page_431">431</span> -Idea; and thus to give a definition of the subject, so as to make it -clear what we are speaking of; as was then done in regard to <i>Love</i>. -A definition was given of it, what it is: whether the definition -was good or bad, at any rate there was a definition. And hence, in -what followed, we were able to say what was clear and consistent -with itself.</p> - -<p>"And what, Phædrus asks, was the other feature?</p> - -<p>"The dividing the subject into kinds or elements, according to -the nature of the thing itself:—not breaking its natural members, -like a bad carver who cannot hit the joint. So the two discourses -which we have delivered, took the irrational part of the -mind, as their common subject; and as the body has two different -sides, the right and the left, with the same names for its parts; so -the two discourses took the irrational portion of man; and the one -took the left-hand portion, and divided this again, and again subdivided -it, till, among the subdivisions, it found a left-handed kind -of Love, of which nothing but ill was to be said. While the discourse -that followed out the right-hand side of phrenzy, (the -irrational portion of man's nature,) was led to something which -bore the name of <i>Love</i> like the other, but which is divine, and was -praised as the source of the greatest blessing."</p> - -<p>"Now I," Socrates goes on to say, "am a great admirer of these -processes of division and comprehension, by which I endeavour to -speak and to think correctly. And if I can find any one who is -able to see clearly what is by nature reducible to one and manifested -in many elements, I follow his footsteps as a divine guide. -Those who can do this, I call—whether rightly or not, God knows—but -I have hitherto been in the habit of calling them <i>dialectical</i> -men."</p> - -<p>It is of no consequence to our present purpose whether either of -the discourses of Socrates in the Phædrus, or the two together, as -is here assumed, do contain a just division and subdivision of that -part of the human soul which is distinguishable from Reason, and -do thus exhibit, in its true relations, the affection of Love. It is -evident that division and subdivision of this kind is here presented -as, in Plato's opinion, a most valuable method; and those who -could successfully practise this method are those whom he admires -as dialectical men. This is here his <i>Dialectic</i>.</p> - -<p>(<i>Sophistes.</i>) We are naturally led to ask whether this method of -dividing a subject as the best way of examining it, be in any other -part of the Platonic Dialogues more fully explained than it is in -the Phædrus; or whether any rules are given for this kind of -Dialectic.</p> - -<p><span class="pagenum" id="Page_432">432</span></p> - -<p>To this we may reply, that in the Dialogue entitled <i>The Sophist</i>, -a method of dividing a subject, in order to examine it, is explained -and exemplified with extraordinary copiousness and ingenuity. -The object proposed in that Dialogue is, to define what a Sophist -is; and with that view, the principal speaker, (who is represented -as an Eleatic stranger,) begins by first exemplifying what is his -method of framing a definition, and by applying it to define an -<i>Angler</i>. The course followed, though it now reads like a burlesque -of philosophical methods, appears to have been at that time a <i>bona -fide</i> attempt to be philosophical and methodical. It proceeds thus:</p> - -<p>"We have to inquire concerning <i>Angling</i>. Is it an Art? It is. -Now what kind of art? All art is an art of making or an art of -getting: (<i>Poietic</i> or <i>Ktetic</i>.) It is Ktetic. Now the art of getting, -is the art of getting by exchange or by capture: (<i>Metabletic</i> or -<i>Chirotic</i>.) Getting by capture is by contest or by chase: (<i>Agonistic</i> -or <i>Thereutic</i>.) Getting by chase is a chase of lifeless or of living -things: (the first has no name, the second is <i>Zootheric</i>.) The chase -of living things is the chase of land animals or of water animals: -(<i>Pezotheric</i> or <i>Enygrotheric</i>.) Chase of water animals is of birds -or of fish: (<i>Ornithothereutic</i> and <i>Halieutic</i>.) Chase of fish is by -inclosing or by striking them: (<i>Hercotheric</i> or <i>Plectic</i>.) We strike -them by day with pointed instruments, or by night, using torches: -(hence the division <i>Ankistreutic</i> and <i>Pyreutic</i>.) Of Ankistreutic, one -kind consists in spearing the fish downwards from above, the other -in twitching them upwards from below: (these two arts are <i>Triodontic</i> -and <i>Aspalieutic</i>.) And thus we have, what we sought, the -notion and the description of angling: namely that it is a Ktetic, -Chirotic, Thereutic, Zootheric, Enygrotheric, Halieutic, Plectic, -Ankistreutic, Aspalieutic Art."</p> - -<p>Several other examples are given of this ingenious mode of definition, -but they are all introduced with reference to the definition of -the Sophist. And it will further illustrate this method to show -how, according to it, the Sophist is related to the Angler.</p> - -<p>The Sophistical Art is an art of getting, by capture, living things, -namely men. It is thus a Ktetic, Chirotic, Thereutic art, and so far -agrees with that of the Angler. But here the two arts diverge, -since that of the Sophist is Pezotheric, that of the Angler Enygrotheric. -To determine the Sophist still more exactly, observe that -the chase of land animals is either of tame animals (including man) -or of wild animals: (<i>Hemerotheric</i> and <i>Agriotheric</i>.) The chase of -tame animals is either by violence, (as kidnapping, tyranny, and war -in general,) or by persuasion, (as by the arts of speech;) that is, it -is <i>Biaiotheric</i> or <i>Pithanurgic</i>. The art of persuasion is a private or<span class="pagenum" id="Page_433">433</span> -a public proceeding: (<i>Idiothereutic</i> or <i>Demosiothereutic</i>.) The art of -private persuasion is accompanied with the giving of presents, (as -lovers do,) or with the receiving of pay: (thus it is <i>Dorophoric</i> or -<i>Mistharneutic</i>.) To receive pay as the result of persuasion, is the -course, either of those who merely earn their bread by supplying -pleasure, namely flatterers, whose art is <i>Hedyntic</i>; or of those who -profess for pay to teach virtue. And who are they? Plainly the -Sophists. And thus <i>Sophistic</i> is that kind of Ktetic, Chirotic, -Thereutic, Zootheric, Pezotheric, Hemerotheric, Pithanurgic, Idiothereutic, -Mistharneutic art, which professes to teach virtue, and -takes money on that account.</p> - -<p>The same process is pursued along several other lines of inquiry: -and at the end of each of them the Sophist is detected, involved in -a number of somewhat obnoxious characteristics. This process of -division it will be observed, is at every step bifurcate, or as it is -called, <i>dichotomous</i>. Applied as it is in these examples, it is rather -the vehicle of satire than of philosophy. Yet, I have no doubt that -this bifurcate method was admired by some of the philosophers of -Plato's time, as a clever and effective philosophical invention. We -may the more readily believe this, inasmuch as one of the most acute -persons of our own time, who has come nearer than any other to -the ancient heads of sects in the submission with which his followers -have accepted his doctrines, has taken up this Dichotomous Method, -and praised it as the only philosophical mode of dividing a subject. -I refer to Mr. Jeremy Bentham's <i>Chrestomathia</i> (published -originally in 1816), in which this exhaustive bifurcate method, as he -calls it, was applied to classify sciences and arts, with a view to a -scheme of education. How exactly the method, as recommended by -him, agrees with the method illustrated in the <i>Sophist</i>, an examination -of any of his examples will show. Thus to take Mineralogy as -an example: according to Bentham, Ontology is Cœnoscopic or -Idioscopic: the Idioscopic is Somatoscopic or Pneumatoscopic; the -Somatoscopic is Pososcopic or Poioscopic: Poioscopic is Physiurgoscopic -or Anthropurgoscopic: Physiurgoscopic is Uranoscopic or -Epigeoscopic: Epigeoscopic is Abioscopic or Embioscopic. And -thus Mineralogy is the Science Idioscopic, Somatoscopic, Poioscopic, -Physiurgoscopic, Epigeoscopic, Abioscopic: inasmuch as it is the -science which regards bodies, with reference to their qualities,—bodies, -namely, the works of nature, terrestrial, lifeless.</p> - -<p>I conceive that this bifurcate method is not really philosophical or -valuable: but that is not our business here. What we have to consider -is whether this is what Plato meant by the term <i>Dialectic</i>.</p> - -<p>The general description of Dialectic in the <i>Sophistes</i> agrees very<span class="pagenum" id="Page_434">434</span> -closely with that quoted from the <i>Phædrus</i>, that it is the separation -of a subject according to its natural divisions.</p> - -<p>Thus, see in the Sophist the passage § 83: "To divide a subject -according to the kinds of things, so as neither to make the same -kind different nor different kinds identical, is the office of the -Dialectical Science." And this is illustrated by observing that it -is the office of the science of Grammar to determine what letters -may be combined and what may not; it is the office of the science of -Music to determine what sounds differing as acute and grave, may -be combined, and what may not: and in like manner it is the office -of the science of Dialectic to determine what <i>kinds</i> may be combined -in one subject and what may not. And the proof is still further -explained.</p> - -<p>In many of the Platonic Dialogues, the Dialectic which Socrates -is thus represented as approving, appears to include the form of -Dialogue, as well as the subdivision of the subject into its various -branches. Socrates is presented as attaching so much importance to -this form, that in the Protagoras (§ 65) he rises to depart, because -his opponent will not conform to this practice. And generally in -Plato, Dialectic is opposed to Rhetoric, as a string of short questions -and answers to a continuous dissertation.</p> - -<p>Xenophon also seems to imply (<i>Mem.</i> <span class="smcap">IV.</span> 5, 11) that Socrates -included in his notion of Dialectic the form of Dialogue as well as -the division of the subject.</p> - -<p>But that the method of close Dialogue was not called <i>Dialectic</i> -by the author of the <i>Sophist</i>, we have good evidence in the work -itself. Among other notions which are analysed by the bifurcate -division here exhibited, is that of getting by contest (<i>Agonistic</i>, -previously given as a division of <i>Ktetic</i>). Now getting by contest -may be by peaceful trial of superiority, or by fight: (<i>Hamilletic</i> or -<i>Machelic</i>). The fight may be of body against body, or of words -against words: these may be called <i>Biastic</i> and <i>Amphisbetic</i>. The -fight of words about right and wrong, may be by long discourses -opposed to each other, as in judicial cases; or by short questions -and answers: the former may be called <i>Dicanic</i>, the latter <i>Antilogic</i>. -Of these colloquies, about right and wrong, some are -natural and spontaneous, others artificial and studied: the former -need no special name; the latter are commonly called <i>Eristic</i>. Of -Eristic colloquies, some are a source of expense to those who hold -them, some of gain: that is, they are <i>Chrematophthoric</i> or <i>Chrematistic</i>: -the former, the occupation of those who talk for pleasure's -and for company's sake, is <i>Adoleschic</i>, wasteful garrulity; the -latter, that of those who talk for the sake of gain, is <i>Sophistic</i>.<span class="pagenum" id="Page_435">435</span> -And thus Sophistic is an art Eristic, which is part of Antilogic, -which is part of Amphisbetic, which is part of Agonistic, which is -part of Chirotic, which is a part of Ktetic. (§ 23.)</p> - -<p>We may notice here an indication that satire rather than exact -reason directs these analyses; in that Sophistic, which was before -a part of the <i>thereutic</i> branch of <i>chirotic</i> and <i>ktetic</i>, is here a part of -the other branch, <i>agonistic</i>.</p> - -<p>But the remark which I especially wish to make here is, that the -art of discussing points of right and wrong by short questions and -answers, being here brought into view, is not called <i>Dialectic</i>, -which we might have expected; but <i>Antilogic</i>. It would seem -therefore that the Author of the Sophist did not understand by -<i>Dialectic</i> such a process as Socrates describes in Xenophon; (<i>Mem.</i> -<span class="smcap">IV.</span> 5, 11, 12;) where he says it was called <i>Dialectic</i>, because it was -followed by persons <i>dividing things into their kinds in conversation</i>: -(κοινῇ βουλεύεσθαι διαλέγοντας:)or such as the Socrates of Plato -insisted upon in the Protagoras and the Gorgias. Of the two -elements which the Dialectical Process of Socrates implied, Division -of the subject and Dialogue, the author of the <i>Sophistes</i> does -not claim the name of <i>Dialectic</i> for either, and seems to reject it -for the second.</p> - -<p>But without insisting upon the name, are we to suppose that the -Dichotomous Method of the <i>Sophistes</i> Dialogue, (I may add of the -<i>Politicus</i>, for the method is the same in this Dialogue also,) is the -method of division of a subject according to its natural members, of -which Plato speaks in the <i>Phædrus</i>?</p> - -<p>If the <i>Sophistes</i> be the work of Plato, the answer is difficult -either way. If this method be Plato's <i>Dialectic</i>, how came he to -omit to say so there? how came he even to seem to deny it? But -on the other hand, if this dichotomous division be a different process -from the division called <i>Dialectic</i> in the Phædrus, had Plato -two methods of division of a subject? and yet has he never spoken -of them as two, or marked their distinction?</p> - -<p>This difficulty would be removed if we were to adopt the opinion, -to which others, on other grounds, have been led, that the Sophistes, -though of Plato's time, is not Plato's work. The grounds of this -opinion are,—that the doctrines of the Sophistes are not Platonic: -(the doctrine of Ideas is strongly impugned and weakly defended:) -Socrates is not the principal speaker, but an Eleatic stranger: and -there is, in the Dialogue, none of the dramatic character which we -generally have in Plato. The Dialogue seems to be the work of -some Eleatic opponent of Plato, rather than his.</p> - -<p>(<i>Rep.</i> B. <span class="smcap">VII.</span>) But we can have no doubt that the <i>Phædrus</i><span class="pagenum" id="Page_436">436</span> -contains Plato's real view of the nature of Dialectic, as to its form; -let us see how this agrees with the view of Dialectic, as to its -matter and object, given in the seventh Book of the <i>Republic</i>.</p> - -<p>According to Plato, Real Existences are the objects of the exact -sciences (as number and figure, of Arithmetic and Geometry). -The things which are the objects of sense transitory phenomena, -which have no reality, because no permanence. Dialectic -deals with Realities in a more general manner. This doctrine is -everywhere inculcated by Plato, and particularly in this part of the -<i>Republic</i>. He does not tell us how we are to obtain a view of the -higher realities, which are the objects of Dialectic: only he here -assumes that it will result from the education which he enjoins. -He says (§ 13) that the Dialectic Process (ἡ διαλεκτικὴ μέθοδος) -alone leads to true science: it makes no assumptions, but goes to -First Principles, that its doctrines may be firmly grounded: and -thus it purges the eye of the soul, which was immersed in barbaric -mud, and turns it upward; using for this purpose the aid of the -sciences which have been mentioned. But when Glaucon inquires -about the details of this Dialectic, Socrates says he will not then -answer the inquiry. We may venture to say, that it does not appear -that he had any answer ready.</p> - -<p>Let us consider for a moment what is said about a philosophy -rendering a reason for the First Principles of each Science, which -the Science itself cannot do. That there is room for such a branch -of philosophy in some sciences, we easily see. Geometry, for -instance, proceeds from Axioms, Definitions and Postulates; but by -the very nature of these terms, does not prove these First Principles. -These—the Axioms, Definitions and Postulates,—are, I -conceive, what Plato here calls the <i>Hypotheses</i> upon which Geometry -proceeds, and for which it is not the business of Geometry to -render a reason. According to him, it is the business of "Dialectic" -to give a just account of these "Hypotheses." What then is -<i>Dialectic?</i></p> - -<p>(<i>Aristotle.</i>) It is, I think, well worthy of remark, that Aristotle, -giving an account in many respects different from that of Plato, of -the nature of Dialectic, is still led in the same manner to consider -Dialectic as the branch of philosophy which renders a reason for -First Principles. In the <i>Topics</i>, we have a distinction drawn between -reasoning demonstrative, and reasoning dialectical: and the -distinction is this:—(<i>Top</i>. <span class="smcap">I.</span> 1) that demonstration is by syllogisms -from true first principles, or from true deductions from such principles; -and that the Dialectical Syllogism is that which syllogizes -from probable propositions (ἠξ ἠνδόξων). And he adds that<span class="pagenum" id="Page_437">437</span> -probable propositions are those which are accepted by all, or by the -greatest part, or by the wise. In the next chapter, he speaks of -the uses of Dialectic, which, he says, are three, mental discipline, -debates, and philosophical science. And he adds (<i>Top</i>. <span class="smcap">I.</span> 2, 6) -that it is also useful with reference to the First Principles in each -Science: for from the appropriate Principles of each science we -cannot deduce anything concerning First Principles, since these -principles are the beginning of reasoning. But from the probable -principles in each province of science we must reason concerning -First Principles: and this is either the peculiar office of Dialectic, -or the office most appropriate to it; for it is a process of investigation, -and must lead to the Principles of all methods.</p> - -<p>That a demonstrative science, as such, does not explain the origin -of its own First Principles, is undoubtedly true. Geometry does -not undertake to give a reason for the Axioms, Definitions, and -Postulates. This has been attempted, both in ancient and in modern -times, by the Metaphysicians. But the Metaphysics employed on -such subjects has not commonly been called Dialectic. The term -has certainly been usually employed rather as describing a Method, -than as determining the subject of investigation. Of the Faculty -which apprehends First Principles, both according to Plato and to -Aristotle, I will hereafter say a few words.</p> - -<p>The object of the dichotomous process pursued in the Sophistes, -and its result in each case, is a Definition. Definition also was one -of the main features of the inquiries pursued by Socrates, Induction -being the other; and indeed in many cases Induction was a series -of steps which ended in Definition. And Aristotle also taught a -peculiar method, the object and result of which was the construction -of Definitions:—namely his <i>Categories</i>. This method is one -of division, but very different from the divisions of the Sophistes. -His method begins by dividing the whole subject of possible inquiry -into ten heads or <i>Categories</i>—Substance, Quantity, Quality, Relation, -Place, Time, Position, Habit, Action, Passion. These again are -subdivided: thus Quality is Habit or Disposition, Power, Affection, -Form. And we have an example of the application of this method -to the construction of a Definition in the Ethics; where he determines -Virtue to be a Habit with certain additional limitations.</p> - -<p>Thus the Induction of Socrates, the Dichotomy of the Eleatics, -the Categories of Aristotle, may all be considered as methods by -which we proceed to the construction of Definitions. If, by any -method, Plato could proceed to the construction of a Definition, or -rather of an Idea, of the Absolute Realities on which First Principles -depend, such a method would correspond with the notion of<span class="pagenum" id="Page_438">438</span> -Dialectic in the <i>Republic</i>. And if it was a method of division like -the Eleatic or Aristotelic, it would correspond with the notion of -Dialectic in the <i>Phædrus</i>.</p> - -<p>That Plato's notion, however, cannot have been exactly either of -these is, I think, plain. The colloquial method of stimulating and -testing the progress of the student in Dialectic is implied, in the -sequel of this discussion of the effect of scientific study. And the -method of Dialogue, as the instrument of instruction, being thus -supposed, the continuation of the account in the <i>Republic</i>, implies -that Plato expected persons to be made dialectical by the study of -the exact sciences in a comprehensive spirit. After insisting on -Geometry and other sciences, he says (<i>Rep.</i> <span class="smcap">VII.</span> § 16): "The -synoptical man is dialectical; and he who is not the one, is not -the other."</p> - -<p>But, we may ask, does a knowledge of sciences lead naturally to -a knowledge of Ideas, as absolute realities from which First Principles -flow? And supposing this to be true, as the Platonic Philosophy -supposes, is the Idea of the Good, as the source of moral -truths, to be thus attained to? That it is, is the teaching of -Plato, here and elsewhere; but have the speculations of subsequent -philosophers in the same direction given any confirmation of this -lofty assumption?</p> - -<p>In reply to this inquiry, I should venture to say, that this -assumption appears to be a remnant of the Socratic doctrine from -which Plato began his speculations, that Virtue is a kind of knowledge; -and that all attempts to verify the assumption have failed. -What Plato added to the Socratic notion was, that the inquiry -after The Good, the Supreme Good, was to be aided by the -analogy or suggestions of those sciences which deal with necessary -and eternal truths; the supreme good being of the nature -of those necessary and eternal truths. This notion is a striking -one, as a suggestion, but it has always failed, I think, in the -attempts to work it out. Those who in modern times, as Cudworth -and Samuel Clarke, have supposed an analogy between the necessary -truths of Geometry and the truths of Morality, though they -have used the like expressions concerning the one and the other -class of truths, have failed to convey clear doctrines and steady convictions -to their readers; and have now, I believe, few or no -followers.</p> - -<p>The result of our investigation appears to be, that though Plato -added much to the matter by means of which the mind was to -be improved and disciplined in its research after Principles and -Definitions, he did not establish any form of Method according<span class="pagenum" id="Page_439">439</span> -to which the inquiry must be conducted, and by which it might -be aided. The most definite notion of Dialectic still remained -the same with the original informal view which Socrates had -taken of it, as Xenophon tells us, (<i>Mem.</i> <span class="smcap">IV.</span> 5, 11) when he says: -"He said that Dialectic (τὸ διαλέγεσθαι) was so called because -it is an inquiry pursued by persons who take counsel together, -separating the subjects considered according to their kinds (διαλέγοντας). -He held accordingly that men should try to be well -prepared for such a process, and should pursue it with diligence: -by this means, he thought, they would become good men, fitted -for responsible offices of command, and truly dialectical" (διαλέκτικωτάτους). -And this is, I conceive, the answer to Mr. Grote's -interrogatory exclamation (Vol. <span class="smcap">VIII.</span> p. 577): "Surely the Etymology -here given by Xenophon or Socrates of the word (διαλέγεσθαι) -cannot be considered as satisfactory." The two notions, -of investigatory Dialogue, and Distribution of notions according -to their kinds, which are thus asserted to be connected in etymology, -were, among the followers of Socrates, connected in fact; the -dialectic dialogue was supposed to involve of course the dialectic -division of the subject.</p> -<hr class="chap" /> - -<p><span class="pagenum" id="Page_440">440</span></p> - - - -<h3><a name="APPENDIX_C" id="APPENDIX_C"></a><span class="smcap">Appendix</span> C.<br /> - -OF THE INTELLECTUAL POWERS ACCORDING -TO PLATO.</h3> - -<p class="center">(<i>Cam. Phil. Soc.</i> <span class="smcap">Nov. 10, 1856</span>.)</p> - - -<p class="drop-cap"><span class="smcap">In</span> the Seventh Book of Plato's <i>Republic</i>, we have certain sciences -described as the instruments of a philosophical and intellectual -education; and we have a certain other intellectual employment -spoken of, namely, Dialectic, as the means of carrying the mind -beyond these sciences, and of enabling it to see the sources of -those truths which the sciences assume as their first principles. -These points have been discussed in the two preceding papers. -But this scheme of the highest kind of philosophical education -proceeds upon a certain view of the nature and degrees of knowledge, -and of the powers by which we know; which view had been presented -in a great measure in the Sixth Book; this view I shall -now attempt to illustrate.</p> - -<p>To analyse the knowing powers of man is a task so difficult, that -we need not be surprised if there is much obscurity in this portion -of Plato's writings. But as a reason for examining what he has -said, we must recollect that if there be in it anything on this subject -which was true then, it is true still; and also, that if we know -any truth on that subject now, we shall find something corresponding -to that truth in the best speculations of sagacious ancient -writers, like Plato. It may therefore be worth while to discuss -the Platonic doctrines on this matter, and to inquire how they are -to be expressed in modern phraseology.</p> - -<p>Plato's doctrine will perhaps be most clearly understood, if we -begin by considering the <i>diagram</i> by which he illustrates the -different degrees of knowledge<a name="FNanchor_341" id="FNanchor_341"></a><a href="#Footnote_341" class="fnanchor">[341]</a>. He sets out from the distinction -of <i>visible</i> and <i>intelligible</i> things. There are visible objects, squares -and triangles, for instance; but these are not the squares and triangles -about which the Geometer reasons. The exactness of his -reasoning does not depend on the exactness of his diagrams. He<span class="pagenum" id="Page_441">441</span> -reasons from certain mental squares and triangles, as he conceives -and understands them. "Thus there are visible and there are -intelligible things. There is a visible and an intelligible world<a name="FNanchor_342" id="FNanchor_342"></a><a href="#Footnote_342" class="fnanchor">[342]</a>: -and there are two different regions about which our knowledge is -concerned. Now take a line divided into two unequal segments to -represent these two regions: and again, divide each segment in the -same ratio. The parts of each segment are to represent differences -of clearness and distinctness, and in the visible world these parts -are <i>things</i> and <i>images</i>. By <i>images</i> I mean shadows, and reflections -in water, and in polished bodies; and by <i>things</i>, I mean that of -which these images are the resemblances; as animals, plants, -things made by man. This difference corresponds to the difference -of <i>Knowledge</i> and mere <i>Opinion</i>; and the <i>Opinable</i> is to the <i>Knowable</i> -as the Image to the Reality."</p> - -<p>This analogy is assented to by Glaucon; and thus there is assumed -a ground for a further construction of the diagram.</p> - -<p>"Now," he says, "we have to divide the segment which represents -Intelligible Things in the same way in which we have divided -that which represents Visible Things. The one part must represent -the knowledge which the mind gets by dealing as it were with -images, and by reasoning downwards <i>from</i> Principles; the other -that which it has by dealing with the Ideas themselves, and going -<i>to</i> First Principles.</p> - -<p>"The one part depends upon assumptions or hypotheses<a name="FNanchor_343" id="FNanchor_343"></a><a href="#Footnote_343" class="fnanchor">[343]</a>, the -other is unhypothetical or absolute truth.</p> - -<p>"One kind of Intelligible Things, then, is Conceptions; for instance, -geometrical conceptions of figures, by means of which we -reason downwards, assuming certain First Principles.</p> - -<p>"Now the other kind of Intelligible Things is this:—that which -the Reason includes in virtue of its power of reasoning, when it<span class="pagenum" id="Page_442">442</span> -regards the assumptions of the Sciences as, what they are, assumptions -only; and uses them as occasions and starting points, that -from these it may ascend to the <i>absolute</i>, (ἀνυπόθετον, unhypothetical,) -which does not depend upon assumption, but is the -origin of scientific truth. The Reason takes hold of this first principle -of truth; and availing itself of all the connections and relations -of this principle, it proceeds to the conclusion; using no -sensible image in doing this, but contemplating the Ideas alone; -and with these Ideas the process begins, goes on, and terminates."</p> - -<p>This account of the matter will probably seem to require at least -further explanation; and that accordingly is acknowledged in the -Dialogue itself. Glaucon says:</p> - -<p>"I apprehend your meaning in a certain degree, but not very -clearly, for the matter is somewhat abstruse. You wish to prove -that the knowledge which, by the Reason, we acquire, of Real -Existence and Intelligible Things, is of a higher degree of certainty -than the knowledge which belongs to what are commonly called -Sciences. Such sciences, you say, have certain assumptions for -their bases; and these assumptions are, by the students of such -sciences, apprehended, not by Sense (that is, the Bodily Senses), -but by a Mental Operation,—by Conception. But inasmuch as -such students ascend no higher than the assumptions, and do not go -to the First Principles of Truth, they do not seem to you to have -true knowledge—intuitive insight—<i>Nous</i>—on the subject of their -reasonings, though the subjects are intelligible, along with their -principle. And you call this habit and practice of the Geometers -and others by the name <i>Conception</i>, not <i>Intuition</i><a name="FNanchor_344" id="FNanchor_344"></a><a href="#Footnote_344" class="fnanchor">[344]</a>; taking Conception -to be something between Opinion on the one side, and -Intuitive Insight on the other."</p> - -<p>"You have explained it well, said I. And now consider the -four sections (of the line) of which we have spoken, as corresponding -to four affections in the mind. Intuition, the highest; Conception, -the next; the third, Belief; and the fourth, Conjecture (from -likenesses); and arrange them in order, so that they may have more -or less of certainty, as their objects have more or less of truth<a name="FNanchor_345" id="FNanchor_345"></a><a href="#Footnote_345" class="fnanchor">[345]</a>.</p> - -<p><span class="pagenum" id="Page_443">443</span></p> - -<p>"I understand, said he. I agree to what you say, and I arrange -them as you direct."</p> - -<p>And so the Sixth Book ends: and the Seventh Book opens -with the celebrated image of the Cave, in which men are confined, -and see all external objects only by the shadows which they cast -on the walls of their prison. And this imperfect knowledge of -things is to the true vision of them, which is attained by those -who ascend to the light of day, as the ordinary knowledge of men is -to the knowledge attainable by those whose minds are purged and -illuminated by a true philosophy.</p> - -<p>Confining ourselves at present to the part of Plato's speculations -which we have mentioned, namely, the degrees of knowledge, -and the division of our knowing faculties, we may understand, -and may in a great degree accept, Plato's scheme. We have already -(in the preceding papers) seen that, by the knowledge of real -things, he means, in the first place, the knowledge of universal -and necessary truths, such as Geometry and the other exact sciences -deal with. These <i>we</i> call sciences of Demonstration; and we -are in the habit of contrasting the knowledge which constitutes -such sciences with the knowledge obtained by the Senses, by Experience -or mere Observation. This distinction of Demonstrative -and Empirical knowledge is a cardinal point in Plato's scheme -also; the former alone being allowed to deserve the name of -<i>Knowledge</i>, and the latter being only <i>Opinion</i>. The Objects with -which Demonstration deals may be termed <i>Conceptions</i>, and the -objects with which Observation or Sense has to do, however -much speculation may reduce them to mere Sensations, are commonly -described as <i>Things</i>. Of these Things, there may be Shadows or -Images, as Plato says; and as we may obtain a certain kind of -knowledge, namely Opinion or Belief, by seeing the Things themselves, -we may obtain an inferior kind of Opinion or Belief by seeing -their Images, which kind of opinion we may for the moment call -<i>Conjecture</i>. Whether then we regard the distinctions of knowledge -itself or of the objects of it, we have three terms before us.</p> - -<blockquote> -<p> -If we consider the kinds of knowledge, they are<br /> -Demonstration: Belief: Conjecture.<br /> -If the objects of this knowledge, they are<br /> -Conceptions: Things: Images.<br /> -</p></blockquote> - -<p><span class="pagenum" id="Page_444">444</span></p> - -<p>But in each of these Series, the first term is evidently wanting: for -Demonstration supposes Principles to reason from. Conceptions -suppose some basis in the mind which gives them their evidence. -What then is the first term in each of these two Series?</p> - -<p>The Principles of Demonstration must be seen by <i>Intuition</i>.</p> - -<p>Conceptions derive their properties from certain powers or -attributes of the mind which we may term <i>Ideas</i>.</p> - -<p>Therefore the two series are</p> -<blockquote> -<p> -Intuition: Demonstration: Belief: Conjecture.<br /> -Ideas: Conceptions: Things: Images.<br /> -</p></blockquote> - -<p>Plato further teaches that the two former terms in each Series -belong to the Intelligible, the two latter to the Visible World: -and he supposes that the ratio of these two primary segments -of the line is the same as the ratio in which each segment is -divided<a name="FNanchor_346" id="FNanchor_346"></a><a href="#Footnote_346" class="fnanchor">[346]</a>.</p> - -<p>In using the term <i>Ideas</i> to describe the mental sources from -which Conceptions derive their validity in demonstration, I am -employing a phraseology which I have already introduced in the -<i>Philosophy of the Inductive Sciences</i>. But independently altogether -of this, I do not see what other term could be employed to denote -the mental objects, attributes, or powers, whatever they be, from -which Conceptions derive their evidence, as Demonstrative Truths -derive their evidence from Intuitive Truths.</p> - -<p>That the Scheme just presented is Plato's doctrine on this subject, -I do not conceive there can be any doubt. There is a little want -of precision in his phraseology, arising from his mixing together -the two series. In fact, his final series</p> - -<p class="center"> -<i>Noësis</i>: <i>Dianoia</i>: <i>Pistis</i>: <i>Eikasia</i>;<br /> -</p> - -<p>is made by putting in the second place, instead of <i>Demonstration</i>, -which is the <i>process</i> pursued, or <i>Science</i>, which is the <i>knowledge</i> -obtained, <i>Conception</i>, which is the <i>object</i> with which the mind -deals. Such deviations from exact symmetry and correlation in -speaking of the faculties of the mind, are almost unavoidable in -every language. And there is yet another source of such inaccuracies -of language; for we have to speak, not only of the -process of acquiring knowledge, and of the objects with which -the mind deals, but of the Faculties of the mind which are -thus employed. Thus <i>Intuition</i> is the Process; <i>Ideas</i> are the<span class="pagenum" id="Page_445">445</span> -Object, in the first term of our series. The Faculty also we -may call <i>Intuition</i>; but the Greek offers a distinction. <i>Noësis</i> -is the <i>Process</i> of Intuition; but the <i>Faculty</i> is <i>Nous</i>. If we -wish to preserve this distinction in English, what must we call -the Faculty? I conceive we must call it <i>the Intuitive Reason</i>, a -term well known to our older philosophical writers<a name="FNanchor_347" id="FNanchor_347"></a><a href="#Footnote_347" class="fnanchor">[347]</a>. Again: -taking the second term of the series, <i>Demonstration</i> is the process, -<i>Science</i>, the result; and <i>Conceptions</i> are the objects with which -the mind deals. But what is the <i>Faculty</i> thus employed? What -is the Faculty employed in Demonstration? The same philosophical -writers of whom I spoke would have answered at once, <i>the Discursive -Reason</i>; and I do not know that, even now, we can suggest -any better term. The Faculty employed in acquiring the two lower -kinds of knowledge, the Faculty which deals with Things and -their Images is, of course, <i>Sense</i>, or <i>Sensation</i>.</p> - -<p>The assertion of a Faculty of the mind by which it apprehends -Truth, which Faculty is higher than the Discursive Reason, -as the Truth apprehended by it is higher than mere Demonstrative -Truth, agrees (as it will at once occur to several of my readers) -with the doctrine taught and insisted upon by the late Samuel -Taylor Coleridge. And so far as he was the means of inculcating -this doctrine, which, as we see, is the doctrine of Plato, and I -might add, of Aristotle, and of many other philosophers, let him -have due honour. But in his desire to impress the doctrine upon -men's minds, he combined it with several other tenets, which will -not bear examination. He held that the two Faculties by which -these two kinds of truth are apprehended, and which, as I have -said, our philosophical writers call <i>the Intuitive Reason</i> and <i>the -Discursive Reason</i>, may be called, and ought to be called, respectively, -<i>The Reason</i> and <i>The Understanding</i>; and that the second of these -is of the nature of the <i>Instinct</i> of animals, so as to be something -intermediate between Reason and Instinct. These opinions, I may -venture to say, are altogether erroneous. The Intuitive Reason and -the Discursive Reason are not, by any English writers, called the -Reason and the Understanding; and accordingly, Coleridge has -had to alter all the passages, namely, those taken from Leighton, -Harrington, and Bacon, from which his exposition proceeds. The -Understanding is so far from being especially the Discursive or<span class="pagenum" id="Page_446">446</span> -Reasoning Faculty, that it is, in universal usage, and by our best -writers, <i>opposed</i> to the Discursive or Reasoning Faculty. Thus this -is expressly declared by Sir John Davis in his poem <i>On the Immortality -of the Soul</i>. He says, of the soul,</p> - -<div class="poetry-container"><div class="poetry"><div class="stanza"> - <div class="verse">When she <i>rates</i> things, and moves from ground to ground,</div> - <div class="verse indent4">The name of <i>Reason</i> (<i>Ratio</i>) she acquires from this:</div> - <div class="verse">But when by reason she truth hath found,</div> - <div class="verse indent4">And standeth fixt, she <i>Understanding</i> is.</div> -</div></div></div> - -<p>Instead of the Reason being fixed, and the Understanding discursive, -as Mr. Coleridge says, the Reason is distinctively discursive; -that is, it obtains conclusions by running from one point to another. -This is what is meant by <i>Discursus</i>; or, taking the full term, <i>Discursus -Rationis</i>, <i>Discourse of Reason</i>. Understanding is fixed, that -is, it dwells upon one view of a subject, and not upon the steps by -which that view is obtained. The verb <i>to reason</i>, implies the substantive, -<i>the Reason</i>, though it is not coextensive with it: for as I -have said, there is the Intuitive Reason as well as the Discursive -Reason. But it is by the Faculty of Reason that we are capable of -reasoning; though undoubtedly the practice or the pretence of reasoning -may be carried so far as to seem at variance with reason in -the more familiar sense of the term; as is the case also in French. -Moliere's Crisale says (in the <i>Femmes Savantes</i>),</p> - -<div class="poetry-container"><div class="poetry"><div class="stanza"> - <div class="verse">Raisonner est l'emploi de toute ma maison,</div> - <div class="verse">Et le raisonnement en bannit la Raison.</div> -</div></div></div> - -<p>If Mr. Coleridge's assertion were true, that the Understanding is -the discursive and the Reason the fixed faculty, we should be justified -in saying that <i>The Understanding is the faculty by which we -reason, and the Reason is the faculty by which we understand</i>. But -this is not so.</p> - -<p>Nor is the Understanding of the nature of Instinct, nor does it -approach nearer than the Reason to the nature of Instinct, but the -contrary. The Instincts of animals bear a very obscure resemblance -to any of man's speculative Faculties; but so far as there is -any such resemblance, Instinct is an obscure image of Reason, not -of Understanding. Animals are said to act as if they reasoned, -rather than as if they understood. The verb <i>understand</i> is especially -applied to man as distinguished from animals. Mr. Coleridge tells -a tale from Huber, of certain bees which, to prevent a piece of -honey from falling, balanced it by their weight, while they built a -pillar to support it. They did this by Instinct, not <i>understanding</i> -what they did; men, doing the same, would have <i>understood</i> what -they were doing. Our Translation of the Scriptures, in making<span class="pagenum" id="Page_447">447</span> -it the special distinction of man and animals, that <i>he has Understanding</i> -and they have not, speaks quite consistently with good -philosophy and good English.</p> - -<p>Mr. Coleridge's object in his speculations is nearly the same as -Plato's; namely, to declare that there is a truth of a higher kind -than can be obtained by mere reasoning; and also to claim, as portions -of this higher truth, certain fundamental doctrines of Morality. -Among these, Mr. Coleridge places the Authority of Conscience, -and Plato, the Supreme Good. Mr. Coleridge also holds, as Plato -held, that the Reason of man, in its highest and most comprehensive -form, is a portion of a Supreme and Universal Reason; and leads to -Truth, not in virtue of its special attributes in each person, but by -its own nature.</p> - -<p>Many of the opinions which are combined with these doctrines, -both in Plato and in Coleridge, are such as we should, I think, find -it impossible to accept, upon a careful philosophical examination of -them; but on these I shall not here dwell.</p> - -<p>I will only further observe, that if any one were to doubt whether -the term Νοῦς is rightly rendered <i>Intuitive Reason</i>, we may find -proof of the propriety of such a rendering in the remarkable discussion -concerning the Intellectual Virtues, which we have in the -Sixth Book of the Nicomachean Ethics. It can hardly be questioned -that Aristotle had in his mind, in writing that passage, the -doctrines of Plato, as expounded in the passage just examined, and -similar passages. Aristotle there says that there are five Intellectual -Virtues, or Faculties by which the Mind aims at Truth in -asserting or denying:—namely, <i>Art</i>, <i>Science</i>, <i>Prudence</i>, <i>Wisdom</i>, -<i>Nous</i>. In this enumeration, passing over Art, Prudence, and Wisdom, -as virtues which are mainly concerned from practical life, we -have, in the region of speculative Truth, a distinction propounded -between <i>Science</i> and <i>Nous</i>: and this distinction is further explained -(c. 6) by the remarks that Science reasons with Principles; and that -these Principles cannot be given <i>by</i> Science, because Science reasons -<i>from</i> them; nor by Art, nor Prudence, for these are conversant with -matters contingent, not with matters demonstrable; nor can the -First Principles of the Reasonings of Science be given by Wisdom, -for Wisdom herself has often to reason from Principles. Therefore -the First Principles of Demonstrative Reasoning must be given by -a peculiar Faculty, <i>Nous</i>. As we have said, <i>Intuitive Reason</i> is the -most appropriate English term for this Faculty.</p> - -<p>The view thus given of that higher kind of Knowledge which -Plato and Aristotle place above ordinary Science, as being the -Knowledge of and Faculty of learning First Principles, will enable<span class="pagenum" id="Page_448">448</span> -us to explain some expressions which might otherwise be misunderstood. -Socrates, in the concluding part of this Sixth Book of the -<i>Republic</i>, says, that this kind of knowledge is "that of which the -Reason (λόγος) takes hold, <i>in virtue of its power of reasoning</i><a name="FNanchor_348" id="FNanchor_348"></a><a href="#Footnote_348" class="fnanchor">[348]</a>." -Here we are plainly not to understand that we arrive at First Principles -<i>by reasoning</i>: for the very opposite is true, and is here taught;—namely, -that First Principles are not what we reason <i>to</i>, but what -we reason <i>from</i>. The meaning of this passage plainly is, that First -Principles are those of which the Reason takes hold <i>in virtue of its -power of reasoning</i>;—they are the conditions which must exist in -order to make any reasoning possible:—they are the propositions -which the Reason must involve implicitly, in order that we may -reason explicitly;—they are the intuitive roots of the dialectical -power.</p> - -<p>In accordance with the views now explained, Plato's Diagram -may be thus further expanded. The term ιδέα is not used in this -part of the <i>Republic</i>; but, as is well known, occurs in its peculiar -Platonic sense in the Tenth Book.</p> - - -<div class="center"> -<table border="1" cellpadding="4" cellspacing="0" summary=""> -<tr> - <td align="center"> </td><td align="center" colspan="2">Intelligible World. νοητον.</td> - <td align="center" colspan="2">Visible World. ορατον.</td></tr> -<tr> - <td align="center"><i>Object</i></td> - <td align="center">Ideas<br />ἰδέαι</td> - <td align="center">Conceptions<br />διάνοια</td> - <td align="center">Things<br />ζῶα κ.τ.λ.</td> - <td align="center">Images<br />εἰκἰνες</td></tr> -<tr> - <td align="center"><i>Process</i></td> - <td align="center">Intuition<br />νἰησις</td> - <td align="center">Demonstration<br />ἐπιστήμη</td> - <td align="center">Belief<br />πίστις</td> - <td align="center">Conjecture<br />είκασία</td></tr> -<tr> - <td align="center"><i>Faculty</i></td> - <td align="center">Intuitive Reason<br />νοῦς</td> - <td align="center">Discursive Reason<br />λόγος</td> -<td align="center" colspan="2">Sensation<br />αἴσθησις</td></tr> -</table></div> - -<hr class="chap" /> - -<p><span class="pagenum" id="Page_449">449</span></p> - - -<h3><a name="Appendix_D" id="Appendix_D"></a><span class="smcap">Appendix D.</span><br /> - -CRITICISM OF ARISTOTLE'S ACCOUNT OF -INDUCTION.</h3> - -<p class="center">(<i>Cam. Phil. Soc.</i> <span class="smcap">Feb. 11, 1850</span>.)</p> - - -<p class="drop-cap"><span class="smcap">The</span> Cambridge Philosophical Society has willingly admitted -among its proceedings not only contributions to science, but also -to the philosophy of science; and it is to be presumed that this -willingness will not be less if the speculations concerning the philosophy -of science which are offered to the Society involve a reference -to ancient authors. Induction, the process by which general truths -are collected from particular examples, is one main point in such -philosophy: and the comparison of the views of Induction entertained -by ancient and modern writers has already attracted much -notice. I do not intend now to go into this subject at any length; -but there is a cardinal passage on the subject in Aristotle's <i>Analytics</i>, -(<i>Analyt. Prior.</i> <span class="smcap">II.</span> 25) which I wish to explain and discuss. I will -first translate it, making such emendations as are requisite to render -it intelligible and consistent, of which I shall afterwards give an -account.</p> - -<p>I will number the sentences of this chapter of Aristotle in order -that I may afterwards be able to refer to them readily.</p> - -<p>§ 1. "We must now proceed to observe that we have to examine -not only syllogisms according to the aforesaid <i>figures</i>,—syllogisms -logical and demonstrative,—but also rhetorical syllogisms,—and, -speaking generally, any kind of proof by which belief is influenced, -following any method.</p> - -<p>§ 2. "All belief arises either from Syllogism or from Induction: -[we must now therefore treat of Induction.]</p> - -<p>§ 3. "Induction, and the Inductive Syllogism, is when by means of -one extreme term we infer the other extreme term to be true of the -middle term.</p> - -<p>§ 4. "Thus if <i>A</i>, <i>C</i>, be the extremes, and <i>B</i> the mean, we have -to show, by means of <i>C</i>, that <i>A</i> is true of <i>B</i>.</p> - -<p><span class="pagenum" id="Page_450">450</span></p> - -<p>§ 5. "Thus let <i>A</i> be <i>long-lived</i>; <i>B</i>, <i>that which has no gall-bladder;</i> -and <i>C</i>, particular long-lived animals, as <i>elephant</i>, <i>horse</i>, -<i>mule</i>.</p> - -<p>§ 6. "Then every <i>C</i> is <i>A</i>, for all the animals above named are -long-lived.</p> - -<p>§ 7. "Also every <i>C</i> is <i>B</i>, for all those animals are destitute of -gall-bladder.</p> - -<p>§ 8. "If then <i>B</i> and <i>C</i> are convertible, and the mean (<i>B</i>) does -not extend further than extreme (<i>C</i>), it necessarily follows that -every <i>B</i> is <i>A</i>.</p> - -<p>§ 9. "For it was shown before, that, if any two things be -true of the same, and if either of them be convertible with the extreme, -the other of the things predicated is true of the convertible -(extreme).</p> - -<p>§ 10. "But we must conceive that <i>C</i> consists of a collection of -all the particular cases; for Induction is applied to all the cases.</p> - -<p>§ 11. "But such a syllogism is an inference of a first truth and -immediate proposition.</p> - -<p>§ 12. "For when there is a mean term, there is a demonstrative -syllogism through the mean; but when there is not a mean, there is -proof by Induction.</p> - -<p>§ 13. "And in a certain way, Induction is contrary to Syllogism; -for Syllogism proves, by the middle term, that the extreme is true of -the third thing: but Induction proves, by means of the third thing, -that the extreme is true of the mean.</p> - -<p>§ 14. "And Syllogism concluding by means of a middle term is -prior by nature and more usual to us; but the proof by Induction, -is more luminous."</p> - -<p>I think that the chapter, thus interpreted, is quite coherent and -intelligible; although at first there seems to be some confusion, -from the author sometimes saying that Induction is a kind of Syllogism, -and at other times that it is not. The amount of the doctrine -is this.</p> - -<p>When we collect a general proposition by Induction from particular -cases, as for instance, that all animals destitute of gall-bladder -(<i>acholous</i>), are long-lived, (if this proposition were true, of -which hereafter,) we may express the process in the form of a Syllogism, -if we will agree to make a collection of particular cases our -middle term, and assume that the proposition in which the second -extreme term occurs is convertible. Thus the known propositions -are</p> - -<p> -Elephant, horse, mule, &c., are long-lived.<br /> -Elephant, horse, mule, &c., are <i>acholous</i>.<br /> -</p> - -<p><span class="pagenum" id="Page_451">451</span></p> - -<p>But if we suppose that the latter proposition is convertible, we -shall have these propositions:</p> -<blockquote> -<p> -Elephant, horse, mule, &c., are long-lived.<br /> -All acholous animals are elephant, horse, mule, &c.,<br /> -</p></blockquote> - -<p>from whence we infer, quite rigorously as to <i>form</i>,</p> - -<blockquote><p> -All acholous animals are long-lived.<br /> -</p> -</blockquote> -<p>This mode of putting the Inductive inference shows both the -strong and the weak point of the illustration of Induction by means -of Syllogism. The strong point is this, that we make the inference -perfect as to form, by including an indefinite collection of particular -cases, elephant, horse, mule, &c., in a single term, <i>C</i>. The Syllogism -then is</p> - -<blockquote><p> -All <i>C</i> are long-lived.<br /> -All acholous animals are <i>C</i>.<br /> -Therefore all acholous animals are long-lived.<br /> -</p></blockquote> - -<p>The weak point of this illustration is, that, at least in some -instances, when the number of actual cases is necessarily indefinite, -the representation of them as a single thing involves an unauthorized -step. In order to give the reasoning which really passes in the -mind, we must say</p> - -<blockquote><p> -Elephant, horse, &c., are long-lived.<br /> -All acholous animals are <i>as</i> elephant, horse, &c.,<br /> -Therefore all acholous animals are long-lived.<br /> -</p></blockquote> - -<p>This "<i>as</i>" must be introduced in order that the "all <i>C</i>" of the -first proposition may be justified by the "<i>C</i>" of the second.</p> - -<p>This step is, I say, necessarily unauthorized, where the number of -particular cases is indefinite; as in the instance before us, the species -of acholous animals. We do not know how many such species there -are, yet we wish to be able to assert that <i>all</i> acholous animals are -long-lived. In the proof of such a proposition, put in a syllogistic -form, there must necessarily be a logical defect; and the above discussion -shows that this defect is the substitution of the proposition, -"All acholous animals are <i>as</i> elephant, &c.," for the converse of -the experimentally proved proposition, "elephant, &c., are acholous."</p> - -<p>In instances in which the number of particular cases is limited, -the necessary existence of a logical flaw in the syllogistic translation -of the process is not so evident. But in truth, such a flaw exists in -all cases of Induction <i>proper</i>: (for Induction by <i>mere enumeration</i> -can hardly be called <i>Induction</i>). I will, however, consider for a -moment the instance of a celebrated proposition which has often -been taken as an example of Induction, and in which the number of -particular cases is, or at least is at present supposed to be, limited. -Kepler's laws, for instance the law that the planets describe ellipses,<span class="pagenum" id="Page_452">452</span> -may be regarded as examples of Induction. The law was inferred, -we will suppose, from an examination of the orbits of Mars, Earth, -Venus. And the syllogistic illustration which Aristotle gives, will, -with the necessary addition to it, stand thus,</p> - -<blockquote><p> -Mars, Earth, Venus describe ellipses.<br /> -Mars, Earth, Venus are planets.<br /> -</p></blockquote> - -<p>Assuming the convertibility of this last proposition, <i>and its universality</i>, -(which is the necessary addition in order to make Aristotle's -syllogism valid) we say</p> - -<blockquote><p> -All the planets are as Mars, Earth, Venus.<br /> -</p></blockquote> - -<p>Whence it follows that all the planets describe ellipses.</p> - -<p>If, instead of this assumed universality, the astronomer had made -a real enumeration, and had established the fact of each particular, -he would be able to say</p> - -<blockquote> - -<p>Saturn, Jupiter, Mars, Earth, Venus, Mercury, describe -ellipses.</p> - -<p>Saturn, Jupiter, Mars, Earth, Venus, Mercury are all the -planets.</p></blockquote> - -<p>And he would obviously be entitled to convert the second proposition, -and then to conclude that</p> - -<blockquote><p> -All the planets describe ellipses.<br /> -</p></blockquote> - -<p>But then, if this were given as an illustration of Induction by -means of syllogism, we should have to remark, in the first place, that -the conclusion that "all the planets describe ellipses," adds nothing -to the major proposition, that "S., J., M., E., V., m., do so." It is -merely the same proposition expressed in other words, so long as -S., J., M., E., V., m., are supposed to be all the planets. And in -the next place we have to make a remark which is more important; -that the minor, in such an example, must generally be either a very -precarious truth, or, as appears in this case, a transitory error. For -that the planets known at any time are <i>all</i> the planets, must always -be a doubtful assertion, liable to be overthrown to-night by an astronomical -observation. And the assertion, as received in Kepler's -time, has been overthrown. For Saturn, Jupiter, Mars, Earth, -Venus, Mercury, are not all the planets. Not only have several new -ones been discovered at intervals, as Uranus, Ceres, Juno, Pallas, -Vesta, but we have new ones discovered every day; and any conclusion -depending upon this premiss that <i>A</i>, <i>B</i>, <i>C</i>, <i>D</i>, <i>E</i>, <i>F</i>, <i>G</i>, <i>H</i>, to -<i>Z</i> are all the planets, is likely to be falsified in a few years by the -discovery of <i>A´</i>, <i>B´</i>, <i>C´</i>, &c. If, therefore, this were the syllogistic -analysis of Induction, Kepler's discovery rested upon a false proposition; -and even if the analysis were now made conformable to our -present knowledge, that induction, analysed as above, would still<span class="pagenum" id="Page_453">453</span> -involve a proposition which to-morrow may show to be false. But -yet no one, I suppose, doubts that Kepler's discovery was really a -discovery—the establishment of a scientific truth on solid grounds; -or, that it is a scientific truth for us, notwithstanding that we are -constantly discovering new planets. Therefore the syllogistic analysis -of it now discussed (namely, that which introduces simple enumeration -as a step) is not the right analysis, and does not represent -the grounds of the Inductive Truth, that all the planets describe -ellipses.</p> - -<p>It may be said that all the planets discovered since Kepler's time -conform to his law, and thus confirm his discovery. This we grant: -but they only <i>confirm</i> the discovery, they do not make it; they are -not its groundwork. It was a discovery before these new cases -were known; it was an inductive truth without them. Still, an -objector might urge, if any one of these new planets had contradicted -the law, it would have overturned the discovery. But this is too -boldly said. A discovery which is so precise, so complex (in the -phenomena which it explains), so supported by innumerable observations -extending through space and time, is not so easily overturned. -If we find that Uranus, or that Encke's comet, deviates from Kepler's -and Newton's laws, we do not infer that these laws must be -false; we say that there must be some disturbing cause in these -cases. We seek, and we find these disturbing causes: in the case of -Uranus, a new planet; in the case of Encke's comet, a resisting -medium. Even in this case therefore, though the number of particulars -is limited, the Induction was not made by a simple enumeration -of all the particulars. It was made from a few cases, and when -the law was discerned to be true in these, it was extended to all; the -conversion and assumed universality of the proposition that "these -are planets," giving us the proposition which we need for the syllogistic -exhibition of Induction, "all the planets are as these."</p> - -<p>I venture to say further, that it is plain, that Aristotle did not -regard Induction as the result of simple enumeration. This is plain, -in the first place, from his example. Any proposition with regard -to a special class of animals, cannot be proved by simple enumeration: -for the number of particular cases, that is, of animal species -in the class, is indefinite at any period of zoological discovery, and -must be regarded as infinite. In the next place, Aristotle says (§ 10 -of the above extract), "We must conceive that <i>C</i> consists of a collection -of all the particular cases; for induction is applied to all the -cases." We must <i>conceive</i> (νοεῖν) that <i>C</i> in the major, consists of all -the cases, in order that the conclusion may be true of all the cases; -but we cannot <i>observe</i> all the cases. But the evident proof that -Aristotle does not contemplate in this chapter an Induction by sim<span class="pagenum" id="Page_454">454</span>ple -enumeration, is the contrast in which he places Induction and -Syllogism. For Induction by simple enumeration stands in no contrast -to Syllogism. The Syllogism of such Induction is quite logical -and conclusive. But Induction from a comparatively small number -of particular cases to a general law, does stand in opposition -to Syllogism. It gives us a truth,—a truth which, as Aristotle -says (§ 14), is more luminous than a truth proved syllogistically, -though Syllogism may be <i>more natural and usual</i>. It gives us (§ 11) -immediate propositions, obtained directly from observation, and not -by a chain of reasoning: "first truths," the principles from which -syllogistic reasonings may be deduced. The Syllogism proves by -means of a middle term (§ 13) that the extreme is true of a third -thing: thus, (<i>acholous</i> being the middle term):</p> - -<blockquote><p> -Acholous animals are long-lived:<br /> -All elephants are acholous animals:<br /> -Therefore all elephants are long-lived.<br /> -</p></blockquote> - -<p>But Induction proves by means of a third thing (namely, particular -cases) that the extreme is true of the mean; thus (<i>acholous</i>, still -being the middle term)</p> - -<blockquote><p> -Elephants are long-lived:<br /> -Elephants are acholous animals:<br /> -Therefore acholous animals are long-lived.<br /> -</p></blockquote> - -<p>It may be objected, such reasoning as this is quite inconclusive: -and the answer is, that this is precisely what we, and as I believe, -Aristotle, are here pointing out. Induction <i>is</i> inconclusive <i>as reasoning</i>. -It is not reasoning: it is another way of getting at truth. -As we have seen, no reasoning can prove such an inductive truth as -this, that all planets describe ellipses. It is <i>known</i> from observation, -but it is not <i>demonstrated</i>. Nevertheless, no one doubts its universal -truth, (except, as aforesaid, when disturbing causes intervene). -And thence, Induction is, as Aristotle says, opposed to syllogistic -reasoning, and yet is a means of discovering truth: not only so, but -a means of discovering primary truths, immediately derived from -observation.</p> - -<p>I have elsewhere taught that all Induction involves a <i>Conception</i> -of the mind applied to facts. It may be asked whether this applies -in such a case as that given by Aristotle. And I reply, that -Aristotle's instance is a very instructive example of what I mean. -The Conception which is applied to the facts in order to make the -induction possible is the want of the gall-bladder;—and Aristotle -supplies us with a special term for this conception; <i>acholous</i><a name="FNanchor_349" id="FNanchor_349"></a><a href="#Footnote_349" class="fnanchor">[349]</a>. But,<span class="pagenum" id="Page_455">455</span> -it may be said, that the animals observed, the elephant, horse, mule, -&c., are acholous, is a mere fact of observation, not a Conception. -I reply that it is a <i>Selected</i> Fact, a fact selected and compared in -several cases, which is what we mean by a <i>Conception</i>. That there -is needed for such selection and comparison a certain activity of the -mind, is evident; but this also may become more clear by dwelling -a little further on the subject. Suppose that Aristotle, having a -desire to know what class of animals are long-lived, had dissected -for that purpose many animals; elephants, horses, cows, sheep, -goats, deer and the like. How many resemblances, how many differences, -must he have observed in their anatomy! He was very -likely long in fixing upon any one resemblance which was common -to all the long-lived. Probably he tried several other characters, -before he tried the presence and absence of the gall-bladder:—perhaps, -trying such characters, he found them succeed for a few cases, -and then fail in others, so that he had to reject them as useless for -his purpose. All the while, the absence of the gall-bladder in the -long-lived animals was a fact: but it was of no use to him, because -he had not selected it and drawn it forth from the mass of other -facts. He was looking for a mean term to connect his first extreme, -<i>long-lived</i>, with his second, the special cases. He sought this middle -term in the entrails of the many animals which he used as -extremes: it <i>was</i> there, but he could not find it. The fact existed, -but it was of no use for the purpose of Induction, because it did -not become a special Conception in his mind. He considered the -animals in various points of view, it may be, as ruminant, as -horned, as hoofed, and the contrary; but not as <i>acholous</i> and the -contrary. When he looked at animals in that point of view,—when -he took up that character as the ground of distinction, he -forthwith imagined that he found a separation of long-lived and -short-lived animals. When that Fact became a Conception, he obtained -an inductive truth, or, at any rate, an inductive proposition.</p> - -<p>He obtained an inductive proposition by applying the Conception -<i>acholous</i> to his observation of animals. This Conception divided -them into two classes; and these classes were, he fancied, long-lived -and short-lived respectively. That it was the Conception, and not -the Fact which enabled him to obtain his inductive proposition, is -further plain from this, that the supposed Fact is not a fact. -Acholous animals are not longer-lived than others. The presence -or absence of the gall-bladder is no character of longevity. It is -true, that in one familiar class of animals, the herbivorous kind, -there is a sort of first seeming of the truth of Aristotle's asserted -rule: for the horse and mule which have not the gall-bladder are<span class="pagenum" id="Page_456">456</span> -longer-lived than the cow, sheep, and goat, which have it. But if -we pursue the investigation further, the rule soon fails. The deer-tribe -that want the gall-bladder are not longer-lived than the other -ruminating animals which have it. And as a conspicuous evidence -of the falsity of the rule, man and the elephant are perhaps, for -their size, the longest-lived animals, and of these, man has, and the -elephant has not, the organ in question. The inductive proposition, -then, is false; but what we have mainly to consider is, where the -fallacy enters, according to Aristotle's analysis of Induction into -Syllogism. For the two premisses are still true; that elephants, &c., -are long-lived; and that elephants, &c., are acholous. And it is -plain that the fallacy comes in with that conversion and generalization -of the latter proposition, which we have noted as necessary to -Aristotle's illustration of Induction. When we say "All acholous -animals are as elephants, &c.," that is, as those in their biological -conditions, we say what is not true. Aristotle's condition (§ 8) is -not complied with, that the middle term shall not extend beyond -the extreme. For the character <i>acholous</i> does extend beyond the -elephant and the animals biologically resembling it; it extends to -deer, &c., which are not like elephants and horses, in the point in -question. And thus, we see that the assumed conversion and -generalization of the minor proposition, is the seat of the fallacy of -false Inductions, as it is the seat of the peculiar logical character of -true Inductions.</p> - -<p>As true Inductive Propositions cannot be logically demonstrated -by syllogistic rules, so they cannot be discovered by any rule. There -is no formula for the discovery of inductive truth. It is caught by -a peculiar sagacity, or power of divination, for which no precepts -can be given. But from what has been said, we see that this sagacity -shows itself in the discovery of propositions which are both -<i>true</i>, and <i>convertible</i> in the sense above explained. Both these steps -may be difficult. The former is often very laborious: and when the -labour has been expended, and a true proposition obtained, it may -turn out useless, because the proposition is not convertible. It was -a matter of great labour to Kepler to prove (from calculation of -observations) that Mars moves elliptically. Before he proved this, -he had tried to prove many similar propositions:—that Mars moved -according to the "bisection of the eccentricity,"—according to the -"vicarious hypothesis,"—according to the "physical hypothesis,"—and -the like; but none of these was found to be exactly true. The -proposition that Mars moves elliptically was proved to be true. -But still, there was the question, Is it convertible? Do all the -planets move as Mars moves? This was proved, (suppose,) to be<span class="pagenum" id="Page_457">457</span> -true, for the Earth and Venus. But still the question remains, Do -all the planets move as Mars, Earth, Venus, do? The inductive -generalizing impulse boldly answers, Yes, to this question; though -the rules of Syllogism do not authorize the answer, and though there -remain untried cases. The inductive Philosopher tries the cases as -fast as they occur, in order to confirm his previous conviction; but -if he had to wait for belief and conviction till he had tried every -case, he never could have belief or conviction of such a proposition -at all. He is prepared to modify or add to his inductive truth -according as new cases and new observations instruct him; but he -does not fear that new cases or new observations will overturn an -inductive proposition established by exact comparison of many complex -and various phenomena.</p> - -<p>Aristotle's example offers somewhat similar reflections. He had -to establish a proposition concerning long-lived animals, which -should be true, and should be susceptible of generalized conversion. -To prove that the elephant, horse and mule are destitute of gall-bladder -required, at least, the labour of anatomizing those animals -in the seat of that organ. But this labour was not enough; for he -would find those animals to agree in many other things besides in -being acholous. He must have selected that character somewhat at -a venture. And the guess was wrong, as a little more labour would -have shown him; if for instance he had dissected deer: for they are -acholous, and yet short-lived. A trial of this kind would have shown -him that the extreme term, <i>acholous</i>, did extend beyond the mean, -namely, animals such as elephant, horse, mule; and therefore, that -the conversion was not allowable, and that the Induction was untenable. -In truth, there is no relation between bile and longevity<a name="FNanchor_350" id="FNanchor_350"></a><a href="#Footnote_350" class="fnanchor">[350]</a>, -and this example given by Aristotle of generalization from induction -is an unfortunate one.</p> - -<p><span class="pagenum" id="Page_458">458</span></p> - -<hr class="tb" /> - -<p>In discussing this passage of Aristotle, I have made two alterations -in the text, one of which is necessary on account of the fact; -the other on account of the sense. In the received text, the particular -examples of long-lived animals given are <i>man</i>, horse, and mule -(ἐφ' ᾧ δὲ Γ, τὸ καθέκαστον μακρόβιον, οἷον ἄνθρωπος, καὶ ἵππος, καὶ ἡμίονος). -And it is afterwards said that all these are <i>acholous</i>: -(ἀλλὰ καὶ τὸ Β, τὸ μὴ ἔχον χολὴν, παντὶ ὑπάρχει τῷ Γ). But -man <i>has</i> a gall-bladder: and the fact was well known in Aristotle's -time, for instance, to Hippocrates; so that it is not likely that -Aristotle would have made the mistake which the text contains. -But at any rate, it is a mistake; if not of the transcriber, of Aristotle; -and it is impossible to reason about the passage, without correcting -the mistake. The substitution of ἔλεφας for ἄνθρωπος makes the -reasoning coherent; but of course, any other acholous long-lived -animal would do so equally well.</p> - -<p>The other emendation which I have made is in § 6. In the received -text § 6 and 7 stand thus:</p> - -<blockquote> - -<p>6. Then every <i>C</i> is <i>A</i>, for <i>every acholous animal is long-lived</i></p> - -<p>(τῷ δὴ Γ ὅλω ὑπάρχει τὸ Α, πᾶν γὰρ τὸ ἄχολον μακρόβιον).</p> - -<p>7. Also every <i>C</i> is <i>B</i>, for all <i>C</i> is destitute of bile.</p></blockquote> - -<p>Whence it may be inferred, says Aristotle, under certain conditions, -that every <i>B</i> is <i>A</i> (τὸ Α τῷ Β ὑπάρχειν) that is, that <i>every -acholous animal is long-lived</i>. But this conclusion is, according to -the common reading, identical with the major premiss; so that the -passage is manifestly corrupt. I correct it by substituting for -ἄχολον, Γ; and thus reading πᾶν γὰρ τὸ Γ μακρόβιον "for every -<i>C</i> is long-lived:" just as in the parallel sentence, 7, we have -ἀλλὰ καὶ τὸ Β, τὸ μὴ ἔχον χολην, παντὶ ὑπάρχει τῷ Γ. In this way -the reasoning becomes quite clear. The corrupt substitution of -ἄχολον for Γ may have been made in various ways; which I need -not suggest. As my business is with the sense of the passage, and -as it makes no sense without the change, and very good sense with -it, I cannot hesitate to make the emendation. And these emendations -being made, Aristotle's view of the nature and force of Induction -becomes, I think, perfectly clear and very instructive.</p> - -<p><span class="pagenum" id="Page_459">459</span></p> - -<hr class="tb" /> - - -<p>ADDITIONAL NOTE.</p> - -<p>I take the liberty of adding to this Memoir the following remarks, -for which I am indebted to Mr.Edleston, Fellow of Trinity College.</p> - -<p>Several of the earlier editions of Aristotle have γ instead of -ἄχολον in the passage referred to in the above paper: ex. gr.</p> - -<p>(1) The edition printed at Basle, 1539 (after Erasmus): "τὸ γ."</p> - -<p>(2) Basil (Erasmus) 1550. "τὸ γ."</p> - -<p>(3) Burana's Latin version, Venet. 1552, has "omne enim <i>C</i> -longævum."</p> - -<p>(4) Sylburg, Francf. 1587 "τὸ γ" is printed in brackets thus: -"[τὸ γ] τὸ ἄχολον."</p> - -<p>(5) So also in Casaubon's edition, 1590.</p> - -<p>(6) Casaub. 1605 "τὸ γ," (though the Latin version has "vacans -bile;") not "[τὸ γ] τὸ ἄχολον," as the edition of 1590.</p> - -<p>(7) In the edition printed Aurel. Allobr. 1607, "[τὸ γ] τὸ -ἄχολον," as in (4) and (5).</p> - -<p>(8) Du Val's editions, Paris, 1619, 1629, 1654 "τὸ γ," though in -Pacius's translation in the adjacent column we find "vacans bile."</p> - -<p>(9) In the critical notes to Waitz's edition of the <i>Organon</i> (Lips. -1844) it is stated that "post ἄχολον del. γ. <i>n</i>," implying apparently, -that in the MS. marked <i>n</i>, the letter γ, which had been originally -written after ἄχολον, had been erased.</p> - -<hr class="tb" /> - -<p>The following passages throw light upon the question whether -ἄνθρωπος ought or ought not to be retained in the passage discussed -in the Memoir.</p> - -<p>(A) Aristot. <i>De Animalibus Histor.</i> <span class="smcap">II.</span> 15, 9 (Bekk.), τῶν μὲν -ζωοτόκων καὶ τετραπόδων ἔλαφος οὐκ ἔχει [χολήν] οὐδὲ πρόξ, ἕτι δὲ -ἵππος, ὀρεύς, ὄνος, φώκη καὶ τῶν ὑῶν ἔνιοι.... Ἔχει δὲ καὶ ὁ ἐλέφας τὸ -ῆπαρ ἄχολον μέν, κ.τ.λ.</p> - -<p>(B) Conf. Ib. <span class="smcap">I.</span> 17, 10, 11. (In the beginning of Chap. 16, he -says that the external μορια of man are γνώριμα, "τὰ δ' ἐντὸς τοὐναντίον. -Ἄγνωστα γάρ ἐστι μάλιστα τὰ τῶν ἀνθρώπων, ὡστε δεῖ πρὸς τὰ τῶν ἄλλων μόρια -ζώων ἀνάγοντας σκοπεῖν," ...)</p> - -<p>(C) Id <i>De Part. Animal.</i> <span class="smcap">IV.</span> 2, 2. τὰ μὲν γὰρ ὅλως οὐκ ἕχει χολήν, -οἷον ἱππος και ὀρεύς καὶ ονος καὶ ἔλαφος καὶ πρόξ.....<span class="pagenum" id="Page_460">460</span> -Ἐν δὲ τοῖς γένεσι τοῖς αὐτοῖς τὰ μὲν ἔχειν φαίνεται, τὰ δ' οὐκ -ἔχειν, οἷον ἐν τῷ τῶν μυῶν. Τούτων δ' ἐστὶ καὶ ὁ ἄνθρωπος· -ἔνιοι μὲν γὰρ φαίνονται ἔχοντες χολὴν ἐπὶ του ἥπατος, ἔνιοι δ' -οὐκ ἔχοντες. Διο καὶ γίνεται ἀμφισβήτησις περὶ ὁλου τοῦ γένους· -οἱ γὰρ ἐντυχόντες ὁποτερωσοῦν ἔχουσι περὶ πάντων ὑπολαμβάνουσιν -ὡς ἁπάντων ἐχόντων.....</p> - -<p>(D) Ib. § 11. Διὸ καὶ χαριέστατα λέγουσι τῶν ῶρχαίων ὁι -φάσκοντες αἴτιον εῖναι τοῦ πλείω ζῆν χρόνον το μὴ ἔχειν χολήν, -βλέψαντες ἐπὶ τὰ μωνυχα και τὰς ελαφους· ταῦτα γὰρ -ἄχολά τε καὶ ζῇ πολὺν χρόνον. Ἔτι δὲ καὶ τὰ μὴ ἑωραμένα -ὑπ' ἐκείνων ὁτι οὐκ ἔχει χολήν, οἷον δελφις καὶ κάμηλος, καὶ -ταῦτα τυγχάνει μακρόβια ὄντα. Εὔλογον γάρ, κ.τ.λ.</p> - -<p>(E) The elephant and man are mentioned together as long-lived -animals (<i>De Long. et Brev. Vitæ</i>, <span class="smcap">IV.</span> 2, and <i>De Generat. Animal.</i> -<span class="smcap">IV.</span> 10, 2.)</p> - -<hr class="tb" /> - -<p>The following is the import of these passages:</p> - -<p>(<i>A</i>) "Of viviparous quadrupeds, the deer, roe, horse, mule, ass, -seal, and some of the swine have not the gall-bladder....</p> - -<p>The elephant also has the liver without gall-bladder, &c."</p> - -<p>(<i>B</i>) "The external parts of man are well known: the internal -parts are far from being so. The parts of man are in a great measure -unknown; so that we must judge concerning them by reference -to the analogy of other animals...."</p> - -<p>(<i>C</i>) "Some animals are altogether destitute of gall-bladder, as -the horse, the mule, the ass, the deer, the roe.... But in some kinds -it appears that some have it, and some have it not, as the mice kind. -And among these is man; for some men appear to have a gall-bladder -on the liver, and some not to have one. And thus there is -a doubt as to the species in general; for those who have happened -to examine examples of either kind, hold that all the cases are of -that kind."</p> - -<p>(<i>D</i>) Those of the ancients speak most plausibly, who say that -the absence of the gall-bladder is the cause of long life; looking -at animals with uncloven hoof, and deer: for these are destitute of -gall-bladder, and live a long time. And further, those animals in -which the ancients had not the opportunity of ascertaining that -they have not the gall-bladder, as the dolphin, and the camel, are -also long-lived animals."</p> - -<p><span class="pagenum" id="Page_461">461</span></p> - -<p>It appears, from these passages, that Aristotle was aware that -some persons had asserted man to have a gall-bladder, but that he -also conceived this not to be universally true. He may have inclined -to the opinion, that the opposite case was the more usual, -and may have written ἄνθρωπος in the passage which I have been -discussing. Another mistake of his is the reckoning deer among -long-lived animals.</p> - -<p>It appears probable, from the context of the passages (<i>C</i>) and -(<i>D</i>), that the conjecture of a connexion between absence of the -gall-bladder and length of life was suggested by some such notion -as this:—that the gall, from its bitterness, is the cause of irritation, -mental and bodily, and that irritation is adverse to longevity. The -opinion is ascribed to "the ancients," not claimed by Aristotle as -his own.</p> -<hr class="chap" /> - -<p><span class="pagenum" id="Page_462">462</span></p> - - - -<h3><a name="Appendix_E" id="Appendix_E"></a><span class="smcap">Appendix E.</span><br /> - -ON THE FUNDAMENTAL ANTITHESIS OF -PHILOSOPHY.</h3> - -<p class="center">(<i>Cam. Phil. Soc.</i> <span class="smcap">Feb. 5, 1844.</span>)</p> - - -<p> -<span class="dropcap"><span class="dsmall">1.</span> A</span>LL persons who have attended in any degree to the views -generally current of the nature of reasoning are familiar -with the distinction of <i>necessary</i> truths and <i>truths of experience</i>; -and few such persons, or at least few students of mathematics, -require to have this distinction explained or enforced. All geometricians -are satisfied that the geometrical truths with which they -are conversant are necessarily true: they not only are true, but -they must be true. The meaning of the terms being understood, -and the proof being gone through, the truth of the proposition -must be assented to. That parallelograms upon the same base and -between the same parallels are equal;—that angles in the same -segment are equal;—these are propositions which we learn to be -true by demonstrations deduced from definitions and axioms; and -which, when we have thus learnt them, we see could not be otherwise. -On the other hand, there are other truths which we learn -from experience; as for instance, that the stars revolve round the -pole in one day; and that the moon goes through her phases from -full to full again in thirty days. These truths we see to be true; -but we know them only by experience. Men never could have -discovered them without looking at the stars and the moon; and -having so learnt them, still no one will pretend to say that they are -necessarily true. For aught we can see, things might have been -otherwise; and if we had been placed in another part of the solar -system, then, according to the opinions of astronomers, experience -would have presented them otherwise.</p> - -<p>2. I take the astronomical truths of experience to contrast with -the geometrical necessary truths, as being both of a familiar definite -sort; we may easily find other examples of both kinds of truth. -The truths which regard numbers are necessary truths. It is a -necessary truth, that 27 and 38 are equal to 65; that half the sum<span class="pagenum" id="Page_463">463</span> -of two numbers added to half their difference is equal to the -greater number. On the other hand, that sugar will dissolve in -water; that plants cannot live without light; and in short, the -whole body of our knowledge in chemistry, physiology, and the -other inductive sciences, consists of truths of experience. If there -be any science which offer to us truths of an ambiguous kind, with -regard to which we may for a moment doubt whether they are -necessary or experiential, we will defer the consideration of them -till we have marked the distinction of the two kinds more clearly.</p> - -<p>3. One mode in which we may express the difference of necessary -truths and truths of experience, is, that necessary truths are those -<i>of which we cannot distinctly conceive the contrary</i>. We can very -readily conceive the contrary of experiential truths. We can -conceive the stars moving about the pole or across the sky in any -kind of curves with any velocities; we can conceive the moon -always appearing during the whole month as a luminous disk, as -she might do if her light were inherent and not borrowed. But -we cannot conceive one of the parallelograms on the same base -and between the same parallels larger than the other; for we -find that, if we attempt to do this, when we separate the parallelograms -into parts, we have to conceive one triangle larger than -another, both having all their parts equal; which we cannot -conceive at all, if we conceive the triangles distinctly. We make -this impossibility more clear by conceiving the triangles to be -placed so that two sides of the one coincide with two sides of -the other; and it is then seen, that in order to conceive the triangles -unequal, we must conceive the two bases which have the -same extremities both ways, to be different lines, though both -straight lines. This it is impossible to conceive: we assent to the -impossibility as an axiom, when it is expressed by saying, that two -straight lines cannot inclose a space; and thus we cannot distinctly -conceive the contrary of the proposition just mentioned respecting -parallelograms.</p> - -<p>4. But it is necessary, in applying this distinction, to bear in -mind the terms of it;—that we cannot <i>distinctly</i> conceive the contrary -of a necessary truth. For in a certain loose, indistinct way, -persons conceive the contrary of necessary geometrical truths, when -they erroneously conceive false propositions to be true. Thus, -Hobbes erroneously held that he had discovered a means of geometrically -doubling the cube, as it is called, that is, finding two -mean proportionals between two given lines; a problem which cannot -be solved by plane geometry. Hobbes not only proposed a -construction for this purpose, but obstinately maintained that it<span class="pagenum" id="Page_464">464</span> -was right, when it had been proved to be wrong. But then, the -discussion showed how indistinct the geometrical conceptions of -Hobbes were; for when his critics had proved that one of the lines -in his diagram would not meet the other in the point which his -reasoning supposed, but in another point near to it; he maintained, -in reply, that one of these points was large enough to include -the other, so that they might be considered as the same point. -Such a mode of conceiving the opposite of a geometrical truth, -forms no exception to the assertion, that this opposite cannot be -distinctly conceived.</p> - -<p>5. In like manner, the indistinct conceptions of children and of -rude savages do not invalidate the distinction of necessary and experiential -truths. Children and savages make mistakes even with -regard to numbers; and might easily happen to assert that 27 -and 38 are equal to 63 or 64. But such mistakes cannot make -such arithmetical truths cease to be necessary truths. When any -person conceives these numbers and their addition distinctly, by resolving -them into parts, or in any other way, he sees that their sum -is necessarily 65. If, on the ground of the possibility of children -and savages conceiving something different, it be held that this is -not a necessary truth, it must be held on the same ground, that -it is not a necessary truth that 7 and 4 are equal to 11; for children -and savages might be found so unfamiliar with numbers as not to -reject the assertion that 7 and 4 are 10, or even that 4 and 3 are 6, -or 8. But I suppose that no persons would on such grounds hold -that these arithmetical truths are truths known only by experience.</p> - -<p>6. Necessary truths are established, as has already been said, -by demonstration, proceeding from definitions and axioms, according -to exact and rigorous inferences of reason. Truths of experience -are collected from what we see, also according to inferences -of reason, but proceeding in a less exact and rigorous mode of -proof. The former depend upon the relations of the ideas which -we have in our minds: the latter depend upon the appearances or -phenomena, which present themselves to our senses. Necessary -truths are formed from our thoughts, the elements of the world -within us; experiential truths are collected from things, the elements -of the world without us. The truths of experience, as they -appear to us in the external world, we call Facts; and when we -are able to find among our ideas a train which will conform themselves -to the apparent facts, we call this a Theory.</p> - -<p>7. This distinction and opposition, thus expressed in various -forms; as Necessary and Experiential Truth, Ideas and Senses,<span class="pagenum" id="Page_465">465</span> -Thoughts and Things, Theory and Fact, may be termed the -<i>Fundamental Antithesis of Philosophy</i>; for almost all the discussions -of philosophers have been employed in asserting or denying, -explaining or obscuring this antithesis. It may be expressed in -many other ways; but is not difficult, under all these different -forms, to recognize the same opposition: and the same remarks -apply to it under its various forms, with corresponding modifications. -Thus, as we have already seen, the antithesis agrees with -that of Reasoning and Observation: again, it is identical with the -opposition of Reflection and Sensation: again, sensation deals -with Objects; facts involve Objects, and generally all things without -us are Objects:—Objects of sensation, of observation. On the -other hand, we ourselves who thus observe objects, and in whom -sensation is, may be called the Subjects of sensation and observation. -And this distinction of Subject and Object is one of the most -general ways of expressing the fundamental antithesis, although -not yet perhaps quite familiar in English. I shall not scruple -however to speak of the Subjective and Objective element of this -antithesis, where the expressions are convenient.</p> - -<p>8. All these forms of antithesis, and the familiar references to -them which men make in all discussions, show the fundamental -and necessary character of the antithesis. We can have no knowledge -without the union, no philosophy without the separation, of -the two elements. We can have no knowledge, except we have -both impressions on our senses from the world without, and -thoughts from our minds within:—except we attend to things, and -to our ideas;—except we are passive to receive impressions, and -active to compare, combine, and mould them. But on the other -hand, philosophy seeks to distinguish the impressions of our senses -from the thoughts of our minds;—to point out the difference of -ideas and things;—to separate the active from the passive faculties -of our being. The two elements, sensations and ideas, are both -requisite to the existence of our knowledge, as both matter and -form are requisite to the existence of a body. But philosophy -considers the matter and the form separately. The properties of -the form are the subject of geometry, the properties of the matter -are the subject of chemistry or mechanics.</p> - -<p>9. But though philosophy considers these elements of knowledge -separately, they cannot really be separated, any more than -can matter and form. "We cannot exhibit matter without form, or -form without matter; and just as little can we exhibit sensations -without ideas, or ideas without sensations;—the passive or the -active faculties of the mind detached from each other.</p> - -<p><span class="pagenum" id="Page_466">466</span></p> - -<p>In every act of my knowledge, there must be concerned the -things whereof I know, and thoughts of me who know: I must -both passively receive or have received impressions, and I must -actively combine them and reason on them. No apprehension of -things is purely ideal: no experience of external things is purely -sensational. If they be conceived as <i>things</i>, the mind must have -been awakened to the conviction of things by sensation: if they be -<i>conceived</i> as things, the expressions of the senses must have been -bound together by conceptions. If we <i>think</i> of any <i>thing</i>, we must -recognize the existence both of thoughts and of things. <i>The -fundamental antithesis of philosophy is an antithesis of inseparable -elements.</i></p> - -<p>10. Not only cannot these elements be separately exhibited, but -they cannot be separately conceived and described. The description -of them must always imply their relation; and the names by -which they are denoted will consequently always bear a relative -significance. And thus <i>the terms which denote the fundamental antithesis -of philosophy cannot be applied absolutely and exclusively -in any case</i>. We may illustrate this by a consideration of some of -the common modes of expressing the antithesis of which we speak. -The terms Theory and Fact are often emphatically used as opposed -to each other: and they are rightly so used. But yet it is impossible -to say absolutely in any case, This is a Fact and not a -Theory; this is a Theory and not a Fact, meaning by Theory, true -Theory. Is it a fact or a theory that the stars appear to revolve -round the pole? Is it a fact or a theory that the earth is a globe -revolving round its axis? Is it a fact or a theory that the earth -revolves round the sun? Is it a fact or a theory that the sun -attracts the earth? Is it a fact or a theory that a loadstone attracts -a needle? In all these cases, some persons would answer one way -and some persons another. A person who has never watched the -stars, and has only seen them from time to time, considers their -circular motion round the pole as a theory, just as he considers the -motion of the sun in the ecliptic as a theory, or the apparent -motion of the inferior planets round the sun in the zodiac. A -person who has compared the measures of different parts of the -earth, and who knows that these measures cannot be conceived distinctly -without supposing the earth a globe, considers its globular -form a fact, just as much as the square form of his chamber. A -person to whom the grounds of believing the earth to revolve round -its axis and round the sun, are as familiar as the grounds for believing -the movements of the mail-coaches in this country, conceives -the former events to be facts, just as steadily as the latter.<span class="pagenum" id="Page_467">467</span> -And a person who, believing the fact of the earth's annual motion, -refers it distinctly to its mechanical course, conceives the sun's -attraction as a fact, just as he conceives as a fact the action of the -wind which turns the sails of a mill. We see then, that in these -cases we cannot apply absolutely and exclusively either of the terms, -Fact or Theory. Theory and Fact are the elements which correspond -to our Ideas and our Senses. The Facts are facts so far as -the Ideas have been combined with the sensations and absorbed -in them: the Theories are Theories so far as the Ideas are kept -distinct from the sensations, and so far as it is considered as still -a question whether they can be made to agree with them. A true -Theory is a fact, a Fact is a familiar theory.</p> - -<p>In like manner, if we take the terms Reasoning and Observation; -at first sight they appear to be very distinct. Our observation -of the world without us, our reasonings in our own minds, -appear to be clearly separated and opposed. But yet we shall find -that we cannot apply these terms absolutely and exclusively. I see -a book lying a few feet from me: is this a matter of observation? -At first, perhaps, we might be inclined to say that it clearly is so. -But yet, all of us, who have paid any attention to the process of -vision, and to the mode in which we are enabled to judge of the -distance of objects, and to judge them to be distant objects at all, -know that this judgment involves inferences drawn from various -sensations;—from the impressions on our two eyes;—from our -muscular sensations; and the like. These inferences are of the -nature of reasoning, as much as when we judge of the distance -of an object on the other side of a river by looking at it from different -points, and stepping the distance between them. Or again: we -observe the setting sun illuminate a gilded weathercock; but this is -as much a matter of reasoning as when we observe the phases -of the moon, and infer that she is illuminated by the sun. All observation -involves inferences, and inference is reasoning.</p> - -<p>11. Even the simplest terms by which the antithesis is expressed -cannot be applied: ideas and sensations, thoughts and things, subject -and object, cannot in any case be applied absolutely and exclusively. -Our sensations require ideas to bind them together, -namely, ideas of space, time, number, and the like. If not so -bound together, sensations do not give us any apprehension of -things or objects. All things, all objects, must exist in space and -in time—must be one or many. Now space, time, number, are not -sensations or things. They are something different from, and opposed -to sensations and things. We have termed them ideas. It -may be said they are <i>relations</i> of things, or of sensations. But<span class="pagenum" id="Page_468">468</span> -granting this form of expression, still a <i>relation</i> is not a thing -or a sensation; and therefore we must still have another and -opposite element, along with our sensations. And yet, though -we have thus these two elements in every act of perception, we -cannot designate any portion of the act as absolutely and exclusively -belonging to one of the elements. Perception involves sensation, -along with ideas of time, space, and the like; or, if any -one prefers the expression, involves sensations along with the apprehension -of relations. Perception is sensation, along with such -ideas as make sensation into an apprehension of things or objects.</p> - -<p>12. And as perception of objects implies ideas, as observation -implies reasoning; so, on the other hand, ideas cannot exist where -sensation has not been: reasoning cannot go on when there has not -been previous observation. This is evident from the necessary -order of development of the human faculties. Sensation necessarily -exists from the first moments of our existence, and is constantly -at work. Observation begins before we can suppose the existence -of any reasoning which is not involved in observation. Hence, -at whatever period we consider our ideas, we must consider them -as having been already engaged in connecting our sensations, and -as modified by this employment. By being so employed, our ideas -are unfolded and defined, and such development and definition -cannot be separated from the ideas themselves. We cannot conceive -space without boundaries or forms; now forms involve sensations. -We cannot conceive time without events which mark -the course of time; but events involve sensations. We cannot -conceive number without conceiving things which are numbered; -and things imply sensations. And the forms, things, events, which -are thus implied in our ideas, having been the objects of sensation -constantly in every part of our life, have modified, unfolded -and fixed our ideas, to an extent which we cannot estimate, but -which we must suppose to be essential to the processes which at -present go on in our minds. We cannot say that objects create -ideas; for to perceive objects we must already have ideas. But we -may say, that objects and the constant perception of objects have so -far modified our ideas, that we cannot, even in thought, separate -our ideas from the perception of objects.</p> - -<p>We cannot say of any ideas, as of the idea of space, or time, or -number, that they are absolutely and exclusively ideas. We cannot -conceive what space, or time, or number would be in our minds, -if we had never perceived any thing or things in space or time. -We cannot conceive ourselves in such a condition as never to have -perceived any thing or things in space or time. But, on the other<span class="pagenum" id="Page_469">469</span> -hand, just as little can we conceive ourselves becoming acquainted -with space and time or numbers as objects of sensation. We cannot -reason without having the operations of our minds affected by -previous sensations; but we cannot conceive reasoning to be merely -a series of sensations. In order to be used in reasoning, sensation -must become observation; and, as we have seen, observation -already involves reasoning. In order to be connected by our ideas, -sensations must be things or objects, and things or objects already -include ideas. And thus, as we have said, none of the terms by -which the fundamental antithesis is expressed can be absolutely -and exclusively applied.</p> - -<p>13. I now proceed to make one or two remarks suggested by -the views which have thus been presented. And first I remark, -that since, as we have just seen, none of the terms which express -the fundamental antithesis can be applied absolutely and exclusively, -the absolute application of the antithesis in any particular -case can never be a conclusive or immoveable principle. This -remark is the more necessary to be borne in mind, as the terms of -this antithesis are often used in a vehement and peremptory manner. -Thus we are often told that such a thing is a <i>Fact</i> and not a -Theory, with all the emphasis which, in speaking or writing, tone -or italics or capitals can give. "We see from what has been said, -that when this is urged, before we can estimate the truth, or the -value of the assertion, we must ask to whom is it a fact? what -habits of thought, what previous information, what ideas does it -imply, to conceive the fact as a fact? Does not the apprehension -of the fact imply assumptions which may with equal justice be -called theory, and which are perhaps false theory? in which case, -the fact is no fact. Did not the ancients assert it as a fact, that the -earth stood still, and the stars moved? and can any fact have -stronger apparent evidence to justify persons in asserting it emphatically -than this had? These remarks are by no means urged in -order to show that no fact can be certainly known to be true; but -only to show that no fact can be certainly shown to be a fact -merely by calling it a fact, however emphatically. There is by no -means any ground of general skepticism with regard to truth -involved in the doctrine of the necessary combination of two elements -in all our knowledge. On the contrary, ideas are requisite -to the essence, and things to the reality of our knowledge in every -case. The proportions of geometry and arithmetic are examples of -knowledge respecting our ideas of space and number, with regard -to which there is no room for doubt. The doctrines of astronomy -are examples of truths not less certain respecting the external world.</p> - -<p><span class="pagenum" id="Page_470">470</span></p> - -<p>14. I remark further, that since in every act of knowledge, -observation or perception, both the elements of the fundamental -antithesis are involved, and involved in a manner inseparable even -in our conceptions, it must always be possible to derive one of these -elements from the other, if we are satisfied to accept, as proof of -such derivation, that one always co-exists with and implies the -other. Thus an opponent may say, that our ideas of space, time, -and number, are derived from our sensations or perceptions, because -we never were in a condition in which we had the ideas of space -and time, and had not sensations or perceptions. But then, we -may reply to this, that we no sooner perceive objects than we perceive -them as existing in space and time, and therefore the ideas of -space and time are not derived from the perceptions. In the same -manner, an opponent may say, that all knowledge which is involved -in our reasonings is the result of experience; for instance, our -knowledge of geometry. For every geometrical principle is presented -to us by experience as true; beginning with the simplest, -from which all others are derived by processes of exact reasoning. -But to this we reply, that experience cannot be the origin of such -knowledge; for though experience shows that such principles are -true, it cannot show that they <i>must be</i> true, which we also know. -We never have seen, as a matter of observation, two straight lines -inclosing a space; but we venture to say further, without the -smallest hesitation, that we never shall see it; and if any one were -to tell us that, according to his experience, such a form was often -seen, we should only suppose that he did not know what he was -talking of. No number of acts of experience can add to the certainty -of our knowledge in this respect; which shows that our -knowledge is not made up of acts of experience. We cannot test -such knowledge by experience; for if we were to try to do so, we -must first know that the lines with which we make the trial <i>are</i> -straight; and we have no test of straightness better than this, that -two such lines cannot inclose a space. Since then, experience can -neither destroy, add to, nor test our axiomatic knowledge, such -knowledge cannot be derived from experience. Since no one act of -experience can affect our knowledge, no numbers of acts of experience -can make it.</p> - -<p>15. To this a reply has been offered, that it is a characteristic -property of geometric forms that the ideas of them exactly resemble -the sensations; so that these ideas are as fit subjects of experimentation -as the realities themselves; and that by such experimentation -we learn the truth of the axioms of geometry. I might -very reasonably ask those who use this language to explain how a<span class="pagenum" id="Page_471">471</span> -particular class of ideas can be said to resemble sensations; how, if -they do, we can know it to be so; how we can prove this resemblance -to belong to geometrical ideas and sensations; and how it -comes to be an especial characteristic of those. But I will put the -argument in another way. Experiment can only show what is, -not what must be. If experimentation on ideas shows what must -be, it is different from what is commonly called experience.</p> - -<p>I may add, that not only the mere use of our senses cannot show -that the axioms of geometry <i>must be</i> true, but that, without the -light of our ideas, it cannot even show that they <i>are</i> true. If we -had a segment of a circle a mile long and an inch wide, we should -have two lines inclosing a space; but we could not, by seeing or -touching any part of either of them, discover that it was a bent line.</p> - -<p>16. That mathematical truths are not derived from experience -is perhaps still more evident, if greater evidence be possible, in the -case of numbers. We assert that 7 and 8 are 15. We find it so, if -we try with counters, or in any other way. But we do not, on that -account, say that the knowledge is derived from experience. We -refer to our conceptions of seven, of eight, and of addition, and as -soon as we possess these conceptions distinctly, we see that the -sum must be fifteen. We cannot be said to make a trial, for we -should not believe the apparent result of the trial if it were different. -If any one were to say that the multiplication table is a table of -the results of experience, we should know that he could not be -able to go along with us in our researches into the foundations of -human knowledge; nor, indeed, to pursue with success any speculations -on the subject.</p> - -<p>17. Attempts have also been made to explain the origin of -axiomatic truths by referring them to the association of ideas. But -this is one of the cases in which the word <i>association</i> has been -applied so widely and loosely, that no sense can be attached to it. -Those who have written with any degree of distinctness on the -subject, have truly taught, that the habitual association of the ideas -leads us to believe a connexion of the things: but they have never -told us that this association gave us the power of forming the ideas. -Association may determine belief, but it cannot determine the possibility -of our conceptions. The African king did not believe that -water could become solid, because he had never seen it in that -state. But that accident did not make it impossible to conceive it -so, any more than it is impossible for us to conceive frozen quicksilver, -or melted diamond, or liquefied air; which we may never -have seen, but have no difficulty in conceiving. If there were a -tropical philosopher really incapable of conceiving water solidified,<span class="pagenum" id="Page_472">472</span> -he must have been brought into that mental condition by abstruse -speculations on the necessary relations of solidity and fluidity, not -by the association of ideas.</p> - -<p>18. To return to the results of the nature of the Fundamental -Antithesis. As by assuming universal and indissoluble connexion -of ideas with perceptions, of knowledge with experience, as an -evidence of derivation, we may assert the former to be derived from -the latter, so might we, on the same ground, assert the latter to be -derived from the former. We see all forms in space; and we -might hence assert all forms to be mere modifications of our idea -of space. We see all events happen in time; and we might hence -assert all events to be merely limitations and boundary-marks of -our idea of time. We conceive all collections of things as two or -three, or some other number: it might hence be asserted that we -have an original idea of number, which is reflected in external -things. In this case, as in the other, we are met at once by the -impossibility of this being a complete account of our knowledge. -Our ideas of space, of time, of number, however distinctly reflected -to us with limitations and modifications, must be reflected, limited -and modified by something different from themselves. We must -have visible or tangible forms to limit space, perceived events to -mark time, distinguishable objects to exemplify number. But still, -in forms, and events, and objects, we have a knowledge which they -themselves cannot give us. For we know, without attending to -them, that whatever they are, they will conform and must conform -to the truths of geometry and arithmetic. There is an ideal portion -in all our knowledge of the external world; and if we were -resolved to reduce all our knowledge to one of its two antithetical -elements, we might say that all our knowledge consists in the relation -of our ideas. Wherever there is necessary truth, there must -be something more than sensation can supply: and the necessary -truths of geometry and arithmetic show us that our knowledge of -objects in space and time depends upon necessary relations of ideas, -whatever other element it may involve.</p> - -<p>19. This remark may be carried much further than the domain -of geometry and arithmetic. Our knowledge of matter may at first -sight appear to be altogether derived from the senses. Yet we -cannot derive from the senses our knowledge of a truth which we -accept as universally certain;—namely, that we cannot by any process -add to or diminish the quantity of matter in the world. This -truth neither is nor can be derived from experience; for the experiments -which we make to verify it pre-suppose its truth. When -the philosopher was asked what was the weight of smoke, he bade<span class="pagenum" id="Page_473">473</span> -the inquirer subtract the weight of the ashes from the weight of -the fuel. Every one who thinks clearly of the changes which take -place in matter, assents to the justice of this reply: and this, not -because any one had found by trial that such was the weight of the -smoke produced in combustion, but because the weight lost was -assumed to have gone into some other form of matter, not to have -been destroyed. When men began to use the balance in chemical -analysis, they did not prove by trial, but took for granted, as self-evident, -that the weight of the whole must be found in the aggregate -weight of the elements. Thus it is involved in the idea of -matter that its amount continues unchanged in all changes which -take place in its consistence. This is a necessary truth: and thus -our knowledge of matter, as collected from chemical experiments, -is also a modification of our idea of matter as the material of the -world incapable of addition or diminution.</p> - -<p>20. A similar remark may be made with regard to the mechanical -properties of matter. Our knowledge of these is reduced, in -our reasonings, to principles which we call the laws of motion. -These laws of motion, as I have endeavoured to show<a name="FNanchor_351" id="FNanchor_351"></a><a href="#Footnote_351" class="fnanchor">[351]</a>, depend -upon the idea of Cause, and involve necessary truths, which are -necessarily implied in the idea of cause;—namely, that every -change of motion must have a cause—that the effect is measured -by the cause;—that reaction is equal and opposite to action. -These principles are not derived from experience. No one, I suppose, -would derive from experience the principle, that every event -must have a cause. Every attempt to see the traces of cause in -the world assumes this principle. I do not say that these principles -are anterior to experience; for I have already, I hope, shown, -that neither of the two elements of our knowledge is, or can be, -anterior to the other. But the two elements are co-ordinate in the -development of the human mind; and the ideal element may be -said to be the origin of our knowledge with the more propriety -of the two, inasmuch as our knowledge is the relation of ideas. -The other element of knowledge, in which sensation is concerned, -and which embodies, limits, and defines the necessary truths which -express the relations of our ideas, may be properly termed experience; -and I have, in the discussion just quoted, endeavoured -to show how the principles concerning mechanical causation, -which I have just stated, are, by observation and experiment, -limited and defined, so that they become the laws of motion.<span class="pagenum" id="Page_474">474</span> -And thus we see that such knowledge is derived from ideas, in -a sense quite as general and rigorous, to say the least, as that -in which it is derived from experience.</p> - -<p>21. I will take another example of this; although it is one less -familiar, and the consideration of it perhaps a little more difficult -and obscure. The objects which we find in the world, for instance, -minerals and plants, are of different kinds; and according -to their kinds, they are called by various names, by means of -which we know what we mean when we speak of them. The -discrimination of these kinds of objects, according to their different -forms and other properties, is the business of chemistry and -botany. And this business of discrimination, and of consequent -classification, has been carried on from the first periods of the -development of the human mind, by an industrious and comprehensive -series of observations and experiments; the only way in -which any portion of the task could have been effected. But as the -foundation of all this labour, and as a necessary assumption during -every part of its progress, there has been in men's minds the -principle, that objects are so distinguishable by resemblances and -differences, that they may be named, and known by their names. -This principle is involved in the idea of a Name; and without -it no progress could have been made. The principle may be -briefly stated thus:—Intelligible Names of kinds are possible. If -we suppose this not to be so, language can no longer exist, nor -could the business of human life go on. If instead of having -certain definite kinds of minerals, gold, iron, copper and the like, -of which the external forms and characters are constantly connected -with the same properties and qualities, there were no connexion -between the appearance and the properties of the object;—if -what seemed externally iron might turn out to resemble lead in -its hardness; and what seemed to be gold during many trials, -might at the next trial be found to be like copper; not only all the -uses of these minerals would fail, but they would not be distinguishable -kinds of things, and the names would be unmeaning. -And if this entire uncertainty as to kind and properties prevailed -for all objects, the world would no longer be a world to which language -was applicable. To man, thus unable to distinguish objects -into kinds, and call them by names, all knowledge would be impossible, -and all definite apprehension of external objects would -fade away into an inconceivable confusion. In the very apprehension -of objects as intelligibly sorted, there is involved a principle -which springs within us, contemporaneous, in its efficacy, with our -first intelligent perception of the kinds of things of which the world<span class="pagenum" id="Page_475">475</span> -consists. We assume, as a necessary basis of our knowledge, that -things are of definite kinds; and the aim of chemistry, botany, and -other sciences is to find marks of these kinds; and along with -these, to learn their definitely-distinguished properties. Even here, -therefore, where so large a portion of our knowledge comes from -experience and observation, we cannot proceed without a necessary -truth derived from our ideas, as our fundamental principle -of knowledge.</p> - -<p>22. What the marks are, which distinguish the constant differences -of kinds of things (definite marks, selected from among many -unessential appearances), and what their definite properties are, -when they are so distinguished, are parts of our knowledge to -be learnt from observation, by various processes; for instance, -among others, by chemical analysis. We find the differences of -bodies, as shown by such analysis, to be of this nature:—that there -are various elementary bodies, which, combining in different definite -proportions, form kinds of bodies definitely different. But, in arriving -at this conclusion, we introduce a new idea, that of Elementary -Composition, which is not extracted from the phenomena, but supplied -by the mind, and introduced in order to make the phenomena -intelligible. That this notion of elementary composition is not supplied -by the chemical phenomena of combustion, mixture, &c. as -merely an observed fact, we see from this; that men had in ancient -times performed many experiments in which elementary composition -was concerned, and had not seen the fact. It never was truly seen -till modern times; and when seen, it gave a new aspect to the whole -body of known facts. This idea of elementary composition, then, is -supplied by the mind, in order to make the facts of chemical analysis -and synthesis intelligible <i>as</i> analysis and synthesis. And this -idea being so supplied, there enters into our knowledge along with -it a corresponding necessary principle;—That the elementary composition -of a body determines its kind and properties. This is, I -say, a principle assumed, as a consequence of the idea of composition, -not a result of experience; for when bodies have been divided -into their kinds, we take for granted that the analysis of a single -specimen may serve to determine the analysis of all bodies of the -same kind: and without this assumption, chemical knowledge with -regard to the kinds of bodies would not be possible. It has been -said that we take only one experiment to determine the composition -of any particular kind of body, because we have a thousand experiments -to determine that bodies of the same kind have the same -composition. But this is not so. Our belief in the principle that -bodies of the same kind have the same composition is not established<span class="pagenum" id="Page_476">476</span> -by experiments, but is assumed as a necessary consequence of the -ideas of Kind and of Composition. If, in our experiments, we -found that bodies supposed to be of the same kind had not the same -composition, we should not at all doubt of the principle just stated, -but conclude at once that the bodies were <i>not</i> of the same kind;—that -the marks by which the kinds are distinguished had been -wrongly stated. This is what has very frequently happened in the -course of the investigations of chemists and mineralogists. And -thus we have it, not as an experiential fact, but as a necessary -principle of chemical philosophy, that the Elementary Composition -of a body determines its Kind and Properties.</p> - -<p>23. How bodies differ in their elementary composition, experiment -must teach us, as we have already said, that experiment has -taught us. But as we have also said, whatever be the nature of -this difference, kinds must be definite, in order that language may -be possible: and hence, whatever be the terms in which we are -taught by experiment to express the elementary composition of -bodies, the result must be conformable to this principle, That the -differences of elementary composition are definite. The law to -which we are led by experiment is, that the elements of bodies -continue in definite proportions according to weight. Experiments -add other laws; as for instance, that of multiple proportions in -different kinds of bodies composed of the same elements; but of -these we do not here speak.</p> - -<p>24. We are thus led to see that in our knowledge of mechanics, -chemistry, and the like, there are involved certain necessary principles, -derived from our ideas, and not from experience. But to this -it may be objected, that the parts of our knowledge in which these -principles are involved has, in historical fact, all been acquired by -experience. The laws of motion, the doctrine of definite proportions, -and the like, have all become known by experiment and -observation; and so far from being seen as necessary truths, have -been discovered by long-continued labours and trials, and through -innumerable vicissitudes of confusion, error, and imperfect truth. -This is perfectly true: but does not at all disprove what has been -said. Perception of external objects and experience, experiment -and observation are needed, not only, as we have said, to supply the -objective element of all knowledge—to embody, limit, define, and -modify our ideas; but this intercourse with objects is also requisite -to unfold and fix our ideas themselves. As we have already said, -ideas and facts can never be separated. Our ideas cannot be exercised -and developed in any other form than in their combination -with facts, and therefore the trials, corrections, controversies, by<span class="pagenum" id="Page_477">477</span> -which the matter of our knowledge is collected, is also the only way -in which the form of it can be rightly fashioned. Experience is -requisite to the clearness and distinctness of our ideas, not because -they are derived from experience, but because they can only be -exercised upon experience. And this consideration sufficiently explains -how it is that experiment and observation have been the -means, and the only means, by which men have been led to a -knowledge of the laws of nature. In reality, however, the necessary -principles which flow from our ideas, and which are the basis -of such knowledge, have not only been inevitably assumed in the -course of such investigations, but have been often expressly promulgated -in words by clear-minded philosophers, long before their -true interpretation was assigned by experiment. This has happened -with regard to such principles as those above mentioned; That every -event must have a cause; That reaction is equal and opposite to -action; That the quantity of matter in the world cannot be increased -or diminished: and there would be no difficulty in finding -similar enunciations of the other principles above mentioned;—That -the kinds of things have definite differences, and that these -differences depend upon their elementary composition. In general, -however, it may be allowed, that the necessary principles which -are involved in those laws of nature of which we have a knowledge -become then only clearly known, when the laws of nature are discovered -which thus involve the necessary ideal element.</p> - -<p>25. But since this is allowed, it may be further asked, how we -are to distinguish between the necessary principle which is derived -from our ideas, and the law of nature which is learnt by experience. -And to this we reply, that the necessary principle may be known by -the condition which we have already mentioned as belonging to such -principles: ... that it is impossible distinctly to conceive the contrary. -We cannot conceive an event without a cause, except we abandon -all distinct idea of cause; we cannot distinctly conceive two straight -lines inclosing space; and if we seem to conceive this, it is only -because we conceive indistinctly. We cannot conceive 5 and 3 -making 7 or 9; if a person were to say that he could conceive this, -we should know that he was a person of immature or rude or bewildered -ideas, whose conceptions had no distinctness. And thus -we may take it as the mark of a necessary truth, that we cannot -conceive the contrary distinctly.</p> - -<p>26. If it be asked what is the test of distinct conception (since -it is upon the distinctness of conception that the matter depends), -we may consider what answer we should give to this question if it -were asked with regard to the truths of geometry. If we doubted<span class="pagenum" id="Page_478">478</span> -whether anyone had these distinct conceptions which enable him to -see the necessary nature of geometrical truth, we should inquire if -he could understand the axioms as axioms, and could follow, as -demonstrative, the reasonings which are founded upon them. If -this were so, we should be ready to pronounce that he had distinct -ideas of space, in the sense now supposed. And the same answer -may be given in any other case. That reasoner has distinct conceptions -of mechanical causes who can see the axioms of mechanics as -axioms, and can follow the demonstrations derived from them as -demonstrations. If it be said that the science, as presented to him, -may be erroneously constructed; that the axioms may not be axioms, -and therefore the demonstrations may be futile, we still reply, that -the same might be said with regard to geometry: and yet that the -possibility of this does not lead us to doubt either of the truth or of -the necessary nature of the propositions contained in Euclid's Elements. -We may add further, that although, no doubt, the authors -of elementary books maybe persons of confused minds, who present -as axioms what are not axiomatic truths; yet that in general, what -is presented as an axiom by a thoughtful man, though it may include -some false interpretation or application of our ideas, will also generally -include some principle which really is necessarily true, and -which would still be involved in the axiom, if it were corrected -so as to be true instead of false. And thus we still say, that if -in any department of science a man can conceive distinctly at all, -there are principles the contrary of which he cannot distinctly conceive, -and which are therefore necessary truths.</p> - -<p>27. But on this it may be asked, whether truth can thus depend -upon the particular state of mind of the person who contemplates -it; and whether that can be a necessary truth which is not so to all -men. And to this we again reply, by referring to geometry and -arithmetic. It is plain that truths may be necessary truths which -are not so to all men, when we include men of confused and perplexed -intellects; for to such men it is not a necessary truth that -two straight lines cannot inclose a space, or that 14 and 17 are 31. -It need not be wondered at, therefore, if to such men it does not -appear a necessary truth that reaction is equal and opposite to -action, or that the quantity of matter in the world cannot be -increased or diminished. And this view of knowledge and truth -does not make it depend upon the state of mind of the student, any -more than geometrical knowledge and geometrical truth, by the -confession of all, depend upon that state. We know that a man -cannot have any knowledge of geometry without so much of attention -to the matter of the science, and so much of care in the<span class="pagenum" id="Page_479">479</span> -management of his own thoughts, as is requisite to keep his ideas -distinct and clear. But we do not, on that account, think of maintaining -that geometrical truth depends merely upon the state of -the student's mind. We conceive that he knows it because it is -true, not that it is true because he knows it. We are not surprised -that attention and care and repeated thought should be requisite to -the clear apprehension of truth. For such care and such repetition -are requisite to the distinctness and clearness of our ideas: and yet -the relations of these ideas, and their consequences, are not produced -by the efforts of attention or repetition which we exert. -They are in themselves something which we may discover, but -cannot make or change. The idea of space, for instance, which is -the basis of geometry, cannot give rise to any doubtful propositions. -What is inconsistent with the idea of space cannot be truly obtained -from our ideas by any efforts of thought or curiosity; if we blunder -into any conclusion inconsistent with the idea of space, our knowledge, -so far as this goes, is no knowledge: any more than our -observation of the external world would be knowledge, if, from -haste or inattention, or imperfection of sense, we were to mistake -the object which we see before us.</p> - -<p>28. But further: not only has truth this reality, which makes it -independent of our mistakes, that it must be what is really consistent -with our ideas; but also, a further reality, to which the -term is more obviously applicable, arising from the principle already -explained, that ideas and perceptions are inseparable. For since, -when we contemplate our ideas, they have been frequently embodied -and exemplified in objects, and thus have been fixed and -modified; and since this compound aspect is that under which we -constantly have them before us, and free from which they cannot -be exhibited; our attempts to make our ideas clear and distinct -will constantly lead us to contemplate them as they are manifested -in those external forms in which they are involved. Thus in studying -geometrical truth, we shall be led to contemplate it as exhibited -in visible and tangible figures;—not as if these could be -sources of truth, but as enabling us more readily to compare the -aspects which our ideas, applied to the world of objects, may -assume. And thus we have an additional indication of the reality -of geometrical truth, in the necessary possibility of its being capable -of being exhibited in a visible or tangible form. And yet even this -test by no means supersedes the necessity of distinct ideas, in order -to a knowledge of geometrical truth. For in the case of the duplication -of the cube by Hobbes, mentioned above, the diagram which -he drew made two points appear to coincide, which did not really,<span class="pagenum" id="Page_480">480</span> -and by the nature of our idea of space, coincide; and thus confirmed -him in his error.</p> - -<p><i>Thus the inseparable nature of the Fundamental Antithesis of -Ideas and Things gives reality to our knowledge, and makes objective -reality a corrective of our subjective imperfections in the pursuit -of knowledge. But this objective exhibition of knowledge can by no -means supersede a complete development of the subjective condition, -namely, distinctness of ideas. And that there is a subjective condition, -by no means makes knowledge altogether subjective, and thus -deprives it of reality; because, as we have said, the subjective and -the objective elements are inseparably bound together in the fundamental -antithesis.</i></p> - -<p>29. It would be easy to apply these remarks to other cases, for -instance, to the case of the principle we have just mentioned, that -the differences of elementary composition of different kinds of bodies -must be definite. We have stated that this principle is necessarily -true;—that the contrary proposition cannot be distinctly conceived. -But by whom? Evidently, according to the preceding reasoning, by -a person who distinctly conceives Kinds, as marked by intelligible -names, and Composition, as determining the kinds of bodies. Persons -new to chemical and classificatory science may not possess -these ideas distinctly; or rather, cannot possess them distinctly; -and therefore cannot apprehend the impossibility of conceiving the -opposite of the above principle; just as the schoolboy cannot apprehend -the impossibility of the numbers in his multiplication table -being other than they are. But this inaptitude to conceive, in -either case, does not alter the necessary character of the truth: -although, in one case, the truth is obvious to all except schoolboys -and the like, and the other is probably not clear to any except those -who have attentively studied the philosophy of elementary compositions. -At the same time, this difference of apprehension of the -truth in different persons does not make the truth doubtful or -dependent upon personal qualifications; for in proportion as persons -attain to distinct ideas, they will see the truth; and cannot, -with such ideas, see anything as truth which is not truth. When -the relations of elements in a compound become as familiar to a -person as the relations of factors in a multiplication table, he will -then see what are the necessary axioms of chemistry, as he now sees -the necessary axioms of arithmetic.</p> - -<p>30. There is also one other remark which I will here make. In -the progress of science, both the elements of our knowledge are -constantly expanded and augmented. By the exercise of observation -and experiment, we have a perpetual accumulation of facts, the<span class="pagenum" id="Page_481">481</span> -materials of knowledge, the objective element. By thought and -discussion, we have a perpetual development of man's ideas going -on: theories are framed, the materials of knowledge are shaped into -form; the subjective element is evolved; and by the necessary -coincidence of the objective and subjective elements, the matter and -the form, the theory and the facts, each of these processes furthers -and corrects the other: each element moulds and unfolds the other. -Now it follows, from this constant development of the ideal portion -of our knowledge, that we shall constantly be brought in view of -new Necessary Principles, the expression of the conditions belonging -to the Ideas which enter into our expanding knowledge. These -principles, at first dimly seen and hesitatingly asserted, at last become -clearly and plainly self-evident. Such is the case with the -principles which are the basis of the laws of motion. Such may -soon be the case with the principles which are the basis of the -philosophy of chemistry. Such may hereafter be the case with -the principles which are to be the basis of the philosophy of the -connected and related polarities of chemistry, electricity, galvanism, -magnetism. That knowledge is possible in these cases, we know; -that our knowledge may be reduced to principles, gradually more -simple, we also know; that we have reached the last stage of -simplicity of our principles, few cultivators of the subject will be -disposed to maintain; and that the additional steps which lead -towards very simple and general principles will also lead to principles -which recommend themselves by a kind of axiomatic character, -those who judge from the analogy of the past history of science -will hardly doubt. That the principles thus axiomatic in their -form, do also express some relation of our ideas, of which experiment -and observation have given a true and real interpretation, -is the doctrine which I have here attempted to establish and illustrate -in the most clear and undoubted of the existing sciences; and -the evidence of this doctrine in those cases seems to be unexceptionable, -and to leave no room to doubt that such is the universal -type of the progress of science. Such a doctrine, as we have now -seen, is closely connected with the views here presented of the -nature of the Fundamental Antithesis of Philosophy, which I have -endeavoured to illustrate.</p> -<hr class="chap" /> - -<p><span class="pagenum" id="Page_482">482</span></p> - - - -<h3><a name="Appendix_F" id="Appendix_F"></a><span class="smcap">Appendix F.</span><br /> - -REMARKS ON A REVIEW OF THE PHILOSOPHY -OF THE INDUCTIVE SCIENCES.</h3> - - -<p class="right"> -<i>Trinity Lodge, April 11th, 1844.</i></p> -<p class="pi"> -<span class="smcap">My Dear Herschel</span>, -</p> - -<p class="drop-cap"><span class="smcap">Being</span> about to send you a copy of a paper on a philosophical -question just printed in the Transactions of our Cambridge -Society, I am tempted to add, as a private communication, a few -Remarks on another aspect of the same question. These Remarks -I think I may properly address to you. They will refer to an -Article in the <i>Quarterly Review</i> for June, 1841, respecting my -<i>History</i> and <i>Philosophy</i> of the Inductive Sciences; and without -assigning any other reason, I may say that the interest I know you -to take in speculations on such subjects makes me confident that -you will give a reasonable attention to what I may have to say on -the subject of that Article. With the Reviewal itself, I am so far -from having any quarrel, that when it appeared I received it as -affording all that I hoped from Public Criticism. The degree and -the kind of admiration bestowed upon my works by a writer so -familiar with science, so comprehensive in his views, and so equitable -in his decisions, as the Reviewer manifestly was, I accepted -as giving my work a stamp of acknowledged value which few other -hands could have bestowed.</p> - -<p>You may perhaps recollect, however, that the Reviewer dissented -altogether from some of the general views which I had maintained, -and especially from a general view which is also, in the main, -that presented in the accompanying Memoir, namely, that, besides -Facts, Ideas are an indispensable source of our knowledge; that -Ideas are the ground of necessary truth; that the Idea of Space, in -particular, is the ground of the necessary truths of geometry. This -question, and especially as limited to the last form, will be the subject -of my Remarks in the first place; and I wish to consider the -Reviewer's objections with the respect which their subtlety and -depth of thought well deserve.</p> - -<p><span class="pagenum" id="Page_483">483</span></p> - -<p>The Reviewer makes objections to the account which I have -given of the source whence geometrical truth derives its characters -of being necessary and universal; but he is not one of those metaphysicians -who deny those characters to the truths of geometry. -He allows in the most ample manner that the truths of geometry -<i>are</i> necessary. The question between us therefore is from what -this character is derived. The Reviewer prefers, indeed, to have it -considered that the question is not concerning the necessity, but, as -he says, the universality of these truths; or rather, the nature and -grounds of our conviction of their universality. He might have -said, with equal justice, the nature and grounds of our conviction -of their necessity. For his objection to the term <i>necessity</i> in this -case—"that all the propositions about realities are necessarily true, -since every reality must be consistent with itself," (p. 206)—does not -apply to our conviction of necessity, since we may not be able to -see what are the properties of real things; and therefore may have -no conviction of their necessity. It may be a necessary property of -salt to be soluble, but we see no such necessity; and therefore the -assertion of such a property is not one of the necessary truths with -which we are here concerned. But to turn back to the necessary -or universal truths of geometry, and the ground of those attributes: -The main difference between the Author and the Reviewer is -brought into view, when the Reviewer discusses the general argument -which I had used, in order to show that truths which we see -to be necessary and universal cannot be derived from experience. -The argument is this,—</p> - -<p>"Experience must always consist of a limited number of observations; -and however numerous these may be, they can show nothing -with regard to the infinite number of cases in which the experiment -has not been made.... Truths can only be known to be general, not -universal, if they depend upon experience alone. Experience cannot -bestow that universality which she herself cannot have; nor -that necessity of which she has no comprehension." (<i>Phil.</i> <i>i.</i> pp. -60, 61.)</p> - -<p>Here is that which must be considered as the cardinal argument -on this subject. It is therefore important to attend to the answer -which the Reviewer makes to it. He says,—</p> - -<p>"We conceive that a full answer to this argument is afforded by -the nature of the inductive propensity,—by the irresistible impulse -of the mind to generalize <i>ad infinitum</i>, when nothing in the nature -of limitation or opposition offers itself to the imagination; and by -our involuntary application of the law of continuity to fill up, by -the same ideal substance of truth, every interval which uncontra<span class="pagenum" id="Page_484">484</span>dicted -experience may have left blank in our inductive conclusion." -(p. 207.)</p> - -<p>Now here we have two rival explanations of the same thing,—the -conviction of the universality of geometrical truths. The one -explanation is, that this universality is imposed upon such truths -by their involving a certain element, derived from the universal -mode of activity of the mind when apprehending such truths, which -element I have termed an Idea. The other explanation is, that this -universality arises from the <i>inductive propensity</i>—from the <i>irresistible -impulse to generalize ad infinitum</i>—from the <i>involuntary application -of the law of continuity</i>—from the <i>filling up all intervals with -the same ideal substance of truth</i>.</p> - -<p>With regard to these two explanations, I may observe, that so -far as they are thus stated they do not necessarily differ. They -both agree in expressing this; that the ground of the universality -of geometrical truths is a certain law of the mind's activity, which -determines its procedure when it is concerned in apprehending the -external world. One explanation says, that we impress upon the -external world the relations of our ideas, and thus believe more -than we see,—the other says, that we have an irresistible impulse -to introduce into our conviction a relation between what we do -observe and what we do not, namely, to generalize <i>ad infinitum</i> -from what we do see. One explanation says, that we perceive all -external objects as included in absolute ideal space,—the other, -that we fill up the intervals of the objects which we perceive with -the same ideal substance of truth. Both sets of expressions may -perhaps be admissible; and if admitted, may be understood as expressing -the same opinions, or opinions which have much in common. -The Author's expressions have the advantage, which ought -to belong to them, as the expressions employed in a systematic -work, of being fixed expressions, technical phrases, intentionally -selected, uniformly and steadily employed whenever the occasion -recurs. The Reviewer's expressions are more lively and figurative, -and such as well become an occasional composition; but hardly -such as could be systematically applied to the subject in a regular -treatise. We could not, as a standard and technical phrase, talk of -filling up the intervals of observation with the same ideal substance -of truth; and the inevitable impulse to generalize would hardly -sufficiently express that we generalize according to a certain idea, -namely, the idea of space. Perhaps that which is suggested to us -as the common import of the two sets of expressions may be conveyed -by some other phrase, in a manner free from the objections -which lie against both the Author's and the Critic's terms. Perhaps<span class="pagenum" id="Page_485">485</span> -the mental idea governing our experience, and the irresistible impulse -to generalize our observation, may both be superseded by our -speaking of a law of the mind's <i>activity</i>, which is really implied in -both. There operates, in observing the external world, a law of -the mind's activity, by which it connects its observations; and this -law of the mind's activity may be spoken of either as the idea of -space, or as the irresistible impulse to generalize the relations of -space which it observes. And this expression—<i>the laws of the -mind's activity</i>—thus opposed to that merely passive function by -which the mind receives the impressions of sense, may be applied to -other ideas as well as to the idea of space, and to the impulse to -generalize in other truths as well as those of geometry.</p> - -<p>So far, it would seem, that the Author and the Critic may be brought -into much nearer agreement than at first seemed likely, with regard -to the grounds of the necessity and universality in our knowledge. -But even if we adopt this conciliatory suggestion, and speak of the -necessity and universality of certain truths as arising from the laws -of the mind's activity, we cannot, without producing great confusion, -allow ourselves to say, as the Critic says, that these truths -are thus derived from <i>experience</i>, or from <i>observation</i>. It will, I -say, be found fatal to all philosophical precision of thought and -language, to say that the fundamental truths of geometry, the -axioms, with the conviction of their necessary truth, are derived -from experience. Let us take any axiomatic truth of geometry, -and ask ourselves if this is not so.</p> - -<p>It is, for example, an axiom in geometry that if a straight line -cut one of two parallel straight lines, it must cut the other also. -Is this truth derived or derivable from observation of actual parallel -lines, and a line cutting them, exhibited to our senses? Let those -who say that we do acquire this truth by observation, imagine -to themselves the mode in which the observation must be made. -We have before us two parallel straight lines, and we see that a -straight line which cuts the one cuts the other also. We see this -again in another case, it may be the angles and the distances being -different, and in a third, and in a fourth; and so on; and generalizing, -we are irresistibly led to believe the assertion to be universally -true. But can any one really imagine this to be the mode in which -we arrive at this truth? "We see," says this explanation, "two -parallel straight lines, cut by a third." But how do we know that -the observed lines are parallel? If we apply any test of parallelism, -we must assume some property of parallels, and thus involve some -axiom on the subject, which we have no more right to assume than -the one now under consideration. We should thus destroy our<span class="pagenum" id="Page_486">486</span> -explanation as an account of the mode of arriving at independent -geometrical axioms. But probably those who would give such an -explanation would not do this. They would not suppose that in -observing this property of parallels we try by measurement whether -the lines are parallel. They would say, I conceive, that we suppose -lines to be parallel, and that then we see that the straight line -which cuts the one must cut the other. That when we make this -supposition, we are persuaded of the truth of the conclusion, is -certain. But what I have to remark is, that this being so, the conclusion -is the result, not of observation, but of the hypothesis. -The geometrical truth here spoken of, after this admission, no -longer flows from experience, but from supposition. It is not that -we <i>ascertain</i> the lines to be parallel, and then <i>find</i> that they have -this property: but we <i>suppose</i> the lines to be parallel, and <i>therefore</i> -they have this property. This is not a truth of experience.</p> - -<p>This, it may be said, is so evident that it cannot have been overlooked -by a very acute reasoner, such as you describe your Critic to -be. What, it may be asked, is the answer which he gives to so -palpable an objection as this? How does he understand his assertion -that we learn the truth of geometrical axioms from experience -(p. 208), so as to make it tenable on his own principles? What -account does he give of the origin of such axioms which makes them -in any sense to be derived from experience?</p> - -<p>In justice to the Reviewer's fairness (which is unimpeachable -throughout his argumentation) it must be stated that he does give -an account in which he professes to show how this is done. And -the main step of his explanation consists in introducing the conception -of <i>direction</i>, and <i>unity of direction</i>. He says (p. 208), "The -<i>unity of direction</i>, or that we cannot march from a given point by -more than one path <i>direct to the same object</i>, is a matter of practical -experience, long before it can by possibility become matter of abstract -thought." We might ask here, as in the former case, how -this can be a matter of experience, except we have some independent -test of directness? and we might demand to know what this -test is. Or do we not rather, here as in the other case, <i>suppose</i> the -directness of the path; and is not the singleness of the direct path -a consequence, not of its observed form, but of its hypothetical directness; -and thus by no means a result of experience? But we -may put our remark upon this deduction of the geometrical axiom -in another form. We generalize, it is said, the observations which -we have made ever since we were born. But this term "generalize" -is far too vague to pass for an explanation, without being itself explained. -We are impelled to believe that to be true in general<span class="pagenum" id="Page_487">487</span> -which we see to be true in particular. But how do we see any -truth? How do we pick out any proposition with respect to a -diagram which we see before us? We see in particular, and state -in general, some truth respecting straight lines, or parallel lines, or -concerning direction. But where do we find the conception of -straightness, or parallelism, or direction? These conceptions are -not upon the surface of things. The child does not, from his birth, -see straightness and parallelism so as to know that he sees them. -How then does his experience bear upon a proposition in which -these conceptions are involved? It is said that it is a matter of -experience long before it is a matter of abstract thought. But how -can there be any experience by which we learn these properties of -a straight line, till our thoughts are at least so abstract as to conceive -what straightness is? If it be said that this conception grows -with our experience, and is gradually unfolded with our unfolding -materials of knowledge, so as to give import and significance to -them: I need make no objection to such a statement, except this—that -this power of unfolding out of the mind conceptions which give -meaning to our experience, is something in addition to the mere -employment of our senses upon the external world. It is what I -have called the ideal part of our knowledge. It implies, not only -an impulse to generalize from experience, but also an impulse to -form conceptions by which generalization is possible. It requires, -not only that nothing should oppose the tendency, but that the -direction in which the tendency is to operate should be determined -by the laws of the mind's activity; by an internal, not by an external -agency.</p> - -<p>One main ground on which the Reviewer is disposed to quarrel -with and reject several of the expressions used in the <i>Philosophy</i>;—such -as that space is an idea, a form of our perception, and the -like,—is this; that such expressions appear to deprive the external -world of its reality; to make it, or at least most of its properties, a -creation of the observing mind. He quotes the following argument -which is urged in the <i>Philosophy</i>, in order to prove that space is -not a notion obtained from experience: "Experience gives us information -concerning things without us, but our apprehending them -as without us takes for granted their existence in space. Experience -acquaints us with the form, position, magnitude, &c. of particular -objects, but that they <i>have</i> form, position, magnitude, pre-supposes -that they are in space." From this statement he altogether dissents. -No, says he, "the reason why we apprehend things as without us is -that they <i>are</i> without us. We take for granted that they exist in -space, because they <i>do</i> so exist, and because such their existence is<span class="pagenum" id="Page_488">488</span> -a matter of direct perception, which can neither be explained in -words nor contravened in imagination: because, in short, space is a -<i>reality</i>, and not a mere matter of convention or imagination."</p> - -<p>Now, if by calling space an idea, we suggest any doubt of its -reality and of the reality of the external world, we certainly run the -risk of misleading our readers; for the external world is real if -anything be real: the bodies which exist in space are things, if -things are anywhere to be found. That bodies do exist in space, -and that <i>that</i> is the reason why we apprehend them as existing -in space, I readily grant. But I conceive that the term Idea ought -not to suggest any such doubt of the reality of the knowledge in -which it is involved. Ideas are always, in our knowledge, conjoined -with facts. Our real knowledge is knowledge, because it involves -ideas, real, because it involves facts. We apprehend things as existing -in space because they do so exist: and our idea of space -enables us so to observe them, and so to conceive them.</p> - -<p>But we want, further, a reason why, apprehending them as they -are, we also apprehend, that in certain relations they could not be -otherwise (that two straight linear objects could not inclose a space, -for instance). This circumstance is no way accounted for by saying -that we apprehend them as they are; and is, I presume to say, inexplicable, -except by supposing that it arises from some property -of the observing mind:—an Idea, as I have termed it,—an irresistible -Impulse to generalize, as the Reviewer expresses it. Or, as -I have suggested, we may adopt a third phrase, a Law of the -mind's activity: and in order that no question may remain, whether -we ascribe reality to the objects and relations which we observe, -we may describe it as "a Law of the mind's activity in -apprehending what is." And thus the real existence of the object, -and the ideal element which our apprehension of it introduces, -would both be clearly asserted.</p> - -<p>I am ready to use expressions which recognize the reality of space -and other external things more emphatically than those expressions -which I have employed in the <i>Philosophy</i>, if expressions can be -found which, while they do this, enable us to explain the possibility -of knowledge, and to analyze the structure of truth. It is, indeed, -extremely difficult to find, in speaking of this subject, expressions -which are satisfactory. The reality of the objects which we perceive -is a profound, apparently an insoluble problem<a name="FNanchor_352" id="FNanchor_352"></a><a href="#Footnote_352" class="fnanchor">[352]</a>. We cannot -but suppose that existence is something different from our know<span class="pagenum" id="Page_489">489</span>ledge -of existence:—that which exists, does not exist merely in our -knowing that it does:—truth is truth whether we know it or not. -Yet how can we conceive truth, otherwise than as something known? -How can we conceive things as existing, without conceiving them -as objects of perception? Ideas and Things are constantly opposed, -yet necessarily co-existent. How they are thus opposite and yet -identical, is the ultimate problem of all philosophy. The successive -phases of philosophy have consisted in separating and again uniting -these two opposite elements; in dwelling sometimes upon the one -and sometimes upon the other, as the principal or original or only -element; and then in discovering that such an account of the state -of the case was insufficient. Knowledge requires ideas. Reality -requires things. Ideas and things co-exist. Truth <i>is</i>, and is known. -But the complete explanation of these points appears to be beyond -our reach. At least it is not necessary for the purposes of our -philosophy. The separation of ideas and sensations in order to -discover the conditions of knowledge is our main task. How ideas -and sensations are united so as to form things, does not so immediately -concern us.</p> - -<p>I have stated that we may, without giving up any material portion -of the Philosophy of Science to which I have been led, -express the conclusions in other phraseology; and that instead of -saying that all our knowledge involves certain Fundamental Ideas, -the sources from which all universal truth is derived, we may say -that there are certain Laws of Mental Activity according to which -alone all the real relations of things are apprehended. If this -alteration in the phraseology will make the doctrines more generally -intelligible or acceptable, there is no reason why it should not be -adopted. But I may remark, that a main purpose of the <i>Philosophy</i> -was not merely to prove that there <i>are</i> such Fundamental -Ideas or Laws of mental activity, but to enumerate those of them -which are involved in the existing sciences; and to state the fundamental -truths to which the fundamental ideas lead. This was the -task which was attempted; and if this have been executed with any -tolerable success, it may perhaps be received as a contribution to -the philosophy of science, of which the value is not small, in whatever -terms it be expressed. And this enumeration of fundamental -ideas, and of truths derived from them, must have something to -correspond to it, in any other mode of expressing that view of the -nature of knowledge which we are led to adopt. If instead of -<i>Fundamental Ideas</i>, we speak of Impulses of generalization, or of -<i>Laws of mental activity</i>, we must still distinguish such Impulses, -or such Laws, according to the distinctions of ideas to which the<span class="pagenum" id="Page_490">490</span> -survey of science led us. We shall thus have a series of groups of -Laws, or of classes of generalizing Impulses, corresponding to the -series of Fundamental Ideas already given. If we employ the -language of the Reviewer, we shall have one generalizing Impulse -which suggests relations of Space; another which directs us to -properties of Numbers; another which deals with Time; another -with Cause: another which groups objects according to Likeness; -another which suggests a purpose as a necessary relation among -them; to which may be added, even while we confine ourselves to -the physical sciences, several others, as may be seen in the <i>Philosophy</i>. -Now when the fundamental conditions and elements of -truth are thus arranged into groups, it is not a matter of so much -consequence to decide whether each group shall be said to be bound -together by an idea or by an impulse of generalization; as it is to -see that, if this happen in virtue of ideas, here are so many distinct -ideas which enter into the structure of science, and give universality -to its matter; and again, if this happen in virtue of an irresistible -impulse of generalization in each case, we have so many different -kinds of impulses of generalization. The main purpose in the -<i>Philosophy</i> was to analyze scientific truth into its conditions and -elements; and I did not content myself with saying that those elements -are Sensations and Ideas; the Ideas being that element -which makes universal knowledge conceivable and possible. I went -further: I enumerated the Ideas which thus enter into science. I -showed that in the sciences which I passed in review, the most -acute and profound inquirers had taken for granted that certain -truths in each science are of universal and necessary validity, and -I endeavoured to select the idea in which this universality and -necessity resided, and to separate it from all other ideas involved -in other sciences. If therefore it be thought better to say that those -principles in each science upon which, as upon the axioms in geometry, -the universality and necessity of scientific truth depends, are -arrived at, not by ideas, but by an irresistible impulse of generalization, -those who employ such phraseology, if they make a classification -of such impulses corresponding to my classification of ideas, -will still adopt the greater part of my philosophy, altering only the -phraseology. Or if, as I suggested, instead of "Fundamental -Ideas," we use the phrase "Laws of Mental Activity," then our -primary intellectual Code—the Constitution of our minds, as it -may be termed—will consist of a Body of Laws of which the Titles -correspond with the Fundamental Ideas of the <i>Philosophy</i>.</p> - -<p>My object was, from the writings of the most sagacious and profound -philosophers who have laboured on each science, to extract<span class="pagenum" id="Page_491">491</span> -such a code, such a constitution. If I have in any degree succeeded -in this, the result must have a reality and a value independently of -all forms of expression. Still I do not think that any language can -ever serve for such legislation, in which the two elements of truth -are not distinguished. Even if we adopt the phraseology which I -have just employed, we shall have to recollect that Law and Fact -must be kept distinct, and that the Constitution has its Principles -as well as its History.</p> - -<p>But I will not longer detain you by seeking other modes of expressing -the Fundamental Antithesis to which the accompanying -Memoir refers. The Remarks which I here send you were written -three years ago, on the appearance of the Review which I have -quoted. If I succeed in obtaining for them a few minutes' attention -from you and a few other friends, I shall be glad that they -have been preserved.</p> - -<p class="center"> -I am, my dear Herschel,</p> -<p class="right">always truly yours, </p> -<p class="right">W. WHEWELL.</p> - -<p>P.S. I have abstained from sending you a large portion of my -Remarks as originally written. I had gone on to show that, in -my <i>Philosophy</i>, I had not only enumerated and analyzed a great -number of different Fundamental Ideas which belong to the different -existing sciences, but that I had also shown in what manner these -ideas enter into their respective sciences; namely, by the statement -or use of Axioms, which involve the ideas, and which form the basis -of each science when systematically exhibited. A number of these -Axioms belonging to most of the physical sciences, are stated in the -<i>Philosophy</i>. I might have added also that I have attempted to classify -the historical steps by which such Axioms are brought into -view and applied. But it is not necessary to dwell upon these -points, in order to illustrate the difference and the agreement -between the Reviewer and me.</p> - -<p class="pi"> -<i>Sir John F. W. Herschel, Bart. &c.</i></p> - -<hr class="chap" /> - -<p><span class="pagenum" id="Page_492">492</span></p> - - - -<h3><a name="Appendix_G" id="Appendix_G"></a><span class="smcap">Appendix G.</span><br /> - -OF THE TRANSFORMATION OF HYPOTHESES -IN THE HISTORY OF SCIENCE.</h3> - -<p class="center">(<i>Cam. Phil. Soc.</i> <span class="smcap">May 19, 1851.</span>)</p> - - -<p> -<span class="dropcap"><span class="dsmall">1.</span> T</span>HE history of science suggests the reflection that it is very -difficult for the same person at the same time to do justice -to two conflicting theories. Take for example the Cartesian hypothesis -of vortices and the Newtonian doctrine of universal gravitation. -The adherents of the earlier opinion resisted the evidence -of the Newtonian theory with a degree of obstinacy and captiousness -which now appears to us quite marvellous: while on the other -hand, since the complete triumph of the Newtonians, <i>they</i> have -been unwilling to allow any merit at all to the doctrine of vortices. -It cannot but seem strange, to a calm observer of such changes, -that in a matter which depends upon mathematical proofs, the -whole body of the mathematical world should pass over, as in this -and similar cases they seem to have done, from an opinion confidently -held, to its opposite. No doubt this must be, in part, -ascribed to the lasting effects of education and early prejudice. -The old opinion passes away with the old generation: the new -theory grows to its full vigour when its congenital disciples grow -to be masters. John Bernoulli continues a Cartesian to the last; -Daniel, his son, is a Newtonian from the first. Newton's doctrines -are adopted at once in England, for they are the solution of a problem -at which his contemporaries have been labouring for years. -They find no adherents in France, where Descartes is supposed to -have already explained the constitution of the world; and Fontenelle, -the secretary of the Academy of Sciences at Paris, dies a -Cartesian seventy years after the publication of Newton's <i>Principia</i>. -This is, no doubt, a part of the explanation of the pertinacity with -which opinions are held, both before and after a scientific revolution: -but this is not the whole, nor perhaps the most instructive -aspect of the subject. There is another feature in the change,<span class="pagenum" id="Page_493">493</span> -which explains, in some degree, how it is possible that, in subjects, -mainly at least mathematical, and therefore claiming demonstrative -evidence, mathematicians should hold different and even opposite -opinions. And the object of the present paper is to point out this -feature in the successions of theories, and to illustrate it by some -prominent examples drawn from the history of science.</p> - -<p>2. The feature to which I refer is this; that when a prevalent -theory is found to be untenable, and consequently, is succeeded by -a different, or even by an opposite one, the change is not made -suddenly, or completed at once, at least in the minds of the most -tenacious adherents of the earlier doctrine; but is effected by a -transformation, or series of transformations, of the earlier hypothesis, -by means of which it is gradually brought nearer and -nearer to the second; and thus, the defenders of the ancient doctrine -are able to go on as if still asserting their first opinions, and -to continue to press their points of advantage, if they have any, -against the new theory. They borrow, or imitate, and in some -way accommodate to their original hypothesis, the new explanations -which the new theory gives, of the observed facts; and thus -they maintain a sort of verbal consistency; till the original hypothesis -becomes inextricably confused, or breaks down under the -weight of the auxiliary hypotheses thus fastened upon it, in order -to make it consistent with the facts.</p> - -<p>This often-occurring course of events might be illustrated from -the history of the astronomical theory of epicycles and eccentrics, -as is well known. But my present purpose is to give one or two -brief illustrations of a somewhat similar tendency from other parts -of scientific history; and in the first place, from that part which -has already been referred to, the battle of the Cartesian and Newtonian -systems.</p> - -<p>3. The part of the Cartesian system of vortices which is most -familiarly known to general readers is the explanation of the motions -of the planets by supposing them carried round the sun by a kind of -whirlpool of fluid matter in which they are immersed: and the explanation -of the motions of the satellites round their primaries by -similar subordinate whirlpools, turning round the primary, and -carried, along with it, by the primary vortex. But it should be -borne in mind that a part of the Cartesian hypothesis which was -considered quite as important as the cosmical explanation, was the -explanation which it was held to afford of terrestrial gravity. Terrestrial -gravity was asserted to arise from the motion of the vortex -of subtle matter which revolved round the earth's axis and filled -the surrounding space. It was maintained that by the rotation of<span class="pagenum" id="Page_494">494</span> -such a vortex, the particles of the subtle matter would exert a -centrifugal force, and by virtue of that force, tend to recede from -the center: and it was held that all bodies which were near the -earth, and therefore immersed in the vortex, would be pressed towards -the center by the effort of the subtle matter to recede from -the center<a name="FNanchor_353" id="FNanchor_353"></a><a href="#Footnote_353" class="fnanchor">[353]</a>.</p> - -<p>These two assumed effects of the Cartesian vortices—to carry -bodies in their stream, as straws are carried round by a whirlpool, -and to press bodies to the center by the centrifugal effort of the -whirling matter—must be considered separately, because they were -modified separately, as the progress of discussion drove the Cartesians -from point to point. The former effect indeed, the <i>dragging</i> -force of the vortex, as we may call it, would not bear working out -on mechanical principles at all; for as soon as the law of motion -was acknowledged (which Descartes himself was one of the loudest -in proclaiming), that a body in motion keeps all the motion which it -has, and receives in addition all that is impressed upon it; as soon, -in short, as philosophers rejected the notion of an inertness in -matter which constantly retards its movements,—it was plain that -a planet perpetually dragged onwards in its orbit by a fluid moving -quicker than itself, must be perpetually accelerated; and therefore -could not follow those constantly-recurring cycles of quicker and -slower motion which the planets exhibit to us.</p> - -<p>The Cartesian mathematicians, then, left untouched the calculation -of the progressive motion of the planets; and, clinging to -the assumption that a vortex would produce a tendency of bodies -to the center, made various successive efforts to construct their -vortices in such a manner that the centripetal forces produced by -them should coincide with those which the phenomena required, -and therefore of course, in the end, with those which the Newtonian -theory asserted.</p> - -<p>In truth, the Cartesian vortex was a bad piece of machinery for -producing a central force: from the first, objections were made to -the sufficiency of its mechanism, and most of these objections were -very unsatisfactorily answered, even granting the additional machinery -which its defenders demanded. One formidable objection was -soon started, and continued to the last to be the torment of the -Cartesians. If terrestrial gravity, it was urged, arise from the -centrifugal force of a vortex which revolves about the earth's axis, -terrestrial gravity ought to act in planes perpendicular to the<span class="pagenum" id="Page_495">495</span> -earth's axis, instead of tending to the earth's center. This objection -was taken by James Bernoulli<a name="FNanchor_354" id="FNanchor_354"></a><a href="#Footnote_354" class="fnanchor">[354]</a>, and by Huyghens<a name="FNanchor_355" id="FNanchor_355"></a><a href="#Footnote_355" class="fnanchor">[355]</a> not long -after the publication of Descartes's <i>Principia</i>. Huyghens (who -adopted the theory of vortices with modifications of his own) supposes -that there are particles of the fluid matter which move about -the earth in every possible direction, within the spherical space -which includes terrestrial objects; and that the greater part of -these motions being in spherical surfaces concentric with the earth, -produces a tendency towards the earth's center.</p> - -<p>This was a procedure tolerably arbitrary, but it was the best -which could be done. Saurin, a little later<a name="FNanchor_356" id="FNanchor_356"></a><a href="#Footnote_356" class="fnanchor">[356]</a>, gave nearly the same -solution of this difficulty. The solution, identifying a vortex of -some kind with a central force, made the hypothesis of vortices -applicable wherever central forces existed; but then, in return, it -deprived the image of a vortex of all that clearness and simplicity -which had been its first great recommendation.</p> - -<p>But still there remained difficulties not less formidable. According -to this explanation of gravity, since the tendency of bodies to -the earth's center arose from the superior centrifugal force of the -whirling matter which pushed them inward as water pushes a light -body upward, bodies ought to tend more strongly to the center in -proportion as they are less dense. The rarest bodies should be the -heaviest; contrary to what we find.</p> - -<p>Descartes's original solution of this difficulty has a certain degree -of ingenuity. According to him (<i>Princip.</i> <span class="smcap">IV.</span> 23) a terrestrial body -consists of particles of the <i>third element</i>, and the more it has of such -particles, the more it excludes the parts of the <i>celestial matter</i>, -from the revolution of which matter gravity arises; and therefore -the denser is the terrestrial body, and the heavier it will be.</p> - -<p>But though this might satisfy him, it could not satisfy the mathematicians -who followed him, and tried to reduce his system to -calculation on mechanical principles. For how could they do this, -if the celestial matter, by the operation of which the phenomena of -force and motion were produced, was so entirely different from -ordinary matter, which alone had supplied men with experimental<span class="pagenum" id="Page_496">496</span> -illustrations of mechanical principles? In order that the celestial -matter, by its whirling, might produce the gravity of heavy bodies, -it was mechanically necessary that it must be very dense; and <i>dense</i> -in the ordinary sense of the term; for it was by regarding density -in the ordinary sense of the term that the mechanical necessity had -been established.</p> - -<p>The Cartesians tried to escape this result (Huyghens, <i>Pesanteur</i>, -p. 161, and John Bernoulli, <i>Nouvelles Pensées</i>, Art. 31) by saying -that there were two meanings of <i>density</i> and <i>rarity</i>; that some -fluids might be rare by having their particles far asunder, others, by -having their particles very small though in contact. But it is difficult -to think that they could, as persons well acquainted with -mechanical principles, satisfy themselves with this distinction; for -they could hardly fail to see that the mechanical effect of any portion -of fluid depends upon the total mass moved, not on the size of -its particles.</p> - -<p>Attempts made to exemplify the vortices experimentally only -showed more clearly the force of this difficulty. Huyghens had -found that certain bodies immersed in a whirling fluid tended to -the center of the vortex. But when Saulmon<a name="FNanchor_357" id="FNanchor_357"></a><a href="#Footnote_357" class="fnanchor">[357]</a> a little later made -similar experiments, he had the mortification of finding that the -heaviest bodies had the greatest tendency to recede from the axis -of the vortex. "The result is," as the Secretary of the Academy -(Fontenelle) says, "exactly the opposite of what we could have -wished, for the [Cartesian] system of gravity: but we are not to -despair; sometimes in such researches disappointment leads to ultimate -success."</p> - -<p>But, passing by this difficulty, and assuming that in some way or -other a centripetal force arises from the centrifugal force of the -vortex, the Cartesian mathematicians were naturally led to calculate -the circumstances of the vortex on mechanical principles; especially -Huyghens, who had successfully studied the subject of centrifugal -force. Accordingly, in his little treatise on the <i>Cause of -Gravitation</i> (p. 143), he calculates the velocity of the fluid matter of -the vortex, and finds that, at a point in the equator, it is 17 times -the velocity of the earth's rotation.</p> - -<p>It may naturally be asked, how it comes to pass that a stream of -fluid, dense enough to produce the gravity of bodies by its centrifugal -force, moving with a velocity 17 times that of the earth (and -therefore moving round the earth in 85 minutes), does not sweep<span class="pagenum" id="Page_497">497</span> -all terrestrial objects before it. But to this Huyghens had already -replied (p. 137), that there are particles of the fluid moving <i>in all -directions</i>, and therefore that they neutralize each other's action, so -far as lateral motion is concerned.</p> - -<p>And thus, as early as this treatise of Huyghens, that is, in three -years from the publication of Newton's <i>Principia</i>, a vortex is made -to mean nothing more than some machinery or other for producing -a central force. And this is so much the case, that Huyghens commends -(p. 165), as confirming his own calculation of the velocity of -his vortex, Newton's proof that at the Moon's orbit the centripetal -force is equal to the centrifugal; and that thus, this force is less -than the centripetal force at the earth's surface in the inverse proportion -of the squares of the distances.</p> - -<p>John Bernoulli, in the same manner, but with far less clearness -and less candour, has treated the hypothesis of vortices as being -principally a hypothetical cause of central force. He had repeated -occasions given him of propounding his inventions for propping up -the Cartesian doctrine, by the subjects proposed for prizes by the -Paris Academy of Sciences; in which competition Cartesian speculations -were favourably received. Thus the subject of the Prize -Essays for 1730 was, the explanation of the Elliptical Form of the -planetary orbits and of the Motion of their Aphelia, and the prize -was assigned to John Bernoulli, who gave the explanation on Cartesian -principles. He explains the elliptical figure, not as Descartes -himself had done, by supposing the vortex which carries the planet -round the sun to be itself squeezed into an elliptical form by the -pressure of contiguous vortices; but he supposes the planet, while -it is carried round by the vortex, to have a limited oscillatory -motion to and from the center, produced by its being originally, -not at the distance at which it would float in equilibrium in the -vortex, but above or below that point. On this supposition, the -planet would oscillate to and from the center, Bernoulli says, like -the mercury when deranged in a barometer: and it is evident that -such an oscillation, combined with a motion round the center, -might produce an oval curve, either with a fixed or with a moveable -aphelion. All this however merely amounts to a possibility -that the oval <i>may</i> be an ellipse, not to a proof that it will be so; -nor does Bernoulli advance further.</p> - -<p>It was necessary that the vortices should be adjusted in such -a manner as to account for Kepler's laws; and this was to be done -by making the velocity of each stratum of the vortex depend in -a suitable manner on its radius. The Abbé de Molières attempted -this on the supposition of elliptical vortices, but could not reconcile<span class="pagenum" id="Page_498">498</span> -Kepler's first two laws, of equal elliptical areas in equal times, with -his third law, that the squares of the periodic times are as the cubes -of the mean distances<a name="FNanchor_358" id="FNanchor_358"></a><a href="#Footnote_358" class="fnanchor">[358]</a>. Bernoulli, with his circular vortices, could -accommodate the velocities at different distances so that they should -explain Kepler's laws. He pretended to prove that Newton's investigations -respecting vortices (in the ninth Section of the Second -Book of the <i>Principia</i>) were mechanically erroneous; and in truth, -it must be allowed that, besides several arbitrary assumptions, there -are some errors of reasoning in them. But for the most part, the -more enlightened Cartesians were content to accept Newton's account -of the motions and forces of the solar system as part of their -scheme; and to say only that the hypothesis of vortices explained -the origin of the Newtonian forces; and that thus theirs was a -philosophy of a higher kind. Thus it is asserted (<i>Mém. Acad.</i> 1734), -that M. de Molières retains the beautiful theory of Newton entire, -only he renders it in a sort less Newtonian, by disentangling -it from attraction, and transferring it from a vacuum into a plenum. -This plenum, though not its native region, frees it from the need of -attraction, which is all the better for it. These points were the -main charms of the Cartesian doctrine in the eyes of its followers;—the -getting rid of attractions, which were represented as a revival -of the Aristotelian "occult qualities," "substantial forms," or -whatever else was the most disparaging way of describing the bad -philosophy of the dark ages<a name="FNanchor_359" id="FNanchor_359"></a><a href="#Footnote_359" class="fnanchor">[359]</a>;—and the providing some material -intermedium, by means of which a body may affect another at a -distance; and thus avoid the reproach urged against the Newtonians, -that they made a body act where it was not. And we are the -less called upon to deny that this last feature in the Newtonian -theory was a difficulty, inasmuch as Newton himself was never<span class="pagenum" id="Page_499">499</span> -unwilling to allow that gravity might be merely an effect produced -by some ulterior cause.</p> - -<p>With such admissions on the two sides, it is plain that the Newtonian -and Cartesian systems would coincide, if the hypothesis of -vortices could be modified in such a way as to produce the force -of gravitation. All attempts to do this, however, failed: and -even John Bernoulli, the most obstinate of the mathematical champions -of the vortices, was obliged to give them up. In his Prize -Essay for 1734, (on the Inclinations of the Planetary Orbits<a name="FNanchor_360" id="FNanchor_360"></a><a href="#Footnote_360" class="fnanchor">[360]</a>,) he -says (Art. <span class="smcap">VIII.</span>), "The gravitation of the Planets towards the center -of the Sun and the weight of bodies towards the center of the earth -has not, for its cause, either the attraction of M. Newton, or the -centrifugal force of the matter of the vortex according to M. Descartes;" -and he then goes on to assert that these forces are produced -by a perpetual torrent of matter tending to the center on -all sides, and carrying all bodies with it. Such a hypothesis is very -difficult to refute. It has been taken up in more modern times by -Le Sage<a name="FNanchor_361" id="FNanchor_361"></a><a href="#Footnote_361" class="fnanchor">[361]</a>, with some modifications; and may be made to account -for the principal facts of the universal gravitation of matter. The -great difficulty in the way of such a hypothesis is, the overwhelming -thought of the whole universe filled with torrents of an invisible but -material and tangible substance, rushing in every direction in infinitely -prolonged straight lines and with immense velocity. Whence -can such matter come, and whither can it go? Where can be its -perpetual and infinitely distant fountain, and where the ocean into -which it pours itself when its infinite course is ended? A revolving -whirlpool is easily conceived and easily supplied; but the -central torrent of Bernoulli, the infinite streams of particles of -Le Sage, are an explanation far more inconceivable than the thing -explained.</p> - -<p>But however the hypothesis of vortices, or some hypothesis substituted -for it, was adjusted to explain the facts of attraction to -a center, this was really nearly all that was meant by a vortex<span class="pagenum" id="Page_500">500</span> -or a "tourbillon," when the system was applied. Thus in the case -of the last act of homage to the Cartesian theory which the French -Academy rendered in the distribution of its prizes, the designation -of a Cartesian Essay in 1741 (along with three Newtonian -ones) as worthy of a prize for an explanation of the Tides; the -difference of high and low water was not explained, as Descartes -has explained it, by the pressure, on the ocean, of the terrestrial -vortex, forced into a strait where it passes under the Moon; but -the waters were supposed to rise towards the Moon, the terrestrial -vortex being disturbed and broken by the Moon, and therefore less -effective in forcing them down. And in giving an account of a -Tourmaline from Ceylon (Acad. Sc. 1717), when it has been ascertained -that it attracts and repels substances, the writer adds, as -a matter of course, "It would seem that it has a vortex." As -another example, the elasticity of a body was ascribed to vortices -between its particles: and in general, as I have said, a vortex -implied what we now imply by speaking of a central force.</p> - -<p>4. In the same manner vortices were ascribed to the Magnet, -in order to account for its attractions and repulsions. But we may -note a circumstance which gave a special turn to the hypothesis -of vortices as applied to this subject, and which may serve as a -further illustration of the manner in which a transition may be -made from one to the other of two rival hypotheses.</p> - -<p>If iron filings be brought near a magnet, in such a manner -as to be at liberty to assume the position which its polar action -assigns to them; (for instance, by strewing them upon a sheet of -paper while the two poles of the magnet are close below the paper;) -they will arrange themselves in certain curves, each proceeding -from the N. to the S. pole of the magnet, like the meridians in -a map of the globe. It is easily shown, on the supposition of -magnetic attraction and repulsion, that these <i>magnetic curves</i>, as -they are termed, are each a curve whose tangent at every point is -the direction of a small line or particle, as determined by the -attraction and repulsion of the two poles. But if we suppose a -<i>magnetic vortex</i> constantly to flow out of one pole and into the -other, in streams which follow such curves, it is evident that such a -vortex, being supposed to exercise material pressure and impulse, -would arrange the iron filings in corresponding streams, and would -thus produce the phenomenon which I have described. And the -hypothesis of <i>central torrents</i> of Bernoulli or Le Sage which I have -referred to, would, in its application to magnets, really become this -hypothesis of a magnetic vortex, if we further suppose that the -matter of the torrents which proceed to one pole and from the<span class="pagenum" id="Page_501">501</span> -other, mingles its streams, so as at each point to produce a stream -in the resulting direction. Of course we shall have to suppose two -sets of magnetic torrents;—a boreal torrent, proceeding to the -north pole, and from the south pole of a magnet; and an austral -torrent proceeding to the south and from the north pole:—and -with these suppositions, we make a transition from the hypothesis -of attraction and repulsion, to the Cartesian hypothesis of vortices, -or at least, torrents, which determine bodies to their magnetic -positions by impulse.</p> - -<p>Of course it is to be expected that, in this as in the other case, -when we follow the hypothesis of impulse into detail, it will need to -be loaded with so many subsidiary hypotheses, in order to accommodate -it to the phenomena, that it will no longer seem tenable. -But the plausibility of the hypothesis in its first application cannot -be denied:—for, it may be observed, the two <i>opposite</i> streams -would counteract each other so as to produce no local <i>motion</i>, -only <i>direction</i>. And this case may put us on our guard against -other suggestions of forces acting in curve lines, which may at -first sight appear to be discerned in magnetic and electric phenomena. -Probably such curve lines will all be found to be only -resulting lines, arising from the direct action and combination of -elementary attraction and repulsion.</p> - -<p>5. There is another case in which it would not be difficult -to devise a mode of transition from one to the other of two rival -theories; namely, in the case of the emission theory and the undulation -theory of Light. Indeed several steps of such a transition -have already appeared in the history of optical speculation; -and the conclusive objection to the emission theory of light, as -to the Cartesian theory of vortices, is, that no amount of additional -hypotheses will reconcile it to the phenomena. Its defenders had -to go on adding one piece of machinery after another, as new -classes of facts came into view, till it became more complex and -unmechanical than the theory of epicycles and eccentrics at its -worst period. Otherwise, as I have said, there was nothing to -prevent the emission theory from migrating into the undulatory -theory, and as the theory of vortices did into the theory of attraction. -For the emissionists allow that rays may <i>interfere</i>; and -that these interferences may be modified by alternate <i>fits</i> in the -rays; now these fits are already a kind of <i>undulation</i>. Then again -the phenomena of polarized light show that the fits or undulations -must have a <i>transverse</i> character: and there is no reason why emitted -rays should not be subject to <i>fits</i> of <i>transverse</i> modification as -well as to any other fits. In short, we may add to the emitted rays<span class="pagenum" id="Page_502">502</span> -of the one theory, all the properties which belong to the undulations -of the other, and thus account for all the phenomena on the -emission theory; with this limitation only, that the emission will -have no share in the explanation, and the undulations will have -the whole. If, instead of conceiving the universe full of a <i>stationary</i> -ether, we suppose it to be full of etherial particles moving -in every direction; and if we suppose, in the one case and in the -other, this ether to be susceptible of undulations proceeding from -every luminous point; the results of the two hypotheses will be the -same; and all we shall have to say is, that the supposition of the -emissive motion of the particles is superfluous and useless.</p> - -<p>6. This view of the manner in which rival theories pass into one -another appears to be so unfamiliar to those who have only slightly -attended to the history of science, that I have thought it might be -worth while to illustrate it by a few examples.</p> - -<p>It might be said, for instance, by such persons<a name="FNanchor_362" id="FNanchor_362"></a><a href="#Footnote_362" class="fnanchor">[362]</a>, "Either the -planets are not moved by vortices, or they do not move by the law -by which heavy bodies fall. It is impossible that both opinions can -be true." But it appears, by what has been said above, that the -Cartesians did hold both opinions to be true; and one with just as -much reason as the other, on their assumptions. It might be said -in the same manner, "Either it is false that the planets are made to -describe their orbits by the above quasi-Cartesian theory of Bernoulli, -or it is false that they obey the Newtonian theory of gravitation." -But this would be said quite erroneously; for if the hypothesis -of Bernoulli be true, it is so because it agrees in its result -with the theory of Newton. It is not only possible that both -opinions may be true, but it is certain that if the first be so, the -second is. It might be said again, "Either the planets describe -their orbits by an inherent virtue, or according to the Newton -theory." But this again would be erroneous, for the Newtonian -doctrine decided nothing as to whether the force of gravitation -was inherent or not. Cotes held that it was, though Newton -strongly protested against being supposed to hold such an opinion. -The word <i>inherent</i> is no part of the physical theory, and will be -asserted or denied according to our metaphysical views of the -essential attributes of matter and force.</p> - -<p>Of course, the possibility of two rival hypotheses being true, -one of which takes the explanation a step higher than the other, -is not affected by the impossibility of two contradictory asser<span class="pagenum" id="Page_503">503</span>tions -of the <i>same order</i> of generality being both true. If there -be a new-discovered comet, and if one astronomer asserts that -it will return once in <i>every</i> twenty years, and another, that it -will return once in every thirty years, both cannot be right. -But if an astronomer says that though its interval was in the last -instance 30 years, it will only be 20 years to the next return, in -consequence of perturbation and resistance, he may be perfectly -right.</p> - -<p>And thus, when different and rival explanations of the same -phenomena are held, till one of them, though long defended by -ingenious men, is at last driven out of the field by the pressure of -facts, the defeated hypothesis is transformed before it is extinguished. -Before it has disappeared, it has been modified so as to -have all palpable falsities squeezed out of it, and subsidiary provisions -added, in order to reconcile it with the phenomena. It has, -in short, been penetrated, infiltrated, and metamorphosed by the -surrounding medium of truth, before the merely arbitrary and erroneous -residuum has been finally ejected out of the body of permanent -and certain knowledge.</p> -<hr class="chap" /> - -<p><span class="pagenum" id="Page_504">504</span></p> - - - -<h3><a name="Appendix_H" id="Appendix_H"></a><span class="smcap">Appendix H.</span><br /> - -ON HEGEL'S CRITICISM OF NEWTON'S -PRINCIPIA.</h3> - -<p class="center">(<i>Cam. Phil. Soc.</i> <span class="smcap">May 21, 1849</span>.)</p> - - -<p class="drop-cap"><span class="smcap">The</span> Newtonian doctrine of universal gravitation, as the cause of -the motions which take place in the solar system, is so entirely -established in our minds, and the fallacy of all the ordinary arguments -against it is so clearly understood among us, that it would -undoubtedly be deemed a waste of time to argue such questions in -this place, so far as physical truth is concerned. But since in other -parts of Europe, there are teachers of philosophy whose reputation -and influence are very great, and who are sometimes referred to -among our own countrymen as the authors of new and valuable -views of truth, and who yet reject the Newtonian opinions, and deny -the validity of the proofs commonly given of them, it may be worth -while to attend for a few minutes to the declarations of such -teachers, as a feature in the present condition of European philosophy. -I the more readily assume that the Cambridge Philosophical -Society will not think a communication on such a subject devoid of -interest, in consequence of the favourable reception which it has -given to philosophical speculations still more abstract, which I have -on previous occasions offered to it. I will therefore proceed to -make some remarks on the opinions concerning the Newtonian -doctrine of gravitation, delivered by the celebrated Hegel, of Berlin, -than whom no philosopher in modern, and perhaps hardly any even -in ancient times, has had his teaching received with more reverential -submission by his disciples, or been followed by a more numerous -and zealous band of scholars bent upon diffusing and applying his -principles.</p> - -<p>The passages to which I shall principally refer are taken from one -of his works which is called the <i>Encyclopædia</i> (Encyklopädie), of -which the First Part is <i>the Science of Logic</i>, the Second, the <i>Philosophy -of Nature</i>, the Third, the <i>Philosophy of Spirit</i>. The Second Part,<span class="pagenum" id="Page_505">505</span> -with which I am here concerned, has for an <i>aliter</i> title, <i>Lectures on -Natural Philosophy</i> (Vorlesungen über Natur-philosophie), and -would through its whole extent offer abundant material for criticism, -by referring it to principles with which we are here familiar: but I -shall for the present confine myself to that part which refers to the -subject which I have mentioned, the Newtonian Doctrine of Gravitation, -§ 269, 270, of the work. Nor shall I, with regard to this -part, think it necessary to give a continuous and complete criticism -of all the passages bearing upon the subject; but only such specimens, -and such remarks thereon, as may suffice to show in a general -manner the value and the character of Hegel's declarations on such -questions. I do not pretend to offer here any opinion upon the -value and character of Hegel's philosophy in general: but I think -it not unlikely that some impression on that head may be suggested -by the examination, here offered, of some points in which we can -have no doubt where the truth lies; and I am not at all persuaded -that a like examination of many other parts of the Hegelian -<i>Encyclopædia</i>, would not confirm the impression which we shall -receive from the parts now to be considered.</p> - -<p>Hegel both criticises the Newtonian doctrines, or what he states -as such; and also, not denying the truth of the laws of phenomena -which he refers to, for instance Kepler's laws, offers his own proof -of these laws. I shall make a few brief remarks on each of these -portions of the pages before me. And I would beg it to be understood -that where I may happen to put my remarks in a short, and -what may seem a peremptory form, I do so for the sake of saving -time; knowing that among us, upon subjects so familiar, a few -words will suffice. For the same reason, I shall take passages from -Hegel, not in the order in which they occur, but in the order in -which they best illustrate what I have to say. I shall do Hegel no -injustice by this mode of proceeding: for I will annex a faithful -translation, so far as I can make one, of the whole of the passages -referred to, with the context.</p> - -<p>No one will be surprised that a German, or indeed any lover of -science, should speak with admiration of the discovery of Kepler's -laws, as a great event in the history of Astronomy, and a glorious -distinction to the discoverer. But to say that the glory of the discovery -of the proof of these laws has been unjustly transferred from -Kepler to Newton, is quite another matter. This is what Hegel -says (<i>a</i>)<a name="FNanchor_363" id="FNanchor_363"></a><a href="#Footnote_363" class="fnanchor">[363]</a>. And we have to consider the reasons which he assigns -for saying so.</p> - -<p><span class="pagenum" id="Page_506">506</span></p> - -<p>He says (<i>b</i>) that "it is allowed by mathematicians that the Newtonian -Formula maybe derived from the Keplerian laws," and hence -he seems to infer that the Newtonian law is not an additional truth. -That is, he does not allow that the discovery of the cause which -produces a certain phenomenal law is anything additional to the -discovery of the law itself.</p> - -<p>"The Newtonian formula may be derived from the Keplerian -law." It was professedly so derived; but derived by introducing -the Idea of <i>Force</i>, which Idea and its consequences were not introduced -and developed till after Kepler's time.</p> - -<p>"The Newtonian formula may be derived from the Keplerian -law." And the Keplerian law may be derived, and was derived, -from the observations of the Greek astronomers and their successors; -but was not the less a new and great discovery on that -account.</p> - -<p>But let us see what he says further of this derivation of the Newtonian -"formula" from the Keplerian Law. It is evident that by -calling it a <i>formula</i>, he means to imply, what he also asserts, that it -is no new law, but only a new form (and a bad one) of a previously -known truth.</p> - -<p>How is the Newtonian "formula," that is, the law of the inverse -squares of the central force, derived from the Keplerian law of the -cubes of the distances proportional to the squares of the times? -This, says Hegel, is the "immediate derivation." (<i>c</i>).—By Kepler's -law, <i>A</i> being the distance and <i>T</i> the periodic time, <i>A</i><sup>3</sup>/<i>T</i><sup>2</sup> is constant. -But Newton <i>calls</i> <i>A</i>/<i>T</i><sup>2</sup> universal gravitation; whence it easily follows -that gravitation is inversely as <i>A</i><sup>2</sup>.</p> - -<p>This is Hegel's way of representing Newton's proof. Reading -it, any one who had never read the <i>Principia</i> might suppose that -Newton <i>defined</i> gravitation to be <i>A</i>/<i>T</i><sup>2</sup>. We, who have read the -<i>Principia</i>, know that Newton <i>proves</i> that in circles, the <i>central -force</i> (not the <i>universal gravitation</i>) is as <i>A</i>/<i>T</i><sup>2</sup>: that he proves this, -by setting out from the idea of force, as that which deflects a body -from the tangent, and makes it describe a curved line: and that in -this way, he passes from Kepler's laws of mere motion to his own -law of Force.</p> - -<p>But Hegel does not see any value in this. Such a mode of -treating the subject he says (<i>i</i>) "offers to us a tangled web, formed -of the Lines of the mere geometrical construction, to which a<span class="pagenum" id="Page_507">507</span> -physical meaning of independent forces is given." That a <i>measure</i> -of forces is <i>found</i> in such lines as the sagitta of the arc described in -a given time, (not such a <i>meaning</i> arbitrarily <i>given</i> to them,) is -certainly true, and is very distinctly proved in Newton, and in all our -elementary books.</p> - -<p>But, says Hegel, as further showing the artificial nature of the -Newtonian formulæ, (<i>h</i>) "Analysis has long been able to derive the -Newtonian expression and the laws therewith connected out of the -Form of the Keplerian Laws;" an assertion, to verify which he -refers to Francœur's <i>Mécanique</i>. This is apparently in order to show -that the "lines" of the Newtonian construction are superfluous. -We know very well that analysis does not always refer to visible -representations of such lines: but we know too, (and Francœur -would testify to this also,) that the analytical proofs contain equivalents -to the Newtonian lines. We, in this place, are too familiar -with the substitution of analytical for geometrical proofs, to be led -to suppose that such a substitution affects the substance of the -truth proved. The conversion of Newton's geometrical proofs of -his discoveries into analytical processes by succeeding writers, has -not made them cease to be discoveries: and accordingly, those -who have taken the most prominent share in such a conversion, -have been the most ardent admirers of Newton's genius and good -fortune.</p> - -<p>So much for Newton's comparison of the Forces in different circular -orbits, and for Hegel's power of understanding and criticising -it. Now let us look at the motion in different parts of the same -elliptical orbit, as a further illustration of the value of Hegel's -criticism. In an elliptical orbit the velocity alternately increases -and diminishes. This follows necessarily from Kepler's law of the -equal description of the areas, and so Newton explains it. Hegel, -however, treats of this acceleration and retardation as a separate -fact, and talks of another explanation of it, founded upon Centripetal -and Centrifugal Force (<i>o</i>). Where he finds this explanation, -I know not; certainly not in Newton, who in the second and third -section of the <i>Principia</i> explains the variation of the velocity in a -quite different manner, as I have said; and nowhere, I think, employs -centrifugal force in his explanations. However, the notion -of centrifugal as acting along with centripetal force is introduced -in some treatises, and may undoubtedly be used with perfect truth -and propriety. How far Hegel can judge when it is so used, we -may see from what he says of the confusion produced by such an -explanation, which is, he says, a maximum. In the first place, he -speaks of the motion being <i>uniformly</i> accelerated and retarded in<span class="pagenum" id="Page_508">508</span> -an elliptical orbit, which, in any exact use of the word <i>uniformly</i>, -it is not. But passing by this, he proceeds to criticise an explanation, -not of the variable velocity of the body in its orbit, but of the -alternate access and recess of the body to and from the center. -Let us overlook this confusion also, and see what is the value of his -criticism on the explanation. He says (<i>p</i>), "according to this explanation, -in the motion of a planet from the aphelion to the perihelion, -the centrifugal is less than the centripetal force; and in the -perihelion itself the centripetal force is supposed suddenly to -become greater than the centrifugal;" and so, of course, the body -re-ascends to the aphelion.</p> - -<p>Now I will not say that this explanation has never been given in -a book professing to be scientific; but I have never seen it given; -and it never can have been given but by a very ignorant and foolish -person. It goes upon the utterly unmechanical supposition that -the approach of a body to the center at any moment depends solely -upon the excess of the centripetal over the centrifugal force; and -reversely. But the most elementary knowledge of mechanics shows -us that when a body is moving <i>obliquely</i> to the distance from the -center, it approaches to or recedes from the center in virtue of this -obliquity, even if no force at all act. And the total approach to -the center is the approach due to this cause, <i>plus</i> the approach due -to the centripetal force, <i>minus</i> the recess due to the centrifugal force. -At the aphelion, the centripetal is greater than the centrifugal -force; and <i>hence</i> the motion becomes oblique; and <i>then</i>, the body -approaches to the center on <i>both</i> accounts, and approaches on -account of the obliquity of the path even when the centrifugal has -become greater than the centripetal force, which it becomes before -the body reaches the perihelion. This reasoning is so elementary, -that when a person who cannot see this, writes on the subject with -an air of authority, I do not see what can be done but to point out -the oversight and leave it.</p> - -<p>But there is, says Hegel (<i>q</i>), another way of explaining the motion -by means of centripetal and centrifugal forces. The two forces -are supposed to increase and decrease gradually, according to different -laws. In this case, there must be a point where they are equal, -and in equilibrio; and this being the case, they will always continue -equal, for there will be no reason for their going out of equilibrium.</p> - -<p>This, which is put as <i>another</i> mode of explanation, is, in fact, the -same mode; for, as I have already said, the centrifugal force, which -is less than the centripetal at the aphelion, becomes the greater of -the two before the perihelion; and there is an intermediate position, -at which the two forces are equal. But at this point, is there no<span class="pagenum" id="Page_509">509</span> -reason why, being equal, the forces should become unequal? Reason -abundant: for the body, being there, moves in a line oblique to the -distance, and so changes its distance; and the centripetal and centrifugal -force, depending upon the distance by different laws, they -forthwith become unequal.</p> - -<p>But these modes of explanation, by means of the centripetal and -centrifugal forces and their relation, are not necessary to Newton's -doctrine, and are nowhere used by Newton; and undoubtedly much -confusion has been produced in other minds, as well as Hegel's, by -speaking of the centrifugal force, which is a mere intrinsic geometrical -result of a body's curvilinear motion round a center, in conjunction -with centripetal force, which is an extrinsic force, acting -upon the body and urging it to the center. Neither Newton, nor -any intelligent Newtonian, ever spoke of the centripetal and centrifugal -force as two distinct forces both extrinsic to the motion, -which Hegel accuses them of doing. (<i>n</i>)</p> - -<p>I have spoken of the third and second of Kepler's laws; of Newton's -explanations of them, and of Hegel's criticism. Let us now, -in the same manner, consider the first law, that the planets move -in ellipses. Newton's proof that this was the result of a central -force varying inversely as the square of the distance, was the solution -of a problem at which his contemporaries had laboured in vain, -and is commonly looked upon as an important step. "But," says -Hegel, (<i>d</i>) "the proof gives a conic section generally, whereas the -main point which ought to be proved is, that the path of the body -is an ellipse only, not a circle or any other conic section." Certainly -if Newton <i>had</i> proved that a planet cannot move in a circle, -(which Hegel says he ought to have done), his system would have -perplexed astronomers, since there are planets which move in orbits -hardly distinguishable from circles, and the variation of the extremity -from planet to planet shows that there is nothing to prevent -the excentricity vanishing and the orbit becoming a circle.</p> - -<p>"But," says Hegel again, (<i>e</i>) "the conditions which make the -path to be an ellipse rather than any other conic section, are empirical -and extraneous;—the supposed casual strength of the impulsion -originally received." Certainly the circumstances which -determine the amount of excentricity of a planet's orbit are derived -from experience, or rather, observation. It is not a part of -Newton's system to determine <i>à priori</i> what the excentricity of a -planet's orbit must be. A system that professes to do this will -undoubtedly be one very different from his. And as our knowledge -of the excentricity is derived from observation, it is, in that sense, -empirical and casual. The strength of the original impulsion is a<span class="pagenum" id="Page_510">510</span> -hypothetical and impartial way of expressing this result of observation. -And as we see no reason why the excentricity should be of -any certain magnitude, we see none why the fraction which expresses -the excentricity should not become as large as unity, that -is, why the orbit should not become a parabola; and accordingly, -some of the bodies which revolve about the same appear to move -in orbits of this form: so little is the motion in an ellipse, as Hegel -says, (<i>f</i>) "the only thing to be proved."</p> - -<p>But Hegel himself has offered proof of Kepler's laws, to which, -considering his objections to Newton's proofs, we cannot help -turning with some curiosity.</p> - -<p>And first, let us look at the proof of the Proposition which we -have been considering, that the path of a planet is necessarily an -ellipse. I will translate Hegel's language as well as I can; but -without answering for the correctness of my translation, since it -does not appear to me to conform to the first condition of translation, -of being intelligible. The translation however, such as it -is, may help us to form some opinion of the validity and value of -Hegel's proofs as compared with Newton's. (<i>r</i>)</p> - -<p>"For absolutely uniform motion, the circle is the only path.... -The circle is the line returning into itself in which all the radii -are equal; there is, for it, only one determining quantity, the -radius.</p> - -<p>"But in free motion, the determination according to space and -to time come into view with differences. There must be a difference -in the spatial aspect in itself, and therefore the form requires -two determining quantities. Hence the form of the path -returning into itself is an ellipse."</p> - -<p>Now even if we could regard this as reasoning, the conclusion -does not in the smallest degree follow. A curve returning into -itself and determined by two quantities, may have innumerable -forms besides the ellipse; for instance, any <i>oval</i> form whatever, -besides that of the conic section.</p> - -<p>But why must the curve be a curve returning into itself? Hegel -has professed to prove this previously (<i>m</i>) from "the determination -of particularity and individuality of the bodies in general, so that -they have partly a center in themselves, and partly at the same -time their center in another." Without seeking to find any precise -meaning in this, we may ask whether it proves the impossibility of -the orbits with moveable apses, (which do not return into themselves,) -such as the planets (affected by perturbations) really do -describe, and such as we know that bodies must describe in all -cases, except when the force varies exactly as the square of the<span class="pagenum" id="Page_511">511</span> -distance? It appears to do so: and it proves this impossibility of -known facts at least as much as it proves anything.</p> - -<p>Let us now look at Hegel's proof of Kepler's second law, that -the elliptical sectors swept by the radius vector are proportional to -the time. It is this: (<i>s</i>).</p> - -<p>"In the circle, the arc or angle which is included by the two -radii is independent of them. But in the motion [of a planet] as -determined by the conception, the distance from the center and the -arc run over in a certain time must be compounded in one determination, -and must make out a whole. This whole is the sector, -a space of two dimensions. And hence the arc is essentially a -Function of the radius vector; and the former (the arc) being -unequal, brings with it the inequality of the radii."</p> - -<p>As was said in the former case, if we could regard this as reasoning, -it would not prove the conclusion, but only, that the arc is -<i>some function or other</i> of the radii.</p> - -<p>Hegel indeed offers (<i>t</i>) a reason why there must be an arc involved. -This arises, he says, from "the determinateness [of the -nature of motion], at one while as time in the root, at another -while as space in the square. But here the quadratic character of -the space is, by the returning of the line of motion into itself, -limited to a sector."</p> - -<p>Probably my readers have had a sufficient specimen of Hegel's -mode of dealing with these matters. I will however add his proof -of Kepler's third law, that the cubes of the distances are as the -squares of the times.</p> - -<p>Hegel's proof in this case (<i>u</i>) has a reference to a previous doctrine -concerning falling bodies, in which time and space have, he -says, a relation to each other as root and square. Falling bodies -however are the case of only <i>half-free</i> motion, and the determination -is incomplete.</p> - -<p>"But in the case of absolute motion, the domain of <i>free</i> masses, -the determination attains its totality. The time as the root is a -mere empirical magnitude: but as a component of the developed -Totality, it is a Totality in itself: it produces itself, and therein has -a reference to itself. And in this process, Time, being itself the -dimensionless element, only comes to a formal identity with itself -and reaches the square: Space, on the other hand, as a positive -external relation, comes to the full dimensions of the conception of -space, that is, the cube. The Realization of the two conceptions -(space and time) preserves their original difference. This is the -third Keplerian law, the relation of the Cubes of the distances to -the squares of the times."</p> - -<p><span class="pagenum" id="Page_512">512</span></p> - -<p>"And this," he adds, (<i>v</i>) with remarkable complacency, "represents -simply and immediately <i>the reason of the thing</i>:—while on -the contrary, the Newtonian Formula, by means of which the Law -is changed into a Law for the Force of Gravity, shows the distortion -and inversion of <i>Reflexion</i>, which stops half-way."</p> - -<p>I am not able to assign any precise meaning to the <i>Reflexion</i>, -which is here used as a term of condemnation, applicable especially -to the Newtonian doctrine. It is repeatedly applied in the same -manner by Hegel. Thus he says, (<i>g</i>) "that what Kepler expresses -in a simple and sublime manner in the form of Laws of the Celestial -Motions, Newton has metamorphosed into the <i>Reflexion-Form</i> -of the Force of Gravitation."</p> - -<p>Though Hegel thus denies Newton all merit with regard to the -explanation of Kepler's laws by means of the gravitation of the -planets to the sun, he allows that to the Keplerian Laws Newton -added the Principle of Perturbations (<i>k</i>). This Principle he accepts -to a certain extent, transforming the expression of it after his -peculiar fashion. "It lies," he says, (<i>l</i>) "in this: that matter in -general assigns a center for itself: the collective bodies of the system -recognise a reference to their sun, and all the individual bodies, -according to the relative positions into which they are brought by -their motions, form a momentary relation of their gravity towards -each other."</p> - -<p>This must appear to us a very loose and insufficient way of -stating the Principle of Perturbations, but loose as it is, it recognises -that the Perturbations depend upon the gravity of the planets one -to another, and to the sun. And if the Perturbations depend upon -these forces, one can hardly suppose that any one who allows this -will deny that the primary undisturbed motions depend upon these -forces, and must be explained by means of them; yet this is what -Hegel denies.</p> - -<p>It is evident, on looking at Hegel's mode of reasoning on such -subjects, that his views approach towards those of Aristotle and the -Aristotelians; according to which motions were divided into <i>natural</i> -and <i>unnatural</i>;—the <i>celestial motions</i> were circular and uniform -in their nature;—and the like. Perhaps it may be worth -while to show how completely Hegel adheres to these ancient -views, by an extract from the additions to the Articles on Celestial -Motions, made in the last edition of the <i>Encyclopædia</i>. He -says (<i>w</i>),</p> - -<p>"The motion of the heavenly bodies is not a being pulled this -way and that, as is imagined (by the Newtonians). <i>They go along, -as the ancients said, like blessed gods.</i> The celestial conformity is<span class="pagenum" id="Page_513">513</span> -not such a one as has the principle of rest or motion external to -itself. It is not right to say because a stone is inert, and the whole -earth consists of stones, and the other heavenly bodies are of the -same nature as the earth, therefore the heavenly bodies are inert. -This conclusion makes the properties of the whole the same as -those of the part. Impulse, Pressure, Resistance, Friction, Pulling, -and the like, are valid only for other than celestial matter."</p> - -<p>There can be no doubt that this is a very different doctrine from -that of Newton.</p> - -<p>I will only add to these specimens of Hegel's physics, a specimen -of the logic by which he refutes the Newtonian argument which -has just been adduced; namely, that the celestial bodies are matter, -and that matter, as we see in terrestrial matter, is inert. He -says (<i>x</i>),</p> - -<p>"Doubtless both are matter, as a good thought and a bad thought -are both thoughts; but the bad one is not therefore good, because -it is a thought."</p> - - -<h3><a id="APPENDIX_TO_THE_MEMOIR"></a>APPENDIX TO THE MEMOIR ON HEGEL'S CRITICISM -OF NEWTON'S PRINCIPIA.</h3> - -<p class="center"><span class="smcap">Hegel.</span> <i>Encyclopædia</i> (2nd Ed. 1827), Part <span class="smcap">XI.</span> p. 250.</p> - -<p class="center">C. <i>Absolute Mechanics.</i></p> - -<p class="center">§ 269.</p> - -<p class="drop-cap"><span class="smcap">Gravitation</span> is the true and determinate conception of material -Corporeity, which (Conception) is realized to the Idea (zur -Idee). <i>General</i> Corporeity is separable essentially into <i>particular</i> -Bodies, and connects itself with the Element of <i>Individuality</i> or -subjectivity, as apparent (phenomenal) presence in the <i>Motion</i>, -which by this means is immediately a system of <i>several Bodies</i>.</p> - -<p>Universal gravitation must, as to itself, be recognised as a profound -thought, although it was principally as apprehended in the -sphere of Reflexion that it eminently attracted notice and confidence -on account of the quantitative determinations therewith connected, -and was supposed to find its confirmation in <i>Experiments</i> -(Erfahrung) pursued from the Solar System down to the phenomena<span class="pagenum" id="Page_514">514</span> -of Capillary Tubes.—But Gravitation contradicts immediately the -Law of Inertia, for in virtue of it (Gravitation) matter tends <i>out of -itself</i> to the other (matter).—In the <i>Conception of Weight</i>, there -are, as has been shown, involved the two elements—Self-existence, -and Continuity, which takes away self-existence. These elements -of the Conception, however, experience a fate, as particular forces, -corresponding to Attractive and Repulsive Force, and are thereby -apprehended in nearer determination, as <i>Centripetal</i> and <i>Centrifugal -Force</i>, which (Forces) like weight, <i>act upon Bodies</i>, independent -of each other, and are supposed to come in contact accidentally -in a third thing, Body. By this means, what there is of profound -in the thought of universal weight is again reduced to nothing; -and Conception and Reason cannot make their way into the doctrine -of absolute motion, so long as the so highly-prized discoveries -of Forces are dominant there. In the conclusion which contains the -<i>Idea</i> of Weight, namely, [contains this Idea] as the Conception -which, in the case of motion, enters into external Reality through -the particularity of the Bodies, and at the same time into this -[Reality] and into their Ideality and self-regarding Reflexion, -(Reflexion-in-sich), the rational identity and inseparability of the -elements is involved, which at other times are represented as independent. -Motion itself, as such, has only its meaning and existence -in a system of <i>several</i> bodies, and those, such as stand in relation to -each other according to different determinations.</p> - -<p class="center">§ 270.</p> - -<p>As to what concerns bodies in which the conception of gravity -(weight) is realized free by itself, we say that they have for the -determinations of their different nature the elements (momente) of -their conception. One [conception of this kind] is the <i>universal</i> -center of the abstract reference [of a body] to itself. Opposite to -this [conception] stands the immediate, extrinsic, centerless <i>Individuality</i>, -appearing as <i>Corporeity</i> similarly independent. Those -[Bodies] however which are particular, which stand in the determination -of extrinsic, and at the same time of intrinsic relation, are -centers for themselves, and [also] have a reference to the first as to -their essential unity.</p> - -<blockquote> <p>The Planetary Bodies, as the immediately concrete, are -in their existence the most complete. Men are accustomed -to take the Sun as the most excellent, inasmuch as the understanding -prefers the abstract to the concrete, and in like -manner the fixed stars are esteemed higher than the Bodies<span class="pagenum" id="Page_515">515</span> -of the Solar System. Centerless Corporeity, as belonging to -externality, naturally separates itself into the opposition of the -lunar and the cometary Body. The laws of absolutely free -motion, as is well known, were discovered by Kepler;—a discovery -of immortal fame. Kepler has proved these laws in -this sense, that for the empirical data he found their general -expression. Since then, it has become a common way of -<span class="sni"><span class="hidev">|</span>(<i>a</i>)<span class="hidev">|</span></span>speaking to say that Newton first found out the proof of these -Laws. It has rarely happened that fame has been more unjustly -transferred from the first discoverer to another person. -On this subject I make the following remarks.</p> - -<p>1. That it is allowed by Mathematicians that the Newtonian -Formulæ may be derived from the Keplerian Laws. -<span class="sni"><span class="hidev">|</span>(<i>b</i>)<span class="hidev">|</span></span>The completely immediate derivation is this: In the third -<span class="sni"><span class="hidev">|</span>(<i>c</i>)<span class="hidev">|</span></span>Keplerian Law, <i>A</i><sup>3</sup>/<i>T</i><sup>2</sup> is the constant quantity. This being put -as <i>A.A</i><sup>2</sup>/<i>T</i><sup>2</sup> and calling, with Newton, <i>A</i>/<i>T</i><sup>2</sup> universal Gravitation, -his expression of the effect of gravity in the reciprocal -ratio of the square of the distances is obvious.</p> - -<p><span class="sni"><span class="hidev">|</span>(<i>d</i>)<span class="hidev">|</span></span>2. That the Newtonian proof of the Proposition that a body -subjected to the Law of Gravitation moves about the central -body in an <i>Ellipse</i>, gives a <i>Conic Section</i> generally, while the -main Proposition which ought to be proved is that the fall -of such a Body is <i>not</i> a <i>Circle or any other Conic Section</i>, -but an <i>Ellipse only</i>. Moreover, there are objections which -may be made against this proof in itself (<i>Princ. Math.</i> I. 1. -Sect. <span class="smcap">II.</span> Prop. 1); and although it is the foundation of the -Newtonian Theory, analysis has no longer any need of it. -The conditions which in the sequel make the path of the -Body to a determinate Conic Section, are referred to an <i>empirical</i> -circumstance, namely, a particular position of the Body -at a determined moment of time, and the <i>casual</i> strength of an -<span class="sni"><span class="hidev">|</span>(<i>f</i>)<span class="hidev">|</span></span><i>impulsion</i> which it is supposed to have received originally; so -that the circumstance which makes the Curve be an Ellipse, -which alone ought to be the thing proved, is extraneous to the -Formula.</p> - -<p>3. That the Newtonian Law of the so-called Force of Gravitation -is in like manner only proved from experience by Induction.</p> - -<p><span class="sni"><span class="hidev">|</span>(<i>g</i>)<span class="hidev">|</span></span>The sum of the difference is this, that what Kepler expressed -in a simple and sublime manner in the Form of <i>Laws</i><span class="pagenum" id="Page_516">516</span> -<i>of the Celestial Motions</i>, Newton has metamorphosed into the -<i>Reflection-Form</i> of the <i>Force of Gravitation</i>. If the Newtonian -Form has not only its convenience but its necessity -in reference to the analytical method, this is only a difference -<span class="sni"><span class="hidev">|</span>(<i>h</i>)<span class="hidev">|</span></span>of the mathematical formulæ; Analysis has long been able to -derive the Newtonian expression, and the Propositions therewith -connected, out of the Form of the Keplerian Laws; (on -this subject I refer to the elegant exposition in <span class="sni"><span class="hidev">|</span>(<i>i</i>)<span class="hidev">|</span></span><i>Francœur's -Traité Elém. de Mécanique</i>, Liv. <span class="smcap">II.</span> Ch. xi. n. 4.)—The old -method of so-called proof is conspicuous as offering to us a -tangled web, formed of the <i>Lines</i> of the mere geometrical -construction, to which a physical meaning of <i>independent -Forces</i> is given; and of empty Reflexion-determinations of -the already mentioned <i>Accelerating Force</i> and <i>Vis Inertiæ</i>, -and especially of the relation of the so-called gravitation itself -to the centripetal force and centrifugal force, and so on.</p> - -<p>The remarks which are here made would undoubtedly have -need of a further explication to show how well founded they -are: in a Compendium, propositions of this kind which do not -agree with that which is assumed, can only have the shape of -assertions. Indeed, since they contradict such high authorities, -they must appear as something worse, as presumptuous -assertions. I will not, on this subject, support myself by saying, -by the bye, that an interest in these subjects has occupied -me for 25 years; but it is more precisely to the purpose to -remark, that the distinctions and determinations which Mathematical -Analysis introduces, and the course which it must -take according to its method, is altogether different from that -which a physical reality must have. The Presuppositions, the -Course, and the Results, which the Analysis necessarily has -and gives, remain quite extraneous to the considerations which -determine the physical value and the signification of those determinations -and of that course. To this it is that attention -should be directed. We have to do with a consciousness -relative to the deluging of physical Mechanics with an <i>inconceivable</i> -(unsäglichen) <i>Metaphysic</i>, which—contrary to experience -and conception—has those mathematical determinations -alone for its source.</p> - -<p>It is recognized that what Newton—besides the foundation -of the analytical treatment, the development of which, by the -bye, has of itself rendered superfluous, or indeed rejected -much which belonged to Newton's essential Principles and -glory—has added to the Keplerian Laws is the Principle of<span class="pagenum" id="Page_517">517</span> -<i>Perturbations</i>,—a Principle whose importance we may here -accept thus far (hier in sofern anzuführen ist); namely, so -<span class="sni"><span class="hidev">|</span>(<i>k</i>)<span class="hidev">|</span></span>far as it rests upon the Proposition that the so-called attraction -is an operation of all the individual parts of bodies, as -being material. <span class="sni"><span class="hidev">|</span>(<i>l</i>)<span class="hidev">|</span></span>It lies in this, that matter in general assigns -a center for itself (sich das centrum setzt), and the figure of -the body is an element in the determination of its place; that -collective bodies of the system recognize a reference to their -Sun (sich ihre Sonne setzen), but also the individual bodies -themselves, according to the relative position with regard to -each other into which they come by their general motion, -form a momentary relation of their gravity (schwere) <i>towards -each other</i>, and are related to each other not only in abstract -spatial relations, but at the same time assign to themselves a -joint center, which however is again resolved [into the general -center] in the universal system.</p> - -<p>As to what concerns the features of the path, to show how -the fundamental determinations of Free Motion are connected -<i>with the Conception</i>, cannot here be undertaken in a satisfactory -and detailed manner, and must therefore be left to its fate. -The proof from reason of the quantitative determinations of -free motion can only rest upon the <i>determinations</i> of <i>Conceptions</i> -of space and time, the elements whose relation (intrinsic -not extrinsic) motion is.</p> - -<p><span class="sni"><span class="hidev">|</span>(<i>m</i>)<span class="hidev">|</span></span>That, <i>in the first place</i>, the motion in general is a motion -<i>returning into itself</i>, is founded on the determination of particularity -and individuality of the bodies in general (§ 269), so that -partly they have a center in themselves, and partly at the same -time their center in another. These are the determinations of -Conceptions which form the basis of the false representatives -<span class="sni"><span class="hidev">|</span>(<i>n</i>)<span class="hidev">|</span></span>of Centripetal Force and Centrifugal Force, as if each of -these were self-existing, extraneous to the other, and independent -of it; and as if they only came in contact in their -operations and consequently <i>externally</i>. They are, as has -already been mentioned, the Lines which must be drawn for -the mathematical determinations, transformed into physical -realities.</p> - -<p>Further, this motion is <i>uniformly accelerated</i>, (and—as -returning into itself—in turn uniformly retarded). In motion -as <i>free</i>, Time and Space enter as <i>different</i> things which are to -make themselves effective in the determination of the motion -<span class="sni"><span class="hidev">|</span>(<i>o</i>)<span class="hidev">|</span></span>(§ 266, note). In the so-called <i>Explanation</i> of the uniformly -accelerated and retarded motion, by means of the alternate<span class="pagenum" id="Page_518">518</span> -decrease and increase of the magnitude of the Centripetal -Force and Centrifugal Force, the <i>confusion</i> which the assumption -of such independent Forces produces is at its greatest -<span class="sni"><span class="hidev">|</span>(<i>p</i>)<span class="hidev">|</span></span>height. According to this explanation, in the motion of a -Planet from the Aphelion to the Perihelion, the centrifugal -is <i>less</i> than the centripetal force, and on the contrary, in the -Perihelion itself, the centrifugal force is supposed to become -greater than the centripetal. For the motion from the Perihelion -to the Aphelion, this representation makes the forces -pass into the opposite relation in the same manner. It is apparent -that such a sudden conversion of the preponderance -which a force has obtained over another, into an inferiority to -the other, cannot be anything taken out of the nature of -Forces. On the contrary it must be concluded, that a preponderance -which one Force has obtained over another must -not only be preserved, but must go onwards to the complete -annihilation of the other Force, and the motion must either, -by the Preponderance of the Centripetal Force, proceed till it -ends in rest, that is, in the Collision of the Planet with the -Central Body, or till by the Preponderance of the Centrifugal -<span class="sni"><span class="hidev">|</span>(<i>q</i>)<span class="hidev">|</span></span>Force it ends in a straight line. But now, if in place of the -suddenness of the conversion, we suppose a gradual increase -of the Force in question, then, since rather the other Force -ought to be assumed as increasing, we lose the opposition -which is assumed for the sake of the explanation; and if the -increase of the one is assumed to be different from that of the -other, (which is the case in some representations,) then there -is found at the mean distance between the apsides a point in -which the Forces are <i>in equilibrio</i>. And the transition of the -Forces out of Equilibrium is a thing just as little without any -sufficient reason as the aforesaid suddenness of inversion. -And in the whole of this kind of explanation, we see that the -mode of remedying a bad mode of dealing with a subject leads -to newer and greater confusion.—A similar confusion makes -its appearance in the explanation of the phænomenon that -the pendulum oscillates more slowly at the equator. This -phænomenon is ascribed to the Centrifugal Force, which it is -asserted must then be greater; but it is easy to see that we -may just as well ascribe it to the augmented gravity, inasmuch -as that holds the pendulum more strongly to the perpendicular -line of rest.</p> - -<p><span class="pagenum" id="Page_519">519</span></p> - - -<p class="center">§ 240.</p> - -<p><span class="sni"><span class="hidev">|</span>(<i>r</i>)<span class="hidev">|</span></span>And now first, as to what concerns the <i>Form of the Path</i>, -the <i>Circle</i> only can be conceived as the path of an <i>absolutely -uniform</i> motion. <i>Conceivable</i>, as people express it, no doubt -it is, that an increasing and diminishing motion should take -place in a circle. But this conceivableness or possibility means -only an abstract capability of being represented, which leaves -out of sight that Determinate Thing on which the question -turns.</p> - -<p>The Circle is the line returning into itself in which all the -radii are <i>equal</i>, that is, it is completely determined by means of -the radius. There is only <i>one</i> Determination, and that is the -<i>whole</i> Determination.</p> - -<p>But in free motion, in which the Determinations according -to space and according to time come into view with Differences, -in a qualitative relation to each other, this Relation -appears in the spatial aspect as a <i>Difference</i> thereof in itself, -which therefore requires two Determinations. Hereby the -Form of the path returning into itself is essentially an -<i>Ellipse</i>.</p> - - - - - -<p><span class="sni"><span class="hidev">|</span>(<i>s</i>)<span class="hidev">|</span></span>The abstract Determinations which produces the circle -appears also in this way, that the arc or angle which is included -by two Radii is independent of them, a magnitude with -regard to them completely empirical. But since in the motion -as determined by the Conception, the distance from the -center, and the arc which is run over in a certain time, must -be comprehended in one determinateness, [<i>and</i>] make out a -whole, this is the sector, a space-determination of two dimensions: -in this way, the arc is essentially a Function of the -Radius Vector; and the former (the arc) being unequal, brings -with it the inequality of the Radii. That the determination -with regard to the space by means of the time appears as a -Determination of two Dimensions,—as a Superficies-Determination,—agrees -<span class="sni"><span class="hidev">|</span>(<i>t</i>)<span class="hidev">|</span></span>with what was said before (§ 266) respecting -Falling Bodies, with regard to the exposition of the same -Determinateness, at one while as Time in the root, at another -while as Space in the Square. Here, however, the Quadratic -character of the space is, by the returning of the Line of -motion into itself, limited to a Sector. These are, as may be -seen, the general principles on which the Keplerian Law, that -in equal times equal sectors are cut off, rests.</p> - -<p>This Law becomes, as is clear, only the relation of the arc -to the Radius Vector, and the Time enters there as the abstract<span class="pagenum" id="Page_520">520</span> -Unity, in which the different Sectors are compared, because -as Unity it is the Determining Element. But the further -relation is that of the Time, not as Unity, but as a Quantity -in general,—as the time of Revolution—to the magnitude of -the Path, or, what is the same thing, the distance from the -center. As Root and Square, we saw that Time and Space -had a relation to each other, in the case of Falling Bodies, the -case of half-free motion—because that [<i>motion</i>] is determined -on one side by the conception, on the other by external -[<i>conditions</i>]. But in the case of absolute motion—the domain -<span class="sni"><span class="hidev">|</span>(<i>u</i>)<span class="hidev">|</span></span>of <i>free</i> masses—the determination attains its Totality. The -Time as the Root is a mere empirical magnitude; but as a -component (moment) of the developed Totality, it is a Totality -in itself,—it produces itself, and therein has a reference to -itself; as the Dimensionless Element in itself, it only comes -to a formal identity with itself, the Square; Space, on the -other hand, as the positive Distribution (aussereinander) -[<i>comes</i>] to the Dimension of the Conception, <i>the</i> <span class="smcap">Cube</span>. Their -<span class="sni"><span class="hidev">|</span>(<i>v</i>)<span class="hidev">|</span></span>Realization preserves their original difference. This is the -third Keplerian Law, the relation of the <i>Cubes</i> of the <i>Distances</i> -to the <i>Squares</i> of the <i>Times</i>;—a Law which is so great -on this account, that it represents so simply and immediately -<i>Reason as belonging to the thing</i>: while on the contrary the -Newtonian Formula, by means of which the Law is changed -into a Law for the Force of Gravity, shows the Distortion, -Perversion and Inversion of <i>Reflexion</i> which stops half-way.</p> - -<p class="center">Additions to new Edition. § 269.</p> - -<p>The center has no sense without the circumference, nor the -circumference without the center. This makes all physical -hypotheses vanish which sometimes proceed from the center, -sometimes from the particular bodies, and sometimes assign -this, sometimes that, as the original [cause of motion] ... It is -silly (läppisch) to suppose that the centrifugal force, as a -tendency to fly off in a Tangent, has been produced by a -lateral projection, a projectile force, an impulse which they -have retained ever since they set out on their journey (von -Haus aus). Such casualty of the motion produced by external -causes belongs to inert matter; as when a stone fastened -to a thread which is thrown transversely tries to fly -from the thread. We are not to talk in this way of Forces. -If we will speak of Force, there is one Force, whose elements<span class="pagenum" id="Page_521">521</span> -do not draw bodies to different sides as if they were two -<span class="sni"><span class="hidev">|</span>(<i>w</i>)<span class="hidev">|</span></span>Forces. The motion of the heavenly bodies is not a being -pulled this way or that, such as is thus imagined; it is free -motion: they go along, as the ancients said, as blessed Gods -(sie gehen als selige Götter einher). The celestial corporeity -is not such a one as has the principle of rest or motion external -to itself. Because stone is inert, and all the earth -consists of stones, and the other heavenly bodies are of the -same nature,—is a conclusion which makes the properties of -the whole the same as those of the part. Impulse, Pressure, -Resistance, Friction, Pulling, and the like, are valid only for -<span class="sni"><span class="hidev">|</span>(<i>x</i>)<span class="hidev">|</span></span>an existence of matter other than the celestial. Doubtless -that which is common to the two is matter, as a good thought -and a bad thought are both thoughts; but the bad one is not -therefore good, because it is a thought.</p></blockquote> -<hr class="chap" /> - -<p><span class="pagenum" id="Page_522">522</span></p> - - - -<h3><a name="Appendix_K" id="Appendix_K"></a><span class="smcap">Appendix K.</span><br /> - -DEMONSTRATION THAT ALL MATTER IS -HEAVY.</h3> - -<p class="center">(<i>Cam. Phil. Soc.</i> <span class="smcap">Feb. 22, 1841.</span>)</p> - - -<p class="drop-cap"><span class="smcap">The</span> discussion of the nature of the grounds and proofs of the -most general propositions which the physical sciences include, -belongs rather to Metaphysics than to that course of experimental -and mathematical investigation by which the sciences are formed. -But such discussions seem by no means unfitted to occupy the attention -of the cultivators of physical science. The ideal, as well as -the experimental side of our knowledge must be carefully studied -and scrutinized, in order that its true import may be seen; and -this province of human speculation has been perhaps of late unjustly -depreciated and neglected by men of science. Yet it can be -prosecuted in the most advantageous manner by them only: for no -one can speculate securely and rightly respecting the nature and -proofs of the truths of science without a steady possession of some -large and solid portions of such truths. A man must be a mathematician, -a mechanical philosopher, a natural historian, in order -that he may philosophize well concerning mathematics, and mechanics, -and natural history; and the mere metaphysician who -without such preparation and fitness sets himself to determine -the grounds of mathematical or mechanical truths, or the principles -of classification, will be liable to be led into error at every -step. He must speculate by means of general terms, which he will -not be able to use as instruments of discovering and conveying -philosophical truth, because he cannot, in his own mind, habitually -and familiarly, embody their import in special examples.</p> - -<p>Acting upon such views, I have already laid before the Philosophical -Society of Cambridge essays on such subjects as I here refer -to; especially a memoir "On the Nature of the Truth of the Laws -of Motion," which was printed by the Society in its Transactions.<span class="pagenum" id="Page_523">523</span> -This memoir appears to have excited in other places, notice of such -a kind as to show that the minds of many speculative persons are -ready for and inclined towards the discussion of such questions. -I am therefore the more willing to bring under consideration -another subject of a kind closely related to the one just mentioned.</p> - -<p>The general questions which all such discussions suggest, are -(in the existing phase of English philosophy) whether certain proposed -scientific truths, (as the laws of motion,) be <i>necessary</i> truths; -and if they are necessary, (which I have attempted to show that in -a certain sense they are,) <i>on what ground</i> their necessity rests. -These questions may be discussed in a general form, as I have -elsewhere attempted to show. But it may be instructive also to -follow the general arguments into the form which they assume in -special cases; and to exhibit, in a distinct shape, the incongruities -into which the opposite false doctrine leads us, when applied to particular -examples. This accordingly is what I propose to do in the -present memoir, with regard to the proposition stated at the head -of this paper, namely, that <i>all matter is heavy</i>.</p> - -<p>At first sight it may appear a doctrine altogether untenable to -assert that this proposition is a necessary truth: for, it may be -urged, we have no difficulty in conceiving matter which is not -heavy; so that matter without weight is a conception not inconsistent -with itself; which it must be if the reverse were a necessary -truth. It may be added, that the possibility of conceiving matter -without weight was shown in the controversy which ended in the -downfall of the phlogiston theory of chemical composition; for -some of the reasoners on this subject asserted phlogiston to be a -body with positive levity instead of gravity, which hypothesis, however -false, shows that such a supposition is possible. Again, it -may be said that <i>weight</i> and <i>inertia</i> are two separate properties -of matter: that mathematicians measure the quantity of matter -by the inertia, and that we learn by experiment only that the -weight is proportional to the inertia; Newton's experiments with -pendulums of different materials having been made with this very -object.</p> - -<p>I proceed to reply to these arguments. And first, as to the -possibility of conceiving matter without weight, and the argument -thence deduced, that the universal gravity of matter is not a necessary -truth, I remark, that it is indeed just, to say that we cannot -even distinctly conceive the contrary of a necessary truth to be -true; but that this impossibility can be asserted only of those perfectly -distinct conceptions which result from a complete develop<span class="pagenum" id="Page_524">524</span>ment -of the fundamental idea and its consequences. Till we reach -this stage of development, the obscurity and indistinctness may -prevent our perceiving absolute contradictions, though they exist. -We have abundant store of examples of this, even in geometry and -arithmetic; where the truths are universally allowed to be necessary, -and where the relations which are impossible, are also inconceivable, -that is, not conceivable distinctly. Such relations, though -not distinctly conceivable, still often appear conceivable and possible, -owing to the indistinctness of our ideas. Who, at the first -outset of his geometrical studies, sees any impossibility in supposing -the side and the diagonal of a square to have a common measure? -Yet they can be rigorously proved to be incommensurable, -and therefore the attempt distinctly to conceive a common measure -of them must fail. The attempts at the geometrical duplication of -the cube, and the supposed solutions, (as that of Hobbes,) have -involved absolute contradictions; yet this has not prevented their -being long and obstinately entertained by men, even of minds acute -and clear in other respects. And the same might be shewn to -be the case in arithmetic. It is plain, therefore, that we cannot, -from the supposed possibility of conceiving matter without weight, -infer that the contrary may not be a necessary truth.</p> - -<p>Our power of judging, from the compatibility or incompatibility -of our conceptions, whether certain propositions respecting the -relations of ideas are true or not, must depend entirely, as I have -said, upon the degree of development which such ideas have undergone -in our minds. Some of the relations of our conceptions on -any subject are evident upon the first steady contemplation of the -fundamental idea by a sound mind: these are the <i>axioms</i> of the -subject. Other propositions may be deduced from the axioms by -strict logical reasoning. These propositions are no less <i>necessary</i> -than the axioms, though to common minds their <i>evidence</i> is very -different. Yet as we become familiar with the steps by which these -ulterior truths are deduced from the axioms, <i>their</i> truth also becomes -evident, and the contrary becomes inconceivable. When a -person has familiarized himself with the first twenty-six propositions -of Euclid, and not till then, it becomes evident to him, that -parallelograms on the same base and between the same parallels -are equal; and he cannot even conceive the contrary. When he -has a little further cultivated his geometrical powers, the equality -of the square on the hypothenuse of a right-angled triangle to the -squares on the sides, becomes also evident; the steps by which it is -demonstrated being so familiar to the mind as to be apprehended -without a conscious act. And thus, the contrary of a necessary<span class="pagenum" id="Page_525">525</span> -truth cannot be distinctly conceived; but the incapacity of forming -such a conception is a condition which depends upon cultivation, -being intimately connected with the power of rapidly and clearly -perceiving the connection of the necessary truth under consideration -with the elementary principles on which it depends. And thus, -again, it may be that there is an absolute impossibility of conceiving -matter without weight; but then, this impossibility may not be -apparent, till we have traced our fundamental conceptions of matter -into some of their consequences.</p> - -<p>The question then occurs, whether we can, by any steps of reasoning, -point out an inconsistency in the conception of matter -without weight. This I conceive we may do, and this I shall -attempt to show.</p> - -<p>The general mode of stating the argument is this:—the quantity -of matter is measured by those sensible properties of matter which -undergo quantitative addition, subtraction and division, as the matter -is added, subtracted and divided. The quantity of matter cannot -be known in any other way. But this mode of measuring the -quantity of matter, in order to be true at all, must be universally -true. If it were only partially true, the limits within which it is -to be applied would be arbitrary; and therefore the whole procedure -would be arbitrary, and, as a method of obtaining philosophical -truth, altogether futile.</p> - -<p>We may unfold this argument further. Let the contrary be supposed, -of that which we assert to be true: namely, let it be supposed -that while all other kinds of matter are heavy (and of course -heavy in proportion to the quantity of matter), there is one kind of -matter which is absolutely destitute of weight; as, for instance, -phlogiston, or any other element. Then where this <i>weightless</i> -element (as we may term it) is mixed with <i>weighty</i> elements, we -shall have a compound, in which the weight is no longer proportional -to the quantity of matter. If, for example, 2 measures of -heavy matter unite with one measure of phlogiston, the weight is -as 2, and the quantity of matter as 3. In all such cases, therefore, -the weight ceases to be the measure of the quantity of matter. -And as the proportion of the weighty and the weightless matter -may vary in innumerable degrees in such compounds, the weight -affords no criterion at all of the quantity of matter in them. And -the smallest admixture of the weightless element is sufficient to -prevent the weight from being taken as the measure of the quantity -of matter.</p> - -<p>But on this hypothesis, how are we to distinguish such compounds -from bodies consisting purely of heavy matter? How are<span class="pagenum" id="Page_526">526</span> -we to satisfy ourselves that there is not, in every body, some admixture, -small or great, of the weightless element? If we call this -element <i>phlogiston</i>, how shall we know that the bodies with which -we have to do are, any of them, absolutely free from phlogiston?</p> - -<p>We cannot refer to the weight for any such assurance; for by -supposition the presence and absence of phlogiston makes no difference -in the weight. Nor can any other properties secure us at -least from a very small admixture; for to assert that a mixture of -1 in 100 or 1 in 10 of phlogiston would always manifest itself in -the properties of the body, must be an arbitrary procedure, till we -have proved this assertion by experiment: and we cannot do this -till we have learnt some mode of measuring the quantities of matter -in bodies and parts of bodies; which is exactly what we question -the possibility of, in the present hypothesis.</p> - -<p>Thus, if we assume the existence of an element, <i>phlogiston</i>, -devoid of weight, we cannot be sure that every body does not contain -some portion of this element; while we see that if there be an -admixture of such an element, the weight is no longer any criterion -of the quantity of matter. And thus we have proved, that if there -be any kind of matter which is not heavy, the weight can no longer -avail us, <i>in any case or to any extent</i>, as a measure of the quantity -of matter.</p> - -<p>I may remark, that the same conclusion is easily extended to the -case in which phlogiston is supposed to have absolute levity; for in -that case, a certain mixture of phlogiston and of heavy matter -would have no weight, and might be substituted for phlogiston in -the preceding reasoning.</p> - -<p>I may remark, also, that the same conclusion would follow by -the same reasoning, if any kind of matter, instead of being void of -weight, were heavy, indeed, but not <i>so</i> heavy, in proportion to its -quantity of matter, as other kinds.</p> - -<p>On all these hypotheses there would be no possibility of measuring -quantity of matter by weight at all, in any case, or to any extent.</p> - -<p>But it may be urged, that we have not yet reduced the hypothesis -of matter without weight to a contradiction; for that mathematicians -measure quantity of matter, not by weight, but by the -other property, of which we have spoken, inertia.</p> - -<p>To this I reply, that, practically speaking, quantity of matter is -always measured by weight, both by mechanicians and chemists: -and as we have proved that this procedure is utterly insecure in all -cases, on the hypothesis of weightless matter, the practice rests -upon a conviction that the hypothesis is false. And yet the practice -is universal. Every experimenter measures quantity of matter<span class="pagenum" id="Page_527">527</span> -by the balance. No one has ever thought of measuring quantity of -matter by its inertia practically: no one has constructed a measure -of quantity of matter in which the matter produces its indications -of quantity by its motion. When we have to take into account the -inertia of a body, we inquire what its weight is, and assume this as -the measure of the inertia; but we never take the contrary course, -and ascertain the inertia first in order to determine by that means -the weight.</p> - -<p>But it may be asked, Is it not then true, and an important -scientific truth, that the <i>quantity of matter</i> is measured by the -<i>inertia</i>? Is it not true, and proved by experiment, that the <i>weight</i> -is <i>proportional</i> to the <i>inertia</i>? If this be not the result of Newton's -experiments mentioned above, what, it may be demanded, do they -prove?</p> - -<p>To these questions I reply: It is true that quantity of matter is -measured by the inertia, for it is true that inertia is as the quantity -of matter. This truth is indeed one of the laws of motion. That -weight is proportional to inertia is proved by experiment, as far as -the laws of motion are so proved: and Newton's experiments prove -one of the laws of motion, so far as any experiments can prove -them, or are needed to prove them.</p> - -<p>That inertia is proportional to weight, is a law equivalent to that -law which asserts, that when pressure produces motion in a given -body, the velocity produced in a given time is as the pressure. For -if the velocity be as the pressure, when the body is given, the -velocity will be constant if the inertia also be as the pressure. For -the inertia is understood to be that property of bodies to which, -<i>ceteris paribus</i>, the velocity impressed is <i>inversely</i> proportional. One -body has twice as much inertia as another, if, when the same force -acts upon it for the same time, it acquires but half the velocity. -This is the fundamental conception of <i>inertia</i>.</p> - -<p>In Newton's pendulum experiments, the pressure producing motion -was a certain resolved part of the weight, and was proportional -to the weight. It appeared by the experiments, that whatever were -the material of which the pendulum was formed, the rate of oscillation -was the same; that is, the velocity acquired was the same. -Hence the inertia of the different bodies must have been in each -case as the weight: and thus this assertion is true of all different -kinds of bodies.</p> - -<p>Thus it appears that the assertion, that inertia is universally -proportional to weight, is equivalent to the law of motion, that the -velocity is as the pressure. The conception of inertia (of which, -as we have said, the fundamental conception is, that the velocity<span class="pagenum" id="Page_528">528</span> -impressed is inversely proportional to the inertia,) connects the -two propositions so as to make them identical.</p> - -<p>Hence our argument with regard to the universal gravity of -matter brings us to the above law of motion, and is proved by -Newton's experiments in the same sense in which that law of motion -is so proved.</p> - -<p>Perhaps some persons might conceive that the identity of weight -and inertia is obvious at once; for both are merely resistance to -motion;—inertia, resistance to all motion (or change of motion)—weight, -resistance to motion upwards.</p> - -<p>But there is a difference in these two kinds of resistance to -motion. Inertia is instantaneous, weight is continuous resistance. -Any momentary impulse which acts upon a free body overcomes its -inertia, for it changes its motion; and this change once effected, -the inertia opposes any return to the former condition, as well as -any additional change. The inertia is thus overcome by a momentary -force. But the weight can only be overcome by a continuous -force like itself. If an impulse act in opposition to the weight, it -may for a moment neutralize or overcome the weight; but if it be -not continued, the weight resumes its effect, and restores the condition -which existed before the impulse acted.</p> - -<p>But weight not only produces rest, when it is resisted, but motion, -when it is not resisted. Weight is measured by the reaction -which would balance it; but when unbalanced, it produces motion, -and the velocity of this motion increases constantly. Now what -determines the velocity thus produced in a given time, or its rate of -increase? What determines it to have one magnitude rather than -another? To this we must evidently reply, <i>the inertia</i>. When -weight produces motion, the inertia is the reaction which makes the -motion determinate. The accumulated motion produced by the -action of unbalanced weight is as determinate a condition as the -equilibrium produced by balanced weight. In both cases the condition -of the body acted on is determined by the opposition of the -action and reaction.</p> - -<p>Hence inertia is the reaction which opposes the weight, when -unbalanced. But by the conception of action and reaction, (as -mutually determining and determined,) they are measured by each -other: and hence the inertia is necessarily proportional to the -weight.</p> - -<p>But when we have reached this conclusion, the original objection -may be again urged against it. It may be said, that there must be -some fallacy in this reasoning, for it proves a state of things to be -necessary when we can so easily conceive a contrary state of things.<span class="pagenum" id="Page_529">529</span> -Is it denied, the opponent may ask, that we can readily imagine -a state of things in which bodies have no weight? Is not the -uniform tendency of all bodies in the same direction not only not -necessary, but not even true? For they do in reality tend, not -with equal forces in parallel lines, but to a center with unequal -forces, according to their position: and we can conceive these -differences of intensity and direction in the force to be greater -than they really are; and can with equal ease suppose the force to -disappear altogether.</p> - -<p>To this I reply, that certainly we may conceive the weight of -bodies to vary in intensity and direction, and by an additional effort -of imagination, may conceive the weight to vanish: but that in all -these suppositions, even in the extreme one, we must suppose the -rule to be universal. If <i>any</i> bodies have weight, <i>all</i> bodies must -have weight. If the direction of weight be different in different -points, this direction must still vary according to the <i>law of continuity</i>; -and the same is true of the intensity of the weight. For if -this were not so, the rest and motion, the velocity and direction, -the permanence and change of bodies, as to their mechanical condition, -would be arbitrary and incoherent: they would not be subject -to mechanical ideas; that is, not to ideas at all: and hence -these conditions of objects would in fact be inconceivable. In -order that the universe may be possible, that is, may fall under the -conditions of intelligible conceptions, we must be able to conceive a -body at rest. But the rest of bodies (except in the absolute negation -of all force) implies the equilibrium of opposite forces. And -one of these opposite forces must be a <i>general</i> force, as weight, in -order that the universe may be governed by general conditions. -And this general force, by the conception of force, may produce -motion, as well as equilibrium; and this motion again must be -determined, and determined by general conditions; which cannot -be, except the communication of motion be regulated by an inertia -proportional to the weight.</p> - -<p>But it will be asked, Is it then pretended that Newton's experiment, -by which it was intended to prove inertia proportional to -weight, does really prove nothing but what may be demonstrated <i>à -priori</i>? Could we know, without experiment, that all bodies,—gold, -iron, wood, cork,—have inertia proportional to their weight? -And to this we reply, that experiment holds the same place in the -establishment of this, as of the other fundamental doctrines of -mechanics. Intercourse with the external world is requisite for -developing our ideas; measurement of phenomena is needed to fix -our conceptions and to render them precise: but the result of our<span class="pagenum" id="Page_530">530</span> -experimental studies is, that we reach a position in which our convictions -do not rest upon experiment. We learn by observation -truths of which we afterwards see the necessity. This is the case -with the laws of motion, as I have repeatedly endeavoured to show. -The same will appear to be the case with the proposition, that -bodies of different kinds have their inertia proportional to their -weight.</p> - -<p>For bodies <i>of the same kind</i> have their inertia proportional to -their weight, both quantities being proportional to the quantity of -matter. And if we compress the same quantity of matter into half -the space, neither the weight nor the inertia is altered, because -these depend on the quantity of matter alone. But in this way we -obtain a body of <i>twice the density</i>; and in the same manner we -obtain a body of any other density. Therefore whatever be the -density, the inertia is proportional to the quantity of matter. But -the mechanical relations of bodies cannot depend upon any difference -of <i>kind</i>, <i>except</i> a difference of density. For if we suppose -any fundamental difference of mechanical nature in the particles or -component elements of bodies, we are led to the same conclusion, -of arbitrary, and therefore impossible, results, which we deduced -from this supposition with regard to weight. Therefore all bodies -of different density, and hence, all bodies whatever, must have their -inertia proportional to their weight.</p> - -<p>Hence we see, that the propositions, that all bodies are heavy, -and that inertia is proportional to weight, necessarily follow from -those fundamental ideas which we unavoidably employ in all attempts -to reason concerning the mechanical relations of bodies. This conclusion -may perhaps appear the more startling to many, because -they have been accustomed to expect that fundamental ideas and -their relations should be self-evident at our first contemplation of -them. This, however, is far from being the case, as I have already -shown. It is not the <i>first</i>, but the most complete and developed -condition of our conceptions which enables us to see what are -axiomatic truths in each province of human speculation. Our fundamental -ideas are necessary conditions of knowledge, universal -forms of intuition, inherent types of mental development; they -may even be termed, if any one chooses, results of connate intellectual -tendencies; but we cannot term them <i>innate</i> ideas, without -calling up a large array of false opinions. For innate ideas were -considered as capable of composition, but by no means of simplification: -as most perfect in their original condition; as to be found, if -any where, in the most uneducated and most uncultivated minds; -as the same in all ages, nations, and stages of intellectual culture;<span class="pagenum" id="Page_531">531</span> -as capable of being referred to at once, and made the basis of our -reasonings, without any special acuteness or effort: in all which -circumstances the Fundamental Ideas of which we have spoken, -are opposed to Innate Ideas so understood.</p> - -<p>I shall not, however, here prosecute this subject. I will only -remark, that Fundamental Ideas, as we view them, are not only -not innate, in any usual or useful sense, but they are not necessarily -<i>ultimate</i> elements of our knowledge. They are the results of our -analysis so far as we have yet prosecuted it; but they may themselves -subsequently be analysed. It may hereafter appear, that -what we have treated as different Fundamental Ideas have, in fact, -a connexion, at some point below the structure which we erect -upon them. For instance, we treat of the mechanical ideas of force, -matter, and the like, as distinct from the idea of substance. Yet -the principle of measuring the quantity of matter by its weight, -which we have deduced from mechanical ideas, is applied to determine -the substances which enter into the composition of bodies. -The idea of substance supplies the axiom, that the whole quantity -of matter of a compound body is equal to the sum of the quantities -of matter of its elements. The mechanical ideas of force and matter -lead us to infer that the quantity both of the whole and its parts -must be measured by their weights. <i>Substance</i> may, for some purposes, -be described as that to which properties belong; <i>matter</i> in -like manner may be described as that which resists force. The -former involves the Idea of permanent Being; the latter, the Idea -of Causation. There may be some elevated point of view from -which these ideas may be seen to run together. But even if this be -so, it will by no means affect the validity of reasonings founded -upon these notions, when duly determined and developed. If we -once adopt a view of the nature of knowledge which makes necessary -truth possible at all, we need be little embarrassed by finding -how closely connected different necessary truths are; and how often, -in exploring towards their roots, different branches appear to spring -from the same stem.</p> - - -<p class="center">END OF THE APPENDIX.</p> -</div> -<hr class="chap" /> - -<p><span class="pagenum" id="Page_532">532</span></p> - - -<p class="center"> -Cambridge:<br /> -PRINTED BY C. J. CLAY, M.A.<br /> -AT THE UNIVERSITY PRESS.<br /> -</p> -<hr class="chap" /> - -<p><span class="pagenum" id="Page_1a">1a</span></p> - - - -<h3><a name="WORKS_BY" id="WORKS_BY"></a>WORKS BY<br /> - -WILLIAM WHEWELL, D.D. F.R.S.<br /> - -<small>MASTER OF TRINITY COLLEGE, CAMBRIDGE</small>.</h3> - - -<div class="hang"> - -<p>HISTORY OF THE INDUCTIVE SCIENCES. -Third and Cheaper Edition. 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PARKER <span class="smcap">AND</span> SON, <span class="smcap">West Strand</span>. -</p> - - - -<div class="footnotes"> -<h3>FOOTNOTES:</h3> - -<div class="footnote"> - -<p><a id="Footnote_1" href="#FNanchor_1" class="label">1</a> - <i>Metaph.</i> xii. 4.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_2" href="#FNanchor_2" class="label">2</a> - Diog. Laert. <i>Vit. Plat.</i></p></div> - -<div class="footnote"> - -<p><a id="Footnote_3" href="#FNanchor_3" class="label">3</a> - T. ii. p. 16, c, d. ed. Bekker, t. v. p. 437.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_4" href="#FNanchor_4" class="label">4</a> - See the remarks on this phrase in the next chapter.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_5" href="#FNanchor_5" class="label">5</a> - <i>Hist. Ind. Sc.</i> b. iii. c. ii.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_6" href="#FNanchor_6" class="label">6</a> - This matter is further discussed in the Appendix, Essay A.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_7" href="#FNanchor_7" class="label">7</a> - These matters are further discussed in the Appendix, Essay B.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_8" href="#FNanchor_8" class="label">8</a> - See Appendix, Essay B.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_9" href="#FNanchor_9" class="label">9</a> - <i>Hist. Ind. Sc.</i> b. ii. Additions to 3rd Ed.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_10" href="#FNanchor_10" class="label">10</a> - See these views further discussed in the Appendix, Essay C.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_11" href="#FNanchor_11" class="label">11</a> - <i>Metaph.</i> xii. 4.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_12" href="#FNanchor_12" class="label">12</a> - <i>Hist. Ind. Sc.</i> b. i. c. iii. sect. 2.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_13" href="#FNanchor_13" class="label">13</a> - <i>Analyt. Prior.</i> i. 30.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_14" href="#FNanchor_14" class="label">14</a> - <i>Analyt. Post.</i> i. 18.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_15" href="#FNanchor_15" class="label">15</a> - <i>Analyt. Prior.</i> ii. 23, περι της επαγωγης.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_16" href="#FNanchor_16" class="label">16</a> - <i>Analyt. Post.</i> ii. 19.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_17" href="#FNanchor_17" class="label">17</a> - But the best reading seems to be -not ἔν τι but ἔτι: and the clause must -be rendered "both to perceive and to -retain the perception in the mind." -This correction does not disturb the -general sense of the passage, that -the first principles of science are -obtained by finding the One in the -Many.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_18" href="#FNanchor_18" class="label">18</a> - <i>Analyt. Post.</i> i. 34.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_19" href="#FNanchor_19" class="label">19</a> - <i>Ibid.</i> ii. 19.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_20" href="#FNanchor_20" class="label">20</a> - <i>Analyt. Prior.</i> ii. 25.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_21" href="#FNanchor_21" class="label">21</a> - See on this subject Appendix, Essay D.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_22" href="#FNanchor_22" class="label">22</a> - See the chapter on Certain Characteristics of Scientific Induction in -the <i>Phil. Ind. Sc.</i> or in the <i>Nov. Org. Renov.</i></p></div> - -<div class="footnote"> - -<p><a id="Footnote_23" href="#FNanchor_23" class="label">23</a> - <i>Phil. Ind. Sc.</i> b. viii. c. i. art. 11, or <i>Hist. Sc. Id.</i> b. viii.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_24" href="#FNanchor_24" class="label">24</a> - B. i. c. xi. sect. 2.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_25" href="#FNanchor_25" class="label">25</a> - B. iii. c. i. sect. 9.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_26" href="#FNanchor_26" class="label">26</a> - <i>De Cælo</i>, ii. 13.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_27" href="#FNanchor_27" class="label">27</a> - <i>Ibid.</i> ii. 10.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_28" href="#FNanchor_28" class="label">28</a> - xii. 8.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_29" href="#FNanchor_29" class="label">29</a> - B. xvi. c. vi.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_30" href="#FNanchor_30" class="label">30</a> - <i>On the Classification of Mammalia, &c.: a Lecture delivered at Cambridge</i>, -May 10, 1859, p. 3.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_31" href="#FNanchor_31" class="label">31</a> - B. i. c. xi.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_32" href="#FNanchor_32" class="label">32</a> - <i>History of Scientific Ideas</i>, and <i>Novum Organum Renovatum</i>.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_33" href="#FNanchor_33" class="label">33</a> - The remainder of this chapter is new in the present edition.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_34" href="#FNanchor_34" class="label">34</a> - <i>Hist. of Greece</i>, Part ii. chap. 68.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_35" href="#FNanchor_35" class="label">35</a> - <i>De Antiqua Medicina</i>, c. 20.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_36" href="#FNanchor_36" class="label">36</a> - Lib. i. c. 9.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_37" href="#FNanchor_37" class="label">37</a> - <i>De Elem.</i> i. 6.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_38" href="#FNanchor_38" class="label">38</a> - In former editions I have not done justice to this passage.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_39" href="#FNanchor_39" class="label">39</a> - <i>Hist. Ind. Sc.</i> Addition to Introduction in Third Edition.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_40" href="#FNanchor_40" class="label">40</a> - Lib. i. <i>Fast.</i></p></div> - -<div class="footnote"> - -<p><a id="Footnote_41" href="#FNanchor_41" class="label">41</a> - <i>Hist. Nat.</i> i. 75.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_42" href="#FNanchor_42" class="label">42</a> - <i>Quæst. Nat.</i> vii. 25.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_43" href="#FNanchor_43" class="label">43</a> - <i>Quæst. Nat.</i> vii. 30, 31.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_44" href="#FNanchor_44" class="label">44</a> - <i>Ibid.</i> iii. 7.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_45" href="#FNanchor_45" class="label">45</a> - <i>Hist. Ind. Sc.</i> b. iii. c. iv. sect. 8.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_46" href="#FNanchor_46" class="label">46</a> - <i>Ibid.</i> b. ix. c. ii.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_47" href="#FNanchor_47" class="label">47</a> - See <i>Hist. Ind. Sc.</i> b. iv. c. i.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_48" href="#FNanchor_48" class="label">48</a> - See the opinion of Aquinas, in Degerando, <i>Hist. Com. des Syst.</i> iv. 499; -of Duns Scotus, <i>ibid.</i> iv. 523.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_49" href="#FNanchor_49" class="label">49</a> - <i>Liber Excerptionum</i>, Lib. i. c. i.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_50" href="#FNanchor_50" class="label">50</a> - <i>Tr. Ex.</i> Lib. i. c. vii.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_51" href="#FNanchor_51" class="label">51</a> - Tenneman, viii. 461.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_52" href="#FNanchor_52" class="label">52</a> - <i>Mores Catholici, or Ages of Faith</i>, viii. p. 247.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_53" href="#FNanchor_53" class="label">53</a> - Tenneman, viii. 460.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_54" href="#FNanchor_54" class="label">54</a> - If there were any doubt on this -subject, we might refer to the writers -who afterwards questioned the supremacy -of Aristotle, and who with -one voice assert that an infallible -authority had been claimed for him. -Thus Laurentius Valla: "Quo minus -ferendi sunt recentes Peripatetici, -qui nullius sectæ hominibus interdicunt -libertate ab Aristotele dissentiendi, -quasi sophos hic, non philosophus." -<i>Pref. in Dial.</i> (Tenneman, ix. -29.) So Ludovicus Vives: "Sunt ex -philosophis et ex theologis qui non -solum quo Aristoteles pervenit extremum -esse aiunt naturæ, sed quâ -pervenit eam rectissimam esse omnium -et certissimam in natura viam." -(Tenneman, ix. 43.) We might urge -too, the evasions practised by philosophical -Reformers, through fear of -the dogmatism to which they had to -submit; for example, the protestation -of Telesius at the end of the -Proem to his work, <i>De Rerum Natura</i>: -"Nec tamen, si quid eorum -quæ nobis posita sunt, sacris literis, -Catholicæve ecclesiæ decretis non -cohæreat, tenendum id, quin penitus -rejiciendum asseveramus contendimusque. -Neque enim <i>humana</i> modo -<i>ratio</i> quævis, sed <i>ipse</i> etiam <i>sensus</i> -illis <i>posthabendus</i>, et si illis non congruat, -abnegandus omnino et ipse -etiam est sensus."</p></div> - -<div class="footnote"> - -<p><a id="Footnote_55" href="#FNanchor_55" class="label">55</a> - <i>Ages of Faith</i>, viii. 247: to the author of which I am obliged for this -quotation.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_56" href="#FNanchor_56" class="label">56</a> - Algazel. See <i>Hist. Ind. Sc.</i> b. iv. c. i.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_57" href="#FNanchor_57" class="label">57</a> - Tenneman, viii. 830.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_58" href="#FNanchor_58" class="label">58</a> - Degerando, iv. 535.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_59" href="#FNanchor_59" class="label">59</a> - Leibnitz's expressions are, (<i>Op.</i> t. -vi. p. 16): "Quand j'étais jeune, je -prenois quelque a l'<i>Art</i> de Lulle, mais -je crus y entrevoir bien des défectuosités, -dont j'ai dit quelque chose dans -un petit Essai d'écolier intitulé <i>De -Arte Combinatoria</i>, publié en 1666, et -qui a été réimprimé après malgré moi. -Mais comme je ne méprise rien facilement, -excepté les arts divinatoires -que ne sont que des tromperies toutes -pures, j'ai trouvé quelque chose d'estimable -encore dans l'<i>Art</i> de Lulle."</p></div> - -<div class="footnote"> - -<p><a id="Footnote_60" href="#FNanchor_60" class="label">60</a> - <i>Works</i>, vii. 296.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_61" href="#FNanchor_61" class="label">61</a> - <i>Fratris Rogeri Bacon, Ordinis Minorum</i>, -Opus Majus, <i>ad Clementem -Quartum, Pontificem Romanum, ex -MS. Codice Dubliniensi cum aliis quibusdam -collato, nunc primum edidit</i> -S. Jebb, M.D. Londini, 1733.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_62" href="#FNanchor_62" class="label">62</a> - <i>Opus Majus</i>, Præf.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_63" href="#FNanchor_63" class="label">63</a> - Contents of Roger Bacon's <i>Opus -Majus</i>. -</p> -<p> -Part I. On the four causes of human -ignorance:—Authority, Custom, -Popular Opinion, and the Pride -of supposed Knowledge. -</p> -<p> -Part II. On the source of perfect -wisdom in the Sacred Scripture. -</p> -<p> -Part III. On the Usefulness of -Grammar. -</p> -<p> -Part IV. On the Usefulness of Mathematics. -</p> -<p> -(1) The necessity of Mathematics in -Human Things (published separately -as the <i>Specula Mathematica</i>). -</p> -<p> -(2) The necessity of Mathematics in -Divine Things.—1<sup>o</sup>. This study -has occupied holy men: 2<sup>o</sup>. -Geography: 3<sup>o</sup>. Chronology: 4<sup>o</sup>. -Cycles; the Golden Number, -&c.: 5<sup>o</sup>. Natural Phenomena, -as the Rainbow: 6<sup>o</sup>. Arithmetic: -7<sup>o</sup>. Music. -</p> -<p> -(3) The necessity of Mathematics in -Ecclesiastical Things. 1<sup>o</sup>. The -Certification of Faith: 2<sup>o</sup>. The -Correction of the Calendar. -</p> -<p> -(4) The necessity of Mathematics in -the State.—1<sup>o</sup>. Of Climates: 2<sup>o</sup>. -Hydrography: 3<sup>o</sup>. Geography: -4<sup>o</sup>. Astrology. -</p> -<p> -Part V. On Perspective (published -separately as <i>Perspectiva</i>). -</p> -<p> -(1) The organs of vision. -</p> -<p> -(2) Vision in straight lines. -</p> -<p> -(3) Vision reflected and refracted. -</p> -<p> -(4) De multiplicatione specierum -(on the propagation of the impressions -of light, heat, &c.) -</p> -<p> -Part VI. On Experimental Science. -</p></div> - -<div class="footnote"> - -<p><a id="Footnote_64" href="#FNanchor_64" class="label">64</a> - <i>Op. Maj.</i> p. 1.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_65" href="#FNanchor_65" class="label">65</a> - <i>Ibid.</i> p. 2.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_66" href="#FNanchor_66" class="label">66</a> - <i>Ibid.</i> p. 10.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_67" href="#FNanchor_67" class="label">67</a> - I will give a specimen. <i>Opus -Majus</i>, c. viii. p. 35: "These two kinds -of philosophers, the Ionic and Italic, -ramified through many sects and -various successors, till they came to -the doctrine of Aristotle, who corrected -and changed the propositions -of all his predecessors, and attempted -to perfect philosophy. In the [Italic] -succession, Pythagoras, Archytas Tarentinus -and Timæus are most prominently -mentioned. But the principal -philosophers, as Socrates, Plato, -and Aristotle, did not descend from -this line, but were Ionics and true -Greeks, of whom the first was Thales -Milesius.... Socrates, according to Augustine -in his 8th book, is related to -have been a disciple of Archelaus. -This Socrates is called the father of -the great philosophers, since he was -the master of Plato and Aristotle, from -whom all the sects of philosophers -descended.... Plato, first learning what -Socrates and Greece could teach, made -a laborious voyage to Egypt, to Archytas -of Tarentum and Timæus, as -says Jerome to Paulinus. And this -Plato is, according to holy men, preferred -to all philosophers, because he -has written many excellent things concerning -God, and morality, and a future -life, which agree with the divine -wisdom of God. And Aristotle was -born before the death of Socrates, -since he was his hearer for three -years, as we read in the life of -Aristotle.... This Aristotle, being -made the master of Alexander the -Great, sent two thousand men into -all regions of the earth, to search out -the nature of things, as Pliny relates -in the 8th book of his <i>Naturalia</i>, and -composed a thousand books, as we -read in his life."</p></div> - -<div class="footnote"> - -<p><a id="Footnote_68" href="#FNanchor_68" class="label">68</a> - <i>Ibid.</i> p. 36.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_69" href="#FNanchor_69" class="label">69</a> - <i>Autonomaticè.</i></p></div> - -<div class="footnote"> - -<p><a id="Footnote_70" href="#FNanchor_70" class="label">70</a> - <i>Op. Maj.</i> p. 46.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_71" href="#FNanchor_71" class="label">71</a> - See <i>Pref.</i> to Jebb's edition. The -passages, there quoted, however, are -not extracts from the <i>Opus Majus</i>, but -(apparently) from the <i>Opus Minus</i> -(<i>MS. Cott.</i> Tib. c. 5.) "Si haberem -potestatem supra libros Aristotelis, -ego facerem omnes cremari; quia non -est nisi temporis amissio studere in -illis, et causa erroris, et multiplicatio -ignorantiæ ultra id quod valeat explicari.... -Vulgus studentum cum -capitibus suis non habet unde excitetur -ad aliquid dignum, et ideo languet -et <i>asininat</i> circa male translata, -et tempus et studium amittit in omnibus -et expensas."</p></div> - -<div class="footnote"> - -<p><a id="Footnote_72" href="#FNanchor_72" class="label">72</a> - Part ii.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_73" href="#FNanchor_73" class="label">73</a> - Parts iv. v. and vi.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_74" href="#FNanchor_74" class="label">74</a> - <i>Op. Maj.</i> p. 476.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_75" href="#FNanchor_75" class="label">75</a> - <i>Op. Maj.</i> p. 15.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_76" href="#FNanchor_76" class="label">76</a> - <i>Ibid.</i> p. 445, see also p. 448. -"Scientiæ aliæ sciunt sua principia -invenire per experimenta, sed conclusiones per argumenta facta ex -principiis inventis. Si vero debeant -habere experientiam conclusionum -suarum particularem et completam, -tunc oportet quod habeant per adjutorium -istius scientiæ nobilis (experimentalis)."</p></div> - -<div class="footnote"> - -<p><a id="Footnote_77" href="#FNanchor_77" class="label">77</a> - <i>Op. Maj.</i> p. 60.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_78" href="#FNanchor_78" class="label">78</a> - <i>Ibid.</i> p. 64.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_79" href="#FNanchor_79" class="label">79</a> - "Veritates magnificas in terminis -aliarum scientiarum in quas per -nullam viam possunt illæ scientiæ, -hæc sola scientiarum domina speculativarum, -potest dare." <i>Op. Maj.</i> -p. 465.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_80" href="#FNanchor_80" class="label">80</a> - One of the ingredients of a preparation -here mentioned, is the flesh of a dragon, which it appears is used -as food by the Ethiopians. The mode -of preparing this food cannot fail to -amuse the reader. "Where there are -good flying dragons, by the art which -they possess, they draw them out of -their dens, and have bridles and saddles -in readiness, and they ride upon -them, and make them bound about -in the air in a violent manner, that -the hardness and toughness of the -flesh may be reduced, as boars are -hunted and bulls are baited before -they are killed for eating." <i>Op. Maj.</i> -p. 470.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_81" href="#FNanchor_81" class="label">81</a> - <i>Op. Maj.</i> p. 473.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_82" href="#FNanchor_82" class="label">82</a> - Quoted by Jebb, <i>Pref.</i> to <i>Op. Maj.</i></p></div> - -<div class="footnote"> - -<p><a id="Footnote_83" href="#FNanchor_83" class="label">83</a> - Mosheim, <i>Hist.</i> iii. 161.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_84" href="#FNanchor_84" class="label">84</a> - <i>Op. Maj.</i> p. 57.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_85" href="#FNanchor_85" class="label">85</a> - Mosheim, iii. 161.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_86" href="#FNanchor_86" class="label">86</a> - Gratian published the <i>Decretals</i> -in the twelfth century; and the Canon -and Civil Law became a regular study -in the universities soon afterwards.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_87" href="#FNanchor_87" class="label">87</a> - Tenneman, ix. 4.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_88" href="#FNanchor_88" class="label">88</a> - Tenneman, ix. 25.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_89" href="#FNanchor_89" class="label">89</a> - "Jam nobis manifestum est terram istam in veritate moveri," &c.—<i>De -Doctâ Ignorantiâ</i>, lib. ii. c. xii.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_90" href="#FNanchor_90" class="label">90</a> - <i>De Doct. Ignor.</i> lib. i. c. i.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_91" href="#FNanchor_91" class="label">91</a> - <i>De Conjecturis</i>, lib. i. c. iii. iv.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_92" href="#FNanchor_92" class="label">92</a> - Born in 1433.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_93" href="#FNanchor_93" class="label">93</a> - Born 1529, died 1597.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_94" href="#FNanchor_94" class="label">94</a> - <i>Aristoteles Exotericus</i>, p. 50.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_95" href="#FNanchor_95" class="label">95</a> - Tiraboschi, t. vii. pt. ii. p. 411.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_96" href="#FNanchor_96" class="label">96</a> - "Franciscus Patricius, novam veram -integram de universis conditurus -philosophiam, sequentia uti verissima -prænuntiare est ausus. Prænunciata -ordine persecutus, divinis oraculis, -geometricis rationibus, clarissimisque -experimentis comprobavit. -</p> - -<p> -Ante primum nihil,<br /> -Post primum omnia,<br /> -A principio omnia," &c.<br /> -</p> - -<p> -His other works are <i>Panaugia</i>, <i>Pancosmia</i>, -<i>Dissertations Peripateticæ</i>.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_97" href="#FNanchor_97" class="label">97</a> - Tiraboschi, t. vii. pt. ii. p. 411.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_98" href="#FNanchor_98" class="label">98</a> - <i>Dissert. Perip.</i> t. ii. lib. v. sub fin.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_99" href="#FNanchor_99" class="label">99</a> - Tenneman, ix. 148.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_100" href="#FNanchor_100" class="label">100</a> - Tenneman, ix. 167.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_101" href="#FNanchor_101" class="label">101</a> - <i>Ibid.</i> 158.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_102" href="#FNanchor_102" class="label">102</a> - Agrippa, <i>De Occult. Phil.</i> lib. i. c. l.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_103" href="#FNanchor_103" class="label">103</a> - Written in 1526.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_104" href="#FNanchor_104" class="label">104</a> - Philip Aurelius Theophrastus -Bombastus von Hohenheim, also -called Paracelsus Eremita, born at -Einsiedlen in Switzerland, in 1493.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_105" href="#FNanchor_105" class="label">105</a> - <i>Hist. Sc. Id.</i> b. ix. c. 2. sect. 1. The Mystical School of Biology.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_106" href="#FNanchor_106" class="label">106</a> - Tenneman, ix. 221.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_107" href="#FNanchor_107" class="label">107</a> - Tenneman, ix. 265.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_108" href="#FNanchor_108" class="label">108</a> - Bernardini Telesii Consentini <i>De -Rerum Natura juxta propria Principia</i>.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_109" href="#FNanchor_109" class="label">109</a> - I take this account from Tenneman: -this Proem was omitted in subsequent -editions of Telesius, and is -not in the one which I have consulted. -Tenneman, <i>Gesch. d. Phil.</i> ix. 280.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_110" href="#FNanchor_110" class="label">110</a> - Proem.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_111" href="#FNanchor_111" class="label">111</a> - "De Principiis atque Originibus -secundum fabulas Cupidinis et Cœli: -sive Parmenidis et Telesii et præcipuè -Democriti Philosophia tractata in -Fabula de Cupidine."</p></div> - -<div class="footnote"> - -<p><a id="Footnote_112" href="#FNanchor_112" class="label">112</a> - "Talia sunt qualia possunt esse -ea quæ ab intellectu sibi permisso, -nec ab experimentis continenter et -gradatim sublevato, profecta videntur."</p></div> - -<div class="footnote"> - -<p><a id="Footnote_113" href="#FNanchor_113" class="label">113</a> - Thom. Campanella <i>de Libris propriis</i>, -as quoted in Tenneman, ix. 291.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_114" href="#FNanchor_114" class="label">114</a> - <i>Economisti Italiani</i>, t. i. p. xxxiii.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_115" href="#FNanchor_115" class="label">115</a> - Tenneman, ix. 305.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_116" href="#FNanchor_116" class="label">116</a> - <i>Hist. Ind. Sc.</i> b. xvi. c. iii. sect. 2.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_117" href="#FNanchor_117" class="label">117</a> - <i>Ibid.</i> b. xvii. c. ii. sect. 1.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_118" href="#FNanchor_118" class="label">118</a> - <i>Quæst. Peripat.</i> i. 1.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_119" href="#FNanchor_119" class="label">119</a> - Tenneman, ix. 108.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_120" href="#FNanchor_120" class="label">120</a> - <i>Hist. Ind. Sc.</i> b. v. c. iii. sect. 2.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_121" href="#FNanchor_121" class="label">121</a> - Tenneman, ix. 420. "Quæcunque ab Aristotele dicta essent commenticia -esse." Freigius, <i>Vita Petri Rami</i>, p. 10.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_122" href="#FNanchor_122" class="label">122</a> - Rami, <i>Animadv. Aristot.</i> i. iv.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_123" href="#FNanchor_123" class="label">123</a> - See <i>Hist. Ind. Sc.</i> b. iv. c. iv. sect. 4.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_124" href="#FNanchor_124" class="label">124</a> - Tenneman, ix. 230.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_125" href="#FNanchor_125" class="label">125</a> - <i>Ibid.</i> 108.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_126" href="#FNanchor_126" class="label">126</a> - Tenneman, ix. 246.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_127" href="#FNanchor_127" class="label">127</a> - Melancthon, <i>De Anima</i>, p. 207, quoted in Tenneman, ix. 121.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_128" href="#FNanchor_128" class="label">128</a> - His works have never been published, -and exist in manuscript in the -library of the Institute at Paris. Some -extracts were published by Venturi, -<i>Essai sur les Ouvrages de Leonard da -Vinci</i>. Paris, 1797.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_129" href="#FNanchor_129" class="label">129</a> - Leonardo died in 1520, at the age -of 78.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_130" href="#FNanchor_130" class="label">130</a> - Paul III. in 1543.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_131" href="#FNanchor_131" class="label">131</a> - <i>Hist. Ind. Sc.</i> b. v. c. ii.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_132" href="#FNanchor_132" class="label">132</a> - Born 1537, died 1619.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_133" href="#FNanchor_133" class="label">133</a> - <i>Hist. Ind. Sc.</i> b. xvii. c. ii. sect. 1.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_134" href="#FNanchor_134" class="label">134</a> - Fabricius, <i>De Motu Locali</i>, p. 182.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_135" href="#FNanchor_135" class="label">135</a> - p. 199.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_136" href="#FNanchor_136" class="label">136</a> - <i>Speculationum Liber</i>, p. 195.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_137" href="#FNanchor_137" class="label">137</a> - <i>Ibid.</i> p. 169.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_138" href="#FNanchor_138" class="label">138</a> - Gulielmi Gilberti, <i>Colcestriensis, Medici Londinensis, De Magnete, Magneticisque -Corporibus, et de Magno Magnete Tellure, Physiologia Nova, plurimis -et Argumentis et Experimentis demonstrata</i>.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_139" href="#FNanchor_139" class="label">139</a> - <i>Hist. Ind. Sc.</i> b. xii. c. i.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_140" href="#FNanchor_140" class="label">140</a> - Pref.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_141" href="#FNanchor_141" class="label">141</a> - <i>De Magnete</i>, lib. vi. c. 3, 4.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_142" href="#FNanchor_142" class="label">142</a> - <i>Nov. Org.</i> b. i.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_143" href="#FNanchor_143" class="label">143</a> - B. i. Aph. 64.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_144" href="#FNanchor_144" class="label">144</a> - Vol. ix. 185.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_145" href="#FNanchor_145" class="label">145</a> - <i>De Magnete</i>, p. 60.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_146" href="#FNanchor_146" class="label">146</a> - B. iii. c. 4.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_147" href="#FNanchor_147" class="label">147</a> - <i>Nov. Org.</i> b. ii. Aph. 48.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_148" href="#FNanchor_148" class="label">148</a> - Drinkwater's <i>Life of Galileo</i>, p. 18.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_149" href="#FNanchor_149" class="label">149</a> - <i>Life of Galileo</i>, p. 9.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_150" href="#FNanchor_150" class="label">150</a> - <i>Hist. Ind. Sc.</i> b. vi. c. ii. sect. 5.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_151" href="#FNanchor_151" class="label">151</a> - <i>Life of Galileo</i>, p. 29.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_152" href="#FNanchor_152" class="label">152</a> - <i>Ibid.</i> p. 33.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_153" href="#FNanchor_153" class="label">153</a> - <i>Il Saggiatore</i>, ii. 247.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_154" href="#FNanchor_154" class="label">154</a> - <i>Il Saggiatore</i>, ii. 200.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_155" href="#FNanchor_155" class="label">155</a> - <i>Ibid.</i> i. 501.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_156" href="#FNanchor_156" class="label">156</a> - <i>Hist. Ind. Sc.</i> b. vi. c. ii. sect. 2.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_157" href="#FNanchor_157" class="label">157</a> - <i>Hist. Ind. Sc.</i> b. vi. c. ii. sect. 4.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_158" href="#FNanchor_158" class="label">158</a> - <i>Ibid.</i> b. v. c. iv. sect. 1.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_159" href="#FNanchor_159" class="label">159</a> - <i>De Stell. Mart.</i> p. iv. c. 51 (1609); Drinkwater's <i>Kepler</i>, p. 33.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_160" href="#FNanchor_160" class="label">160</a> - Published 1604. <i>Hist. Ind. Sc.</i> b. ix. c. ii.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_161" href="#FNanchor_161" class="label">161</a> - <i>Hist. Ind. Sc.</i> b. v. c. iv. sect. i.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_162" href="#FNanchor_162" class="label">162</a> - <i>Hist. Ind. Sc.</i> b. vii. c. vi. sect 1.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_163" href="#FNanchor_163" class="label">163</a> - <i>De Stell. Mart.</i> p. 11. c. 19.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_164" href="#FNanchor_164" class="label">164</a> - <i>Hist. Ind. Sc.</i> b. ii. c. iv. sect. 6.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_165" href="#FNanchor_165" class="label">165</a> - <i>Ibid.</i> sect. 8.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_166" href="#FNanchor_166" class="label">166</a> - Montucla, i. 566.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_167" href="#FNanchor_167" class="label">167</a> - <i>De Augm.</i> lib. iv. c. 1.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_168" href="#FNanchor_168" class="label">168</a> - And in other passages: thus, "Ego enim buccinator tantum pugnam -non ineo." <i>Nov. Org.</i> lib. iv. c. i.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_169" href="#FNanchor_169" class="label">169</a> - Lib. 1. Aphor. 78 <i>et seq.</i></p></div> - -<div class="footnote"> - -<p><a id="Footnote_170" href="#FNanchor_170" class="label">170</a> - <i>Aug. Sc.</i> Lib. iii. c. 4. p. 194. So -in other places, as <i>Nov. Org.</i> i. Aph. -104. "De scientiis tum demum bene -sperandum est quando per scalam -veram et per gradus continuos, et -non intermissos aut hiulcos a particularibus -ascendetur ad axiomata -minora, et deinde ad media, alia -aliis superiora, et postremo demum -ad generalissima."</p></div> - -<div class="footnote"> - -<p><a id="Footnote_171" href="#FNanchor_171" class="label">171</a> - <i>Nov. Org.</i> 1. Aph. 22.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_172" href="#FNanchor_172" class="label">172</a> - <i>Ib.</i> Aph. 20.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_173" href="#FNanchor_173" class="label">173</a> - 1 Ax. 15.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_174" href="#FNanchor_174" class="label">174</a> - <i>Nov. Org.</i> lib. ii. Aph. 19.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_175" href="#FNanchor_175" class="label">175</a> - <i>Inst. Mag.</i> par. iii. (vol. viii. p. 244).</p></div> - -<div class="footnote"> - -<p><a id="Footnote_176" href="#FNanchor_176" class="label">176</a> - <i>Hist. Ind. Sc.</i> b. x. c. i.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_177" href="#FNanchor_177" class="label">177</a> - <i>Ib.</i> c. iv.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_178" href="#FNanchor_178" class="label">178</a> - <i>Nov. Org.</i> lib. i. Aph. 61.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_179" href="#FNanchor_179" class="label">179</a> - <i>Nov. Org.</i> lib. ii. Aph. 10.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_180" href="#FNanchor_180" class="label">180</a> - Aph. 11.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_181" href="#FNanchor_181" class="label">181</a> - Aph. 15, p. 105.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_182" href="#FNanchor_182" class="label">182</a> - Page 110.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_183" href="#FNanchor_183" class="label">183</a> - Herschel, <i>On the Study of Nat. Phil.</i> Art. 192.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_184" href="#FNanchor_184" class="label">184</a> - <i>Nov. Org.</i> lib. i. Aph. 40.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_185" href="#FNanchor_185" class="label">185</a> - <i>Nov. Org.</i> lib. i. Ax. 103.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_186" href="#FNanchor_186" class="label">186</a> - <i>Edinb. Rev.</i> No. cxxxii. p. 65.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_187" href="#FNanchor_187" class="label">187</a> - <i>Ib.</i></p></div> - -<div class="footnote"> - -<p><a id="Footnote_188" href="#FNanchor_188" class="label">188</a> - Pref. to the <i>Nat. Hist.</i> i. 243.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_189" href="#FNanchor_189" class="label">189</a> - <i>Nov. Org.</i> lib. i. Aph. 19.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_190" href="#FNanchor_190" class="label">190</a> - <i>Ibid.</i> lib. i. Aph. 20.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_191" href="#FNanchor_191" class="label">191</a> - Aph. 27.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_192" href="#FNanchor_192" class="label">192</a> - <i>Ib.</i> 28.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_193" href="#FNanchor_193" class="label">193</a> - Aph. 104. So Aph. 105. "In constituendo axiomate forma <i>inductionis</i> -alia quam adhuc in usu fuit excogitanda est," &c.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_194" href="#FNanchor_194" class="label">194</a> - <i>Ep. ad P. Fulgentium.</i> <i>Op.</i> x. 330.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_195" href="#FNanchor_195" class="label">195</a> - <i>Nov. Org.</i> i. Aph. 113.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_196" href="#FNanchor_196" class="label">196</a> - See the motto to Kant's <i>Kritik der Reinen Vernunft</i>.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_197" href="#FNanchor_197" class="label">197</a> - <i>Œuvres Philosophiques de Bacon, -&c.</i> par M. N. Bouillet, 3 Tomes. -</p> -<p> -<i>Examen de la Philosophie de Bacon</i> -(<i>Œuvres Posthumes</i> du Comte J. de -Maistre). -</p> -<p> -<i>Bacon, sa Vie, son Temps, sa Philosophie</i>, -par Charles de Remusat. -</p> -<p> -<i>Histoire de la Vie et des Ouvrages -de François Bacon</i>, par J. B. de Vaugelles. -</p> -<p> -<i>Franz Baco von Verulam</i>, von -Kuno Fischer. -</p> -<p> -<i>The Works of Francis Bacon</i>, collected -and edited by James Spedding, -Robert Leslie Ellis, and Douglas -Denon Heath.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_198" href="#FNanchor_198" class="label">198</a> - Note to Aph. xviii.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_199" href="#FNanchor_199" class="label">199</a> - Pref. to the <i>Parasceue</i>, Vol. i. p. 382.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_200" href="#FNanchor_200" class="label">200</a> - <i>Anatomical Exercitations concerning -the Generation of Living Creatures</i>, -1653. Preface.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_201" href="#FNanchor_201" class="label">201</a> - He used similar expressions in -conversation. George Ent, who edited -his <i>Generation of Animals</i>, visited -him, "at that time residing not far -from the city; and found him very -intent upon the perscrutation of -nature's works, and with a countenance -as cheerful, as mind unperturbed; -Democritus-like, chiefly -searching into the cause of natural -things." In the course of conversation -the writer said, "It hath always -been your choice about the secrets of -Nature, to consult Nature herself." -"'Tis true," replied he; "and I have -constantly been of opinion that from -thence we might acquire not only the -knowledge of those less considerable -secrets of Nature, but even a certain -admiration of that Supreme Essence, -the Creator. And though I have -ever been ready to acknowledge, that -many things have been discovered -by learned men of former times; yet -do I still believe that the number of -those which remain yet concealed in -the darkness of impervestigable Nature -is much greater. Nay, I cannot -forbear to wonder, and sometimes -smile at those, who persuade themselves, -that all things were so consummately -and absolutely delivered -by Aristotle, Galen, or some other -great name, as that nothing was left -to the superaddition of any that succeeded."</p></div> - -<div class="footnote"> - -<p><a id="Footnote_202" href="#FNanchor_202" class="label">202</a> - Lib. i. c. 2, 3.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_203" href="#FNanchor_203" class="label">203</a> - <i>Anal. Post.</i> ii.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_204" href="#FNanchor_204" class="label">204</a> - Pars iii. p. 45.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_205" href="#FNanchor_205" class="label">205</a> - See <i>Hist. Ind. Sc.</i> b. vi. c. ii.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_206" href="#FNanchor_206" class="label">206</a> - Cap. i. ii.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_207" href="#FNanchor_207" class="label">207</a> - <i>Hist. Ind. Sc.</i> b. ix. c. ii.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_208" href="#FNanchor_208" class="label">208</a> - <i>Meteorum</i>, c. viii. p. 187.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_209" href="#FNanchor_209" class="label">209</a> - Mackintosh, <i>Dissertation on Ethical Science</i>.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_210" href="#FNanchor_210" class="label">210</a> - <i>Hist. Ind. Sc.</i> b. vii. c. i.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_211" href="#FNanchor_211" class="label">211</a> - Castelli, Torricelli, Viviani, Baliani, Gassendi, Mersenne, Borelli, Cavalleri.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_212" href="#FNanchor_212" class="label">212</a> - <i>De Plenitudine Mundi, in qua defenditur Cartesiana Philosophia contra -sententias Francisci Baconi, Th. Hobbii et Sethi Wardi.</i></p></div> - -<div class="footnote"> - -<p><a id="Footnote_213" href="#FNanchor_213" class="label">213</a> - Bacon's <i>Works</i>, vol. ii. 111.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_214" href="#FNanchor_214" class="label">214</a> - <i>Hist. Ind. Sc.</i> b. vii. c. i.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_215" href="#FNanchor_215" class="label">215</a> - <i>Nov. Org.</i> lib. ii. Aph. 2.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_216" href="#FNanchor_216" class="label">216</a> - <i>Ib.</i> lib. ii. Aph. 45.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_217" href="#FNanchor_217" class="label">217</a> - <i>Optics</i>, qu. 31, near the end.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_218" href="#FNanchor_218" class="label">218</a> - Qu. 28.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_219" href="#FNanchor_219" class="label">219</a> - <i>Hist. Ind. Sc.</i> b. v. and b. vii.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_220" href="#FNanchor_220" class="label">220</a> - <i>Optics</i>, qu. 31.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_221" href="#FNanchor_221" class="label">221</a> - <i>History of Ideas</i>, b. iii. c. x.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_222" href="#FNanchor_222" class="label">222</a> - <i>Ibid.</i> b. iii. c. ix. x. xi.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_223" href="#FNanchor_223" class="label">223</a> - <i>Opticks</i>, qu. 31.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_224" href="#FNanchor_224" class="label">224</a> - <i>Nov. Org.</i> l. ii. Aph. 2. "Licet -enim in natura nihil existet præter -corpora individua, edentia actus puros -individuos ex lege; in doctrinis -tamen illa ipsa lex, ejusque inquisitio, -et inventio, et explicatio, pro -fundamento est tam ad sciendum -quam ad operandum. Eam autem -<i>legem</i>, ejusque <i>paragraphos, formarum</i> -nomine intelligimus; præsertim -cum hoc vocabulum invaluerit, et -familiariter occurrat." -</p> -<p> -Aph. 17. "Eadem res est <i>forma</i> -calidi vel <i>forma</i> luminis, et <i>lex</i> calidi -aut <i>lex</i> luminis."</p></div> - -<div class="footnote"> - -<p><a id="Footnote_225" href="#FNanchor_225" class="label">225</a> - <i>Essay</i>, b. xi. c. iv. sect. 3.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_226" href="#FNanchor_226" class="label">226</a> - <i>Ibid.</i> c. xiii. sect. 22.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_227" href="#FNanchor_227" class="label">227</a> - <i>History of Ideas</i>, b. iii. c. iii. Modern Opinions respecting the Idea of -Cause.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_228" href="#FNanchor_228" class="label">228</a> - <i>Ibid.</i> b. i. c. iv.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_229" href="#FNanchor_229" class="label">229</a> - <i>Langue des Calculs</i>, p. 1.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_230" href="#FNanchor_230" class="label">230</a> - <i>Grammaire</i>, p. xxxvi.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_231" href="#FNanchor_231" class="label">231</a> - Since the selection and construction -of terms is thus a matter of so -much consequence in the formation -of science, it is proper that systematic -rules, founded upon sound principles, -should be laid down for the -performance of this operation. Some -such rules are accordingly suggested -in b. iv. of the <i>Nov. Org. Ren.</i></p></div> - -<div class="footnote"> - -<p><a id="Footnote_232" href="#FNanchor_232" class="label">232</a> - <i>Disc. Prélim.</i> p. viii.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_233" href="#FNanchor_233" class="label">233</a> - Helvetius <i>Sur l'Homme</i>, c. xxiii.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_234" href="#FNanchor_234" class="label">234</a> - P. xiii.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_235" href="#FNanchor_235" class="label">235</a> - See Mr.Sharpe's <i>Essays</i>.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_236" href="#FNanchor_236" class="label">236</a> - Price's <i>Essays</i>, p. 16.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_237" href="#FNanchor_237" class="label">237</a> - P. 18.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_238" href="#FNanchor_238" class="label">238</a> - Reid, <i>Essays on the Powers of the Human Mind</i>, iii. 31.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_239" href="#FNanchor_239" class="label">239</a> - Stewart, <i>Outlines of Moral Phil.</i> p. 138.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_240" href="#FNanchor_240" class="label">240</a> - Whately, <i>Polit. Econ.</i> p. 76.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_241" href="#FNanchor_241" class="label">241</a> - Cousin, <i>Fragmens Philosophiques</i>, i. 53.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_242" href="#FNanchor_242" class="label">242</a> - <i>Ibid.</i> i. 67.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_243" href="#FNanchor_243" class="label">243</a> - See also the vigorous critique of Locke's <i>Essay</i>, by Lemaistre, <i>Soirées de -St. Petersbourg</i>.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_244" href="#FNanchor_244" class="label">244</a> - Ampère, <i>Essai</i>, p. 210.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_245" href="#FNanchor_245" class="label">245</a> - <i>Kritik der Reinen Vernunft</i>, Pref. p. xv.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_246" href="#FNanchor_246" class="label">246</a> - The sensational system never -acquired in Germany the ascendancy -which it obtained in England and -France; but I am compelled here to -pass over the history of philosophy -in Germany, except so far as it affects -ourselves.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_247" href="#FNanchor_247" class="label">247</a> - i. p. 14.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_248" href="#FNanchor_248" class="label">248</a> - i. p. 7.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_249" href="#FNanchor_249" class="label">249</a> - <i>Hist. Ind. Sc.</i> b. xi. c. vii.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_250" href="#FNanchor_250" class="label">250</a> - P. 15.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_251" href="#FNanchor_251" class="label">251</a> - P. 16.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_252" href="#FNanchor_252" class="label">252</a> - M. Comte's statement is so entirely -at variance with the fact that -I must quote it here. (<i>Phil. Pos.</i> -vol. i. p. 705.) -</p> -<p> -"Le second théorème général de -dynamique consiste dans le célèbre -et important <i>principe des aires</i>, dont -le première idée est due à Kepler, qui découvrit et démontra forte simplement -cette propriété pour le cas -du mouvement d'une molecule unique, -ou en d'autres terms, d'un -corps dont tous les points se meuvent -identiquement. Kepler établit, -par les considérations les plus élémentaires, -qui si la force accélératrice -totale dont une molecule est animée -tend constamment vers un point fixé, -le rayon vecteur du mobile décrit -autour de ce point des aires égales en -temps egaux, de telle sorte que l'aire -décrite au bout d'un temps quelconque -croît proportionellement à ce -temps. Il fit voir en outre que réciproquement, -si une semblable relation -a été vérifiée dans le mouvement -d'un corps par rapport à un -certain point, c'est une preuve suffisante -de l'action sur le corps d'un force -dirigée sans cesse vers ce point." -</p> -<p> -There is not a trace of the above -propositions in the work <i>De Stellâ -Martis</i>, which contains Kepler's discovery -of his law, nor, I am convinced, -in any other of Kepler's -works. He is everywhere constant -to his conceptions of the <i>magnetic</i> -virtue residing in the sun, by means -of which the sun, revolving on his -axis, carries the planets round with -him. M. Comte's statement so exactly -expresses <i>Newton's</i> propositions, that -one is led to suspect some extraordinary -mistake, by which what should -have been said of the one was transferred -to the other.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_253" href="#FNanchor_253" class="label">253</a> - Vol. ii. p. 433.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_254" href="#FNanchor_254" class="label">254</a> - Vol. ii. 640.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_255" href="#FNanchor_255" class="label">255</a> - I venture to offer this problem;—to -express the <i>laws of the phenomena</i> -of diffraction without the hypothesis -of undulations;—as a challenge to -any one who holds such hypothesis -to be unphilosophical.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_256" href="#FNanchor_256" class="label">256</a> - ii. p. 641.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_257" href="#FNanchor_257" class="label">257</a> - ii. p. 673.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_258" href="#FNanchor_258" class="label">258</a> - <i>Hist. Ind. Sc.</i> ii. 489, b. x. c. i.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_259" href="#FNanchor_259" class="label">259</a> - ii. p. 561.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_260" href="#FNanchor_260" class="label">260</a> - i. 50.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_261" href="#FNanchor_261" class="label">261</a> - i. 41.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_262" href="#FNanchor_262" class="label">262</a> - ii. 433.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_263" href="#FNanchor_263" class="label">263</a> - <i>Phil. Pos.</i> ii. 392-398.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_264" href="#FNanchor_264" class="label">264</a> - [<i>A System of Logic, Ratiocinative -and Inductive, being a connected view -of the Principles of Evidence, and of -the Methods of Scientific Investigation.</i> -By John Stuart Mill.]</p></div> - -<div class="footnote"> - -<p><a id="Footnote_265" href="#FNanchor_265" class="label">265</a> - These Remarks were published -in 1849, under the title <i>Of Induction, -with especial reference to Mr. J. S. -Mill's System of Logic</i>.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_266" href="#FNanchor_266" class="label">266</a> - My references are throughout -(except when otherwise expressed) to -the volume and the page of Mr. Mill's -first edition of his <i>Logic</i>.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_267" href="#FNanchor_267" class="label">267</a> - On this subject see an Essay <i>On the Transformation of Hypotheses</i>, -given in the Appendix.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_268" href="#FNanchor_268" class="label">268</a> - B. vii. c. iii. sect. 3.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_269" href="#FNanchor_269" class="label">269</a> - B. iii. c. ix. art. 7.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_270" href="#FNanchor_270" class="label">270</a> - B. i. c. iii.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_271" href="#FNanchor_271" class="label">271</a> - B. iii. c. viii.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_272" href="#FNanchor_272" class="label">272</a> - <i>Discourse</i>, Art. 192.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_273" href="#FNanchor_273" class="label">273</a> - B. xi. c. xi.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_274" href="#FNanchor_274" class="label">274</a> - <i>Phil.</i> b. xiii. c. ix. art. 7.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_275" href="#FNanchor_275" class="label">275</a> - B. xiii. c. viii.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_276" href="#FNanchor_276" class="label">276</a> - Given also in the <i>Phil. Ind. Sc.</i> b. xiii. c. vii. sect. 17.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_277" href="#FNanchor_277" class="label">277</a> - <i>Ibid.</i> b. vi. c. iv.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_278" href="#FNanchor_278" class="label">278</a> - See <i>Hist. Ind. Sc.</i> b. xii. note <span class="smcap">D</span>, in the second edition.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_279" href="#FNanchor_279" class="label">279</a> - There are some points in my doctrines -on the subject of the Classificatory -Sciences to which Mr. Mill -objects, (ii. 314, &c.), but there is -nothing which I think it necessary -to remark here, except one point. -After speaking of Classification of -organized beings in general, Mr. Mill -notices (ii. 321) as an additional subject, -the arrangement of natural -groups into a Natural Series; and he -says, that "all who have attempted -a theory of natural arrangement, including -among the rest Mr. Whewell, -have stopped short of this: all except -M. Comte." On this I have to observe, -that I stopped short of, or -rather passed by, the doctrine of a -Series of organized beings, because I -thought it bad and narrow philosophy: -and that I sufficiently indicated -that I did this. In the <i>History</i> -(b. xvi. c. vi.) I have spoken of the -doctrine of Circular Progression propounded -by Mr. Macleay, and have -said, "so far as this view <i>negatives</i> a -mere <i>linear</i> progression in nature, -which would place each genus in contact -with the preceding and succeeding -ones, and so far as it requires us -to attend to the more varied and -ramified resemblances, there can be -no doubt that it is supported by the -result of all the attempts to form -natural systems." And with regard -to the difference between Cuvier and -M. de Blainville, to which Mr. Mill -refers (ii. 321), I certainly cannot -think that M. Comte's suffrage can -add any weight to the opinion of -either of those great naturalists.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_280" href="#FNanchor_280" class="label">280</a> - <i>Hist. Ind. Sc.</i> b. x. note (<span class="smcap">VA</span>) in -the second edition.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_281" href="#FNanchor_281" class="label">281</a> - B. xi. c. v. art. 11.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_282" href="#FNanchor_282" class="label">282</a> - I have given elsewhere (see last -chapter) reasons why I cannot assign -to M. Comte's <i>Philosophie Positive</i> -any great value as a contribution to -the philosophy of science. In this -judgment I conceive that I am supported -by the best philosophers of -our time. M. Comte owes, I think, -much of the notice which has been -given to him to his including, as Mr. -Mill does, the science of society and -of human nature in his scheme, -and to his boldness in dealing with -these. He appears to have been received -with deference as a mathematician: -but Sir John Herschel has -shown that a supposed astronomical -discovery of his is a mere assumption. -I conceive that I have shown -that his representation of the history -of science is erroneous, both in its -details and in its generalities. His -distinction of the three stages of sciences, -the theological, metaphysical, -and positive, is not at all supported -by the facts of scientific history. -Real discoveries always involve what -he calls <i>metaphysics</i>; and the doctrine -of final causes in physiology, -the main element of science which -can properly be called <i>theological</i>, -is retained at the end, as well as the -beginning of the science, by all except -a peculiar school.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_283" href="#FNanchor_283" class="label">283</a> - I have also, in the same place, -given the Inductive Pyramid for the -science of Optics. These Pyramids -are necessarily inverted in their form, -in order that, in reading in the ordinary -way, we may proceed <i>to</i> the -vertex. <i>Phil. Ind. Sc.</i> b. xi. c. vi.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_284" href="#FNanchor_284" class="label">284</a> - <i>Cosmos</i>, vol. ii. note 35.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_285" href="#FNanchor_285" class="label">285</a> - The reader will probably recollect -that as <i>Induction</i> means the inference -of general propositions from -particular cases, <i>Deduction</i> means the -inference by the application of general -propositions to particular cases, -and by combining such applications; -as when from the most general principles -of Geometry or of Mechanics, -we prove some less general theorem; -for instance, the number of the possible -regular solids, or the principle of -<i>vis viva</i>.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_286" href="#FNanchor_286" class="label">286</a> - B. vi. c. v.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_287" href="#FNanchor_287" class="label">287</a> - c. vi.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_288" href="#FNanchor_288" class="label">288</a> - <i>Hist.</i> b. vi. c. vi. sect. 13.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_289" href="#FNanchor_289" class="label">289</a> - <i>Hist. Ind. Sc.</i> b. viii.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_290" href="#FNanchor_290" class="label">290</a> - Reprinted in the Appendix to this volume.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_291" href="#FNanchor_291" class="label">291</a> - <i>Phil. Pos.</i> t. iv. p. 264.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_292" href="#FNanchor_292" class="label">292</a> - <i>Logic</i>, b. vi. c. 3.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_293" href="#FNanchor_293" class="label">293</a> - Jones, <i>On Rent</i>, 1833.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_294" href="#FNanchor_294" class="label">294</a> - <i>Literary Remains</i>, 1859.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_295" href="#FNanchor_295" class="label">295</a> - The substance of this and the -next chapter was printed as a communication -to the Cambridge Phil. -Soc. in 1840.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_296" href="#FNanchor_296" class="label">296</a> - Or in the earlier editions, in the -<i>Philosophy of the Inductive Sciences</i>.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_297" href="#FNanchor_297" class="label">297</a> - <i>Phil. of Biol.</i> c. v.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_298" href="#FNanchor_298" class="label">298</a> - <i>Hist. Ind. Sc.</i> b. ix. c. iii.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_299" href="#FNanchor_299" class="label">299</a> - <i>Ibid.</i> b. vii. c. ii.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_300" href="#FNanchor_300" class="label">300</a> - Sir W. Hamilton's Note on the <i>Philosophy of the Unconditioned</i>.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_301" href="#FNanchor_301" class="label">301</a> - Werenfels in Mr. Mansel's <i>Bampton Lectures</i>, lect. ii. Note 15.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_302" href="#FNanchor_302" class="label">302</a> - <i>Scholium Generale</i> at the end of the <i>Principia</i>.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_303" href="#FNanchor_303" class="label">303</a> - B. iv. c. i.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_304" href="#FNanchor_304" class="label">304</a> - Reid's <i>Works</i>, Supplementary Dissertation D.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_305" href="#FNanchor_305" class="label">305</a> - <i>Hist. Sc. Id.</i> b. iii.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_306" href="#FNanchor_306" class="label">306</a> - <i>Hist. Sc. Id.</i> b. vi. c. iii.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_307" href="#FNanchor_307" class="label">307</a> - The remarks contained in this -chapter have for the most part been -already printed and circulated in a -<i>Letter to the Author of Prolegomena -Logica</i>, 1852.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_308" href="#FNanchor_308" class="label">308</a> - <i>Biographical History of Philosophy</i>, -1846. In a more recent edition -the author of this work has modified -his expressions, but still employs -himself in arguing against Dr. Whewell, -in order to overthrow Kant. -So far as his arguments affect my -philosophy, they are, as I conceive, -answered in the various expositions -which I have given of that philosophy.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_309" href="#FNanchor_309" class="label">309</a> - B. ii. The Philosophy of the -Pure Sciences. Chap. ii. Of the Idea -of Space. Chap. iii. Of some peculiarities -of the Idea of Space. Chap. -vii. Of the Idea of Time. Chap. viii. -Of some peculiarities of the Idea of -Time.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_310" href="#FNanchor_310" class="label">310</a> - <i>Prolegomena Logica</i>, by H. L. Mansel, M.A. 1851.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_311" href="#FNanchor_311" class="label">311</a> - <i>Logic</i>, i p. 273, 3rd edit.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_312" href="#FNanchor_312" class="label">312</a> - No. 193, p. 29.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_313" href="#FNanchor_313" class="label">313</a> - <i>Prol. Log.</i> p. 123.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_314" href="#FNanchor_314" class="label">314</a> - See <i>Phil. Ind. Sc.</i> b. vi. c. iii.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_315" href="#FNanchor_315" class="label">315</a> - Kant.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_316" href="#FNanchor_316" class="label">316</a> - Republished as <i>The History of Scientific Ideas</i>.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_317" href="#FNanchor_317" class="label">317</a> - Given in the <i>Novum Organon Renovatum</i>.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_318" href="#FNanchor_318" class="label">318</a> - <i>Nov. Org. Ren.</i> Aph. cv.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_319" href="#FNanchor_319" class="label">319</a> - <i>Hist. Sc. Id.</i> b. ix. c. vi.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_320" href="#FNanchor_320" class="label">320</a> - <i>Hist. Ind. Sc.</i> b. xviii. c. vi. sect. 5</p></div> - -<div class="footnote"> - -<p><a id="Footnote_321" href="#FNanchor_321" class="label">321</a> - P. 116. "No amount of human knowledge can be adequate which does -not solve the phenomena of these absolute certainties."</p></div> - -<div class="footnote"> - -<p><a id="Footnote_322" href="#FNanchor_322" class="label">322</a> - Prof. Butler, Lect. ix. Second -Series, p. 136, appears to think that -Plato had sufficient grounds (of a -theological kind) for the assumption -of such Ideas; but I see no trace of -them.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_323" href="#FNanchor_323" class="label">323</a> - I am aware that this translation -is different from the common translation. -It appears to me to be consistent -with the habit of the Greek -language. It slightly leans in favour -of my view; but I do not conceive -that the argument would be perceptibly -weaker, if the common interpretation -were adopted.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_324" href="#FNanchor_324" class="label">324</a> - In the <i>First Alcibiades</i>, Pythodorus -is mentioned as having paid -100 minæ to Zeno for his instructions -(119 <span class="smcap">A</span>).</p></div> - -<div class="footnote"> - -<p><a id="Footnote_325" href="#FNanchor_325" class="label">325</a> - P. 183 e.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_326" href="#FNanchor_326" class="label">326</a> - <i>Deip.</i> xi. c. 15, p. 105.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_327" href="#FNanchor_327" class="label">327</a> - Accedit et illud quod naturalis -philosophia in iis ipsis viris, qui ei -incubuerunt, vacantem et integrum -hominem, præsertim his recentioribus -temporibus, vix nacta sit; nisi -forte quis monachi alicujus in cellula, -aut nobilis in villula lucubrantis, -exemplum adduxerit; sed facta est -demum naturalis philosophia instar -transitus cujusdam et pontisternii ad -alia. Atque magna ista scientiarum -mater ad officia ancillæ detrusa est; -quæ medicinæ aut mathematicis operibus -ministrat, et rursus quæ adolescentium -immatura ingenia lavat -et imbuat velut tinctura quadam -prima, ut aliam postea felicius et -commodius excipiant.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_328" href="#FNanchor_328" class="label">328</a> - -μεταξὺ οἰκονομίας καὶ χρεματισμοῦ, -between house-keeping and -money-getting.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_329" href="#FNanchor_329" class="label">329</a> - τὸ περὶ τοὺς λόγους.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_330" href="#FNanchor_330" class="label">330</a> - The Sciences are to draw the -mind from that which grows and -perishes to that which really is: - μάθημα ψυχῆς ὁλκὸν ἀπὸ τοῦ γιγνομένου ἐπι τὸ ὅν.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_331" href="#FNanchor_331" class="label">331</a> -ἐπὶ θέαν τῆς τῶν ἀριθμῶν φύσεως.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_332" href="#FNanchor_332" class="label">332</a> - τῇ νοηήσει αὐτῇ.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_333" href="#FNanchor_333" class="label">333</a> - He adds "and for the sake of -war;" this point I have passed by. -Plato does not really ascribe much -weight to this use of Science, as we -see in what he says of Geometry and -Astronomy.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_334" href="#FNanchor_334" class="label">334</a> - ἀρθῶς ἕχει -ἑξῆς μετὰ δευτέραν αὕξην τρίτην λαμβάνειν, ἕστι δέ που τοῦτο περὶ τὴν -τῶν κύβων αύξην καὶ τὸ βάθους μέτεχον.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_335" href="#FNanchor_335" class="label">335</a> - ἀντίστροφον αὐτοῦ.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_336" href="#FNanchor_336" class="label">336</a> - πρὸς ἐναρμόνιον φορὰν ὦτα παγῆναι.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_337" href="#FNanchor_337" class="label">337</a> - πυκνώματα ἄ ττα.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_338" href="#FNanchor_338" class="label">338</a> - τίνες ξύμφωνοι ἀριθμοὶ, &c.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_339" href="#FNanchor_339" class="label">339</a> - -Η καὶ διαλεκτικὸν καλεῖς τὸν λόγον ἐκάστου λαμβάνοντα -τῆς οὐσίας; (§ 14).</p></div> - -<div class="footnote"> - -<p><a id="Footnote_340" href="#FNanchor_340" class="label">340</a> - - ὥσπερ θριγγὸς τοῖς μαθήμασιν ἡ διαλεκτικὴ ἦμιν ἐπάνω -κεῖσθαι. (§ 14).]</p></div> - -<div class="footnote"> - -<p><a id="Footnote_341" href="#FNanchor_341" class="label">341</a> - <i>Pol</i>. vi. § 19.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_342" href="#FNanchor_342" class="label">342</a> - He adds, "This <i>oraton</i>, this visible -world, I will not say has any -connexion with <i>ouranon</i>, heaven, -that I may not be accused of playing -upon words."</p></div> - -<div class="footnote"> - -<p><a id="Footnote_343" href="#FNanchor_343" class="label">343</a> - It is plain that Plato, by <i>Hypotheses</i>, -in this place, means the usual -foundations of Arithmetic and Geometry; -namely, Definitions and Postulates. -He says that "the arithmeticians -and geometers take as hypotheses -(hυποθεμενοι) odd and even, and -the three kinds of angles (right, acute, -and obtuse); and figures, (as a triangle, -a square,) and the like." I say -his "hypotheses" are the Definitions -and Postulates, not the Axioms: for -the Axioms of Arithmetic and Geometry -belong to the Higher Faculty, -which ascends to First Principles. -But this Faculty operates rather in -using these axioms than in enunciating -them. It knows them implicitly -rather than expresses them explicitly.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_344" href="#FNanchor_344" class="label">344</a> - διάνοιαν άλλ' οὐ νοῦν.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_345" href="#FNanchor_345" class="label">345</a> - The Diagram, as here described, would be this: -</p> - - - -<div class="center"> -<table border="1" cellpadding="4" cellspacing="0" summary=""> -<tr><td align="center" colspan="2"> <i>Intelligible World.</i></td><td align="center" colspan="2"><i>Visible World.</i></td></tr> -<tr><td align="center">Intuition.</td><td align="center">Conception.</td><td align="center">Things.</td><td align="center">Images.</td></tr> -</table></div> - -<p> -Plato supposes the whole, and each of the two parts, to be divided in the -same ratio, in order that the <i>analogy</i> of the division in each case may be -represented.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_346" href="#FNanchor_346" class="label">346</a> - The four segments might be as 4: 2: 2: 1; or as 9: 6: 6: 4; or generally, -as <i>a</i>: <i>ar</i>: <i>ar</i>: <i>ar</i><sup>2</sup>.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_347" href="#FNanchor_347" class="label">347</a> - -</p> -<p> - -<span style="margin-left: 4.5em;">Hence the mind Reason receives</span><br /> -Intuitive or Discursive.<br /> -</p> - -<p> - -<span class="smcap">Milton.</span><br /> -</p></div> - -<div class="footnote"> - -<p><a id="Footnote_348" href="#FNanchor_348" class="label">348</a> -τῇ τοῦ διαλέγεσθαι δυνόμει.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_349" href="#FNanchor_349" class="label">349</a> - This term occurs in other parts of Aristotle. See the additional Note.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_350" href="#FNanchor_350" class="label">350</a> - Mr. Owen, to whom I am indebted -for the physiological part of -this criticism, tells me, "All mammalia -have bile, the carnivora in -greater proportion than the herbivora: -the gall-bladder is a comparatively -unimportant accessory to the -biliary apparatus; adjusting it to -certain modifications of stomach and -intestine: there is no relation between -natural longevity and bile. -Neither has the presence or absence -of the gall-bladder any connexion -with age. Man and the elephant are -perhaps for their size the longest -lived animals, and the latest at coming -to maturity: one has the gall-bladder, -and the other not."</p></div> - -<div class="footnote"> - -<p><a id="Footnote_351" href="#FNanchor_351" class="label">351</a> - <i>Hist. Sc. Ind.</i> b. iii.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_352" href="#FNanchor_352" class="label">352</a> - These remarks were written in 1841. The accompanying Memoir contains -a further discussion of this problem.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_353" href="#FNanchor_353" class="label">353</a> - Cartes. <i>Princip.</i> iv. 23.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_354" href="#FNanchor_354" class="label">354</a> - Jac. Bernoulli, <i>Nouvelles Pensées -sur le Système de M. Descartes</i>, op. t. -i. p. 239 (1686).</p></div> - -<div class="footnote"> - -<p><a id="Footnote_355" href="#FNanchor_355" class="label">355</a> - <i>De la Cause de la Pesanteur</i> (1689), -p. 135.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_356" href="#FNanchor_356" class="label">356</a> - <i>Journal des Savans</i>, 1703. Mém. -Acad. Par. 1709. -</p> -<p> -Bulfinger, in 1726 (Acad. Petrop.), -conceived that by making a sphere -revolve at the same time about two -axes at right angles to each other, -every particle would describe a great -circle; but this is not so.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_357" href="#FNanchor_357" class="label">357</a> - Acad. Par. 1714, <i>Hist.</i> p. 106.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_358" href="#FNanchor_358" class="label">358</a> - Acad. Par. 1733.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_359" href="#FNanchor_359" class="label">359</a> - Acad. Sc. 1709. If we abandon -the clear principles of mechanics, the -writer says, "toute la lumière que -nous pouvons avoir est éteinte, et -nous voilà replongés de nouveau -dans les anciennes ténèbres du Peripatetisme, -dont le Ciel nous veuille -preserver!" -</p> -<p> -It was also objected to the Newtonian -system, that it did not account -for the remarkable facts, that all the -motions of the primary planets, all -the motions of the satellites, and all -the motions of rotation, including -that of the sun, are in the same direction, -and nearly in the same plane; -facts which have been urged by Laplace -as so strongly recommending -the Nebular Hypothesis; and that -hypothesis is, in truth, a hypothesis -of vortices respecting the <i>origin</i> of -the system of the world.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_360" href="#FNanchor_360" class="label">360</a> - <i>Nouvelle Physique Céleste</i>, Op. t. -iii. p. 163. -</p> -<p> -The deviation of the orbits of the -planets from the plane of the sun's -equator was of course a difficulty in -the system which supposed that they -were carried round by the vortices -which the sun's rotation caused, or -at least rendered evident. Bernoulli's -explanation consists in supposing the -planets to have a sort of <i>leeway</i> (<i>dérive -des vaisseaux</i>) in the stream of -the vortex.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_361" href="#FNanchor_361" class="label">361</a> - See <i>Hist. Sc. Ideas</i>, b. iii. c. ix. -Art. 7.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_362" href="#FNanchor_362" class="label">362</a> - See Mill's <i>Logic</i>, vol. i. p. 311, 2nd ed.</p></div> - -<div class="footnote"> - -<p><a id="Footnote_363" href="#FNanchor_363" class="label">363</a> - These letters refer to passages in the Translation annexed to this Memoir.</p></div></div> - - - -<div class="transnote"> - -<h3>Transcriber's Notes</h3> - -<p>Obvious typographical errors have been silently corrected. Other -variations in spelling, punctuation and hyphenation remain unchanged.</p> - -<p>In the Table of Contents Chap. XV item 5. "And justly" is not present in the text. It -has been removed and the numbering adjusted accordingly.</p> - - -</div> - - - - - - - - -<pre> - - - - - -End of the Project Gutenberg EBook of On the Philosophy of Discovery, -Chapters Historical and Critica, by William Whewell - -*** END OF THIS PROJECT GUTENBERG EBOOK PHILOSOPHY OF DISCOVERY *** - -***** This file should be named 51555-h.htm or 51555-h.zip ***** -This and all associated files of various formats will be found in: - http://www.gutenberg.org/5/1/5/5/51555/ - -Produced by Sonya Schermann, Les Galloway and the Online -Distributed Proofreading Team at http://www.pgdp.net (This -file was produced from images generously made available -by The Internet Archive) - - -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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