{"collection":"philosophy-ethics","full_text_available":true,"graph_url":"https://unchartedknowledge.5gfusion.net/v2/api/page/gutenberg_51555/graph","html_url":"https://unchartedknowledge.5gfusion.net/v2/page/gutenberg_51555","id":"gutenberg_51555","license":"Public Domain (US)","rights_basis":"gutenberg_metadata_copyright_false","source":"gutenberg","source_url":"https://www.gutenberg.org/ebooks/51555","summary":null,"tags":["Category: History - Other","Category: Philosophy & Ethics","Philosophy -- History","Science -- History","Science -- Philosophy"],"text":"ON THE\n\n                              PHILOSOPHY\n\n                                  OF\n\n                              DISCOVERY.\n\n\n\n\n                              Cambridge:\n\n                      PRINTED BY C. J. CLAY, M.A.\n\n                       AT THE UNIVERSITY PRESS.\n\n\n\n\n                                ON THE\n\n                       PHILOSOPHY OF DISCOVERY,\n\n                   CHAPTERS HISTORICAL AND CRITICAL;\n\n                                  BY\n\n                         WILLIAM WHEWELL, D.D.\n\n               MASTER OF TRINITY COLLEGE, CAMBRIDGE, AND\n           CORRESPONDING MEMBER OF THE INSTITUTE OF FRANCE.\n\n             INCLUDING THE COMPLETION OF THE THIRD EDITION\n             OF THE PHILOSOPHY OF THE INDUCTIVE SCIENCES.\n\n                            [Illustration: Hand passing torch to hand]\n\n                 \u039b\u0391\u039c\u03a0\u0391\u0394\u0399\u0391 \u0395\u03a7\u039f\u039d\u03a4\u0395\u03a3 \u0394\u0399\u0391\u0394\u03a9\u03a3\u039f\u03a5\u03a3\u0399\u039d \u0391\u039b\u039b\u0397\u039b\u039f\u0399\u03a3\n\n                                LONDON:\n\n                 JOHN W. PARKER AND SON, WEST STRAND.\n\n                                 1860.\n\n\n\n\nThe following are the latest editions of the series of works which has\nbeen published connected with the present subject:\n\n  _History of the Inductive Sciences_, 3 Vols. 1857.\n  _History of Scientific Ideas_, 2 Vols. 1858.\n  _Novum Organon Renovatum_, 1 Vol. 1858.\n  _On the Philosophy of Discovery_, 1 Vol. 1860.\n\nTo the _History of the Inductive Sciences_ are appended two Indexes (in\nVol. 1.), an Index of Proper Names, and an Index of Technical Terms.\nThese Indexes, and the Tables of Contents of the other works, will\nenable the reader to refer to any person or event included in this\nseries.\n\n\n\n\nPREFACE\n\n\nThe two works which I entitled _The History of the Inductive Sciences_,\nand _The Philosophy of the Inductive Sciences_, were intended to\npresent to the reader a view of the steps by which those portions of\nhuman knowledge which are held to be most certain and stable have\nbeen acquired, and of the philosophical principles which are involved\nin those steps. Each of these steps was a scientific _Discovery_, in\nwhich a _new_ conception was applied in order to bind together observed\nfacts. And though the conjunction of the observed facts was in each\ncase an example of logical _Induction_, it was not the inductive\nprocess merely, but the _novelty_ of the result in each case which gave\nits peculiar character to the History; and the Philosophy at which\nI aimed was not the Philosophy of Induction, but the _Philosophy of\nDiscovery_. In the present edition I have described this as my object\nin my Title.\n\nA great part of the present volume consists of chapters which composed\nthe twelfth Book of the Philosophy in former editions, which Book was\nthen described as a 'Review of Opinions on the nature of Knowledge\nand the Method of seeking it.' I have added to this part several new\nchapters, on Plato, Aristotle, the Arabian Philosophers, Francis Bacon,\nMr. Mill, Mr. Mansel, the late Sir William Hamilton, and the German\nphilosophers Kant, Fichte, Schelling and Hegel. I might, if time had\nallowed, have added a new chapter on Roger Bacon, founded on his _Opus\nMinus_ and other works, recently published for the first time under the\ndirection of the Master of the Rolls; a valuable contribution to the\nhistory of philosophy. But the review of this work would not materially\nalter the estimate of Roger Bacon which I had derived from the _Opus\nMajus_.\n\nBut besides these historical and critical surveys of the philosophy of\nothers, I have ventured to introduce some new views of my own; namely,\nviews which bear upon the philosophy of religion. I have done so under\nthe conviction that no philosophy of the universe can satisfy the minds\nof thoughtful men which does not deal with such questions as inevitably\nforce themselves on our notice, respecting the Author and the Object\nof the universe; and also under the conviction that every philosophy\nof the universe which has any consistency must suggest answers, at\nleast conjectural, to such questions. No _Cosmos_ is complete from\nwhich the question of Deity is excluded; and all Cosmology has a side\nturned towards Theology. Though I am aware therefore how easy it is, on\nthis subject, to give offence and to incur obloquy, I have not thought\nit right to abstain from following out my philosophical principles\nto their results in this department of speculation. The results do\nnot differ materially from those at which many pious and thoughtful\nspeculators have arrived in previous ages of the world; though they\nhave here, as seems to me, something of novelty in their connection\nwith the philosophy of science. But this point I willingly leave to the\ncalm decision of competent judges.\n\nI have added in an Appendix various Essays, previously published at\ndifferent times, which may serve perhaps to illustrate some points of\nthe history and philosophy of science.\n\n  TRINITY LODGE,\n\n  _February 8, 1856_.\n\n\n\n\n                                  ON\n\n                     THE PHILOSOPHY OF DISCOVERY.\n\n\n\n\nCONTENTS.\n\n The chapters marked thus * appear now for the first time.\n\n The chapters marked thus \u2020 have appeared in other works.\n\n\n  CHAP. I. INTRODUCTION.\n\n  CHAP. II. PLATO.\n\n  CHAP. III. * ADDITIONAL REMARKS ON PLATO.\n            1. The Doctrine of Ideas.\n            2. The Doctrine of the One and Many.\n            3. The notion of the nature and aim of Science.\n            4. The Survey of existing Sciences.\n            5. The Constitution of the human Mind.\n\n  CHAP. IV. ARISTOTLE.\n\n  CHAP. V. * ADDITIONAL REMARKS ON ARISTOTLE.\n            1. Induction.\n            2. Invention.\n            3. The One in the Many.\n            4. The \"Five Words.\"\n            5. Aristotle's contribution to the Physical Sciences.\n            6. Aristotle's Astronomy.\n            7. Aristotle on Classification.\n            8. F. Bacon on Aristotle.\n            9. Discovery of Causes.\n           10. Plato and Aristotle.\n           11. Aristotle against Plato's _Ideas_.\n\n  CHAP. VI. THE LATER GREEKS.\n\n  CHAP. VII. THE ROMANS.\n\n  CHAP. VIII. * ARABIAN PHILOSOPHERS.\n\n  CHAP. IX. THE SCHOOLMEN OF THE MIDDLE AGES.\n\n  CHAP. X. THE INNOVATORS OF THE MIDDLE AGES.\n             Raymond Lully.\n\n  CHAP. XI. THE INNOVATORS OF THE MIDDLE AGES--_continued_.\n             Roger Bacon.\n\n  CHAP. XII. THE REVIVAL OF PLATONISM.\n             1. Causes of Delay in the Advance of Knowledge.\n             2. Causes of Progress.\n             3. Hermolaus Barbarus, &c.\n             4. Nicolaus Cusanus.\n             5. Manilius Ficinus.\n             6. Francis Patricius.\n             7. Picus, Agrippa, &c.\n             8. Paracelsus, Fludd, &c.\n\n  CHAP. XIII. THE THEORETICAL REFORMERS OF SCIENCE.\n             1. Bernardinus Telesius.\n             2. Thomas Campanella.\n             3. Andrew C\u00e6salpinus.\n             4. Giordano Bruno.\n             5. Peter Ramus.\n             6. The Reformers in General.\n             7. Melancthon.\n\n  CHAP. XIV. THE PRACTICAL REFORMERS OF SCIENCE.\n             1. Character of the Practical Reformers.\n             2. Leonardo da Vinci.\n             3. Copernicus.\n             4. Fabricius.\n             5. Maurolycus.\n             6. Benedetti.\n             7. Gilbert.\n             8. Galileo.\n             9. Kepler.\n            10. Tycho.\n\n  CHAP. XV. FRANCIS BACON.\n             1. (I.) General Remarks.\n             2. Common estimate of him.\n             3. We consider only Physical Science.\n             4. He is placed at the head of the change:\n             5. (II.) _He proclaims a New Era_;\n             6. (III.) _By a Change of Method_;\n             7. Including successive Steps;\n             8. Gradually ascending.\n             9. (IV.) _He contrasts the Old and the New Method._\n            10. (V.) _Has he neglected Ideas?_\n            11. No.\n            12. Examples of Ideas treated by him.\n            13. He has failed in applying his Method;\n            14. (VI.) _To the Cause of Heat._\n            15. He seeks Causes before Laws.\n            16. (VII.) _His Technical Form worthless._\n            17. He is confused by words.\n            18. His \"Instances.\"\n            19. Contain some good Suggestions.\n            20. (VIII.) _His \"Idols.\"_\n            21. (IX.) _His view of Utility._\n            22. (X.) _His Hopefulness._\n            23. (XI.) _His Piety._\n\n  CHAP. XVI. * ADDITIONAL REMARKS ON FRANCIS BACON.\n             1. Mr. Ellis's views.\n             2. Mr. Spedding's views.\n\n  CHAP. XVII. FROM BACON TO NEWTON.\n             1. Harvey.\n             2. Descartes.\n             3. Gassendi.\n             4. Actual Progress in Science.\n             5. Otto Guericke, &c.\n             6. Hooke.\n             7. Royal Society.\n             8. Bacon's _New Atalantis_.\n             9. Cowley.\n            10. Barrow.\n\n  CHAP. XVIII. NEWTON.\n             1. Animating effect of his Discoveries.\n             2. They confirm Bacon's views.\n             3. Newton shuns Hypotheses.\n             4. His views of Inductive Philosophy.\n             5. His \"Rules of Philosophizing.\"\n             6. _The First Rule._\n             7. What is a \"True Cause\"?\n             8. _Such_ as are real?\n             9. Or _those_ which are proved?\n            10. Use of the Rule.\n            11. Rule otherwise expressed.\n            12. _The Second Rule._\n            13. What are Events \"of the same kind\"?\n            14. _The Third Rule_:\n            15. Not safe.\n            16. _The Fourth Rule._\n            17. Occult Qualities.\n            18. Ridiculed.\n            19. Distinction of Laws and Causes.\n\n  CHAP. XIX. LOCKE AND HIS FRENCH FOLLOWERS.\n             1. Cause of Locke's popularity.\n             2. Sensational School.\n             3. His inconsistencies.\n             4. Condillac, &c.\n             5. Importance of Language.\n             6. Ground of this.\n             7. The Encyclopedists.\n             8. Helvetius.\n             9. Value of Arts.\n            10. Tendency to Reaction.\n\n  CHAP. XX. THE REACTION AGAINST THE SENSATIONAL SCHOOL.\n             1. \"Nisi intellectus ipse.\"\n             2. Price's \"Review.\"\n             3. Stewart defends Price.\n             4. Archbishop Whately.\n             5. Laromigui\u00e8re.\n             6. M. Cousin.\n             7. M. Amp\u00e8re.\n             8. His Classification of Sciences.\n             9. Kant's Reform of Philosophy.\n            10. Its Effect in Germany.\n\n  CHAP. XXI. FURTHER ADVANCE OF THE SENSATIONAL SCHOOL.\n                M. Auguste Comte.\n             1. M. Comte on three States of Science.\n             2. M. Comte rejects the Search of Causes.\n             3. Causes in Physics.\n             4. Causes in other Sciences.\n             5. M. Comte's Practical Philosophy.\n             6. M. Comte on Hypotheses.\n             7. M. Comte's Classification of Sciences.\n\n  CHAP. XXII. \u2020 MR. MILL'S LOGIC.\n             (I.) What is Induction? \u00a7\u00a7 1-14.\n            (II.) Induction or Description, \u00a7\u00a7 15-23.\n           (III.) In Discovery a new Conception is introduced, \u00a7\u00a7 24-37.\n            (IV.) Mr. Mill's Four Methods of Inquiry, \u00a7\u00a7 38-40.\n             (V.) His Examples, \u00a7\u00a7 41-48.\n            (VI.) Mr. Mill against Hypotheses, \u00a7\u00a7 49, 50.\n           (VII.) Against prediction of Facts, \u00a7\u00a7 51-53.\n          (VIII.) Newton's Vera Causa, \u00a7\u00a7 54, 55.\n            (IX.) Successive Generalizations, \u00a7\u00a7 56-62.\n             (X.) Mr. Mill's Hope from Deductions, \u00a7\u00a7 63-67.\n            (XI.) Fundamental opposition of our Doctrines, \u00a7\u00a7 68-71.\n           (XII.) Absurdities in Mr. Mill's Logic, \u00a7\u00a7 72-74.\n\n  CHAP. XXIII. * POLITICAL ECONOMY AS AN INDUCTIVE SCIENCE.\n             1. Moral Sciences.\n             2. Political Economy.\n             3. Wages, Profits, and Rents.\n             4. Premature Generalizations.\n             5. Correction of these by Induction--Rent.\n             6.     \"      Wages.\n             7.     \"      Population.\n\n  CHAP. XXIV. \u2020 MODERN GERMAN PHILOSOPHY.\n            (I.) Science is the Idealization of Facts, \u00a7\u00a7 1-8.\n           (II.) Successive German Philosophies.\n                 Kant, Fichte, Schelling, Hegel, \u00a7\u00a7 9-16.\n\n  CHAP. XXV. \u2020 THE FUNDAMENTAL ANTITHESIS AS IT EXISTS IN THE MORAL WORLD.\n                 Moral Progress is the Realization of Ideas.\n\n  CHAP. XXVI. * OF THE \"PHILOSOPHY OF THE INFINITE.\"\n                 God is Eternal.\n\n  CHAP. XXVII. * SIR WILLIAM HAMILTON ON INERTIA AND WEIGHT.\n             1. Primary and Secondary Qualities.\n             2. Meaning of the Distinction.\n             3. Sir W. Hamilton adds \"Secundo-Primary.\"\n             4. Inertia.\n             5. Sir W. Hamilton's arguments and reply.\n             6. Gravity.\n                Sir W. Hamilton's arguments and reply.\n\n  CHAP. XXVIII. \u2020 INFLUENCE OF GERMAN SYSTEMS OF PHILOSOPHY IN BRITAIN.\n             1. Stewart on Kant.\n             2. Mr. G. H. Lewes on Kant.\n           4-6. Mr. Mansel on Kant.\n                His objection to our Fundamental Ideas, and Reply.\n          7-10. New Axioms are possible.\n         11-13. Mr. Mansel's Kantianism.\n         14-16. Axioms are not from experience.\n\n  CHAP. XXIX. * NECESSARY TRUTH IS PROGRESSIVE.\n             Objections considered.\n\n  CHAP. XXX. * THE THEOLOGICAL BEARING OF THE PHILOSOPHY OF DISCOVERY.\n           1-4. How can necessary truths be actual?\n          5, 6. Small extent of necessary truth.\n             7. How did things come to be as they are?\n             8. View of the Theist.\n          9-12. Is this Platonism?\n            13. Idea of Time.\n        14, 15. Ideas of Force and Matter.\n            16. Creation of Matter.\n            17. Platonic Ideas.\n         18-21. Idea of Kind.\n            22. Idea of Substance.\n            23. Idea of Final Cause.\n        24, 25. Human immeasurably inferior to Divine.\n            26. Science advances towards the Divine Ideas.\n            27. Recapitulation.\n\n  CHAP. XXXI. * MAN'S KNOWLEDGE OF GOD.\n          1, 2. Opinions.\n             3. From Nature we learn something of God.\n           4-6. Though but little.\n          7, 8. From ourselves we learn something concerning God.\n          9-11. Objections answered.\n            12. Creation.\n            13. End of the World.\n            14. Moral and Theological views enter.\n\n  CHAP. XXXII. * ANALOGIES OF PHYSICAL AND RELIGIOUS PHILOSOPHY.\n          1, 2. Idealization of Facts and Realization of Ideas;\n          3, 4. Both imperfect.\n          5, 6. Divine Ideas perfect.\n           7-9. Realization of Divine Love.\n         10-13. Realization of Divine Justice.\n            14. Analogy of Physical and Moral Philosophy.\n        15, 16. Supernatural Beginning, Middle, and End indicated.\n            17. Suggestion of a Future State.\n         18-20. Confirmation from the Intellect of Man.\n            21. From the Moral Nature of Man.\n\n\n  APPENDIX.\n\n                                                   PAGE\n\n  APPEND. A. OF THE PLATONIC THEORY OF IDEAS        403\n          B. ON PLATO'S SURVEY OF THE SCIENCES      417\n         BB. ON PLATO'S NOTION OF DIALECTIC         429\n          C. OF THE INTELLECTUAL POWERS ACCORDING\n                 TO PLATO                           440\n          D. CRITICISM OF ARISTOTLE'S ACCOUNT OF\n                 INDUCTION                          449\n          E. ON THE FUNDAMENTAL ANTITHESIS OF\n                 PHILOSOPHY                         462\n          F. REMARKS ON A REVIEW OF THE PHILOSOPHY\n                 OF THE INDUCTIVE SCIENCES          482\n          G. ON THE TRANSFORMATION OF HYPOTHESES\n                 IN THE HISTORY OF SCIENCE          492\n          H. ON HEGEL'S CRITICISM OF NEWTON'S\n                 PRINCIPIA                          504\n               Appendix to the Memoir on Hegel's Criticism\n                 of Newton's Principia              513\n          K. DEMONSTRATION THAT ALL MATTER IS\n                 HEAVY                              522\n\n\n\n\n                                ON THE\n                              PHILOSOPHY\n                                  OF\n                              DISCOVERY.\n\n\n    W\u00e4r' nicht das Auge sonnenhaft\n    Wie k\u00f6nnten wir das Licht erblicken?\n    Lebt' nicht in uns des Gottes eigne Kraft\n    Wie k\u00f6nnte uns das G\u00f6ttliche entz\u00fccken?\n                                       GOETHE.\n\n    Were nothing sunlike in the Eye\n    How could we Light itself descry?\n    Were nothing godlike in the Mind\n    How could we God in Nature find?\n\n\nCHAPTER I.\n\nINTRODUCTION.\n\n\nBy the examination of the elements of human thought in which I have\nbeen engaged, and by a consideration of the history of the most clear\nand certain parts of our knowledge, I have been led to doctrines\nrespecting the progress of that exact and systematic knowledge which\nwe call Science; and these doctrines I have endeavoured to lay before\nthe reader in the History of the Sciences and of Scientific Ideas. The\nquestions on which I have thus ventured to pronounce have had a strong\ninterest for man from the earliest period of his intellectual progress,\nand have been the subjects of lively discussion and bold speculation in\nevery age. I conceive that in the doctrines to which these researches\nhave conducted us, we have a far better hope that we possess a body of\npermanent truths than the earlier essays on the same subjects could\nfurnish. For we have not taken our examples of knowledge at hazard,\nas earlier speculators did, and were almost compelled to do; but have\ndrawn our materials from the vast store of unquestioned truths which\nmodern science offers to us: and we have formed our judgment concerning\nthe nature and progress of knowledge by considering what such science\nis, and how it has reached its present condition. But though we have\nthus pursued our speculations concerning knowledge with advantages\nwhich earlier writers did not possess, it is still both interesting\nand instructive for us to regard the opinions upon this subject which\nhave been delivered by the philosophers of past times. It is especially\ninteresting to see some of the truths which we have endeavoured to\nexpound, gradually dawning in men's minds, and assuming the clear\nand permanent form in which we can now contemplate them. I shall\ntherefore, in the ensuing chapters, pass in review many of the opinions\nof the writers of various ages concerning the mode by which man best\nacquires the truest knowledge; and I shall endeavour, as we proceed,\nto appreciate the real value of such judgments, and their place in the\nprogress of sound philosophy.\n\nIn this estimate of the opinions of others, I shall be guided by\nthose general doctrines which I have, as I trust, established in the\nhistories already published. And without attempting here to give any\nsummary of these doctrines, I may remark that there are two main\nprinciples by which speculations on such subjects in all ages are\nconnected and related to each other; namely, the opposition of _Ideas_\nand _Sensations_, and the distinction of _practical_ and _speculative_\nknowledge. The opposition of Ideas and Sensations is exhibited to us\nin the antithesis of Theory and Fact, which are necessarily considered\nas distinct and of opposite natures, and yet necessarily identical,\nand constituting Science by their identity. In like manner, although\npractical knowledge is in substance identical with speculative, (for\nall knowledge is speculation,) there is a distinction between the two\nin their history, and in the subjects by which they are exemplified,\nwhich distinction is quite essential in judging of the philosophical\nviews of the ancients. The alternatives of identity and diversity,\nin these two antitheses,--the successive separation, opposition, and\nreunion of principles which thus arise,--have produced, (as they may\neasily be imagined capable of doing,) a long and varied series of\nsystems concerning the nature of knowledge; among which we shall have\nto guide our course by the aid of the views already presented.\n\nI am far from undertaking, or wishing, to review the whole series of\nopinions which thus come under our notice; and I do not even attempt to\nexamine all the principal authors who have written on such subjects. I\nmerely wish to select some of the most considerable forms which, such\nopinions have assumed, and to point out in some measure the progress\nof truth from age to age. In doing this, I can only endeavour to seize\nsome of the most prominent features of each time and of each step, and\nI must pass rapidly from classical antiquity to those which we have\ncalled the dark ages, and from them to modern times. At each of these\nperiods the modifications of opinion, and the speculations with which\nthey were connected, formed a vast and tangled maze, the byways of\nwhich our plan does not allow us to enter. We shall esteem ourselves\nbut too fortunate, if we can discover the single track by which ancient\nled to modern philosophy.\n\nI must also repeat that my survey of philosophical writers is here\nconfined to this one point,--their opinions on the nature of knowledge\nand the method of science. I with some effort avoid entering upon other\nparts of the philosophy of those authors of whom I speak; I knowingly\npass by those portions of their speculations which are in many cases\nthe most interesting and celebrated;--their opinions concerning the\nhuman soul, the Divine Governor of the world, the foundations or\nleading doctrines of politics, religion, and general philosophy. I\nam desirous that my reader should bear this in mind, since he must\notherwise be offended with the scanty and partial view which I give in\nthis place of the philosophers whom I enumerate.\n\n\n\n\nCHAPTER II.\n\nPLATO.\n\n\nThere would be small advantage in beginning our examination earlier\nthan the period of the Socratic School at Athens; for although the\nspirit of inquiry on such subjects had awakened in Greece at an earlier\nperiod, and although the peculiar aptitude of the Grecian mind for\nsuch researches had shown itself repeatedly in subtle distinctions\nand acute reasonings, all the positive results of these early efforts\nwere contained in a more definite form in the reasonings of the\nPlatonic age. Before that time, the Greeks did not possess plain and\nfamiliar examples of exact knowledge, such as the truths of Arithmetic,\nGeometry, Astronomy and Optics became in the school of Plato; nor\nwere the antitheses of which we spoke above, so distinctly and fully\nunfolded as we find them in Plato's works.\n\nThe question which hinges upon one of these antitheses, occupies\na prominent place in several of the Platonic dialogues; namely,\nwhether our knowledge be obtained by means of Sensation or of Ideas.\nOne of the doctrines which Plato most earnestly inculcated upon his\ncountrymen was, that we do not _know_ concerning sensible objects, but\nconcerning ideas. The first attempts of the Greeks at metaphysical\nanalysis had given rise to a school which maintained that material\nobjects are the only realities. In opposition to this, arose another\nschool, which taught that material objects have no permanent reality,\nbut are ever waxing and waning, constantly changing their substance.\n\"And hence,\" as Aristotle says[1], \"arose the doctrine of ideas which\nthe Platonists held. For they assented to the opinion of Heraclitus,\nthat all sensible objects are in a constant state of flux. So that if\nthere is to be any knowledge and science, it must be concerning some\npermanent natures, different from the sensible natures of objects;\nfor there can be no permanent science respecting that which is\nperpetually changing. It happened that Socrates turned his speculations\nto the moral virtues, and was the first philosopher who endeavoured\nto give universal definitions of such matters. He wished to reason\nsystematically, and therefore he tried to establish definitions, for\ndefinitions are the basis of systematic reasoning. There are two things\nwhich may justly be looked upon as steps in philosophy due to Socrates;\ninductive reasonings, and universal definitions;--both of them steps\nwhich belong to the foundations of science. Socrates, however, did not\nmake universals, or definitions separable from the objects; but his\nfollowers separated them, and these essences they termed _Ideas_.\" And\nthe same account is given by other writers[2]. \"Some existences are\nsensible, some intelligible: and according to Plato, if we wish to\nunderstand the principles of things, we must first separate the _ideas_\nfrom the _things_, such as the ideas of Similarity, Unity, Number,\nMagnitude, Position, Motion: second, that we must assume an absolute\nFair, Good, Just, and the like: third, that we must consider the ideas\nof relation, as Knowledge, Power: recollecting that the Things which\nwe perceive have this or that appellation applied to them because\nthey partake of this or that Idea; those things being _just_ which\nparticipate in the idea of The Just, those being _beautiful_, which\ncontain the idea of The Beautiful.\" And many of the arguments by which\nthis doctrine was maintained are to be found in the Platonic dialogues.\nThus the opinion that true knowledge consists in sensation, which had\nbeen asserted by Protagoras and others, is refuted in the _The\u00e6tetus_:\nand, we may add, so victoriously refuted, that the arguments there\nput forth have ever since exercised a strong influence upon the\nspeculative world. It may be remarked that in the minds of Plato and\nof those who have since pursued the same paths of speculation, the\ninterest of such discussions as those we are now referring to, was by\nno means limited to their bearing upon mere theory; but was closely\nconnected with those great questions of morals which have always a\npractical import. Those who asserted that the only foundation of\nknowledge was sensation, asserted also that the only foundation of\nvirtue was the desire of pleasure. And in Plato, the metaphysical\npart of the disquisitions concerning knowledge in general, though\nindependent in its principles, always seems to be subordinate in its\npurpose to the questions concerning the knowledge of our duty.\n\nSince Plato thus looked upon the Ideas which were involved in each\ndepartment of knowledge as forming its only essential part, it was\nnatural that he should look upon the study of Ideas as the true mode\nof pursuing knowledge. This he himself describes in the _Philebus_[3].\n\"The best way of arriving at truth is not very difficult to point out,\nbut most hard to pursue. All the arts which have ever been discovered,\nwere revealed in this manner. It is a gift of the gods to man, which,\nas I conceive, they sent down by some Prometheus, as by Prometheus\nthey gave us the light of fire; and the ancients, more clear-sighted\nthan we, and less removed from the gods, handed down this traditionary\ndoctrine: that whatever is said to be, comes of One and of Many, and\ncomprehends in itself the Finite and the Infinite in coalition\n(being One Kind, and consisting of Infinite Individuals). And this\nbeing the state of things, we must, in each case, endeavour to seize\nthe One Idea (the idea of the Kind) as the chief point; for we shall\nfind that it is there. And when we have seized this one thing, we may\nthen consider how it comprehends in itself two, or three, or any other\nnumber; and, again, examine each of these ramifications separately;\ntill at last we perceive, not only that One is at the same time One\nand Many, but also _how many_. And when we have thus filled up the\ninterval between the Infinite and the One, we may consider that we\nhave done with each one. The gods then, as I have said, taught us by\ntradition thus to contemplate, and to learn, and to teach one another.\nBut the philosophers of the present day seize upon the One, at hazard,\ntoo soon or too late, and then immediately snatch at the Infinite; but\nthe intermediate steps escape them, in which resides the distinction\nbetween a truly logical and a mere disputatious discussion.\"\n\nIt would seem that what the author here describes as the most perfect\nform of exposition, is that which refers each object to its place in\na classification containing a complete series of subordinations, and\nwhich gives a definition of each class. We have repeatedly remarked\nthat, in sciences of classification, each new definition which gives a\ntenable and distinct separation of classes is an important advance in\nour knowledge; but that such definitions are rather the last than the\nfirst step in each advance. In the progress of real knowledge, these\ndefinitions are always the results of a laborious study of individual\ncases, and are never arrived at by a pure effort of thought, which is\nwhat Plato appears to have imagined as the true mode of philosophizing.\nAnd still less do the advances of other sciences consist in seizing\nat once upon the highest generality, and filling in afterwards all\nthe intermediate steps between that and the special instances. On the\ncontrary, as we have seen, the ascents from particular to general are\nall successive; and each step of this ascent requires time, and labour,\nand a patient examination of actual facts and objects.\n\nIt would, of course, be absurd to blame Plato for having inadequate\nviews of the nature of progressive knowledge, at the time when\nknowledge could hardly be said to have begun its progress. But we\nalready find in his speculations, as appears in the passages just\nquoted from his writings, several points brought into view which will\nrequire our continued attention as we proceed. In overlooking the\nnecessity of a gradual and successive advance from the less general to\nthe more general truths, Plato shared in a dimness of vision[4] which\nprevailed among philosophers to the time of Francis Bacon. In thinking\ntoo slightly of the study of actual nature, he manifested a bias from\nwhich the human intellect freed itself in the vigorous struggles which\nterminated the dark ages. In pointing out that all knowledge implies\na unity of what we observe as manifold, which unity is given by the\nmind, Plato taught a lesson which has of late been too obscurely\nacknowledged, the recoil by which men repaired their long neglect of\nfacts having carried them for a while so far as to think that facts\nwere the whole of our knowledge. And in analysing this principle of\nUnity, by which we thus connect sensible things, into various Ideas,\nsuch as Number, Magnitude, Position, Motion, he made a highly important\nstep, which it has been the business of philosophers in succeeding\ntimes to complete and to follow out.\n\nBut the efficacy of Plato's speculations in their bearing upon physical\nscience, and upon theory in general, was much weakened by the confusion\nof practical with theoretical knowledge, which arose from the ethical\npropensities of the Socratic school. In the Platonic Dialogues, Art and\nScience are constantly spoken of indiscriminately. The skill possessed\nby the Painter, the Architect, the Shoemaker, is considered as a just\nexample of human science, no less than the knowledge which the geometer\nor the astronomer possesses of the theoretical truths with which he\nis conversant. Not only so; but traditionary and mythological tales,\nmystical imaginations and fantastical etymologies, are mixed up, as\nno less choice ingredients, with the most acute logical analyses, and\nthe most exact conduct of metaphysical controversies. There is no\ndistinction made between the knowledge possessed by the theoretical\npsychologist and the physician, the philosophical teacher of morals\nand the legislator or the administrator of law. This, indeed, is the\nless to be wondered at, since even in our own time the same confusion\nis very commonly made by persons not otherwise ignorant or uncultured.\n\nOn the other hand, we may remark finally, that Plato's admiration of\nIdeas was not a barren imagination, even so far as regarded physical\nscience. For, as we have seen[5], he had a very important share in\nthe introduction of the theory of epicycles, having been the first to\npropose to astronomers in a distinct form, the problem of which that\ntheory was the solution; namely, \"to explain the celestial phenomena\nby the combination of equable circular motions.\" This demand of an\nideal hypothesis which should exactly express the phenomena (as well\nas they could then be observed), and from which, by the interposition\nof suitable steps, all special cases might be deduced, falls in well\nwith those views respecting the proper mode of seeking knowledge\nwhich we have quoted from the _Philebus_. And the Idea which could\nthus represent and replace all the particular Facts, being not only\nsought but found, we may readily suppose that the philosopher was, by\nthis event, strongly confirmed in his persuasion that such an Idea\nwas indeed what the inquirer ought to seek. In this conviction all\nhis genuine followers up to modern times have participated; and thus,\nthough they have avoided the error of those who hold that facts alone\nare valuable as the elements of our knowledge, they have frequently run\ninto the opposite error of too much despising and neglecting facts, and\nof thinking that the business of the inquirer after truth was only a\nprofound and constant contemplation of the conceptions of his own mind.\nBut of this hereafter.\n\nFOOTNOTES:\n\n[Footnote 1: _Metaph._ xii. 4.]\n\n[Footnote 2: Diog. Laert. _Vit. Plat._]\n\n[Footnote 3: T. ii. p. 16, c, d. ed. Bekker, t. v. p. 437.]\n\n[Footnote 4: See the remarks on this phrase in the next chapter.]\n\n[Footnote 5: _Hist. Ind. Sc._ b. iii. c. ii.]\n\n\n\n\nCHAPTER III.\n\nADDITIONAL REMARKS ON PLATO.\n\n\nThe leading points in Plato's writings which bear upon the philosophy\nof discovery are these:\n\n  1. The Doctrine of Ideas.\n  2. The Doctrine of the One and the Many.\n  3. The notion of the nature and aim of Science.\n  4. The survey of existing Sciences.\n\n1. The Doctrine of Ideas is an attempt to solve a problem which in all\nages forces itself upon the notice of thoughtful men; namely, How can\ncertain and permanent knowledge be possible for man, since all his\nknowledge must be derived from transient and fluctuating sensations?\nAnd the answer given by this doctrine is, that certain and permanent\nknowledge is _not_ derived from _Sensations_, but from _Ideas_. There\nare in the mind certain elements of knowledge which are not derived\nfrom sensation, and are only imperfectly exemplified in sensible\nobjects; and when we reason concerning sensible things so as to obtain\nreal knowledge, we do so by considering such things as partaking of\nthe qualities of the Ideas concerning which there can be truth. The\nsciences of Geometry and Arithmetic show that there _are_ truths which\nman can know; and the Doctrine of Ideas explains how this is possible.\n\nSo far the Doctrine of Ideas answers its primary purpose, and is a\nreply (by no means the least intelligible and satisfactory reply) to\na question still agitated among philosophers: What is the ground of\ngeometrical (and other necessary) truth?\n\nBut Plato seems, in many of his writings, to extend this doctrine much\nfurther; and to assume, not only Ideas of Space and its properties,\nfrom which geometrical truths are derived; but of Relations, as the\nRelations of Like and Unlike, Greater and Less; and of mere material\nobjects, as Tables and Chairs. Now to assume Ideas of such things as\nthese solves no difficulty and is supported by no argument. In this\nrespect the Ideal theory is of no value in Science.\n\nIt is curious that we have a very acute refutation of the Ideal theory\nin this sense, not only in Aristotle, the open opponent of Plato on\nthis subject, but in the Platonic writings themselves: namely, in the\nDialogue entitled _Parmenides_; which, on this and on other accounts, I\nconsider to be the work not of Plato, but of an opponent of Plato[6].\n\n\n2. I have spoken, in the preceding chapter, of Plato's doctrine that\ntruth is to be obtained by discerning the One in the Many. This\nexpression is used, it would seem, in a somewhat large and fluctuating\nway, to mean several things; as for instance, finding the one _kind_ in\nmany _individuals_ (for instance, the one idea of dog in many dogs);\nor the one _law_ in many _phenomena_ (for instance, the eccentrics and\nepicycles in many planets). In any interpretation, it is too loose and\nindefinite a rule to be of much value in the formation of sciences,\nthough it has been recently again propounded as important in modern\ntimes.\n\n\n3. I have said, in the preceding chapter, that Plato, though he saw\nthat scientific truths of great generality might be obtained and\nwere to be arrived at by philosophers, overlooked the necessity of a\n_gradual_ and _successive_ advance from the less general to the more\ngeneral; and I have described this as a 'dimness of vision.' I must now\nacknowledge that this is not a very appropriate phrase; for not only\nno acuteness of vision could have enabled Plato to see that gradual\ngeneralization in science of which, as yet, no example had appeared;\nbut it was very fortunate for the progress of truth, at that time, that\nPlato had imagined to himself the object of science to be general\nand sublime truths which prove themselves to be true by the light of\ntheir own generality and symmetry. It is worth while to illustrate this\nnotice of Plato by some references to his writings.\n\nIn the Sixth Book of the _Republic_, Plato treats of the then existing\nsciences as the instruments of a philosophical education. Among the\nmost conspicuous of these is astronomy. He there ridicules the notion\nthat astronomy is a sublime science because it makes men look _upward_.\nHe asserts that the really sublime science is that which makes men look\nat the _realities_, which are suggested by the appearances seen in the\nheavens: namely, the spheres which revolve and carry the luminaries\nin their revolutions. Now it was no doubt the determined search for\nsuch \"realities\" as these which gave birth to the Greek _Astronomy_,\nthat first and critical step in the progress of science. Plato, by his\nexhortations, if not by his suggestions, contributed effectually, as\nI conceive, to this step in science. In the same manner he requires\na science of _Harmonics_ which shall be free from the defects and\ninaccuracies which occur in actual instruments. This belief that the\nuniverse was full of mathematical relations, and that these were the\ntrue objects of scientific research, gave a vigour, largeness of mind,\nand confidence to the Greek speculators which no more cautious view of\nthe problem of scientific discovery could have supplied. It was well\nthat this advanced guard in the army of discoverers was filled with\nindomitable courage, boundless hopes, and creative minds.\n\nBut we must not forget that this disposition to what Bacon calls\n_anticipation_ was full of danger as well as of hope. It led Plato\ninto error, as it led Kepler afterwards, and many others in all ages\nof scientific activity. It led Plato into error, for instance, when it\nled him to assert (in the _Tim\u00e6us_) that the four elements, Earth, Air,\nFire and Water, have, for the forms of their particles respectively,\nthe Cube, the Icosahedron, the Pyramid, and the Octahedron; and again,\nwhen it led him to despise the practical controversies of the musicians\nof his time; which controversies were, in fact, the proof of the\ntruth of the mathematical theory of Harmonics. And in like manner it\nled Kepler into error when it led him to believe that he had found the\nreason of the number, size and motion of the planetary orbits in the\napplication of the five regular solids to the frame of the universe[7].\n\nHow far the caution in forming hypotheses which Bacon's writings urge\nupon us is more severe than suits the present prospects of science,\nwe may hereafter consider; but it is plainly very conceivable that\na boldness in the invention and application of hypotheses which was\npropitious to science in its infancy, may be one of the greatest\ndangers of its more mature period: and further, that the happy effect\nof such a temper depended entirely upon the candour, skill and labour\nwith which the hypotheses were compared with the observed phenomena.\n\n\n4. Plato has given a survey of the sciences of his time as Francis\nBacon has of _his_. Indeed Plato has given two such surveys: one,\nin the _Republic_, in reviewing, as I have said, the elements of a\nphilosophical education; the other in the _Tim\u00e6us_, as the portions\nof a theological view of the universe--such as has been called a\n_Theodic\u00e6a_, a justification of God. In the former passage of Plato,\nthe sciences enumerated are Arithmetic, Plane Geometry, Solid Geometry,\nAstronomy and Harmonics[8]. In the _Tim\u00e6us_ we have a further notice\nof many other subjects, in a way which is intended, I conceive, to\ninclude such knowledge as Plato had then arrived at on the various\nparts of the universe. The subjects there referred to are, as I have\nelsewhere stated[9], these: light and heat, water, ice, gold, gems,\nrust and other natural objects:--odours, taste, hearing, lights,\ncolour, and the powers of sense in general:--the parts and organs of\nthe body, as the bones, the marrow, the brain, flesh, muscles, tendons,\nligaments and nerves; the skin, the hair, the nails; the veins and\narteries; respiration; generation; and in short, every obvious point\nof physiology. But the opinions thus delivered in the _Tim\u00e6us_ on the\nlatter subject have little to do with the progress of real knowledge.\nThe doctrines, on the other hand, which depend upon geometrical and\narithmetical relations are portions or preludes of the sciences which\nthe fulness of time brought forth.\n\n\n5. I may, as further bearing upon the Platonic notion of science,\nnotice Plato's view of the constitution of the human mind. According\nto him the Ideas which are the constituents of science form an\nIntelligible World, while the visible and tangible things which we\nperceive by our senses form the Visible World. In the visible world we\nhave shadows and reflections of actual objects, and by these shadows\nand reflections we may judge of the objects, even when we cannot do\nso directly; as when men in a dark cavern judge of external objects\nby the shadows which they cast into the cavern. In like manner in the\nIntelligible World there are conceptions which are the usual objects of\nhuman thought, and about which we reason; but these are only shadows\nand reflections of the Ideas which are the real sources of truth.\nAnd the Reasoning Faculty, the Discursive Reason, the _Logos_, which\nthus deals with conceptions, is subordinate to the Intuitive Faculty,\nthe Intuitive Reason, the _Nous_, which apprehends Ideas[10]. This\nrecognition of a Faculty in man which contemplates the foundations--the\n_Fundamental Ideas_--of science, and by apprehending such Ideas, makes\nscience possible, is consentaneous to the philosophy which I have\nall along presented, as the view taught us by a careful study of the\nhistory and nature of science. That new Fundamental Ideas are unfolded,\nand the Intuitive Faculty developed and enlarged by the progress of\nscience and by an intimate acquaintance with its reasonings, Plato\nappears to have discerned in some measure, though dimly. And this is\nthe less wonderful, inasmuch as this gradual and successive extension\nof the field of Intuitive Truth, in proportion as we become familiar\nwith a larger amount of derived truth, is even now accepted by few,\nthough proved by the reasonings of the greatest scientific discoverers\nin every age.\n\nThe leading defect in Plato's view of the nature of real science is his\nnot seeing fully the extent to which experience and observation are the\nbasis of all our knowledge of the universe. He considers the luminaries\nwhich appear in the heavens to be not the true objects of astronomy,\nbut only some imperfect adumbration of them;--mere diagrams which may\nassist us in the study of a higher truth, as beautiful diagrams might\nillustrate the truths of geometry, but would not prove them. This\nnotion of an astronomy which is an astronomy of Theories and not of\nFacts, is not tenable, for Theories _are_ Facts. Theories and Facts\nare equally _real_; true Theories are Facts, and Facts are familiar\nTheories. But when Plato says that astronomy is a series of problems\nsuggested by visible things, he uses expressions quite conformable\nto the true philosophy of science; and the like is true of all other\nsciences.\n\nFOOTNOTES:\n\n[Footnote 6: This matter is further discussed in the Appendix, Essay A.]\n\n[Footnote 7: These matters are further discussed in the Appendix, Essay\nB.]\n\n[Footnote 8: See Appendix, Essay B.]\n\n[Footnote 9: _Hist. Ind. Sc._ b. ii. Additions to 3rd Ed.]\n\n[Footnote 10: See these views further discussed in the Appendix, Essay\nC.]\n\n\n\n\nCHAPTER IV.\n\nARISTOTLE.\n\n\nThe views of Aristotle with regard to the foundations of human\nknowledge are very different from those of his tutor Plato, and are\neven by himself put in opposition to them. He dissents altogether\nfrom the Platonic doctrine that Ideas are the true materials of our\nknowledge; and after giving, respecting the origin of this doctrine,\nthe account which we quoted in the last chapter, he goes on to reason\nagainst it. \"Thus,\" he says[11], \"they devised Ideas of all things\nwhich are spoken of as universals: much as if any one having to count a\nnumber of objects, should think that he could not do it while they were\nfew, and should expect to count them by making them more numerous. For\nthe kinds of things are almost more numerous than the special sensible\nobjects, by seeking the causes of which they were led to their Ideas.\"\nHe then goes on to urge several other reasons against the assumption of\nIdeas and the use of them in philosophical researches.\n\nAristotle himself establishes his doctrines by trains of reasoning. But\nreasoning must proceed from certain First Principles; and the question\nthen arises, Whence are these First Principles obtained? To this he\nreplies, that they are the result of _Experience_, and he even employs\nthe same technical expression by which we at this day describe the\nprocess of collecting these principles from observed facts;--that they\nare obtained by _Induction_. I have already quoted passages in which\nthis statement is made[12]. \"The way of reasoning,\" he says[13], \"is\nthe same in philosophy, and in any art or science: we must collect\nthe _facts_ (\u03c4\u1f70 \u1f51\u03c0\u1f70\u03c1\u03c7\u03bf\u03bd\u03c4\u03b1), and the things to which the facts happen,\nand must have as large a supply of these as possible, and then we must\nexamine them according to the terms of our syllogisms.\" ... \"There are\npeculiar principles in each science; and in each case these principles\nmust be obtained from _experience_. Thus astronomical observation\nsupplies the principles of astronomical science. For the phenomena\nbeing rightly taken, the demonstrations of astronomy were discovered;\nand the same is the case with any other Art or Science. So that if\nthe facts in each case be taken, it is our business to construct the\ndemonstrations. For if _in our natural history_ (\u03ba\u03b1\u03c4\u1f70 \u03c4\u1f70\u03bd \u1f31\u03c3\u03c4\u03bf\u03c1\u03af \u03b1\u03bd)\nwe have omitted none of the facts and properties which belong to the\nsubject, we shall learn what we can demonstrate and what we cannot.\"\nAnd again[14], \"It is manifest that if any sensation be wanting, there\nmust be some knowledge wanting, which we are thus prevented from\nhaving. For we acquire knowledge either _by Induction_ (\u1f10\u03c0\u03b1\u03b3\u03c9\u03b3\u1fc6) or\nby Demonstration: and Demonstration is from universals, but Induction\nfrom particulars. It is impossible to have universal theoretical\npropositions except by Induction: and we cannot make inductions without\nhaving sensation; for sensation has to do with particulars.\"\n\nIt is easy to show that Aristotle uses the term _Induction_, as we use\nit, to express the process of collecting a general proposition from\nparticular cases in which it is exemplified. Thus in a passage which\nwe have already quoted[15], he says, \"Induction, and Syllogism from\nInduction, is when we attribute one extreme term to the middle by means\nof the other.\" The import of this technical phraseology will further\nappear by the example which he gives: \"We find that several animals\nwhich are deficient in bile are long-lived, as man, the horse, the\nmule; hence we infer that _all_ animals which are deficient in bile are\nlong-lived.\"\n\nWe may observe, however, that both Aristotle's notion of induction,\nand many other parts of his philosophy, are obscure and imperfect, in\nconsequence of his refusing to contemplate ideas as something distinct\nfrom sensation. It thus happens that he always assumes the ideas\nwhich enter into his proposition as _given_; and considers it as the\nphilosopher's business to determine whether such propositions are true\nor not: whereas the most important feature in induction is, as we have\nsaid, the _introduction_ of a new idea, and not its employment when\nonce introduced. That the mind in this manner gives unity to that which\nis manifold,--that we are thus led to speculative principles which have\nan evidence higher than any others,--and that a peculiar sagacity in\nsome men seizes upon the conceptions by which the facts may be bound\ninto true propositions,--are doctrines which form no essential part\nof the philosophy of the Stagirite, although such views are sometimes\nrecognized, more or less clearly, in his expressions. Thus he says[16],\n\"There can be no knowledge when the sensation does not continue in\nthe mind. For this purpose, it is necessary both to perceive, and to\nhave some _unity_ in the mind (\u03b1\u1f30\u03c3\u03b8\u03b1\u03bd\u03bf\u03bc\u03ad\u03bd\u03bf\u03b9\u03c2 \u03b5\u03c7\u03b5\u03b9\u03bd \u1f14\u03bd \u03c4\u03b9[17] \u1f10\u03bd \u03c4\u1fc7\n\u03c8\u03c5\u03c7\u1fc7); and many such perceptions having taken place, some difference\nis then perceived: and from the remembrance of these arises Reason.\nThus from Sensation comes Memory, and from Memory of the same thing\noften repeated comes Experience: for many acts of Memory make up one\nExperience. And from Experience, or from any Universal Notion which\ntakes a permanent place in the mind,--from the _unity in the manifold_,\nthe same some one thing being found in many facts,--springs the first\nprinciple of Art and of Science; of Art, if it be employed about\nproduction; of Science, if about existence.\"\n\nI will add to this, Aristotle's notice of _Sagacity_; since, although\nlittle or no further reference is made to this quality in his\nphilosophy, the passage fixes our attention upon an important step in\nthe formation of knowledge. \"Sagacity\" (\u1f00\u03b3\u03c7\u03af\u03bd\u03bf\u03b9\u03b1), he says[18], \"is a\nhitting by guess (\u03b5\u1f50\u03c3\u03c4\u03bf\u03c7\u03af\u03b1 \u03c4\u03b9\u03c2) upon the middle term (the conception\ncommon to two cases) in an inappreciable time. As for example, if any\none seeing that the bright side of the moon is always towards the sun,\nsuddenly perceives why this is; namely, because the moon shines by the\nlight of the sun:--or if he sees a person talking with a rich man, he\nguesses that he is borrowing money;--or conjectures that two persons\nare friends, because they are enemies of the same person.\"--To consider\nonly the first of these examples;--the conception here introduced,\nthat of a body shining by the light which another casts upon it, is\nnot contained in the observed facts, but introduced by the mind. It\nis, in short, that conception which, in the act of induction, the mind\nsuperadds to the phenomena as they are presented by the senses: and to\ninvent such appropriate conceptions, such \"eustochies,\" is, indeed, the\nprecise office of inductive sagacity.\n\nAt the end of this work (the _Later Analytics_) Aristotle ascribes\nour knowledge of principles to Intellect (\u03bd\u03bf\u1fe6\u03c2), or, as it appears\nnecessary to translate the word, _Intuition_[19]. \"Since, of our\nintellectual habits by which we aim at truth, some are always true, but\nsome admit of being false, as Opinion and Reasoning, but Science and\nIntuition are always true; and since there is nothing which is more\ncertain than Science except Intuition; and since Principles are better\nknown to us than the Deductions from them; and since all Science is\nconnected by reasoning, we cannot have Science respecting Principles.\nConsidering this then, and that the beginning of Demonstration cannot\nbe Demonstration, nor the beginning of Science, Science; and since, as\nwe have said, there is no other kind of truth, Intuition must be the\nbeginning of Science.\"\n\nWhat is here said, is, no doubt, in accordance with the doctrines which\nwe have endeavoured to establish respecting the nature of Science,\nif by this _Intuition_ we understand that contemplation of certain\nFundamental Ideas, which is the basis of all rigorous knowledge. But\nnotwithstanding this apparent approximation, Aristotle was far from\nhaving an habitual and practical possession of the principles which he\nthus touches upon. He did not, in reality, construct his philosophy by\ngiving Unity to that which was manifold, or by seeking in Intuition\nprinciples which might be the basis of Demonstration; nor did he\ncollect, in each subject, fundamental propositions by an induction\nof particulars. He rather endeavoured to divide than to unite; he\nemployed himself, not in combining facts, but in analysing notions;\nand the criterion to which he referred his analysis was, not the facts\nof our experience, but our habits of language. Thus his opinions\nrested, not upon sound inductions, gathered in each case from the\nphenomena by means of appropriate Ideas; but upon the loose and vague\ngeneralizations which are implied in the common use of speech.\n\nYet Aristotle was so far consistent with his own doctrine of the\nderivation of knowledge from experience, that he made in almost\nevery province of human knowledge, a vast collection of such special\nfacts as the experience of his time supplied. These collections are\nalmost unrivalled, even to the present day, especially in Natural\nHistory; in other departments, when to the facts we must add the right\nInductive Idea, in order to obtain truth, we find little of value\nin the Aristotelic works. But in those parts which refer to Natural\nHistory, we find not only an immense and varied collection of facts and\nobservations, but a sagacity and acuteness in classification which it\nis impossible not to admire. This indeed appears to have been the most\neminent faculty in Aristotle's mind.\n\nThe influence of Aristotle in succeeding ages will come under our\nnotice shortly.\n\n\nFOOTNOTES:\n\n[Footnote 11: _Metaph._ xii. 4.]\n\n[Footnote 12: _Hist. Ind. Sc._ b. i. c. iii. sect. 2.]\n\n[Footnote 13: _Analyt. Prior._ i. 30.]\n\n[Footnote 14: _Analyt. Post._ i. 18.]\n\n[Footnote 15: _Analyt. Prior._ ii. 23, \u03c0\u03b5\u03c1\u1f76 \u03c4\u1fc6\u03c2 \u1f10\u03c0\u03b1\u03b3\u03c9\u03b3\u1fc6\u03c2.]\n\n[Footnote 16: _Analyt. Post._ ii. 19.]\n\n[Footnote 17: But the best reading seems to be not \u1f14\u03bd \u03c4\u03b9 but \u1f14\u03c4\u03b9:\nand the clause must be rendered \"both to perceive and to retain the\nperception in the mind.\" This correction does not disturb the general\nsense of the passage, that the first principles of science are obtained\nby finding the One in the Many.]\n\n[Footnote 18: _Analyt. Post._ i. 34.]\n\n[Footnote 19: _Ibid._ ii. 19.]\n\n\n\n\nCHAPTER V.\n\nADDITIONAL REMARKS ON ARISTOTLE.\n\n\n1. One of the most conspicuous points in Aristotle's doctrines as\nbearing upon the philosophy of Science is his account of that mode of\nattaining truth which is called _Induction_; for we are accustomed\nto consider Induction as the process by which our Sciences have been\nformed; and we call them collectively the _Inductive Sciences_.\nAristotle often speaks of Induction, as for instance, when he says that\nSocrates introduced the frequent use of it. But the cardinal passage\non this subject is in his _Analytics_, in which he compares Syllogism\nand Induction as two modes of drawing conclusions[20]. He there says\nthat all belief arises either from Syllogism or from Induction: and\nadds that Induction is, when by means of one extreme term we infer\nthe other extreme to be true of the middle term. The example which\nhe gives is this: knowing that particular animals are long-lived, as\nelephant, horse, mule; and finding that these animals agree in having\nno gall-bladder; we infer, by _Induction_, that _all_ animals which\nhave no gall-bladder are long-lived. This may be done, he says, if the\nmiddle and the second extreme are convertible: as the following formal\nstatement may show.\n\n  Elephant, horse, mule, &c. are long-lived.\n  Elephant, horse, mule, &c. are all gall-less.\n\nIf we might convert this proposition, and say\n\nAll gall-less animals are as elephant, horse, mule, &c.:\n\nwe might infer _syllogistically_ that\n\nAll gall-less animals are long-lived.\n\nAnd though we cannot infer this syllogistically, we infer it by\nInduction, when we have a sufficient amount of instances[21].\n\nI have already elsewhere given this account of Induction, as a process\nemployed in the formation of our knowledge[22]. What I have now to\nremark concerning Aristotle is, that it does not appear to have\noccurred to him, that in establishing such a proposition as that which\nhe gives as his instance, the main difficulty is the _discovery_ of\na _middle term_ which will allow us to frame such a proposition as\nwe need. The zoologist who wanted to know what kind of animals are\nlong-lived, might guess long before he guessed that the absence of the\ngall-bladder supplied the requisite middle term; (if the proposition\nwere true; which it is not.) And in like manner in other cases, it\nis difficult to find a middle term, which enables us to collect a\nproposition by Induction. And herein consists the imperfection of his\nview of the subject; which considers the main point to be the proof\nof the proposition when the conceptions are _given_, whereas the main\npoint really is, the _discovery_ of conceptions which will make a true\nproposition possible.\n\n\n2. Since the main characteristic of the steps which have occurred in\nthe formation of the physical sciences, is not merely that they are\npropositions collected by Induction, but by the introduction of a _new_\nconception; it has been suggested that it is not a characteristic\ndesignation of these Sciences to call them _Inductive Sciences_. Almost\nevery discovery involves in it the introduction of a new conception,\nas the element of a new proposition; and the novelty of the conception\nis more characteristic of the stages of discovery than the inductive\napplication of it. Hence as bearing upon the Philosophy of Discovery,\nthe statements of Aristotle concerning Induction, though acute and\nvaluable, are not so valuable as they might seem. Even Francis Bacon,\nit has been asserted, erred in the same way (and of course with less\nexcuse) in asserting Induction, of a certain kind, to be the great\ninstrument for the promotion of knowledge, and in overlooking the\nnecessity of the _Invention_ which gives Induction its value.\n\n\n3. The invention or discovery of a conception by which many facts\nof observation are conjoined so as to make them the materials of a\nproposition, is called in Plato, as we have seen, _finding the One in\nthe Many_.\n\nIn the passage quoted from the _Later Analytics_, Aristotle uses the\nsame expression, and speaks very justly respecting the formation of\nknowledge. Indeed the _Titles_ of the chapters of this and many parts\nof Aristotle's works would lead us to expect just such a Philosophy\nof Discovery as is the object of our study at present. Thus we have,\n_Anal. Post._ B. II. chap. 13: \"How we are to hunt (\u03b8\u03b7\u03c1\u03b5\u03cd\u03b5\u03b9\u03bd) the\npredications of a Definition.\" Chap. 14: \"Precepts for the invention\nof Problems and of a Middle Term:\" and the like. But when we come to\nread these chapters, they contain little that is of value, and resolve\nthemselves mostly into permutations of Aristotle's logical phraseology.\n\n\n4. The part of the Aristotelian philosophy which has most permanently\nretained its place in modern Sciences is a part of which a use has been\nmade quite different from that which was originally contemplated. The\n\"Five words\" which are explained in the Introduction to Aristotle's\n_Categories_: namely, the words _Genus_, _Species_, _Difference_,\n_Property_, _Accident_, were introduced mainly that they might be used\nin the propositions of which Syllogisms consist, and might thus be the\nelements of reasoning. But it has so happened that these words are\nrarely used in Sciences of Reasoning, but are abundantly and commonly\nused in the Sciences of Classification, as I have explained in\nspeaking of the Classificatory Sciences[23].\n\n\n5. Of Aristotle's actual contributions to the Physical Sciences I have\nspoken in the History of those Sciences[24]. I have[25] stated that\nhe conceived the globular form of the earth so clearly and gave so\nforcibly the arguments for that doctrine, that we may look upon him as\nthe most effective teacher of it. Also in the Appendix to that History,\npublished in the third edition, I have given Aristotle's account of the\nRainbow, as a further example of his industrious accumulation of facts,\nand of his liability to error in his facts.\n\n\n6. We do not find Aristotle so much impressed as we might have expected\nby that great monument of Grecian ingenuity, the theory of epicycles\nand excentrics which his predecessor Plato urged so strongly upon the\nattention of his contemporaries. Aristotle proves, as I have said,\nthe globular form of the earth by good and sufficient arguments. He\nalso proves by arguments which seem to him quite conclusive[26], that\nthe earth is in the center of the universe, and immoveable. As to the\nmotions of the rest of the planets, he says little. The questions\nof their order, and their distances, and the like, belong, he says,\nto Astrology[27]. He remarks only that the revolution of the heaven\nitself, the outermost revolution, is simple and the quickest of all:\nthat the revolutions of the others are slower, each moving in a\ndirection opposite to the heaven in its own circle: and that it is\nreasonable that those which are nearest to the first revolution should\ntake the longest time in describing their own circle, and those that\nare furthest off, the least time, and the intermediate ones in the\norder of their distances, \"as also the mathematicians show.\"\n\nIn the _Metaphysics_[28] he enumerates the circular movements which\nhad been introduced by the astronomers Eudoxus and Calippus for the\nexplanation of the phenomena presented by the sun, moon and planets.\nThese, he says, amount to fifty-five; and this, he says, must be the\nnumber of essences and principles which exist in the universe.\n\n\n7. In the Sciences of Classification, and especially in the\nclassification of animals, higher claims have been made for Aristotle,\nwhich I have discussed in the History[29]. I have there attempted to\nshow that Aristotle's classification, inasmuch as it enumerates all\nthe parts of animals, may be said to contain the _materials_ of every\nsubsequent classification: but that it cannot be said to anticipate\nany modern system, because the different grades of classification are\nnot made _subordinate_ to one another as a _system_ of classification\nrequires. I have the satisfaction of finding Mr. Owen agreeing with me\nin these views[30].\n\n\n8. Francis Bacon's criticism on Aristotle which I have quoted in the\nAppendix to the History[31], is severe, and I think evidently the\nresult of prejudice. He disparages Aristotle in comparison with the\nother philosophers of Greece. 'Their systems,' he says, 'had some\nsavour of experience, and nature, and bodily things; while the Physics\nof Aristotle, in general, sound only of Logical Terms.\n\n'Nor let anyone be moved by this: that in his books _Of Animals_,\nand in his _Problems_, and in others of his tracts, there is often a\nquoting of experiments. For he had made up his mind beforehand; and did\nnot consult experience in order to make right propositions and axioms,\nbut when he had settled his system to his will, he twisted experience\nround and made her bend to his system.'\n\nI do not think that this can be said with any truth. I know no\ninstances in which Aristotle has twisted experience round, and made\nher bend to his system. In his _Problems_, he is so far from giving\ndogmatical solutions of the questions proposed, that in most cases, he\npropounds two or three solutions as mere suggestions and conjectures.\nAnd both in his History of Animals, as I have said, and in others of\nhis works, the want of system gives them an incoherent and tumultuary\ncharacter, which even a false system would have advantageously removed;\nfor, as I have said elsewhere, it is easier to translate a false system\ninto a true one, than to introduce system into a mass of confusion.\n\n\n9. It is curious that a fundamental error into which Aristotle fell in\nhis view of the conditions which determine the formation of Science\nis very nearly the same as one of Francis Bacon's leading mistakes.\nAristotle says, that Science consists in knowing the _causes_ of\nthings, as Bacon aims at acquiring a knowledge of the _forms_ or\n_essences_ of things and their qualities. But the history of all the\nsciences teaches us that sciences do not begin with such knowledge, and\nthat in few cases only do they ever attain to it. Sciences begin by a\nknowledge of the _laws_ of _phenomena_, and proceed by the discovery\nof the scientific ideas by which the phenomena are colligated, as I\nhave shown in other works[32]. The discovery of causes is not beyond\nthe human powers, as some have taught. Those who thus speak disregard\nthe lessons taught by the history of Physical Astronomy, of Geology, of\nPhysical Optics, Thermotics and other sciences. But the discovery of\ncauses, and of the essential forms of qualities, is a triumph reserved\nfor the later stages of each Science, when the knowledge of the laws of\nphenomena has already made great progress. It was not to be expected\nthat Aristotle would discern this truth, when, as yet, there was no\nScience extant in which it had been exemplified. Yet in Astronomy, the\ntheory of epicycles and excentrics had immense value, and even has\nstill, as representing the laws of phenomena; while the attempt to find\nin it, as Aristotle wished to do, the ultimate causes of the motions\nof the universe, could only mislead. The Aristotelian maxim, which\nsounds so plausible, and has been so generally accepted, that \"to know\ntruly is to know the causes of things,\" is a bad guide in scientific\nresearch. Instead of it we might substitute this: that \"though we may\naspire to know at last _why_ things are, we must be content for a long\ntime with knowing _how_ they are.\"\n\n\n10. Hence if we are asked whether Plato or Aristotle had the truer\nviews of the nature and property of Science, we must give the\npreference to Plato; for though his notion of a real Intelligible\nWorld, of which the Visible world was a fleeting and changeable shadow,\nwas extravagant, yet it led him to seek to determine the forms of the\nIntelligible Things, which are really the laws of visible phenomena;\nwhile Aristotle was led to pass lightly over such laws, because they\ndid not at once reveal the causes which produced the phenomena.\n\n\n11. Aristotle, throughout his works, takes numerous occasions to\nargue against Plato's doctrine of Ideas. Yet these Ideas, so far as\nthey were the Intelligible Forms of Visible Things, were really fit\nobjects of philosophical research; and the search after them had a\npowerful influence in promoting the progress of Science. And we may\nsee in the effect of this search the answer to many of Aristotle's\nstrongest arguments. For instance, Aristotle says that Plato, by way of\nexplaining things, adds to them as many Ideas, and that this is just\nas if a man having to reckon a large number, were to begin by adding\nto it another large number. It is plain that to this we may reply,\nthat the adopting the Ideas of Cycles, along with the motions of the\nPlanets, does really explain the motions; and that the Cycles are not\nsimply added to the phenomena, but include and supersede the phenomena:\na finite number of Cycles include and represent an infinite number of\nseparate phenomena.\n\nTo Aristotle's argument that Ideas cannot be the Causes or Principles\nof Things, we should reply, that though they cannot be this, they may\nnevertheless be, and must be, the Conditions and Principles of our\nKnowledge, which is what we want them to be.\n\nI have given an account of the main features of Aristotle's philosophy,\nso far as it concerns the Physical Sciences, in the History of the\nInductive Sciences, Book I.\n\n\nFOOTNOTES:\n\n[Footnote 20: _Analyt. Prior._ ii. 25.]\n\n[Footnote 21: See on this subject Appendix, Essay D.]\n\n[Footnote 22: See the chapter on Certain Characteristics of Scientific\nInduction in the _Phil. Ind. Sc._ or in the _Nov. Org. Renov._]\n\n[Footnote 23: _Phil. Ind. Sc._ b. viii. c. i. art. 11, or _Hist. Sc.\nId._ b. viii.]\n\n[Footnote 24: B. i. c. xi. sect. 2.]\n\n[Footnote 25: B. iii. c. i. sect. 9.]\n\n[Footnote 26: _De C\u00e6lo_, ii. 13.]\n\n[Footnote 27: _Ibid._ ii. 10.]\n\n[Footnote 28: xii. 8.]\n\n[Footnote 29: B. xvi. c. vi.]\n\n[Footnote 30: _On the Classification of Mammalia, &c.: a Lecture\ndelivered at Cambridge_, May 10, 1859, p. 3.]\n\n[Footnote 31: B. i. c. xi.]\n\n[Footnote 32: _History of Scientific Ideas_, and _Novum Organum\nRenovatum_.]\n\n\n\n\nCHAPTER VI.\n\nTHE LATER GREEKS.\n\n\nThus while Plato was disposed to seek the essence of our knowledge\nin Ideas alone, Aristotle, slighting this source of truth, looked to\nExperience as the beginning of Science; and he attempted to obtain, by\ndivision and deduction, all that Experience did not immediately supply.\nAnd thus, with these two great names, began that struggle of opposite\nopinions which has ever since that time agitated the speculative\nworld, as men have urged the claims of Ideas or of Experience to our\nrespect, and as alternately each of these elements of knowledge has\nbeen elevated above its due place, while the other has been unduly\ndepressed. We shall see the successive turns of this balanced struggle\nin the remaining portions of this review.\n\nBut we may observe that practically the influence of Plato predominated\nrather than that of Aristotle, in the remaining part of the history\nof ancient philosophy. It was, indeed, an habitual subject of dispute\namong men of letters, whether the sources of true knowledge are\nto be found in the Senses or in the Mind; the Epicureans taking\none side of this alternative, and the Academics another, while the\nStoics in a certain manner included both elements in their view. But\nnone of these sects showed their persuasion that the materials of\nknowledge were to be found in the domain of Sense, by seeking them\nthere. No one appears to have thought of following the example of\nAristotle, and gathering together a store of observed facts. We may\nexcept, perhaps, assertions belonging to some provinces of Natural\nHistory, which were collected by various writers: but in these, the\nmixed character of the statements, the want of discrimination in\nthe estimate of evidence, the credulity and love of the marvellous\nwhich the authors for the most part displayed, showed that instead\nof improving upon the example of Aristotle, they were wandering\nfurther and further from the path of real knowledge. And while they\nthus collected, with so little judgment, such statements as offered\nthemselves, it hardly appears to have occurred to any one to enlarge\nthe stores of observation by the aid of experiment; and to learn\nwhat the laws of nature were, by trying what were their results in\nparticular cases. They used no instruments for obtaining an insight\ninto the constitution of the universe, except logical distinctions\nand discussions; and proceeded as if the phenomena familiar to their\npredecessors must contain all that was needed as a basis for natural\nphilosophy. By thus contenting themselves with the facts which the\nearlier philosophers had contemplated, they were led also to confine\nthemselves to the ideas which those philosophers had put forth. For\nall the most remarkable alternatives of hypothesis, so far as they\ncould be constructed with a slight and common knowledge of phenomena,\nhad been promulgated by the acute and profound thinkers who gave the\nfirst impulse to philosophy: and it was not given to man to add much\nto the original inventions of _their_ minds till he had undergone\nanew a long discipline of observation, and of thought employed upon\nobservation. Thus the later authors of the Greek Schools became little\nbetter than commentators on the earlier; and the commonplaces with\nwhich the different schools carried on their debates,--the constantly\nrecurring argument, with its known attendant answer,--the distinctions\ndrawn finer and finer and leading to nothing,--render the speculations\nof those times a _scholastic_ philosophy, in the same sense in which\nwe employ the term when we speak of the labours of the middle ages. It\nwill be understood that I now refer to that which is here my subject,\nthe opinions concerning our knowledge of nature, and the methods in\nuse for the purpose of obtaining such knowledge. Whether the moral\nspeculations of the ancient world were of the same stationary kind,\ngoing their round in a limited circle, like their metaphysics and\nphysics, must be considered on some other occasion. [33] Mr. Grote,\nin his very interesting discussion of Socrates's teaching, notices\nalso[34] the teaching of Hippocrates, which he conceives to have in\none respect the same tendency as the philosophy of Socrates; namely,\nto turn away from the vague aggregate of doctrines and guesses which\nconstituted the Physical Philosophy of that time, and to pursue instead\na special and more practical course of inquiry: Hippocrates selecting\nMedicine and Socrates selecting Ethics. By this limitation of their\nsubject, they avoided some of the errors of their predecessors. For,\nas Mr. Grote has also remarked, \"the earlier speculators, Anaxagoras,\nEmpedocles, Democritus, the Pythagoreans, all had still present to\ntheir minds the vast and undivided problems which have been transmitted\ndown from the old poets; bending their minds to the invention of some\nsystem which would explain them all at once, or assist the imagination\nin conceiving both how the Kosmos first began and how it continued to\nmove on.\" There could be no better remedy for this ambitious error of\nthe human mind than to have a definite subject of study, such as the\ndiseases and the health of the human body. Accordingly, we see that the\nstudy of medicine did draw its cultivators away from this ancient but\nunprofitable field. Hippocrates[35] condemns those who, as Empedocles,\nset themselves to make out what man was from the beginning, how he\nbegan first to exist, and in what manner he was constructed. This is,\nhe says, no part of medicine. In like manner he blames and refutes\nthose who make some simple element, Hot, or Cold, or Moist, or Dry, the\ncause of diseases, and give medical precepts professing to be founded\non this hypothesis.\n\nThese passages are marked by the prudence which practical study\nsuggests to a calm and clear-sighted man. They can hardly be said to\nhave opened the way to a Science of Medicine; for in the sense in which\nwe here use the word _Science_, namely, a collection of general truths\ninferred from facts by successive discoverers, we have even yet no\nScience of Medicine. The question with regard to the number and nature\nof the Elements of which bodies are composed began to be agitated, as\nwe have seen, at a very early period of Greek philosophy, and continued\nlong to be regarded as a chief point of physiological doctrine. In\nGalen's work we have a treatise entitled, _On the Elements according\nto Hippocrates_; and the writer explains[36] that though Hippocrates\nhas not written any work with the title _On the Elements_, yet that\nhe has in his _Treatise on the Nature of Man_ shown his opinion on\nthat subject. That the doctrine of the Four Elements, Hot, Cold,\nMoist, Dry, subsisted long in the schools, we have evidence in Galen.\nHe tells us[37] that when he was a student of nineteen years old a\nteacher urged this lore upon him, and regarded him as very contentious\nand perverse, because he offered objections to it. His account of the\nDialogue between him and the teacher is curious. But in Hippocrates the\ndoctrine of these four elements is replaced, in a great measure, by the\ndoctrine of the Four Humours of which the human body is constituted;\nnamely, Blood, Phlegm, Yellow Bile and Black Bile. Galen dwells with\nemphasis upon Hippocrates's proof that there must be more than one such\nelement[38].\n\n\"What,\" he asks, \"is the method of finding the Elements of bodies?\nThere can, in my opinion, be no other than that which was introduced by\nHippocrates; namely, we must inquire whether there be only one element,\neverywhere the same in kind, or whether there are more than one,\nvarious and unlike each other. And if the Element be not one only, but\nseveral, various and dissimilar, we must inquire in the second place,\nhow many elements there are, and what, and of what kind they are, and\nhow related in their association.\n\n\"Now that the First Element is not one only of which both our bodies\nand those of all other creatures were produced, Hippocrates shows\nfrom these considerations. And it is better first to put down his own\nexpressions and then to expound them. 'I assert that if man consisted\nof one element only he could not fall sick; for there would be nothing\nwhich could derange his health, if he were all of one Element.'\"\n\nThe doctrine of One Element did not prevail much after the time of\nHippocrates: the doctrine of Four Elements continued, as I have said,\nlong to hold possession of the Schools, but does not appear as an\nimportant part of the doctrine of Hippocrates. The doctrine of the Four\nHumours (Blood, Phlegm, Yellow Bile and Black Bile) is more peculiarly\nhis, and long retained its place as a principle of physiological\nScience.\n\nBut we are here not so much concerned with his discoveries in medicine\nas with his views respecting the method of acquiring sound knowledge,\nand in this respect, as has been said, he recommends by his practice\na prudent limitation of the field of inquiry, a rejection of wide,\nambitious, general assertions, and a practical study of his proper\nfield.\n\nIn ascribing these merits to Hippocrates's medical speculations as\nto the ethical speculations of his contemporary Socrates, we assign\nconsiderable philosophical value to Hippocrates, no less than to\nSocrates. These merits were at that time the great virtues of physical\nas well as of ethical philosophy. But, as Mr. Grote well observes, the\ncommunity of character which then subsisted between the physical and\nethical speculations prevailing at that time, ceased to obtain in later\ntimes. Indeed, it ceased to exist just at that time, in consequence of\nthe establishment of scientific astronomy by the exertions of Plato\nand his contemporaries. From that time the Common Sense (as we call it)\nof a man like Socrates, though it might be a good guide in ethics, was\nnot a good guide in physics. I have shown elsewhere[39] how the Common\nSense of Socrates was worthless in matters of astronomy. From that time\none of the great intellectual lessons was, that in order to understand\nthe external world, we must indeed observe carefully, but we must also\nguess boldly. Discovery here required an inventive mind like Plato's\nto deal with and arrange new and varied facts. But in ethics all the\nfacts were old and familiar, and the generalizations of language by\nwhich they were grouped as Virtues and Vices, and the like, were common\nand well-known words. Here was no room for invention; and thus in the\nethical speculations of Socrates or of any other moral teacher, we are\nnot to look for any contributions to the Philosophy of Discovery.\n\nNor do I find anything on this subject among later Greek writers,\nbeyond the commendation of such intellectual virtues as Hippocrates and\nGalen, and other medical writers, schooled by the practice of their\nart, enjoined and praised. But before we quit the ancients I will point\nout some peculiarities which may be noticed in the Roman disciples of\nthe Greek philosophy.\n\n\nFOOTNOTES:\n\n[Footnote 33: The remainder of this chapter is new in the present\nedition.]\n\n[Footnote 34: _Hist. of Greece_, Part ii. chap. 68.]\n\n[Footnote 35: _De Antiqua Medicina_, c. 20.]\n\n[Footnote 36: Lib. i. c. 9.]\n\n[Footnote 37: _De Elem._ i. 6.]\n\n[Footnote 38: In former editions I have not done justice to this\npassage.]\n\n[Footnote 39: _Hist. Ind. Sc._ Addition to Introduction in Third\nEdition.]\n\n\n\n\nCHAPTER VII.\n\nTHE ROMANS.\n\n\nThe Romans had no philosophy but that which they borrowed from the\nGreeks; and what they thus received, they hardly made entirely their\nown. The vast and profound question of which we have been speaking,\nthe relation between Existence and our Knowledge of what exists, they\nnever appear to have fathomed, even so far as to discern how wide and\ndeep it is. In the development of the ideas by which nature is to be\nunderstood, they went no further than their Greek masters had gone,\nnor indeed was more to be looked for. And in the practical habit of\naccumulating observed facts as materials for knowledge, they were much\nless discriminating and more credulous than their Greek predecessors.\nThe descent from Aristotle to Pliny, in the judiciousness of the\nauthors and the value of their collections of facts, is immense.\n\nSince the Romans were thus servile followers of their Greek teachers,\nand little acquainted with any example of new truths collected from\nthe world around them, it was not to be expected that they could have\nany just conception of that long and magnificent ascent from one set\nof truths to others of higher order and wider compass, which the\nhistory of science began to exhibit when the human mind recovered\nits progressive habits. Yet some dim presentiment of the splendid\ncareer thus destined for the intellect of man appears from time to\ntime to have arisen in their minds. Perhaps the circumstance which\nmost powerfully contributed to suggest this vision, was the vast\nintellectual progress which they were themselves conscious of having\nmade, through the introduction of the Greek philosophy; and to this\nmay be added, perhaps, some other features of national character. Their\ntemper was too stubborn to acquiesce in the absolute authority of the\nGreek philosophy, although their minds were not inventive enough to\nestablish a rival by its side. And the wonderful progress of their\npolitical power had given them a hope in the progress of man which\nthe Greeks never possessed. The Roman, as he believed the fortune of\nhis State to be destined for eternity, believed also in the immortal\ndestiny and endless advance of that Intellectual Republic of which he\nhad been admitted a denizen.\n\nIt is easy to find examples of such feelings as I have endeavoured\nto describe. The enthusiasm with which Lucretius and Virgil speak of\nphysical knowledge, manifestly arises in a great measure from the\ndelight which they had felt in becoming acquainted with the Greek\ntheories.\n\n    Me vero primum dulces ante omnia Mus\u00e6\n    Quarum sacra fero ingenti perculsus amore\n    Accipiant, c\u0153lique vias et sidera monstrent,\n    Defectus Solis varios, Lun\u00e6que labores!...\n    Felix qui potuit rerum cognoscere causas!\n\n    Ye sacred Muses, with whose beauty fir'd,\n    My soul is ravisht and my brain inspir'd:\n    Whose Priest I am, whose holy fillets wear,\n    Would you your Poet's first petition hear,\n    Give me the ways of wand'ring stars to know,\n    The depth of Heaven above and Earth below;\n    Teach me the various labours of the Moon,\n    And whence proceed th' eclipses of the Sun;\n    Why flowing Tides prevail upon the main,\n    And in what dark abyss they shrink again;\n    What shakes the solid Earth; what cause delays\n    The Summer Nights; and shortens Winter Days....\n      Happy the man who, studying Nature's Laws,\n    Through known effects can trace the secret cause!\n\nOvid[40] expresses a similar feeling.\n\n    Felices animos quibus h\u00e6c cognoscere primis\n      Inque domos superas scandere cura fuit!...\n    Admovere oculis distantia sidera nostris\n      \u00c6theraque ingenio supposuere suo.\n    Sic petitur c\u0153lum: non ut ferat Ossam Olympus\n      Summaque Peliacus sidera tanget apex.\n\n    Thrice happy souls! to whom 'twas given to rise\n    To truths like these, and scale the spangled skies!\n    Far distant stars to clearest view they brought,\n    And girdled ether with their chain of thought.\n    So heaven is reached:--not as of old they tried\n    By mountains piled on mountains in their pride.\n\n\nAnd from the whole tenour of these and similar passages, it is evident\nthat the intellectual pleasure which arises from our first introduction\nto a beautiful physical theory had a main share in producing this\nenthusiasm at the contemplation of the victories of science; although\nundoubtedly the moral philosophy, which was never separated from the\nnatural philosophy, and the triumph over superstitious fears, which\na knowledge of nature was supposed to furnish, added warmth to the\nfeeling of exultation.\n\nWe may trace a similar impression in the ardent expressions which\nPliny[41] makes use of in speaking of the early astronomers, and which\nwe have quoted in the _History_. \"Great men! elevated above the common\nstandard of human nature, by discovering the laws which celestial\noccurrences obey, and by freeing the wretched mind of man from the\nfears which eclipses inspired.\"\n\nThis exulting contemplation of what science had done, naturally led the\nmind to an anticipation of further achievements still to be performed.\nExpressions of this feeling occur in Seneca, and are of the most\nremarkable kind, as the following example will show[42]:\n\n\"Why do we wonder that comets, so rare a phenomenon, have not yet had\ntheir laws assigned?--that we should know so little of their beginning\nand their end, when their recurrence is at wide intervals? It is not\nyet fifteen hundred years since Greece,\n\n  Stellis numeros et nomina fecit,\n\n'reckoned the stars, and gave them names.' There are still many nations\nwhich are acquainted with the heavens by sight only; which do not yet\nknow why the moon disappears, why she is eclipsed. It is but lately\nthat among us philosophy has reduced these matters to a certainty. The\nday shall come when the course of time and the labour of a maturer age\nshall bring to light what is yet concealed. One generation, even if it\ndevoted itself to the skies, is not enough for researches so extensive.\nHow then can it be so, when we divide this scanty allowance of years\ninto no equal shares between our studies and our vices? These things\nthen must be explained by a long succession of inquiries. We have but\njust begun to know how arise the morning and evening appearances,\nthe stations, the progressions, and the retrogradations of the fixed\nstars which put themselves in our way;--which appearing perpetually\nin another and another place compel us to be curious. Some one will\nhereafter demonstrate in what region the comets wander; why they move\nso far asunder from the rest; of what size and nature they are. Let\nus be content with what we have discovered: let posterity contribute\nits share to truth.\" Again he adds[43] in the same strain: \"Let us\nnot wonder that what lies so deep is brought out so slowly. How many\nanimals have become known for the first time in this age! And the\nmembers of future generations shall know many of which we are ignorant.\nMany things are reserved for ages to come, when our memory shall\nhave passed away. The world would be a small thing indeed, if it did\nnot contain matter of inquiry _for_ all the world. Eleusis reserves\nsomething for the second visit of the worshipper. _So too Nature\ndoes not at once disclose all_ HER _mysteries_. We think ourselves\ninitiated; we are but in the vestibule. The arcana are not thrown open\nwithout distinction and without reserve. This age will see some things;\nthat which comes after us, others.\"\n\nWhile we admire the happy coincidence of these conjectures with the\nsoundest views which the history of science teaches us, we must not\nforget that they are merely conjectures, suggested by very vague\nimpressions, and associated with very scanty conceptions of the laws\nof nature. Seneca's _Natural Questions_, from which the above extract\nis taken, contains a series of dissertations on various subjects of\nNatural Philosophy; as Meteors, Rainbows, Lightnings, Springs, Rivers,\nSnow, Hail, Rain, Wind, Earthquakes and Comets. In the whole of these\ndissertations, the statements are loose, and the explanations of little\nor no value. Perhaps it may be worth our while to notice a case in\nwhich he refers to an observation of his own, although his conclusion\nfrom it be erroneous. He is arguing[44] against the opinion that\nSprings arise from the water which falls in rain. \"In the first place,\"\nhe says, \"I, a very diligent digger in my vineyard, affirm that no rain\nis so heavy as to moisten the earth to the depth of more than ten feet.\nAll the moisture is consumed in this outer crust, and descends not to\nthe lower part.\" We have here something of the nature of an experiment;\nand indeed, as we may readily conceive, the instinct which impels man\nto seek truth by experiment can never be altogether extinguished.\nSeneca's experiment was deprived of its value by the indistinctness of\nhis ideas, which led him to rest in the crude conception of the water\nbeing \"consumed\" in the superficial crust of the earth.\n\nIt is unnecessary to pursue further the reasonings of the Romans on\nsuch subjects, and we now proceed to the ages which succeeded the fall\nof their empire.\n\n\nFOOTNOTES:\n\n[Footnote 40: Lib. i. _Fast._]\n\n[Footnote 41: _Hist. Nat._ i. 75.]\n\n[Footnote 42: _Qu\u00e6st. Nat._ vii. 25.]\n\n[Footnote 43: _Qu\u00e6st. Nat._ vii. 30, 31.]\n\n[Footnote 44: _Ibid._ iii. 7.]\n\n\n\n\nCHAPTER VIII.\n\nARABIAN PHILOSOPHERS.\n\n\nI have noticed certain additions to Physical Science made by the\nArabians; namely, in Astronomy[45]. The discovery of the motion of\nthe Sun's Apogee by Albategnius, and the discovery of the Moon's\n_Variation_ by Aboul-Wefa; and in Optics[46] the assertion of Alhazen\nthat the angle of refraction is not proportional to the angle of\nincidence, as Ptolemy had supposed: and certain steps in the philosophy\nof vision. We must also suppose, as the Arabic word _alkali_ reminds\nus, that the Arabians contributed to lay the foundations of chemistry.\nThe question which we have here to ask is, whether the Arabians made\nany steps beyond their predecessors in the philosophy of discovery.\nAnd to this question, I conceive the answer must be this: that among\nthem as among the Greeks, those who practically observed nature, and\nespecially those who made discoveries in Science, must have had a\npractical acquaintance with some of the maxims which are exemplified\nin the formation of Science. To discover that the Apogee of the Sun\nwas 17 degrees distant from the point where Ptolemy had placed it,\nAlbategnius made careful observations, and referred them to the theory\nof the eccentric, so as to verify or correct that theory. And when, in\nthe eleventh century, Arzachel found the Apogee to be less advanced\nthan Albategnius had found it, he proceeded again to correct the\ntheory by introducing a new movement of the equinoctial points, which\nwas called the _Trepidation_. It appeared afterwards, however, that,\nin doing this, he had had too much confidence in the observations of\nhis predecessors, and that no such movement as the Trepidation really\nexisted. In like manner to correct Ptolemy's law of refraction, Alhazen\nhad recourse to experiment: but he did not put his experiments in the\nform of a Table, as Ptolemy had done. If he had done this, he might\npossibly have discovered the law of sines, which Snell afterwards\ndiscovered.\n\nBut though the Arabian philosophers thus, in some cases, observed\nfacts, and referred those facts to general mathematical laws, it does\nnot appear that they were led to put in any new or striking general\nform such maxims as this: That the progress of Science consists in the\nexact observation of facts and in colligating them by ideas. Those of\nthem who were dissatisfied with the existing philosophy as barren and\nuseless (for instance Algazel[47]), were led to point at the faults\nand contradictions of that philosophy, but did not attempt, so far\nas I know, to substitute for it anything better. If they rejected\nAristotle's _Organon_, they did not attempt to construct a new Organon\nfor themselves.\n\nIndeed they do not appear even to have had sufficient confidence in the\nreal truth of the astronomical theories which they had adopted from the\nGreeks, always to correct and extend those where their observations\nshowed that they required correction and extension. Sometimes they did\nthis, but not generally enough. When Arzachel found by observation\nthe Apogee of the Sun to be situated too far back, he ventured to\ncorrect Ptolemy's statement of its motion. But when Aboul-Wefa had\nreally discovered the _Variation_ of the Moon's motion, he did not\nexpress it by means of an epicycle. If he had done so, he would have\nmade it unnecessary for Tycho Brahe at a later period to make the same\ndiscovery.\n\nThe moral of this incident is the same moral which we have perpetually\nto note as taught us at every step by the history of Science:--namely,\nthe necessity of constant, careful and exact observation of Facts; and\nthe advantage of devising a Theory, (even if it have to be afterwards\nrejected,) by which the Facts shall be bound together into a coherent\nwhole.\n\nFOOTNOTES:\n\n[Footnote 45: _Hist. Ind. Sc._ b. iii. c. iv. sect. 8.]\n\n[Footnote 46: _Ibid._ b. ix. c. ii.]\n\n[Footnote 47: See _Hist. Ind. Sc._ b. iv. c. i.]\n\n\n\n\nCHAPTER IX.\n\nTHE SCHOOLMEN OF THE MIDDLE AGES.\n\n\nIn the _History of the Sciences_ I have devoted a Book to the state\nof Science in the middle ages, and have endeavoured to analyse the\nintellectual defects of that period. Among the characteristic features\nof the human mind during those times, I have noticed Indistinctness of\nIdeas, a Commentatorial Spirit, Mysticism, and Dogmatism. The account\nthere given of this portion of the history of man belongs, in reality,\nrather to the History of Ideas than to the History of Progressive\nScience. For, as we have there remarked, theoretical Science was,\nduring the period of which we speak, almost entirely stationary; and\nthe investigation of the causes of such a state of things may be\nconsidered as a part of that review in which we are now engaged, of the\nvicissitudes of man's acquaintance with the methods of discovery. But\nwhen we offered to the world a history of science, to leave so large a\nchasm unexplained, would have made the series of events seem defective\nand broken; and the survey of the Middle Ages was therefore inserted.\nI would beg to refer to that portion of the former work the reader who\nwishes for information in addition to what is here given.\n\nThe Indistinctness of Ideas and the Commentatorial Disposition of those\nages have already been here brought under our notice. Viewed with\nreference to the opposition between Experience and Ideas, on which\npoint, as we have said, the succession of opinions in a great measure\nturns, it is clear that the commentatorial method belongs to the ideal\nside of the question: for the commentator seeks for such knowledge\nas he values, by analysing and illustrating what his author has said;\nand, content with this material of speculation, does not desire to\nadd to it new stores of experience and observation. And with regard\nto the two other features in the character which we gave to those\nages, we may observe that Dogmatism demands for philosophical theories\nthe submission of mind, due to those revealed religious doctrines\nwhich are to guide our conduct and direct our hopes: while Mysticism\nelevates ideas into realities, and offers them to us as the objects\nof our religious regard. Thus the Mysticism of the middle ages and\ntheir Dogmatism alike arose from not discriminating the offices of\ntheoretical and practical philosophy. Mysticism claimed for ideas the\ndignity and reality of principles of moral action and religious hope:\nDogmatism imposed theoretical opinions respecting speculative points\nwith the imperative tone of rules of conduct and faith.\n\nIf, however, the opposite claims of theory and practice interfered\nwith the progress of science by the confusion they thus occasioned,\nthey did so far more by drawing men away altogether from mere physical\nspeculations. The Christian religion, with its precepts, its hopes, and\nits promises, became the leading subject of men's thoughts; and the\ngreat active truths thus revealed, and the duties thus enjoined, made\nall inquiries of mere curiosity appear frivolous and unworthy of man.\nThe Fathers of the Church sometimes philosophized ill; but far more\ncommonly they were too intent upon the great lessons which they had to\nteach, respecting man's situation in the eyes of his Heavenly Master,\nto philosophize at all respecting things remote from the business of\nlife and of no importance in man's spiritual concerns.\n\nYet man has his intellectual as well as his spiritual wants. He has\nfaculties which demand systems and reasons, as well as precepts and\npromises. The Christian doctor, who knew so much more than the heathen\nphilosopher respecting the Creator and Governor of the universe, was\nnot long content to know or to teach less, respecting the universe\nitself. While it was still maintained that Theology was the only\nreally important study, Theology was so extended and so fashioned as to\ninclude all other knowledge: and after no long time, the Fathers of the\nChurch themselves became the authors of systems of universal knowledge.\n\nBut when this happened, the commentatorial spirit was still in its\nfull vigour. The learned Christians could not, any more than the\nlater Greeks or the Romans, devise, by the mere force of their own\ninvention, new systems, full, comprehensive, and connected, like those\nof the heroic age of philosophy. The same mental tendencies which led\nmen to look for speculative coherence and completeness in the view of\nthe universe, led them also to admire and dwell upon the splendid and\nacute speculations of the Greeks. They were content to find, in those\nimmortal works, the answers to the questions which their curiosity\nprompted; and to seek what further satisfaction they might require,\nin analysing and unfolding the doctrines promulgated by those great\nmasters of knowledge. Thus the Christian doctors became, as to general\nphilosophy, commentators upon the ancient Greek teachers.\n\nAmong these, they selected Aristotle as their peculiar object of\nadmiration and study. The vast store, both of opinions and facts, which\nhis works contain, his acute distinctions, his cogent reasons in some\nportions of his speculations, his symmetrical systems in almost all,\nnaturally commended him to the minds of subtle and curious men. We\nmay add that Plato, who taught men to contemplate Ideas separate from\nThings, was not so well fitted for general acceptance as Aristotle, who\nrejected this separation. For although the due apprehension of this\nopposition of Ideas and Sensations is a necessary step in the progress\nof true philosophy, it requires a clearer view and a more balanced mind\nthan the common herd of students possess; and Aristotle, who evaded the\nnecessary perplexities in which this antithesis involves us, appeared,\nto the temper of those times, the easier and the plainer guide of the\ntwo.\n\nThe Doctors of the middle ages having thus adopted Aristotle as\ntheir master in philosophy, we shall not be surprised to find them\ndeclaring, after him, that experience is the source of our knowledge\nof the visible world. But though, like the Greeks, they thus talked of\nexperiment, like the Greeks, they showed little disposition to discover\nthe laws of nature by observation of facts. This barren and formal\nrecognition of experience or sensation as one source of knowledge,\nnot being illustrated by a practical study of nature, and by real\ntheoretical truths obtained by such a study, remained ever vague,\nwavering, and empty. Such a mere acknowledgment cannot, in any times,\nancient or modern, be considered as indicating a just apprehension of\nthe true basis and nature of science.\n\nIn imperfectly perceiving how, and how far, experience is the source of\nour knowledge of the external world, the teachers of the middle ages\nwere in the dark; but so, on this subject, have been almost all the\nwriters of all ages, with the exception of those who in recent times\nhave had their minds enlightened by contemplating philosophically the\nmodern progress of science. The opinions of the doctors of the middle\nages on such subjects generally had those of Aristotle for their basis;\nbut the subject was often still further analysed and systematized, with\nan acute and methodical skill hardly inferior to that of Aristotle\nhimself.\n\nThe Stagirite, in the beginning of his _Physics_, had made the\nfollowing remarks. \"In all bodies of doctrine which involve principles,\ncauses, or elements, Science and Knowledge arise from the knowledge\nof these; (for we then consider ourselves to _know_ respecting any\nsubject, when we know its first cause, its first principles, its\nultimate elements.) It is evident, therefore, that in seeking a\nknowledge of nature, we must first know what are its principles. But\nthe course of our knowledge is, from the things which are better known\nand more manifest to us, to the things which are more certain and\nevident in nature. For those things which are most evident in truth,\nare not most evident to us. [And consequently we must advance from\nthings obscure in nature, but manifest to us, towards the things which\nare really in nature more clear and certain.] The things which are\nfirst obvious and apparent to us are complex; and from these we obtain,\nby analysis, principles and elements. We must proceed from universals\nto particulars. For the whole is better known to our senses than the\nparts, and for the same reason, the universal better known than the\nparticular. And thus words signify things in a large and indiscriminate\nway, which is afterwards analysed by definition; as we see that the\nchildren at first call all men _father_, and all women _mother_, but\nafterwards learn to distinguish.\"\n\nThere are various assertions contained in this extract which came to\nbe considered as standard maxims, and which occur constantly in the\nwriters of the middle ages. Such are, for instance, the maxim, \"Ver\u00e8\nscire est per causas scire;\" the remark, that compounds are known\nto us before their parts, and the illustration from the expressions\nused by children. Of the mode in which this subject was treated by\nthe schoolmen, we may judge by looking at passages of Thomas Aquinas\nwhich treat of the subject of the human understanding. In the _Summa\nTheologi\u00e6_, the eighty-fifth Question is _On the manner and order of\nunderstanding_, which subject he considers in eight Articles; and\nthese must, even now, be looked upon as exhibiting many of the most\nimportant and interesting points of the subject. They are, _First_,\nWhether our understanding understands by abstracting ideas (_species_)\nfrom appearances; _Second_, Whether intelligible species abstracted\nfrom appearances are related to our understanding as that _which_ we\nunderstand, or that _by which_ we understand; _Third_, Whether our\nunderstanding does naturally understand universals first; _Fourth_,\nWhether our understanding can understand many things at once; _Fifth_,\nWhether our understanding understands by compounding and dividing;\n_Sixth_, Whether the understanding can err; _Seventh_, Whether one\nperson can understand the same thing better than another; _Eighth_,\nWhether our understanding understands the indivisible sooner than\nthe divisible. And in the discussion of the last point, for example,\nreference is made to the passage of Aristotle which we have already\nquoted. \"It may seem,\" he says, \"that we understand the indivisible\nbefore the divisible; for _the Philosopher_ says that we understand\nand know by knowing principles and elements; but indivisibles are the\nprinciples and elements of divisible things. But to this we may reply,\nthat in our receiving of science, principles and elements are not\nalways first; for sometimes from the sensible effects we go on to the\nknowledge of intelligible principles and causes.\" We see that both the\nobjection and the answer are drawn from Aristotle.\n\nWe find the same close imitation of Aristotle in Albertus Magnus, who,\nlike Aquinas, flourished in the thirteenth century. Albertus, indeed,\nwrote treatises corresponding to almost all those of the Stagirite, and\nwas called the _Ape of Aristotle_. In the beginning of his _Physics_,\nhe says, \"Knowledge does not always begin from that which is first\naccording to the nature of things, but from that of which the knowledge\nis easiest. For the human intellect, on account of its relation to the\nsenses (_propter reflexionem quam habet ad sensum_), collects science\nfrom the senses; and thus it is easier for our knowledge to begin from\nthat which we can apprehend by sense, imagination, and intellect, than\nfrom that which we apprehend by intellect alone.\" We see that he has\nsomewhat systematized what he has borrowed.\n\nThis disposition to dwell upon and systematize the leading doctrines\nof metaphysics assumed a more definite and permanent shape in the\nopposition of the Realists and Nominalists. The opposition involved\nin this controversy is, in fact, that fundamental antithesis of Sense\nand Ideas about which philosophy has always been engaged; and of\nwhich we have marked the manifestation in Plato and Aristotle. The\nquestion, What is the object of our thoughts when we reason concerning\nthe external world? must occur to all speculative minds: and the\ndifficulties of the answer are manifest. We must reply, either that our\nown Ideas, or that Sensible Things, are the elements of our knowledge\nof nature. And then the scruples again occur,--how we have any\n_general_ knowledge if our thoughts are fixed on particular objects;\nand, on the other hand,--how we can attain to any _true_ knowledge of\nnature by contemplating ideas which are not identical with objects in\nnature. The two opposite opinions maintained on this subject were, on\nthe one side,--that our general propositions refer to objects which\nare _real_, though divested of the peculiarities of individuals; and,\non the other side,--that in such propositions, individuals are not\nrepresented by any reality, but bound together by a _name_. These two\nviews were held by the Realists and Nominalists respectively: and thus\nthe Realist manifested the adherence to Ideas, and the Nominalist the\nadherence to the impressions of Sense, which have always existed as\nopposite yet correlative tendencies in man.\n\nThe Realists were the prevailing sect in the Scholastic times: for\nexample, both Thomas Aquinas and Duns Scotus, the _Angelical_ and the\n_Subtle_ Doctor, held this opinion, although opposed to each other\nin many of their leading doctrines on other subjects. And as the\nNominalist, fixing his attention upon sensible objects, is obliged to\nconsider what is the _principle of generalization_, in order that the\npossibility of any general proposition may be conceivable; so on the\nother hand, the Realist, beginning with the contemplation of universal\nideas, is compelled to ask what is the _principle of individuation_, in\norder that he may comprehend the application of general propositions\nin each particular instance. This inquiry concerning the principle of\nindividuation was accordingly a problem which occupied all the leading\nminds among the Schoolmen[48]. It will be apparent from what has\nbeen said, that it is only one of the many forms of the fundamental\nantithesis of the Ideas and the Senses, which we have constantly before\nus in this review.\n\nThe recognition of the derivation of our knowledge, in part at least,\nfrom Experience, though always loose and incomplete, appears often\nto be independent of the Peripatetic traditions. Thus Richard of St.\nVictor, a writer of contemplative theology in the twelfth century,\nsays[49], that \"there are three sources of knowledge, experience,\nreason, faith. Some things we prove by experiment, others we collect\nby reasoning, the certainty of others we hold by believing. And\nwith regard to temporal matters, we obtain our knowledge by actual\nexperience; the other guides belong to divine knowledge.\" Richard\nalso propounds a division of human knowledge which is clearly not\nderived directly from the ancients, and which shows that considerable\nattention must have been paid to such speculations. He begins by laying\ndown clearly and broadly the distinction, which, as we have seen, is\nof primary importance, between _practice_ and _theory_. _Practice_,\nhe says, includes seven mechanical arts; those of the clothier, the\narmourer, the navigator, the hunter, the physician, and the player.\n_Theory_ is threefold, divine, natural, doctrinal; and is thus divided\ninto Theology, Physics, and Mathematics. _Mathematics_, he adds,\ntreats of the invisible _forms_ of visible things. We have seen that\nby many profound thinkers this word _forms_ has been selected as best\nfitted to describe those relations of things which are the subject of\nmathematics. Again, Physics discovers causes from their effects and\neffects from their causes. It would not be easy at the present day to\ngive a better account of the object of physical science. But Richard\nof St. Victor makes this account still more remarkably judicious, by\nthe examples to which he alludes; which are earthquakes, the tides,\nthe virtues of plants, the instincts of animals, the classification of\nminerals, plants and reptiles.\n\n    Unde tremor terris, qu\u00e2 vi maria alta tumescant,\n    Herbarum vires, animos irasque ferarum,\n    Omne genus fruticum, lapidum quoque, reptiliumque.\n\nHe further adds[50], \"Physical science ascends from effects to\ncauses, and descends again from causes to effects.\" This declaration\nFrancis Bacon himself might have adopted. It is true, that Richard\nwould probably have been little able to produce any clear and\ndefinite instances of knowledge, in which this ascent and descent\nwere exemplified; but still the statement, even considered as a\nmere conjectural thought, contains a portion of that sagacity and\ncomprehensive power which we admire so much in Bacon.\n\nRichard of St. Victor, who lived in the twelfth century, thus exhibits\nmore vigour and independence of speculative power than Thomas Aquinas,\nAlbertus Magnus, and Duns Scotus, in the thirteenth. In the interval,\nabout the end of the twelfth century, the writings of Aristotle had\nbecome generally known in the West; and had been elevated into the\nstandard of philosophical doctrine, by the divines mentioned above, who\nfelt a reverent sympathy with the systematizing and subtle spirit of\nthe Stagirite as soon as it was made manifest to them. These doctors,\nfollowing the example of their great forerunner, reduced every part\nof human knowledge to a systematic form; the systems which they thus\nframed were presented to men's minds as the only true philosophy, and\ndissent from them was no longer considered to be blameless. It was an\noffence against religion as well as reason to reject the truth, and\nthe truth could be but one. In this manner arose that claim which the\nDoctors of the Church put forth to control men's opinions upon all\nsubjects, and which we have spoken of in the _History of Science_ as\nthe Dogmatism of the Middle Ages. There is no difficulty in giving\nexamples of this characteristic. We may take for instance a Statute of\nthe University of Paris, occasioned by a Bull of Pope John XXI., in\nwhich it is enacted, \"that no Master or Bachelor of any faculty, shall\npresume to read lectures upon any author in a private room, on account\nof the many perils which may arise therefrom; but shall read in public\nplaces, where all may resort, and may faithfully report what is there\ntaught; excepting only books of Grammar and Logic, in which there can\nbe no presumption.\" And certain errors of Brescian are condemned in a\nRescript[51] of the papal Legate Odo, with the following expressions:\n\"Whereas, as we have been informed, certain Logical professors\ntreating of Theology in their disputations, and Theologians treating\nof Logic, contrary to the command of the law are not afraid to mix and\nconfound the lots of the Lord's heritage; we exhort and admonish your\nUniversity, all and singular, that they be content with the landmarks\nof the Sciences and Faculties which our Fathers have fixed; and that\nhaving due fear of the curse pronounced in the law against him who\nremoveth his neighbour's landmark, you hold such sober wisdom according\nto the Apostles, that ye may by no means incur the blame of innovation\nor presumption.\"\n\nThe account which, in the _History of Science_, I gave of Dogmatism as\na characteristic of the middle ages, has been indignantly rejected by\na very pleasing modern writer, who has, with great feeling and great\ndiligence, brought into view the merits and beauties of those times,\ntermed by him _Ages of Faith_. He urges[52] that religious authority\nwas never claimed for physical science: and he quotes from Thomas\nAquinas, a passage in which the author protests against the practice\nof confounding opinions of philosophy with doctrines of faith. We\nmight quote in return the Rescript[53] of Stephen, bishop of Paris,\nin which he declares that there can be but one truth, and rejects\nthe distinction of things being true according to philosophy and not\naccording to the Catholic faith; and it might be added, that among the\nerrors condemned in this document are some of Thomas Aquinas himself.\nWe might further observe, that if no physical doctrines were condemned\nin the times of which we now speak, this was because, on such subjects,\nno new opinions were promulgated, and not because opinion was free.\nAs soon as new opinions, even on physical subjects, attracted general\nnotice, they were prohibited by authority, as we see in the case of\nGalileo[54].\n\nBut this disinclination to recognize philosophy as independent of\nreligion, and this disposition to find in new theories, even in\nphysical ones, something contrary to religion or scripture, are, it\nwould seem, very natural tendencies of theologians; and it would be\nunjust to assert that these propensities were confined to the periods\nwhen the authority of papal Rome was highest; or that the spirit which\nhas in a great degree controlled and removed such habits was introduced\nby the Reformation of religion in the sixteenth century. We must trace\nto other causes, the clear and general recognition of Philosophy,\nas distinct from Theology, and independent of her authority. In\nthe earlier ages of the Church, indeed, this separation had been\nacknowledged. St. Augustin says, \"A Christian should beware how he\nspeaks on questions of natural philosophy, as if they were doctrines of\nHoly Scripture; for an infidel who should hear him deliver absurdities\ncould not avoid laughing. Thus the Christian would be confused, and the\ninfidel but little edified; for the infidel would conclude that our\nauthors really entertained these extravagant opinions, and therefore\nthey would despise them, to their own eternal ruin. Therefore the\nopinions of philosophers should never be proposed as dogmas of faith,\nor rejected as contrary to faith, when it is not certain that they are\nso.\" These words are quoted with approbation by Thomas Aquinas, and\nit is said[55], are cited in the same manner in every encyclopedical\nwork of the middle ages. This warning of genuine wisdom was afterwards\nrejected, as we have seen; and it is only in modern times that its\nvalue has again been fully recognized. And this improvement we must\nascribe, mainly, to the progress of physical science. For a great body\nof undeniable truths on physical subjects being accumulated, such as\nhad no reference to nor connexion with the truths of religion, and\nyet such as possessed a strong interest for most men's minds, it was\nimpossible longer to deny that there were wide provinces of knowledge\nwhich were not included in the dominions of Theology, and over which\nshe had no authority. In the fifteenth and sixteenth centuries, the\nfundamental doctrines of mechanics, hydrostatics, optics, magnetics,\nchemistry, were established and promulgated; and along with them,\na vast train of consequences, attractive to the mind by the ideal\nrelations which they exhibited, and striking to the senses by the power\nwhich they gave man over nature. Here was a region in which philosophy\nfelt herself entitled and impelled to assert her independence. From\nthis region, there is a gradation of subjects in which philosophy\nadvances more and more towards the peculiar domain of religion;\nand at some intermediate points there have been, and probably will\nalways be, conflicts respecting the boundary line of the two fields\nof speculation. For the limit is vague and obscure, and appears to\nfluctuate and shift with the progress of time and knowledge.\n\nOur business at present is not with the whole extent and limits\nof philosophy, but with the progress of physical science more\nparticularly, and the methods by which it may be attained: and we are\nendeavouring to trace historically the views which have prevailed\nrespecting such methods, at various periods of man's intellectual\nprogress. Among the most conspicuous of the revolutions which opinions\non this subject have undergone, is the transition from an implicit\ntrust in the internal powers of man's mind to a professed dependence\nupon external observation; and from an unbounded reverence for the\nwisdom of the past, to a fervid expectation of change and improvement.\nThe origin and progress of this disposition of mind;--the introduction\nof a state of things in which men not only obtained a body of\nindestructible truths from experience, and increased it from generation\nto generation, but professedly, and we may say, ostentatiously,\ndeclared such to be the source of their knowledge, and such their\nhopes of its destined career;--the rise, in short, of Experimental\nPhilosophy, not only as a habit, but as a Philosophy of Experience, is\nwhat we must now endeavour to exhibit.\n\n\nFOOTNOTES:\n\n[Footnote 48: See the opinion of Aquinas, in Degerando, _Hist. Com. des\nSyst._ iv. 499; of Duns Scotus, _ibid._ iv. 523.]\n\n[Footnote 49: _Liber Excerptionum_, Lib. i. c. i.]\n\n[Footnote 50: _Tr. Ex._ Lib. i. c. vii.]\n\n[Footnote 51: Tenneman, viii. 461.]\n\n[Footnote 52: _Mores Catholici, or Ages of Faith_, viii. p. 247.]\n\n[Footnote 53: Tenneman, viii. 460.]\n\n[Footnote 54: If there were any doubt on this subject, we might\nrefer to the writers who afterwards questioned the supremacy of\nAristotle, and who with one voice assert that an infallible authority\nhad been claimed for him. Thus Laurentius Valla: \"Quo minus ferendi\nsunt recentes Peripatetici, qui nullius sect\u00e6 hominibus interdicunt\nlibertate ab Aristotele dissentiendi, quasi sophos hic, non\nphilosophus.\" _Pref. in Dial._ (Tenneman, ix. 29.) So Ludovicus Vives:\n\"Sunt ex philosophis et ex theologis qui non solum quo Aristoteles\npervenit extremum esse aiunt natur\u00e6, sed qu\u00e2 pervenit eam rectissimam\nesse omnium et certissimam in natura viam.\" (Tenneman, ix. 43.) We\nmight urge too, the evasions practised by philosophical Reformers,\nthrough fear of the dogmatism to which they had to submit; for example,\nthe protestation of Telesius at the end of the Proem to his work, _De\nRerum Natura_: \"Nec tamen, si quid eorum qu\u00e6 nobis posita sunt, sacris\nliteris, Catholic\u00e6ve ecclesi\u00e6 decretis non coh\u00e6reat, tenendum id, quin\npenitus rejiciendum asseveramus contendimusque. Neque enim _humana_\nmodo _ratio_ qu\u00e6vis, sed _ipse_ etiam _sensus_ illis _posthabendus_, et\nsi illis non congruat, abnegandus omnino et ipse etiam est sensus.\"]\n\n[Footnote 55: _Ages of Faith_, viii. 247: to the author of which I am\nobliged for this quotation.]\n\n\n\n\nCHAPTER X.\n\nTHE INNOVATORS OF THE MIDDLE AGES.\n\n\n_Raymond Lully._\n\n1. _General Remarks._--In the rise of Experimental Philosophy,\nunderstanding the term in the way just now stated, two features have\nalready been alluded to: the disposition to cast off the prevalent\nreverence for the opinions and methods of preceding teachers with an\neager expectation of some vast advantage to be derived from a change;\nand the belief that this improvement must be sought by drawing our\nknowledge from external observation rather than from mere intellectual\nefforts;--_the Insurrection against Authority_, and _the Appeal to\nExperience_. These two movements were closely connected; but they may\neasily be distinguished, and in fact, persons were very prominent in\nthe former part of the task, who had no comprehension of the latter\nprinciple, from which alone the change derives its value. There were\nmany Malcontents who had not the temper, talent or knowledge, which\nfitted them to be Reformers.\n\nThe authority which was questioned, in the struggle of which we speak,\nwas that of the Scholastic System, the combination of Philosophy with\nTheology; of which Aristotle, presented in the form and manner which\nthe Doctors of the Church had imposed upon him, is to be considered\nthe representative. When there was demanded of men a submission of\nthe mind, such as this system claimed, the natural love of freedom in\nman's bosom, and the speculative tendencies of his intellect, rose in\nrebellion, from time to time, against the ruling oppression. We find\nin all periods of the scholastic ages examples of this disposition\nof man to resist overstrained authority; the tendency being mostly,\nhowever, combined with a want of solid thought, and showing itself\nin extravagant pretensions and fantastical systems put forwards by\nthe insurgents. We have pointed out one such opponent[56] of the\nestablished systems, even among the Arabian schoolmen, a more servile\nrace than ever the Europeans were. We may here notice more especially\nan extraordinary character who appeared in the thirteenth century, and\nwho may be considered as belonging to the Prelude of the Reform in\nPhilosophy, although he had no share in the Reform itself.\n\n2. _Raymond Lully._--Raymond Lully is perhaps traditionally best known\nas an Alchemist, of which art he appears to have been a cultivator. But\nthis was only one of the many impulses of a spirit ardently thirsty\nof knowledge and novelty. He had[57], in his youth, been a man of\npleasure, but was driven by a sudden shock of feeling to resolve on a\ncomplete change of life. He plunged into solitude, endeavoured to still\nthe remorse of his conscience by prayer and penance, and soon had his\nsoul possessed by visions which he conceived were vouchsafed to him.\nIn the feeling of religious enthusiasm thus excited, he resolved to\ndevote his life to the diffusion of Christian truth among Heathens and\nMahomedans. For this purpose, at the age of thirty he betook himself\nto the study of Grammar, and of the Arabic language. He breathed\nearnest supplications for an illumination from above; and these were\nanswered by his receiving from heaven, as his admirers declare, his\n_Ars Magna_ by which he was able without labour or effort to learn\nand apply all knowledge. The real state of the case is, that he put\nhimself in opposition to the established systems, and propounded a New\nArt, from which he promised the most wonderful results; but that his\nArt really is merely a mode of combining ideal conceptions without any\nreference to real sources of knowledge, or any possibility of real\nadvantage. In a Treatise addressed, in A.D. 1310, to King Philip of\nFrance, entitled _Liber Lamentationis Duodecim Principiorum Philosophi\u00e6\ncontra Averroistas_, Lully introduced Philosophy, accompanied by her\ntwelve Principles, (Matter, Form, Generation, &c.) uttering loud\ncomplaints against the prevailing system of doctrine; and represents\nher as presenting to the king a petition that she may be upheld and\nrestored by her favourite, the Author. His _Tabula Generalis ad omnes\nScientias applicabilis_ was begun the 15th September, 1292, in the\nHarbour of Tunis, and finished in 1293, at Naples. In order to frame an\nArt of thus tabulating all existing sciences, and indeed all possible\nknowledge, he divides into various classes the conceptions with which\nhe has to deal. The first class contains nine _Absolute Conceptions_:\nGoodness, Greatness, Duration, Power, Wisdom, Will, Virtue, Truth,\nMajesty. The second class has nine _Relative Conceptions_: Difference,\nIdentity, Contrariety, Beginning, Middle, End, Majority, Equality,\nMinority. The third class contains nine _Questions_: Whether? What?\nWhence? Why? How great? How circumstanced? When? Where? and How?\nThe fourth class contains the nine _Most General Subjects_: God,\nAngel, Heaven, Man, _Imaginativum_, _Sensitivum_, _Vegetativum_,\n_Elementativum_, _Instrumentativum_. Then come nine _Pr\u00e6dicaments_,\nnine _Moral Qualities_, and so on. These conceptions are arranged in\nthe compartments of certain concentric moveable circles, and give\nvarious combinations by means of triangles and other figures, and thus\npropositions are constructed.\n\nIt must be clear at once, that real knowledge, which is the union of\nfacts and ideas, can never result from this machinery for shifting\nabout, joining and disjoining, empty conceptions. This, and all similar\nschemes, go upon the supposition that the logical combinations of\nnotions do of themselves compose knowledge; and that really existing\nthings may be arrived at by a successive system of derivation from\nour most general ideas. It is imagined that by distributing the\nnomenclature of abstract ideas according to the place which they can\nhold in our propositions, and by combining them according to certain\nconditions, we may obtain formul\u00e6 including all possible truths, and\nthus fabricate a science in which all sciences are contained. We thus\nobtain the means of talking and writing upon all subjects, without the\ntrouble of thinking: the revolutions of the emblematical figures are\nsubstituted for the operations of the mind. Both exertion of thought,\nand knowledge of facts, become superfluous. And this reflection, adds\nan intelligent author[58], explains the enormous number of books which\nLully is said to have written; for he might have written those even\nduring his sleep, by the aid of a moving power which should keep his\nmachine in motion. Having once devised this invention for manufacturing\nscience, Lully varied it in a thousand ways, and followed it into\na variety of developments. Besides Synoptical Tables, he employs\nGenealogical Trees, each of which he dignifies with the name of the\nTree of Science. The only requisite for the application of his System\nwas a certain agreement in the numbers of the classes into which\ndifferent subjects were distributed; and as this symmetry does not\nreally exist in the operations of our thoughts, some violence was done\nto the natural distinction and subordination of conceptions, in order\nto fit them for the use of the system.\n\nThus Lully, while he professed to teach an Art which was to shed new\nlight upon every part of science, was in fact employed in a pedantic\nand trifling repetition of known truths or truisms; and while he\ncomplained of the errors of existing methods, he proposed in their\nplace one which was far more empty, barren, and worthless, than the\ncustomary processes of human thought. Yet his method is spoken of[59]\nwith some praise by Leibnitz, who indeed rather delighted in the\nregion of ideas and words, than in the world of realities. But Francis\nBacon speaks far otherwise and more justly on this subject[60]. \"It is\nnot to be omitted that some men, swollen with emptiness rather than\nknowledge, have laboured to produce a certain Method, not deserving\nthe name of a legitimate Method, since it is rather a method of\nimposture: which yet is doubtless highly grateful to certain would-be\nphilosophers. This method scatters about certain little drops of\nscience in such a manner that a smatterer may make a perverse and\nostentatious use of them with a certain show of learning. Such was\nthe art of Lully, which consisted of nothing but a mass and heap of\nthe words of each science; with the intention that he who can readily\nproduce the words of any science shall be supposed to know the science\nitself. Such collections are like a rag shop, where you find a patch of\neverything, but nothing which is of any value.\"\n\n\nFOOTNOTES:\n\n[Footnote 56: Algazel. See _Hist. Ind. Sc._ b. iv. c. i.]\n\n[Footnote 57: Tenneman, viii. 830.]\n\n[Footnote 58: Degerando, iv. 535.]\n\n[Footnote 59: Leibnitz's expressions are, (_Op._ t. vi. p. 16): \"Quand\nj'\u00e9tais jeune, je prenois quelque a l'_Art_ de Lulle, mais je crus y\nentrevoir bien des d\u00e9fectuosit\u00e9s, dont j'ai dit quelque chose dans un\npetit Essai d'\u00e9colier intitul\u00e9 _De Arte Combinatoria_, publi\u00e9 en 1666,\net qui a \u00e9t\u00e9 r\u00e9imprim\u00e9 apr\u00e8s malgr\u00e9 moi. Mais comme je ne m\u00e9prise\nrien facilement, except\u00e9 les arts divinatoires que ne sont que des\ntromperies toutes pures, j'ai trouv\u00e9 quelque chose d'estimable encore\ndans l'_Art_ de Lulle.\"]\n\n[Footnote 60: _Works_, vii. 296.]\n\n\n\n\nCHAPTER XI.\n\nTHE INNOVATORS OF THE MIDDLE AGES--CONTINUED.\n\n\n_Roger Bacon._\n\nWe now come to a philosopher of a very different character, who was\nimpelled to declare his dissent from the reigning philosophy by the\nabundance of his knowledge, and by his clear apprehension of the mode\nin which real knowledge had been acquired and must be increased.\n\nRoger Bacon was born in 1214, near Ilchester, in Somersetshire, of\nan old family. In his youth he was a student at Oxford, and made\nextraordinary progress in all branches of learning. He then went to\nthe University of Paris, as was at that time the custom of learned\nEnglishmen, and there received the degree of Doctor of Theology. At\nthe persuasion of Robert Grost\u00eate, bishop of Lincoln, he entered the\nbrotherhood of Franciscans in Oxford, and gave himself up to study\nwith extraordinary fervour. He was termed by his brother monks _Doctor\nMirabilis_. We know from his own works, as well as from the traditions\nconcerning him, that he possessed an intimate acquaintance with all the\nscience of his time which could be acquired from books; and that he had\nmade many remarkable advances by means of his own experimental labours.\nHe was acquainted with Arabic, as well as with the other languages\ncommon in his time. In the title of his works, we find the whole\nrange of science and philosophy, Mathematics and Mechanics, Optics,\nAstronomy, Geography, Chronology, Chemistry, Magic, Music, Medicine,\nGrammar, Logic, Metaphysics, Ethics, and Theology; and judging from\nthose which are published, these works are full of sound and exact\nknowledge. He is, with good reason, supposed to have discovered, or to\nhave had some knowledge of, several of the most remarkable inventions\nwhich were made generally known soon afterwards; as gunpowder, lenses,\nburning specula, telescopes, clocks, the correction of the calendar,\nand the explanation of the rainbow.\n\nThus possessing, in the acquirements and habits of his own mind,\nabundant examples of the nature of knowledge and of the process of\ninvention, Roger Bacon felt also a deep interest in the growth and\nprogress of science, a spirit of inquiry respecting the causes which\nproduced or prevented its advance, and a fervent hope and trust in its\nfuture destinies; and these feelings impelled him to speculate worthily\nand wisely respecting a Reform of the Method of Philosophizing. The\nmanuscripts of his works have existed for nearly six hundred years in\nmany of the libraries of Europe, and especially in those of England;\nand for a long period the very imperfect portions of them which were\ngenerally known, left the character and attainments of the author\nshrouded in a kind of mysterious obscurity. About a century ago,\nhowever, his _Opus Majus_ was published[61] by Dr. S. Jebb, principally\nfrom a manuscript in the Library of Trinity College, Dublin; and this\ncontained most or all of the separate works which were previously\nknown to the public, along with others still more peculiar and\ncharacteristic. We are thus able to judge of Roger Bacon's knowledge\nand of his views, and they are in every way well worthy our attention.\n\nThe _Opus Majus_ is addressed to Pope Clement the Fourth, whom Bacon\nhad known when he was legate in England as Cardinal-bishop of Sabina,\nand who admired the talents of the monk, and pitied him for the\npersecutions to which he was exposed. On his elevation to the papal\nchair, this account of Bacon's labours and views was sent, at the\nearnest request of the pontiff. Besides the _Opus Majus_, he wrote\ntwo others, the _Opus Minus_ and _Opus Tertium_; which were also sent\nto the pope, as the author says[62], \"on account of the danger of\nroads, and the possible loss of the work.\" These works still exist\nunpublished, in the Cottonian and other libraries. The _Opus Majus_ is\na work equally wonderful with regard to its general scheme, and to the\nspecial treatises with which the outlines of the plan are filled up.\nThe professed object of the work is to urge the necessity of a reform\nin the mode of philosophizing, to set forth the reasons why knowledge\nhad not made a greater progress, to draw back attention to the sources\nof knowledge which had been unwisely neglected, to discover other\nsources which were yet almost untouched, and to animate men in the\nundertaking, by a prospect of the vast advantages which it offered.\nIn the development of this plan, all the leading portions of science\nare expounded in the most complete shape which they had at that time\nassumed; and improvements of a very wide and striking kind are proposed\nin some of the principal of these departments. Even if the work had had\nno leading purpose, it would have been highly valuable as a treasure of\nthe most solid knowledge and soundest speculations of the time; even\nif it had contained no such details, it would have been a work most\nremarkable for its general views and scope. It may be considered as,\nat the same time, the _Encyclopedia_ and the _Novum Organon_ of the\nthirteenth century.\n\nSince this work is thus so important in the history of Inductive\nPhilosophy I shall give, in a note, a view[63] of its divisions and\ncontents. But I must now endeavour to point out more especially the way\nin which the various principles, which the reform of scientific method\ninvolved, are here brought into view.\n\nOne of the first points to be noticed for this purpose, is the\nresistance to authority; and at the stage of philosophical history\nwith which we here have to do, this means resistance to the authority\nof Aristotle, as adopted and interpreted by the Doctors of the\nSchools. Bacon's work[64] is divided into Six Parts; and of these\nParts, the First is, Of the four universal Causes of all Human\nIgnorance. The causes thus enumerated[65] are:--the force of unworthy\nauthority;--traditionary habit;--the imperfection of the undisciplined\nsenses;--and the disposition to conceal our ignorance and to make an\nostentatious show of our knowledge. These influences involve every man,\noccupy every condition. They prevent our obtaining the most useful and\nlarge and fair doctrines of wisdom, the secret of all sciences and\narts. He then proceeds to argue, from the testimony of philosophers\nthemselves, that the authority of antiquity, and especially of\nAristotle, is not infallible. \"We find[66] their books full of doubts,\nobscurities, and perplexities. They scarce agree with each other in\none empty question or one worthless sophism, or one operation of\nscience, as one man agrees with another in the practical operations\nof medicine, surgery, and the like arts of Secular men. Indeed,\" he\nadds, \"not only the philosophers, but the saints have fallen into\nerrors which they have afterwards retracted,\" and this he instances\nin Augustin, Jerome, and others. He gives an admirable sketch[67] of\nthe progress of philosophy from the Ionic School to Aristotle; of whom\nhe speaks with great applause. \"Yet,\" he adds[68], \"those who came\nafter him corrected him in some things, and added many things to his\nworks, and shall go on adding to the end of the world.\" Aristotle, he\nadds, is now called peculiarly[69] the Philosopher, \"yet there was a\ntime when his philosophy was silent and unregarded, either on account\nof the rarity of copies of his works, or their difficulty, or from\nenvy; till after the time of Mahomet, when Avicenna and Averroes, and\nothers, recalled this philosophy into the full light of exposition. And\nalthough the Logic and some other works were translated by Boethius\nfrom the Greek, yet the philosophy of Aristotle first received a quick\nincrease among the Latins at the time of Michael Scot; who, in the year\nof our Lord 1230, appeared, bringing with him portions of the books of\nAristotle on Natural Philosophy and Mathematics. And yet a small part\nonly of the works of this author is translated, and a still smaller\npart is in the hands of common students.\" He adds further[70] (in the\nThird Part of the _Opus Majus_, which is a Dissertation on language),\nthat the translations which are current of these writings, are very\nbad and imperfect. With these views, he is moved to express himself\nsomewhat impatiently[71] respecting these works: \"If I had,\" he says,\n\"power over the works of Aristotle, I would have them all burnt; for\nit is only a loss of time to study in them, and a cause of error, and\na multiplication of ignorance beyond expression.\" \"The common herd of\nstudents,\" he says, \"with their heads, have no principle by which they\ncan be excited to any worthy employment; and hence they mope and make\nasses of themselves over their bad translations, and lose their time,\nand trouble, and money.\"\n\nThe remedies which he recommends for these evils, are, in the first\nplace, the study of that only perfect wisdom which is to be found in\nthe sacred Scripture[72], in the next place, the study of mathematics\nand the use of experiment[73]. By the aid of these methods, Bacon\nanticipates the most splendid progress for human knowledge. He takes up\nthe strain of hope and confidence which we have noticed as so peculiar\nin the Roman writers; and quotes some of the passages of Seneca which\nwe adduced in illustration of this:--that the attempts in science were\nat first rude and imperfect, and were afterwards improved;--that the\nday will come, when what is still unknown shall be brought to light by\nthe progress of time and the labours of a longer period;--that one age\ndoes not suffice for inquiries so wide and various;--that the people\nof future times shall know many things unknown to us;--and that the\ntime shall arrive when posterity will wonder that we overlooked what\nwas so obvious. Bacon himself adds anticipations more peculiarly in\nthe spirit of his own time. \"We have seen,\" he says, at the end of the\nwork, \"how Aristotle, by the ways which wisdom teaches, could give to\nAlexander the empire of the world. And this the Church ought to take\ninto consideration against the infidels and rebels, that there may be a\nsparing of Christian blood, and especially on account of the troubles\nthat shall come to pass in the days of Antichrist; which by the grace\nof God, it would be easy to obviate, if prelates and princes would\nencourage study, and join in searching out the secrets of nature and\nart.\"\n\nIt may not be improper to observe here that this belief in the\nappointed progress of knowledge, is not combined with any overweening\nbelief in the unbounded and independent power of the human intellect.\nOn the contrary, one of the lessons which Bacon draws from the state\nand prospects of knowledge, is the duty of faith and humility. \"To\nhim,\" he says[74], \"who denies the truth of the faith because he is\nunable to understand it, I will propose in reply the course of nature,\nand as we have seen it in examples.\" And after giving some instances,\nhe adds, \"These, and the like, ought to move men and to excite them\nto the reception of divine truths. For if, in the vilest objects of\ncreation, truths are found, before which the inward pride of man must\nbow, and believe though it cannot understand, how much more should\nman humble his mind before the glorious truths of God!\" He had before\nsaid[75]: \"Man is incapable of perfect wisdom in this life; it is\nhard for him to ascend towards perfection, easy to glide downwards\nto falsehoods and vanities: let him then not boast of his wisdom, or\nextol his knowledge. What he knows is little and worthless, in respect\nof that which he believes without knowing; and still less, in respect\nof that which he is ignorant of. He is mad who thinks highly of his\nwisdom; he most mad, who exhibits it as something to be wondered at.\"\nHe adds, as another reason for humility, that he has proved by trial,\nhe could teach in one year, to a poor boy, the marrow of all that\nthe most diligent person could acquire in forty years' laborious and\nexpensive study.\n\nTo proceed somewhat more in detail with regard to Roger Bacon's views\nof a Reform in Scientific Inquiry, we may observe that by making\nMathematics and Experiment the two great points of his recommendation,\nhe directed his improvement to the two essential parts of all\nknowledge, Ideas and Facts, and thus took the course which the most\nenlightened philosophy would have suggested. He did not urge the\nprosecution of experiment, to the comparative neglect of the existing\nmathematical sciences and conception; a fault which there is some\nground for ascribing to his great namesake and successor Francis\nBacon: still less did he content himself with a mere protest against\nthe authority of the schools, and a vague demand for change, which\nwas almost all that was done by those who put themselves forward as\nreformers in the intermediate time. Roger Bacon holds his way steadily\nbetween the two poles of human knowledge; which, as we have seen, it\nis far from easy to do. \"There are two modes of knowing,\" says he[76];\n\"by argument, and by experiment. Argument concludes a question; but\nit does not make us feel certain, or acquiesce in the contemplation\nof truth, except the truth be also found to be so by experience.\"\nIt is not easy to express more decidedly the clearly seen union of\nexact conceptions with certain facts, which, as we have explained,\nconstitutes real knowledge.\n\nOne large division of the _Opus Majus_ is \"On the Usefulness of\nMathematics,\" which is shown by a copious enumeration of existing\nbranches of knowledge, as Chronology, Geography, the Calendar and\n(in a separate Part) Optics. There is a chapter[77], in which it is\nproved by reason, that all science requires mathematics. And the\narguments which are used to establish this doctrine, show a most just\nappreciation of the office of mathematics in science. They are such as\nfollows:--That other sciences use examples taken from mathematics as\nthe most evident:--That mathematical knowledge is, as it were, innate\nin us, on which point he refers to the well-known dialogue of Plato,\nas quoted by Cicero:--That this science, being the easiest, offers the\nbest introduction to the more difficult:--That in mathematics, things\nas known to us are identical with things as known to nature:--That\nwe can here entirely avoid doubt and error, and obtain certainty and\ntruth:--That mathematics is prior to other sciences in nature, because\nit takes cognizance of quantity, which is apprehended by intuition,\n(_intuitu intellectus_). \"Moreover,\" he adds[78], \"there have been\nfound famous men, as Robert, bishop of Lincoln, and Brother Adam\nMarshman (de Marisco), and many others, who by the power of mathematics\nhave been able to explain the causes of things; as may be seen in the\nwritings of these men, for instance, concerning the Rainbow and Comets,\nand the generation of heat, and climates, and the celestial bodies.\"\n\nBut undoubtedly the most remarkable portion of the _Opus Majus_ is the\nSixth and last Part, which is entitled \"De Scientia experimentali.\"\nIt is indeed an extraordinary circumstance to find a writer of the\nthirteenth century, not only recognizing experiment as one source\nof knowledge, but urging its claims as something far more important\nthan men had yet been aware of, exemplifying its value by striking\nand just examples, and speaking of its authority with a dignity of\ndiction which sounds like a foremurmur of the Baconian sentences\nuttered nearly four hundred years later. Yet this is the character of\nwhat we here find[79]. \"Experimental science, the sole mistress of\nspeculative sciences, has three great Prerogatives among other parts\nof knowledge: First she tests by experiment the noblest conclusions of\nall other sciences: Next she discovers respecting the notions which\nother sciences deal with, magnificent truths to which these sciences of\nthemselves can by no means attain: her Third dignity is, that she by\nher own power and without respect of other sciences, investigates the\nsecret of nature.\"\n\nThe examples which Bacon gives of these \"Prerogatives\" are very\ncurious, exhibiting, among some error and credulity, sound and clear\nviews. His leading example of the First Prerogative, is the Rainbow,\nof which the cause, as given by Aristotle, is tested by reference to\nexperiment with a skill which is, even to us now, truly admirable.\nThe examples of the Second Prerogative are three:--_first_, the art\nof making an artificial sphere which shall move with the heavens by\nnatural influences, which Bacon trusts may be done, though astronomy\nherself cannot do it--\"et tunc,\" he says, \"thesaurum unius regis\nvaleret hoc instrumentum;\"--_secondly_, the art of prolonging life,\nwhich experiment may teach, though medicine has no means of securing\nit except by regimen[80];--_thirdly_, the art of making gold finer\nthan fine gold, which goes beyond the power of alchemy. The Third\nPrerogative of experimental science, arts independent of the received\nsciences, is exemplified in many curious examples, many of them\nwhimsical traditions. Thus it is said that the character of a people\nmay be altered by altering the air[81]. Alexander, it seems, applied\nto Aristotle to know whether he should exterminate certain nations\nwhich he had discovered, as being irreclaimably barbarous; to which\nthe philosopher replied, \"If you can alter their air, permit them to\nlive, if not, put them to death.\" In this part, we find the suggestion\nthat the fire-works made by children, of saltpetre, might lead to the\ninvention of a formidable military weapon.\n\nIt could not be expected that Roger Bacon, at a time when experimental\nscience hardly existed, could give any _precepts_ for the discovery\nof truth by experiment. But nothing can be a better _example_ of the\nmethod of such investigation, than his inquiry concerning the cause of\nthe Rainbow. Neither Aristotle, nor Avicenna, nor Seneca, he says, have\ngiven us any clear knowledge of this matter, but experimental science\ncan do so. Let the experimenter (_experimentator_) consider the cases\nin which he finds the same colours, as the hexagonal crystals from\nIreland and India; by looking into these he will see colours like those\nof the rainbow. Many think that this arises from some special virtue of\nthese stones and their hexagonal figure; let therefore the experimenter\ngo on, and he will find the same in other transparent stones, in dark\nones as well as in light-coloured. He will find the same effect also\nin other forms than the hexagon, if they be furrowed in the surface,\nas the Irish crystals are. Let him consider too, that he sees the same\ncolours in the drops which are dashed from oars in the sunshine;--and\nin the spray thrown by a millwheel;--and in the dew-drops which lie on\nthe grass in a meadow on a summer-morning;--and if a man takes water\nin his mouth and projects it on one side into a sunbeam;--and if in an\noil-lamp hanging in the air, the rays fall in certain positions upon\nthe surface of the oil;--and in many other ways, are colours produced.\nWe have here a collection of instances, which are almost all examples\nof the same kind as the phenomenon under consideration; and by the help\nof a principle collected by induction from these facts, the colours of\nthe rainbow were afterwards really explained.\n\nWith regard to the form and other circumstances of the bow he is still\nmore precise. He bids us measure the height of the bow and of the sun,\nto show that the center of the bow is exactly opposite to the sun.\nHe explains the circular form of the bow,--its being independent of\nthe form of the cloud, its moving when we move, its flying when we\nfollow,--by its consisting of the reflections from a vast number of\nminute drops. He does not, indeed, trace the course of the rays through\nthe drop, or account for the precise magnitude which the bow assumes;\nbut he approaches to the verge of this part of the explanation; and\nmust be considered as having given a most happy example of experimental\ninquiry into nature, at a time when such examples were exceedingly\nscanty. In this respect, he was more fortunate than Francis Bacon, as\nwe shall hereafter see.\n\nWe know but little of the biography of Roger Bacon, but we have every\nreason to believe that his influence upon his age was not great.\nHe was suspected of magic, and is said to have been put into close\nconfinement in consequence of this charge. In his work he speaks\nof Astrology as a science well worth cultivating. \"But,\" says he,\n\"Theologians and Decretists, not being learned in such matters and\nseeing that evil as well as good may be done, neglect and abhor such\nthings, and reckon them among Magic Arts.\" We have already seen, that\nat the very time when Bacon was thus raising his voice against the\nhabit of blindly following authority, and seeking for all science\nin Aristotle, Thomas Aquinas was employed in fashioning Aristotle's\ntenets into that fixed form in which they became the great impediment\nto the progress of knowledge. It would seem, indeed, that something\nof a struggle between the progressive and stationary powers of the\nhuman mind was going on at this time. Bacon himself says[82], \"Never\nwas there so great an appearance of wisdom, nor so much exercise of\nstudy in so many Faculties, in so many regions, as for this last forty\nyears. Doctors are dispersed everywhere, in every castle, in every\nburgh, and especially by the students of two Orders, (he means the\nFranciscans and Dominicans, who were almost the only religious orders\nthat distinguished themselves by an application to study[83],) which\nhas not happened except for about forty years. And yet there was never\nso much ignorance, so much error.\" And in the part of his work which\nrefers to Mathematics, he says of that study[84], that it is the door\nand the key of the sciences; and that the neglect of it for thirty or\nforty years has entirely ruined the studies of the Latins. According to\nthese statements, some change, disastrous to the fortunes of science,\nmust have taken place about 1230, soon after the foundation of the\nDominican and Franciscan Orders[85]. Nor can we doubt that the adoption\nof the Aristotelian philosophy by these two Orders, in the form in\nwhich the Angelical Doctor had systematized it, was one of the events\nwhich most tended to defer, for three centuries, the reform which Roger\nBacon urged as a matter of crying necessity in his own time.\n\n\nFOOTNOTES:\n\n[Footnote 61: _Fratris Rogeri Bacon, Ordinis Minorum_, Opus Majus, _ad\nClementem Quartum, Pontificem Romanum, ex MS. Codice Dubliniensi cum\naliis quibusdam collato, nunc primum edidit_ S. Jebb, M.D. Londini,\n1733.]\n\n[Footnote 62: _Opus Majus_, Pr\u00e6f.]\n\n[Footnote 63: Contents of Roger Bacon's _Opus Majus_.\n\nPart I. On the four causes of human ignorance:--Authority, Custom,\nPopular Opinion, and the Pride of supposed Knowledge.\n\nPart II. On the source of perfect wisdom in the Sacred Scripture.\n\nPart III. On the Usefulness of Grammar.\n\nPart IV. On the Usefulness of Mathematics.\n\n(1) The necessity of Mathematics in Human Things (published separately\nas the _Specula Mathematica_).\n\n(2) The necessity of Mathematics in Divine Things.--1\u00b0. This study\nhas occupied holy men: 2\u00b0. Geography: 3\u00b0. Chronology: 4\u00b0. Cycles;\nthe Golden Number, &c.: 5\u00b0. Natural Phenomena, as the Rainbow: 6\u00b0.\nArithmetic: 7\u00b0. Music.\n\n(3) The necessity of Mathematics in Ecclesiastical Things.--1\u00b0. The\nCertification of Faith: 2\u00b0. The Correction of the Calendar.\n\n(4) The necessity of Mathematics in the State.--1\u00b0. Of Climates: 2\u00b0.\nHydrography: 3\u00b0. Geography: 4\u00b0. Astrology.\n\nPart V. On Perspective (published separately as _Perspectiva_).\n\n(1) The organs of vision.\n\n(2) Vision in straight lines.\n\n(3) Vision reflected and refracted.\n\n(4) De multiplicatione specierum (on the propagation of the impressions\nof light, heat, &c.)\n\nPart VI. On Experimental Science.]\n\n[Footnote 64: _Op. Maj._ p. 1.]\n\n[Footnote 65: _Ibid._ p. 2.]\n\n[Footnote 66: _Ibid._ p. 10.]\n\n[Footnote 67: I will give a specimen. _Opus Majus_, c. viii. p. 35:\n\"These two kinds of philosophers, the Ionic and Italic, ramified\nthrough many sects and various successors, till they came to the\ndoctrine of Aristotle, who corrected and changed the propositions\nof all his predecessors, and attempted to perfect philosophy. In\nthe [Italic] succession, Pythagoras, Archytas Tarentinus and Tim\u00e6us\nare most prominently mentioned. But the principal philosophers, as\nSocrates, Plato, and Aristotle, did not descend from this line, but\nwere Ionics and true Greeks, of whom the first was Thales Milesius....\nSocrates, according to Augustine in his 8th book, is related to have\nbeen a disciple of Archelaus. This Socrates is called the father of the\ngreat philosophers, since he was the master of Plato and Aristotle,\nfrom whom all the sects of philosophers descended.... Plato, first\nlearning what Socrates and Greece could teach, made a laborious voyage\nto Egypt, to Archytas of Tarentum and Tim\u00e6us, as says Jerome to\nPaulinus. And this Plato is, according to holy men, preferred to all\nphilosophers, because he has written many excellent things concerning\nGod, and morality, and a future life, which agree with the divine\nwisdom of God. And Aristotle was born before the death of Socrates,\nsince he was his hearer for three years, as we read in the life of\nAristotle.... This Aristotle, being made the master of Alexander the\nGreat, sent two thousand men into all regions of the earth, to search\nout the nature of things, as Pliny relates in the 8th book of his\n_Naturalia_, and composed a thousand books, as we read in his life.\"]\n\n[Footnote 68: _Ibid._ p. 36.]\n\n[Footnote 69: _Autonomatic\u00e8._]\n\n[Footnote 70: _Op. Maj._ p. 46.]\n\n[Footnote 71: See _Pref._ to Jebb's edition. The passages, there\nquoted, however, are not extracts from the _Opus Majus_, but\n(apparently) from the _Opus Minus_ (_MS. Cott._ Tib. c. 5.) \"Si haberem\npotestatem supra libros Aristotelis, ego facerem omnes cremari; quia\nnon est nisi temporis amissio studere in illis, et causa erroris, et\nmultiplicatio ignoranti\u00e6 ultra id quod valeat explicari.... Vulgus\nstudentum cum capitibus suis non habet unde excitetur ad aliquid\ndignum, et ideo languet et _asininat_ circa male translata, et tempus\net studium amittit in omnibus et expensas.\"]\n\n[Footnote 72: Part ii.]\n\n[Footnote 73: Parts iv. v. and vi.]\n\n[Footnote 74: _Op. Maj._ p. 476.]\n\n[Footnote 75: _Op. Maj._ p. 15.]\n\n[Footnote 76: _Ibid._ p. 445, see also p. 448. \"Scienti\u00e6 ali\u00e6 sciunt\nsua principia invenire per experimenta, sed conclusiones per argumenta\nfacta ex principiis inventis. Si vero debeant habere experientiam\nconclusionum suarum particularem et completam, tunc oportet quod\nhabeant per adjutorium istius scienti\u00e6 nobilis (experimentalis).\"]\n\n[Footnote 77: _Op. Maj._ p. 60.]\n\n[Footnote 78: _Ibid._ p. 64.]\n\n[Footnote 79: \"Veritates magnificas in terminis aliarum scientiarum in\nquas per nullam viam possunt ill\u00e6 scienti\u00e6, h\u00e6c sola scientiarum domina\nspeculativarum, potest dare.\" _Op. Maj._ p. 465.]\n\n[Footnote 80: One of the ingredients of a preparation here mentioned,\nis the flesh of a dragon, which it appears is used as food by the\nEthiopians. The mode of preparing this food cannot fail to amuse the\nreader. \"Where there are good flying dragons, by the art which they\npossess, they draw them out of their dens, and have bridles and saddles\nin readiness, and they ride upon them, and make them bound about in the\nair in a violent manner, that the hardness and toughness of the flesh\nmay be reduced, as boars are hunted and bulls are baited before they\nare killed for eating.\" _Op. Maj._ p. 470.]\n\n[Footnote 81: _Op. Maj._ p. 473.]\n\n[Footnote 82: Quoted by Jebb, _Pref._ to _Op. Maj._]\n\n[Footnote 83: Mosheim, _Hist._ iii. 161.]\n\n[Footnote 84: _Op. Maj._ p. 57.]\n\n[Footnote 85: Mosheim, iii. 161.]\n\n\n\n\nCHAPTER XII.\n\nTHE REVIVAL OF PLATONISM.\n\n\n1. _Causes of Delay in the Advance of Knowledge._--In the insight\npossessed by learned men into the method by which truth was to be\ndiscovered, the fourteenth and fifteenth centuries went backwards,\nrather than forwards, from the point which had been reached in the\nthirteenth. Roger Bacon had urged them to have recourse to experiment;\nbut they returned with additional and exclusive zeal to the more\nfavourite employment of reasoning upon their own conceptions. He had\ncalled upon them to look at the world without; but their eyes forthwith\nturned back upon the world within. In the constant oscillation of the\nhuman mind between Ideas and Facts, after having for a moment touched\nthe latter, it seemed to swing back more impetuously to the former.\nNot only was the philosophy of Aristotle firmly established for a\nconsiderable period, but when men began to question its authority, they\nattempted to set up in its place a philosophy still more purely ideal,\nthat of Plato. It was not till the actual progress of experimental\nknowledge for some centuries had given it a vast accumulation of force,\nthat it was able to break its way fully into the circle of speculative\nscience. The new Platonist schoolmen had to run their course, the\npractical discoverers had to prove their merit by their works, the\nItalian innovators had to utter their aspirations for a change, before\nthe second Bacon could truly declare that the time for a fundamental\nreform was at length arrived.\n\nIt cannot but seem strange, to any one who attempts to trace the\ngeneral outline of the intellectual progress of man, and who considers\nhim as under the guidance of a Providential sway, that he should\nthus be permitted to wander so long in a wilderness of intellectual\ndarkness; and even to turn back, by a perverse caprice as it might\nseem, when on the very border of the brighter and better land which was\nhis destined inheritance. We do not attempt to solve this difficulty:\nbut such a course of things naturally suggests the thought, that a\nprogress in physical science is not the main object of man's career,\nin the eyes of the Power who directs the fortunes of our race. We\ncan easily conceive that it may have been necessary to man's general\nwelfare that he should continue to turn his eyes inwards upon his own\nheart and faculties, till Law and Duty, Religion and Government, Faith\nand Hope, had been fully incorporated with all the past acquisitions of\nhuman intellect; rather than that he should have rushed on into a train\nof discoveries tending to chain him to the objects and operations of\nthe material world. The systematic Law[86] and philosophical Theology\nwhich acquired their ascendancy in men's minds at the time of which\nwe speak, kept them engaged in a region of speculations which perhaps\nprepared the way for a profounder and wider civilization, for a more\nelevated and spiritual character, than might have been possible without\nsuch a preparation. The great Italian poet of the fourteenth century\nspeaks with strong admiration of the founders of the system which\nprevailed in his time. Thomas, Albert, Gratian, Peter Lombard, occupy\ndistinguished places in the Paradise. The first, who is the poet's\ninstructor, says,--\n\n      Io fui degli agni della santa greggia\n    Che Domenico mena per cammino\n    U' ben s'impingua se non si vaneggia.\n      Questo che m'\u00e8 a destra piu vicino\n    Frate e maestro fummi; ed esso Alberto\n    E di Cologna, ed io Tomas d'Aquino....\n      Quell' altro fiammeggiar esce del riso\n      De Grazian, che l'uno et l'altro foro\n        Ajut\u00f2 si che piace in Paradiso.\n\n      I, then, was of the lambs that Dominic\n    Leads, for his saintly flock, along the way\n    Where well they thrive not swoln with vanity.\n    He nearest on my right-hand brother was\n    And master to me; Albert of Cologne\n    Is this; and of Aquinum Thomas, I....\n    That next resplendence issues from the smile\n    Of Gratian, who to either forum lent\n    Such help as favour wins in Paradise.\n\nIt appears probable that neither poetry, nor painting, nor the other\narts which require for their perfection a lofty and spiritualized\nimagination, would have appeared in the noble and beautiful forms which\nthey assumed in the fourteenth and fifteenth century, if men of genius\nhad, at the beginning of that period, made it their main business\nto discover the laws of nature, and to reduce them to a rigorous\nscientific form. Yet who can doubt that the absence of these touching\nand impressive works would have left one of the best and purest parts\nof man's nature without its due nutriment and development? It may\nperhaps be a necessary condition in the progress of man, that the Arts\nwhich aim at beauty should reach their excellence before the Sciences\nwhich seek speculative truth; and if this be so, we inherit, from the\nmiddle ages, treasures which may well reconcile us to the delay which\ntook place in their cultivation of experimental science.\n\nHowever this may be, it is our business at present to trace the\ncircumstances of this very lingering advance. We have already noticed\nthe contest of the Nominalists and Realists, which was one form,\nthough, with regard to scientific methods, an unprofitable one, of\nthe antithesis of Ideas and Things. Though, therefore, this struggle\ncontinued, we need not dwell upon it. The Nominalists denied the real\nexistence of Ideas, which doctrine was to a great extent implied\nin the prevailing systems; but the controversy in which they thus\nengaged, did not lead them to seek for knowledge in a new field and\nby new methods. The arguments which Occam the Nominalist opposes to\nthose of Duns Scotus the Realist, are marked with the stamp of the\nsame system, and consist only in permutations and combinations of the\nsame elementary conceptions. It was not till the impulse of external\ncircumstances was added to the discontent, which the more stirring\nintellects felt towards the barren dogmatism of their age, that the\nactivity of the human mind was again called into full play, and a new\ncareer of progression entered upon, till then undreamt of, except by a\nfew prophetic spirits.\n\n\n2. _Causes of Progress._--These circumstances were principally the\nrevival of Greek and Roman literature, the invention of Printing, the\nProtestant Reformation, and a great number of curious discoveries and\ninventions in the arts, which were soon succeeded by important steps\nin speculative physical science. Connected with the first of these\nevents, was the rise of a party of learned men who expressed their\ndissatisfaction with the Aristotelian philosophy, as it was then\ntaught, and manifested a strong preference for the views of Plato. It\nis by no means suitable to our plan to give a detailed account of this\nnew Platonic school; but we may notice a few of the writers who belong\nto it, so far at least as to indicate its influence upon the Methods of\npursuing science.\n\nIn the fourteenth century[87], the frequent intercourse of the most\ncultivated persons of the Eastern and Western Empire, the increased\nstudy of the Greek language in Italy, the intellectual activity of the\nItalian States, the discovery of manuscripts of the classical authors,\nwere circumstances which excited or nourished a new and zealous study\nof the works of Greek and Roman genius. The genuine writings of the\nancients, when presented in their native life and beauty, instead of\nbeing seen only in those lifeless fragments and dull transformations\nwhich the scholastic system had exhibited, excited an intense\nenthusiasm. Europe, at that period, might be represented by Plato's\nbeautiful allegory, of a man who, after being long kept in a dark\ncavern, in which his knowledge of the external world is gathered from\nthe images which stream through the chinks of his prison, is at last\nled forth into the full blaze of day. It was inevitable that such a\nchange should animate men's efforts and enlarge their faculties. Greek\nliterature became more and more known, especially by the influence of\nlearned men who came from Constantinople into Italy: these teachers,\nthough they honoured Aristotle, reverenced Plato no less, and had never\nbeen accustomed to follow with servile submission of thought either\nthese or any other leaders. The effect of such influences soon reveals\nitself in the works of that period. Dante has woven into his _Divina\nCommedia_ some of the ideas of Platonism. Petrarch, who had formed his\nmind by the study of Cicero, and had thus been inspired with a profound\nadmiration for the literature of Greece, learnt Greek from Barlaam, a\nmonk who came as ambassador from the Emperor of the East to the Pope,\nin 1339. With this instructor, the poet read the works of Plato; struck\nby their beauty, he contributed, by his writings and his conversation,\nto awake in others an admiration and love for that philosopher, which\nsoon became strongly and extensively prevalent among the learned in\nItaly.\n\n\n3. _Hermolaus Barbarus, &c._--Along with the feeling there prevailed\nalso, among those who had learnt to relish the genuine beauties of\nthe Greek and Latin writers, a strong disgust for the barbarisms in\nwhich the scholastic philosophy was clothed. Hermolaus Barbarus[88],\nwho was born in 1454, at Venice, and had formed his taste by the\nstudy of classical literature, translated, among other learned works,\nThemistius's paraphrastic expositions of the Physics of Aristotle;\nwith the view of trying whether the Aristotelian Natural Philosophy\ncould not be presented in good Latin, which the scholastic teachers\ndenied. In his Preface he expresses great indignation against those\nphilosophers who have written and disputed on philosophical subjects\nin barbarous Latin, and in an uncultured style, so that all refined\nminds are repelled from these studies by weariness and disgust. They\nhave, he says, by this barbarism, endeavoured to secure to themselves,\nin their own province, a supremacy without rivals or opponents. Hence\nthey maintain that mathematics, philosophy, jurisprudence, cannot\nbe expounded in correct Latin;--that between these sciences and the\ngenuine Latin language there is a great gulf, as between things that\ncannot be brought together: and on this ground they blame those who\ncombine the study of philology and eloquence with that of science.\nThis opinion, adds Hermolaus, perverts and ruins our studies; and is\nhighly prejudicial and unworthy in respect to the state. Hermolaus\nawoke in others, as for instance, in John Picus of Mirandula, the same\ndislike to the reigning school philosophy. As an opponent of the same\nkind, we may add Marius Nizolius of Bersallo, a scholar who carried\nhis admiration of Cicero to an exaggerated extent, and who was led,\nby a controversy with the defenders of the scholastic philosophy,\nto publish (1553) a work _On the True Principles and True Method of\nPhilosophizing_. In the title of this work, he professes to give \"the\ntrue principles of almost all arts and sciences, refuting and rejecting\nalmost all the false principles of the Logicians and Metaphysicians.\"\nBut although, in the work, he attacks the scholastic philosophy, he\ndoes little or nothing to justify the large pretensions of his title;\nand he excited, it is said, little notice. It is therefore curious that\nLeibnitz should have thought it worth his while to re-edit this work,\nwhich he did in 1670, adding remarks of his own.\n\n\n4. _Nicolaus Cusanus._--Without dwelling upon this opposition to the\nscholastic system on the ground of taste, I shall notice somewhat\nfurther those writers who put forwards Platonic views, as fitted to\ncomplete or to replace the doctrines of Aristotle. Among these, I may\nplace Nicolaus Cusanus, (so called from Cus, a village on the Moselle,\nwhere he was born in 1401;) who was afterwards raised to the dignity\nof cardinal. We might, indeed, at first be tempted to include Cusanus\namong those persons who were led to reject the old philosophy by being\nthemselves agents in the progressive movement of physical science.\nFor he published, before Copernicus, and independently of him, the\ndoctrine that the earth is in motion[89]. But it should be recollected\nthat in order to see the possibility of this doctrine, and its claims\nto acceptance, no new reference to observation was requisite. The\nHeliocentric System was merely a new mode of representing to the mind\nfacts, with which all astronomers had long been familiar. The system\nmight very easily have been embraced and inculcated by Plato himself;\nas indeed it is said to have been actually taught by Pythagoras. The\nmere adoption of the Heliocentric view, therefore, without attempting\nto realize the system in detail, as Copernicus did, cannot entitle a\nwriter of the fifteenth century to be looked upon as one of the authors\nof the discoveries of that period; and we must consider Cusanus as a\nspeculative anti-Aristotelian, rather than as a practical reformer.\n\nThe title of Cusanus's book, _De Doct\u00e2 Ignoranti\u00e2_, shows how far\nhe was from agreeing with those who conceived that, in the works\nof Aristotle, they had a full and complete system of all human\nknowledge. At the outset of this book[90], he says, after pointing\nout some difficulties in the received philosophy, \"If, therefore,\nthe case be so, (as even the very profound Aristotle, in his _First\nPhilosophy_, affirms,) that in things most manifest by nature, there\nis a difficulty, no less than for an owl to look at the sun; since\nthe appetite of knowledge is not implanted in us in vain, we ought\nto desire to know that we are ignorant. If we can fully attain to\nthis, we shall arrive at _Instructed Ignorance_.\" How far he was from\nplacing the source of knowledge in experience, as opposed to ideas,\nwe may see in the following passage[91] from another work of his,\n_On Conjectures_. \"Conjectures must proceed from our mind, as the\nreal world proceeds from the infinite Divine Reason. For since the\nhuman mind, the lofty likeness of God, participates, as it may, in\nthe fruitfulness of the creative nature, it doth from itself, as the\nimage of the Omnipotent Form, bring forth reasonable thoughts which\nhave a similitude to real existences. Thus the Human Mind exists as a\nconjectural form of the world, as the Divine Mind is its real form.\" We\nhave here the Platonic or ideal side of knowledge put prominently and\nexclusively forwards.\n\n\n5. _Marsilius Ficinus, &c._--A person who had much more influence\non the diffusion of Platonism was Marsilius Ficinus, a physician\nof Florence. In that city there prevailed, at the time of which we\nspeak, the greatest enthusiasm for Plato. George Gemistius Pletho,\nwhen in attendance upon the Council of Florence, had imparted to\nmany persons the doctrines of the Greek philosopher; and, among\nothers, had infused a lively interest on this subject into the elder\nCosmo, the head of the family of the Medici. Cosmo formed the plan\nof founding a Platonic academy. Ficinus[92], well instructed in the\nworks of Plato, Plotinus, Proclus, and other Platonists, was selected\nto further this object, and was employed in translating the works of\nthese authors into Latin. It is not to our present purpose to consider\nthe doctrines of this school, except so far as they bear upon the\nnature and methods of knowledge; and therefore I must pass by, as I\nhave in other instances done, the greater part of their speculations,\nwhich related to the nature of God, the immortality of the soul, the\nprinciples of Goodness and Beauty, and other points of the same order.\nThe object of these and other Platonists of this school, however, was\nnot to expel the authority of Aristotle by that of Plato. Many of\nthem had come to the conviction that the highest ends of philosophy\nwere to be reached only by bringing into accordance the doctrines\nof Plato and of Aristotle. Of this opinion was John Picus, Count of\nMirandula and Concordia; and under this persuasion he employed the\nwhole of his life in labouring upon a work, _De Concordi\u00e2 Platonis et\nAristotelis_, which was not completed at the time of his death, in\n1494; and has never been published. But about a century later, another\nwriter of the same school, Francis Patricius[93], pointing out the\ndiscrepancies between the two Greek teachers, urged the propriety of\ndeposing Aristotle from the supremacy he had so long enjoyed. \"Now all\nthese doctrines, and others not a few,\" he says[94], \"since they are\nPlatonic doctrines, philosophically most true, and consonant with the\nCatholic faith, whilst the Aristotelian tenets are contrary to the\nfaith, and philosophically false, who will not, both as a Christian and\na Philosopher, prefer Plato to Aristotle? And why should not hereafter,\nin all the colleges and monasteries of Europe, the reading and study\nof Plato be introduced? Why should not the philosophy of Aristotle be\nforthwith exiled from such places? Why must men continue to drink the\nmortal poison of impiety from that source?\" with much more in the same\nstrain.\n\nThe Platonic school, of which we have spoken, had, however, reached\nits highest point of prosperity before this time, and was already\ndeclining. About 1500, the Platonists appeared to triumph over the\nPeripatetics[95]; but the death of their great patron, Cardinal\nBessarion, about this time, and we may add, the hollowness of their\nsystem in many points, and its want of fitness for the wants and\nexpectations of the age, turned men's thoughts partly back to the\nestablished Aristotelian doctrines, and partly forwards to schemes of\nbolder and fresher promise.\n\n\n6. _Francis Patricius._--Patricius, of whom we have just spoken, was\none of those who had arrived at the conviction that the formation of\na new philosophy, and not merely the restoration of an old one, was\nneeded. In 1593, appeared his _Nova de Universis Philosophia_; and\nthe mode in which it begins[96] can hardly fail to remind us of the\nexpressions which Francis Bacon soon afterwards used in the opening of\na work of the same nature. \"Francis Patricius, being about to found\nanew the true philosophy of the universe, dared to begin by announcing\nthe following indisputable principles.\" Here, however, the resemblance\nbetween Patricius and true inductive philosophers ends. His principles\nare barren _\u00e0 priori_ axioms; and his system has one main element,\n_Light_, (_Lux_, or _Lumen_,) to which all operations of nature are\nreferred. In general cultivation, and practical knowledge of nature,\nhe was distinguished among his contemporaries. In various passages of\nhis works he relates[97] observations which he had made in the course\nof his travels, in Cyprus, Corfu, Spain, the mountains of the Modenese,\nand Dalmatia, which was his own country; his observations relate to\nlight, the saltness of the sea, its flux and reflux, and other points\nof astronomy, meteorology, and natural history. He speaks of the sex of\nplants[98]; rejects judicial astrology; and notices the astronomical\nsystems of Copernicus, Tycho, Fracastoro, and Torre. But the mode in\nwhich he speaks of experiments proves, what indeed is evident from the\ngeneral scheme of his system, that he had no due appreciation of the\nplace which observation must hold in real and natural philosophy.\n\n\n7. _Picus, Agrippa, &c._--It had been seen in the later philosophical\nhistory of Greece, how readily the ideas of the Platonic school lead\non to a system of unfathomable and unbounded mysticism. John Picus,\nof Mirandula[99], added to the study of Plato and the Neoplatonists,\na mass of allegorical interpretations of the Scriptures, and the\ndreams of the Cabbala, a Jewish system[100], which pretends to explain\nhow all things are an emanation of the Deity. To this his nephew,\nFrancis Picus, added a reference to inward illumination[101], by which\nknowledge is obtained, independently of the progress of reasoning.\nJohn Reuchlin, or Capnio, born 1455; John Baptist Helmont, born 1577;\nFrancis Mercurius Helmont, born 1618, and others, succeeded John Picus\nin his admiration of the Cabbala: while others, as Jacob B\u0153hmen,\nrested upon internal revelations like Francis Picus. And thus we have\na series of mystical writers, continued into modern times, who may\nbe considered as the successors of the Platonic school; and who all\nexhibit views altogether erroneous with regard to the nature and origin\nof knowledge. Among the various dreams of this school are certain wide\nand loose analogies of terrestrial and spiritual things. Thus in the\nwritings of Cornelius Agrippa (who was born 1487, at Cologne) we have\nsuch systems as the following[102]:--\"Since there is a threefold world,\nelemental, celestial, and intellectual, and each lower one is governed\nby that above it, and receives the influence of its powers: so that\nthe very Archetype and Supreme Author transfuses the virtues of his\nomnipotence into us through angels, heavens, stars, elements, animals,\nplants, stones,--into us, I say, for whose service he has framed and\ncreated all these things;--the Magi do not think it irrational that\nwe should be able to ascend by the same degrees, the same worlds, to\nthis Archetype of the world, the Author and First Cause of all, of whom\nall things are, and from whom they proceed; and should not only avail\nourselves of those powers which exist in the nobler works of creation,\nbut also should be able to attract other powers, and add them to these.\"\n\nAgrippa's work, _De Vanitate Scientiarum_, may be said rather to\nhave a skeptical and cynical, than a Platonic, character. It is a\ndeclamation[103], in a melancholy mood, against the condition of the\nsciences in his time. His indignation at the worldly success of men\nwhom he considered inferior to himself, had, he says, metamorphosed him\ninto a dog, as the poets relate of Hecuba of Troy, so that his impulse\nwas to snarl and bark. His professed purpose, however, was to expose\nthe dogmatism, the servility, the self-conceit, and the neglect of\nreligious truth which prevailed in the reigning Schools of philosophy.\nHis views of the nature of science, and the modes of improving its\ncultivation, are too imperfect and vague to allow us to rank him among\nthe reformers of science.\n\n\n8. _Paracelsus, Fludd, &c._--The celebrated Paracelsus[104] put himself\nforwards as a reformer in philosophy, and obtained no small number of\nadherents. He was, in most respects, a shallow and impudent pretender;\nand had small knowledge of the literature or science of his time:\nbut by the tone of his speaking and writing he manifestly belongs\nto the mystical school of which we are now speaking. Perhaps by the\nboldness with which he proposed new systems, and by connecting these\nwith the practical doctrines of medicine, he contributed something to\nthe introduction of a new philosophy. We have seen in the History of\nChemistry that he was the author of the system of Three Principles,\n(salt, sulphur, and mercury,) which replaced the ancient doctrine of\nFour Elements, and prepared the way for a true science of chemistry.\nBut the salt, sulphur, and mercury of Paracelsus were not, he tells his\ndisciples, the visible bodies which we call by those names, but certain\ninvisible, astral, or sidereal elements. The astral salt is the basis\nof the solidity and incombustible parts in bodies; the astral sulphur\nis the source of combustion and vegetation; the astral mercury is the\norigin of fluidity and volatility. And again, these three elements are\nanalogous to the three elements of man,--Body, Spirit, and Soul.\n\nA writer of our own country, belonging to this mystical school, is\nRobert Fludd, or De Fluctibus, who was born in 1571, in Kent, and\nafter pursuing his studies at Oxford, travelled for several years.\nOf all the Theosophists and Mystics, he is by much the most learned;\nand was engaged in various controversies with Mersenne, Gassendi,\nKepler, and others. He thus brings us in contact with the next class\nof philosophers whom we have to consider, the practical reformers\nof philosophy;--those who furthered the cause of science by making,\npromulgating, or defending the great discoveries which now began\nto occupy men. He adopted the principle, which we have noticed\nelsewhere[105], of the analogy of the Macrocosm and Microcosm, the\nworld of nature and the world of man. His system contains such a\nmixture and confusion of physical and metaphysical doctrines as might\nbe expected from his ground-plan, and from his school. Indeed his\nobject, the general object of mystical speculators, is to identify\nphysical with spiritual truths. Yet the influence of the practical\nexperimental philosophy which was now gaining ground in the world may\nbe traced in him. Thus he refers to experiments on distillation to\nprove the existence and relation of the regions of water, air, and\nfire, and of the spirits which correspond to them; and is conceived, by\nsome persons[106], to have anticipated Torricelli in the invention of\nthe Barometer.\n\nWe need no further follow the speculations of this school. We see\nalready abundant reason why the reform of the methods of pursuing\nscience could not proceed from the Platonists. Instead of seeking\nknowledge by experiment, they immersed themselves deeper than even the\nAristotelians had done in traditionary lore, or turned their eyes\ninwards in search of an internal illumination. Some attempts were made\nto remedy the defects of philosophy by a recourse to the doctrines\nof other sects of antiquity, when men began to feel more distinctly\nthe need of a more connected and solid knowledge of nature than the\nestablished system gave them. Among these attempts were those of\nBerigard[107], Magernus, and especially Gassendi, to bring into repute\nthe philosophy of the Ionian school, of Democritus and of Epicurus. But\nthese endeavours were posterior in time to the new impulse given to\nknowledge by Copernicus, Kepler, and Galileo, and were influenced by\nviews arising out of the success of these discoveries, and they must,\ntherefore, be considered hereafter. In the mean time, some independent\nefforts (arising from speculative rather than practical reformers)\nwere made to cast off the yoke of the Aristotelian dogmatism, and to\napprehend the true form of that new philosophy which the most active\nand hopeful minds saw to be needed; and we must give some account of\nthese attempts, before we can commit ourselves to the full stream of\nprogressive philosophy.\n\n\nFOOTNOTES:\n\n[Footnote 86: Gratian published the _Decretals_ in the twelfth century;\nand the Canon and Civil Law became a regular study in the universities\nsoon afterwards.]\n\n[Footnote 87: Tenneman, ix. 4.]\n\n[Footnote 88: Tenneman, ix. 25.]\n\n[Footnote 89: \"Jam nobis manifestum est terram istam in veritate\nmoveri,\" &c.--_De Doct\u00e2 Ignoranti\u00e2_, lib. ii. c. xii.]\n\n[Footnote 90: _De Doct. Ignor._ lib. i. c. i.]\n\n[Footnote 91: _De Conjecturis_, lib. i. c. iii. iv.]\n\n[Footnote 92: Born in 1433.]\n\n[Footnote 93: Born 1529, died 1597.]\n\n[Footnote 94: _Aristoteles Exotericus_, p. 50.]\n\n[Footnote 95: Tiraboschi, t. vii. pt. ii. p. 411.]\n\n[Footnote 96: \"Franciscus Patricius, novam veram integram de universis\nconditurus philosophiam, sequentia uti verissima pr\u00e6nuntiare est\nausus. Pr\u00e6nunciata ordine persecutus, divinis oraculis, geometricis\nrationibus, clarissimisque experimentis comprobavit.\n\n  Ante primum nihil,\n  Post primum omnia,\n  A principio omnia,\" &c.\n\nHis other works are _Panaugia_, _Pancosmia_, _Dissertations\nPeripatetic\u00e6_.]\n\n[Footnote 97: Tiraboschi, t. vii. pt. ii. p. 411.]\n\n[Footnote 98: _Dissert. Perip._ t. ii. lib. v. sub fin.]\n\n[Footnote 99: Tenneman, ix. 148.]\n\n[Footnote 100: Tenneman, ix. 167.]\n\n[Footnote 101: _Ibid._ 158.]\n\n[Footnote 102: Agrippa, _De Occult. Phil._ lib. i. c. l.]\n\n[Footnote 103: Written in 1526.]\n\n[Footnote 104: Philip Aurelius Theophrastus Bombastus von Hohenheim,\nalso called Paracelsus Eremita, born at Einsiedlen in Switzerland, in\n1493.]\n\n[Footnote 105: _Hist. Sc. Id._ b. ix. c. 2. sect. 1. The Mystical\nSchool of Biology.]\n\n[Footnote 106: Tenneman, ix. 221.]\n\n[Footnote 107: Tenneman, ix. 265.]\n\n\n\n\nCHAPTER XIII.\n\nTHE THEORETICAL REFORMERS OF SCIENCE.\n\n\nWe have already seen that Patricius, about the middle of the sixteenth\ncentury, announced his purpose of founding anew the whole fabric\nof philosophy; but that, in executing this plan, he ran into wide\nand baseless hypotheses, suggested by _\u00e0 priori_ conceptions rather\nthan by external observation; and that he was further misled by\nfanciful analogies resembling those which the Platonic mystics loved\nto contemplate. The same time, and the period which followed it,\nproduced several other essays which were of the same nature, with the\nexception of their being free from the peculiar tendencies of the\nPlatonic school: and these insurrections against the authority of\nthe established dogmas, although they did not directly substitute a\nbetter positive system in the place of that which they assailed, shook\nthe authority of the Aristotelian system, and led to its overthrow;\nwhich took place as soon as these theoretical reformers were aided by\npractical reformers.\n\n\n1. _Bernardinus Telesius._--Italy, always, in modern times, fertile in\nthe beginnings of new systems, was the soil on which these innovators\narose. The earliest and most conspicuous of them is Bernardinus\nTelesius, who was born in 1508, at Cosenza, in the kingdom of Naples.\nHis studies, carried on with great zeal and ability, first at Milan\nand then at Rome, made him well acquainted with the knowledge of\nhis times; but his own reflections convinced him that the basis of\nscience, as then received, was altogether erroneous; and led him to\nattempt a reform, with which view, in 1565, he published, at Rome,\nhis work[108], \"_Bernardinus Telesius, of Cosenza, on the Nature of\nThings, according to principles of his own_.\" In the preface of this\nwork he gives a short account[109] of the train of reflection by which\nhe was led to put himself in opposition to the Aristotelian philosophy.\nThis kind of autobiography occurs not unfrequently in the writings of\ntheoretical reformers; and shows how livelily they felt the novelty of\ntheir undertaking. After the storm and sack of Rome in 1527, Telesius\nretired to Padua, as a peaceful seat of the muses; and there studied\nphilosophy and mathematics, with great zeal, under the direction of\nJerome Amalth\u00e6us and Frederic Delphinus. In these studies he made great\nprogress; and the knowledge which he thus acquired threw a new light\nupon his view of the Aristotelian philosophy. He undertook a closer\nexamination of the Physical Doctrines of Aristotle; and as the result\nof this, he was astonished how it could have been possible that so\nmany excellent men, so many nations, and even almost the whole human\nrace, should, for so long a time, have allowed themselves to be carried\naway by a blind reverence for a teacher, who had committed errors so\nnumerous and grave as he perceived to exist in \"the philosopher.\" Along\nwith this view of the insufficiency of the Aristotelian philosophy,\narose, at an early period, the thought of erecting a better system in\nits place. With this purpose he left Padua, when he had received the\ndegree of Doctor, and went to Rome, where he was encouraged in his\ndesign by the approval and friendly exhortations of distinguished men\nof letters, amongst whom were Ubaldino Bandinelli and Giovanni della\nCasa. From Rome he went to his native place, when the incidents and\noccupations of a married life for a while interrupted his philosophical\nproject. But after his wife was dead, and his eldest son grown to\nmanhood, he resumed with ardour the scheme of his youth; again studied\nthe works of Aristotle and other philosophers, and composed and\npublished the first two books of his treatise. The opening to this\nwork sufficiently exhibits the spirit in which it was conceived. Its\nobject is stated in the title to be to show, that \"the construction\nof the world, the magnitude and nature of the bodies contained in\nit, are not to be investigated by reasoning, which was done by the\nancients, but are to be apprehended by the senses, and collected from\nthe things themselves.\" And the Proem is in the same strain. \"They who\nbefore us have inquired concerning the construction of this world and\nof the things which it contains, seem indeed to have prosecuted their\nexamination with protracted vigils and great labour, but _never to have\nlooked at it_.\" And thus, he observes, they found nothing but error.\nThis he ascribes to their presumption. \"For, as it were, attempting\nto rival God in wisdom, and venturing to seek for the principles and\ncauses of the world by the light of their own reason, and thinking they\nhad found what they had only invented, they made an arbitrary world of\ntheir own.\" \"_We_ then,\" he adds, \"not relying on ourselves, and of a\nduller intellect than they, propose to ourselves to turn our regards to\nthe world itself and its parts.\"\n\nThe execution of the work, however, by no means corresponds to the\nannouncement. The doctrines of Aristotle are indeed attacked; and the\nobjections to these, and to other received opinions, form a large\npart of the work. But these objections are supported by _\u00e0 priori_\nreasoning, and not by experiments. And thus, rejecting the Aristotelian\nphysics, he proposes a system at least equally baseless; although, no\ndoubt, grateful to the author from its sweeping and apparently simple\ncharacter. He assumes three principles, Heat, Cold, and Matter: Heat\nis the principle of motion, Cold of immobility, and Matter is the\ncorporeal substratum, in which these incorporeal and active principles\nproduce their effects. It is easy to imagine that, by combining and\nseparating these abstractions in various ways, a sort of account of\nmany natural phenomena may be given; but it is impossible to ascribe\nany real value to such a system. The merit of Telesius must be\nconsidered to consist in his rejection of the Aristotelian errors,\nin his perception of the necessity of a reform in the method of\nphilosophizing, and in his persuasion that this reform must be founded\non experiments rather than on reasoning. When he said[110], \"We propose\nto ourselves to turn our eyes to the world itself, and its parts, their\npassions, actions, operations, and species,\" his view of the course to\nbe followed was right; but his purpose remained but ill fulfilled, by\nthe arbitrary edifice of abstract conceptions which his system exhibits.\n\nFrancis Bacon, who, about half a century later, treated the subject\nof a reform of philosophy in a far more penetrating and masterly\nmanner, has given us his judgment of Telesius. In his view, he takes\nTelesius as the restorer of the Atomic philosophy, which Democritus\nand Parmenides taught among the ancients; and according to his\ncustom, he presents an image of this philosophy in an adaptation of\na portion of ancient mythology[111]. The Celestial Cupid, who with\nC\u0153lus, was the parent of the Gods and of the Universe, is exhibited\nas a representation of matter and its properties, according to the\nDemocritean philosophy. \"Concerning Telesius,\" says Bacon, \"we think\nwell, and acknowledge him as a lover of truth, a useful contributor to\nscience, an amender of some tenets, the first of recent men. But we\nhave to do with him as the restorer of the philosophy of Parmenides,\nto whom much reverence is due.\" With regard to this philosophy,\nhe pronounces a judgment which very truly expresses the cause of\nits rashness and emptiness. \"It is,\" he says, \"such a system[112]\nas naturally proceeds from the intellect, abandoned to its own\nimpulse, and not rising from experience to theory continuously and\nsuccessively.\" Accordingly, he says that, \"Telesius, although learned\nin the Peripatetic philosophy (if that were anything), which indeed, he\nhas turned against the teachers of it, is hindered by his affirmations,\nand is more successful in destroying than in building.\"\n\nThe work of Telesius excited no small notice, and was placed in the\n_Index Expurgatorius_. It made many disciples, a consequence probably\ndue to its spirit of system-making, no less than to its promise of\nreform, or its acuteness of argument; for till trial and reflection\nhave taught man modesty and moderation, he can never be content to\nreceive knowledge in the small successive instalments in which nature\ngives it forth to him. It is the makers of large systems, arranged with\nan _appearance_ of completeness and symmetry, who, principally, give\nrise to Schools of philosophy.\n\n\n2. (_Thomas Campanella_).--Accordingly, Telesius may be looked upon as\nthe founder of a School. His most distinguished successor was Thomas\nCampanella, who was born in 1568, at Stilo, in Calabria. He showed\ngreat talents at an early age, prosecuting his studies at Cosenza,\nthe birth-place of the great opponent of Aristotle and reformer of\nphilosophy. He, too, has given us an account[113] of the course of\nthought by which he was led to become an innovator. \"Being afraid\nthat not genuine truth, but falsehood in the place of truth, was the\ntenant of the Peripatetic School, I examined all the Greek, Latin,\nand Arabic commentators of Aristotle, and hesitated more and more, as\nI sought to learn whether what they have said were also to be read\nin the world itself, which I had been taught by learned men was the\nliving book of God. And as my doctors could not satisfy my scruples,\nI resolved to read all the books of Plato, Pliny, Galen, the Stoics,\nand the Democriteans, and especially those of Telesius; and to compare\nthem with that _first and original writing, the world_; that thus from\nthe primary autograph, I might learn if the copies contained anything\nfalse.\" Campanella probably refers here to an expression of Plato,\nwho says, \"the world is God's epistle to mankind.\" And this image, of\nthe natural world as an original manuscript, while human systems of\nphilosophy are but copies, and may be false ones, became a favourite\nthought of the reformers, and appears repeatedly in their writings from\nthis time. \"When I held my public disputation at Cosenza,\" Campanella\nproceeds, \"and still more, when I conversed privately with the brethren\nof the monastery, I found little satisfaction in their answers; but\nTelesius delighted me, on account of his freedom in philosophizing,\nand because he rested upon the nature of things, and not upon the\nassertions of men.\"\n\nWith these views and feelings, it is not wonderful that Campanella,\nat the early age of twenty-two (1590,) published a work remarkable\nfor the bold promise of its title: \"_Thomas Campanella's Philosophy\ndemonstrated to the senses, against those who have philosophized in an\narbitrary and dogmatical manner, not taking nature for their guide; in\nwhich the errors of Aristotle and his followers are refuted from their\nown assertions and the laws of nature: and all the imaginations feigned\nin the place of nature by the Peripatetics are altogether rejected;\nwith a true defence of Bernardin Telesius of Cosenza, the greatest\nof philosophers; confirmed by the opinions of the ancients, here\nelucidated and defended, especially those of the Platonists_.\"\n\nThis work was written in answer to a book published against Telesius\nby a Neapolitan professor named Marta; and it was the boast of the\nyoung author that he had only employed eleven months in the composition\nof his defence, while his adversary had been engaged eleven years\nin preparing his attack. Campanella found a favourable reception in\nthe house of the Marchese Lavelli, and there employed himself in the\ncomposition of an additional work, entitled _On the Sense of Things\nand Magic_, and in other literary labours. These, however, are full\nof the indications of an enthusiastic temper, inclined to mystical\ndevotion, and of opinions bearing the cast of pantheism. For instance,\nthe title of the book last quoted sets forth as demonstrated in the\ncourse of the work, that \"the world is the living and intelligent\nstatue of God; and that all its parts, and particles of parts, are\nendowed some with a clearer, some with a more obscure sense, such\nas suffices for the preservation of each and of the whole.\" Besides\nthese opinions, which could not fail to make him obnoxious to the\nreligious authorities, Campanella[114] engaged in schemes of political\nrevolution, which involved him in danger and calamity. He took part\nin a conspiracy, of which the object was to cast off the tyranny of\nSpain, and to make Calabria a republic. This design was discovered; and\nCampanella, along with others, was thrown into prison and subjected to\ntorture. He was kept in confinement twenty-seven years; and at last\nobtained his liberation by the interposition of Pope Urban VIII. He\nwas, however, still in danger from the Neapolitan Inquisition; and\nescaped in disguise to Paris, where he received a pension from the\nking, and lived in intercourse with the most eminent men of letters. He\ndied there in 1639.\n\nCampanella was a contemporary of Francis Bacon, whom we must consider\nas belonging to an epoch to which the Calabrian school of innovators\nwas only a prelude. I shall not therefore further follow the connexion\nof writers of this order. Tobias Adami, a Saxon writer, an admirer\nof Campanella's works, employed himself, about 1620, in adapting\nthem to the German public, and in recommending them strongly to\nGerman philosophers. Descartes, and even Bacon, may be considered as\nsuccessors of Campanella; for they too were theoretical reformers; but\nthey enjoyed the advantage of the light which had, in the mean time,\nbeen thrown upon the philosophy of science, by the great practical\nadvances of Kepler, Galileo, and others. To these practical reformers\nwe must soon turn our attention: but we may first notice one or two\nadditional circumstances belonging to our present subject.\n\nCampanella remarks that both the Peripatetics and the Platonists\nconducted the learner to knowledge by a long and circuitous path, which\nhe wished to shorten by setting out from the sense. Without speaking\nof the methods which he proposed, we may notice one maxim[115] of\nconsiderable value which he propounds, and to which we have already\nbeen led. \"We begin to reason from sensible objects, and definition\nis the end and epilogue of science. It is not the beginning of our\nknowing, but only of our teaching.\"\n\n\n3. (_Andrew C\u00e6salpinus._)--The same maxim had already been announced\nby C\u00e6salpinus, a contemporary of Telesius; (he was born at Arezzo in\n1520, and died at Rome in 1603). C\u00e6salpinus is a great name in science,\nthough professedly an Aristotelian. It has been seen in the _History\nof Science_[116], that he formed the first great epoch of the science\nof botany by his systematic arrangement of plants, and that in this\ntask he had no successor for nearly a century. He also approached near\nto the great discovery of the circulation of the blood[117]. He takes\na view of science which includes the remark that we have just quoted\nfrom Campanella: \"We reach perfect knowledge by three steps: Induction,\nDivision, Definition. By Induction, we collect likeness and agreement\nfrom observation; by Division, we collect unlikeness and disagreement;\nby Definition, we learn the proper substance of each object. Induction\nmakes universals from particulars, and offers to the mind all\nintelligible matter; Division discovers the difference of universals,\nand leads to species; Definition resolves species into their principles\nand elements[118].\" Without asserting this to be rigorously correct, it\nis incomparably more true and philosophical than the opposite view,\nwhich represents definition as the beginning of our knowledge; and\nthe establishment of such a doctrine is a material step in inductive\nphilosophy[119].\n\n\n4. (_Giordano Bruno._)--Among the Italian innovators of this time\nwe must notice the unfortunate Giordano Bruno, who was born at Nola\nabout 1550 and burnt at Rome in 1600. He is, however, a reformer of a\ndifferent school from Campanella; for he derives his philosophy from\nIdeas and not from Observation. He represents himself as the author of\na new doctrine, which he terms the _Nolan Philosophy_. He was a zealous\npromulgator and defender of the Copernican system of the universe, as\nwe have noticed in the _History of Science_[120]. Campanella also wrote\nin defence of that system.\n\nIt is worthy of remark that a thought which is often quoted from\nFrancis Bacon, occurs in Bruno's _Cena di Cenere_, published in\n1584; I mean, the notion that the later times are more aged than\nthe earlier. In the course of the dialogue, the Pedant, who is one\nof the interlocutors, says, \"In antiquity is wisdom;\" to which the\nPhilosophical Character replies, \"If you knew what you were talking\nabout, you would see that your principle leads to the opposite result\nof that which you wish to infer;--I mean, that _we_ are older, and have\nlived longer, than our predecessors.\" He then proceeds to apply this,\nby tracing the course of astronomy through the earlier astronomers up\nto Copernicus.\n\n\n5. (_Peter Ramus._)--I will notice one other reformer of this period,\nwho attacked the Aristotelian system on another side, on which it\nwas considered to be most impregnable. This was Peter Ramus,(born in\nPicardy in 1515,) who ventured to denounce the _Logic_ of Aristotle as\nunphilosophical and useless. After showing an extraordinary aptitude\nfor the acquirement of knowledge in his youth, when he proceeded to\nthe degree of Master of Arts, he astonished his examiners by choosing\nfor the subject of the requisite disputation the thesis[121], \"that\nwhat Aristotle has said is all wrong.\" This position, so startling in\n1535, he defended for the whole day, without being defeated. This was,\nhowever, only a formal academical exercise, which did not necessarily\nimply any permanent conviction of the opinion thus expressed. But his\nmind was really labouring to detect and remedy the errors which he\nthus proclaimed. From him, as from the other reformers of this time,\nwe have an account of this mental struggle[122]. He says, in a work on\nthis subject, \"I will candidly and simply explain how I was delivered\nfrom the darkness of Aristotle. When, according to the laws of our\nuniversity, I had spent three years and a half in the Aristotelian\nphilosophy, and was now invested with the philosophical laurel as a\nMaster of Arts, I took an account of the time which I had consumed\nin this study, and considered on what subjects I should employ this\nlogical art of Aristotle, which I had learnt with so much labour and\nnoise, I found it made me not more versed in history or antiquities,\nmore eloquent in discourse, more ready in verse, more wise in any\nsubject. Alas for me! how was I overpowered, how deeply did I groan,\nhow did I deplore my lot and my nature, how did I deem myself to be\nby some unhappy and dismal fate and frame of mind abhorrent from the\nMuses, when I found that I was one who, after all my pains, could\nreap no benefit from that wisdom of which I heard so much, as being\ncontained in the Logic of Aristotle.\" He then relates that he was\nled to the study of the Dialogues of Plato, and was delighted with\nthe kind of analysis of the subjects discussed which Socrates is\nthere represented as executing. \"Well,\" he adds, \"I began thus to\nreflect within myself--(I should have thought it impious to say it to\nanother)--What, I pray you, prevents me from _socratizing_; and from\nasking, without regard to Aristotle's authority, whether Aristotle's\nLogic be true and correct? It may be that that philosopher leads\nus wrong; and if so, no wonder that I cannot find in his books the\ntreasure which is not there. What if his dogmas be mere figments? Do\nI not tease and torment myself in vain, trying to get a harvest from\na barren soil?\" He convinced himself that the Aristotelian logic was\nworthless: and constructed a new system of Logic, founded mainly on the\nPlatonic process of exhausting a subject by analytical classification\nof its parts. Both works, his _Animadversions on Aristotle_, and his\n_Logic_, appeared in 1543. The learned world was startled and shocked\nto find a young man, on his first entrance into life, condemning\nas faulty, fallacious, and useless, that part of Aristotle's works\nwhich had always hitherto been held as a masterpiece of philosophical\nacuteness, and as the Organon of scientific reasoning. And in truth, it\nmust be granted that Ramus does not appear to have understood the real\nnature and object of Aristotle's Logic; while his own system could not\nsupply the place of the old one, and was not of much real value. This\ndissent from the established doctrines was, however, not only condemned\nbut punished. The printing and selling of his books was forbidden\nthrough France; and Ramus was stigmatized by a sentence[123] which\ndeclared him rash, arrogant, impudent, and ignorant, and prohibited\nfrom teaching logic and philosophy. He was, however, afterwards\nrestored to the office of professor: and though much attacked,\npersisted in his plan of reforming, not only Logic but Physics and\nMetaphysics. He made his position still more dangerous by adopting the\nreformed religion; and during the unhappy civil wars of France, he was\ndeprived of his professorship, driven from Paris, and had his library\nplundered. He endeavoured, but in vain, to engage a German professor,\nSchegk, to undertake the reform of the Aristotelian Physics; a portion\nof knowledge in which he felt himself not to be strong. Unhappily for\nhimself, he afterwards returned to Paris, where he perished in the\nmassacre of St. Bartholomew in 1572.\n\nRamus's main objection to the Aristotelian Logic is, that it is not\nthe image of the natural process of thought; an objection which shows\nlittle philosophical insight; for the course by which we obtain\nknowledge may well differ from the order in which our knowledge,\nwhen obtained, is exhibited. We have already seen that Ramus's\ncontemporaries, C\u00e6salpinus and Campanella, had a wiser view; placing\ndefinition as the last step in knowing, but the first in teaching.\nBut the effect which Ramus produced was by no means slight. He aided\npowerfully in turning the minds of men to question the authority of\nAristotle on all points; and had many followers, especially among the\nProtestants. Among the rest, Milton, our great poet, published \"Artis\nLogic\u00e6 plenior Institutio _ad Petri Rami methodum concinnata_;\" but\nthis work, appearing in 1672, belongs to a succeeding period.\n\n\n6. (_The Reformers in general_).--It is impossible not to be struck\nwith the series of misfortunes which assailed the reformers of\nphilosophy of the period we have had to review. Roger Bacon was\nrepeatedly condemned and imprisoned; and, not to speak of others who\nsuffered under the imputation of magical arts, Telesius is said[124] to\nhave been driven from Naples to his native city by calumny and envy;\nC\u00e6salpinus was accused of atheism[125]; Campanella was imprisoned for\ntwenty-seven years and tortured; Giordano Bruno was burnt at Rome as\na heretic; Ramus was persecuted during his life, and finally murdered\nby his personal enemy Jacques Charpentier, in a massacre of which the\nplea was religion. It is true, that for the most part these misfortunes\nwere not principally due to the attempts at philosophical reform, but\nwere connected rather with politics or religion. But we cannot doubt\nthat the spirit which led men to assail the received philosophy, might\nreadily incline them to reject some tenets of the established religion;\nsince the boundary line of these subjects is difficult to draw. And as\nwe have seen, there was in most of the persons of whom we have spoken,\nnot only a well-founded persuasion of the defects of existing systems,\nbut an eager spirit of change, and a sanguine anticipation of some\nwide and lofty philosophy, which was soon to elevate the minds and\nconditions of men. The most unfortunate were, for the most part, the\nleast temperate and judicious reformers. Patricius, who, as we have\nseen, declared himself against the Aristotelian philosophy, lived and\ndied at Rome in peace and honour[126].\n\n\n7. (_Melancthon._)--It is not easy to point out with precision the\nconnexion between the efforts at a Reform in Philosophy, and the great\nReformation of Religion in the sixteenth century. The disposition to\nassert (practically at least) a freedom of thinking, and to reject the\ncorruptions which tradition had introduced and authority maintained,\nnaturally extended its influence from one subject to another; and\nespecially in subjects so nearly connected as theology and philosophy.\nThe Protestants, however, did not reject the Aristotelian system;\nthey only reformed it, by going back to the original works of the\nauthor, and by reducing it to a conformity with Scripture. In this\nreform, Melancthon was the chief author, and wrote works on Logic,\nPhysics, Morals, and Metaphysics, which were used among Protestants.\nOn the subject of the origin of our knowledge, his views contained\na very philosophical improvement of the Aristotelian doctrines. He\nrecognized the importance of Ideas, as well as of Experience. \"We could\nnot,\" he says[127], \"proceed to reason at all, except there were by\nnature innate in man certain fixed points, that is, principles of\nscience;--as Number, the recognition of Order and Proportion, logical,\ngeometrical, physical and moral Principles. Physical principles are\nsuch as these,--everything which exists proceeds from a cause,--a body\ncannot be in two places at once,--time is a continued series of things\nor of motions,--and the like.\" It is not difficult to see that such\nPrinciples partake of the nature of the Fundamental Ideas which we have\nattempted to arrange and enumerate in a previous part of this work.\n\nBefore we proceed to the next chapter, which treats of the Practical\nReformers of Scientific Method, let us for an instant look at the\nstrong persuasion implied in the titles of the works of this period,\nthat the time of a philosophical revolution was at hand. Telesius\npublished _De Rerum Natura juxta propria principia_; Francis Helmont,\n_Philosophia vulgaris refutata_; Patricius, _Nova de Universis\nPhilosophia_; Campanella, _Philosophia sensibus demonstrata, adversus\nerrores Aristotelis_; Bruno professed himself the author of a _Nolan\nPhilosophy_; and Ramus of a _New Logic_. The age announced itself\npregnant; and the eyes of all who took an interest in the intellectual\nfortunes of the race, were looking eagerly for the expected offspring.\n\n\nFOOTNOTES:\n\n[Footnote 108: Bernardini Telesii Consentini _De Rerum Natura juxta\npropria Principia_.]\n\n[Footnote 109: I take this account from Tenneman: this Proem was\nomitted in subsequent editions of Telesius, and is not in the one which\nI have consulted. Tenneman, _Gesch. d. Phil._ ix. 280.]\n\n[Footnote 110: Proem.]\n\n[Footnote 111: \"De Principiis atque Originibus secundum fabulas\nCupidinis et C\u0153li: sive Parmenidis et Telesii et pr\u00e6cipu\u00e8 Democriti\nPhilosophia tractata in Fabula de Cupidine.\"]\n\n[Footnote 112: \"Talia sunt qualia possunt esse ea qu\u00e6 ab intellectu\nsibi permisso, nec ab experimentis continenter et gradatim sublevato,\nprofecta videntur.\"]\n\n[Footnote 113: Thom. Campanella _de Libris propriis_, as quoted in\nTenneman, ix. 291.]\n\n[Footnote 114: _Economisti Italiani_, t. i. p. xxxiii.]\n\n[Footnote 115: Tenneman, ix. 305.]\n\n[Footnote 116: _Hist. Ind. Sc._ b. xvi. c. iii. sect. 2.]\n\n[Footnote 117: _Ibid._ b. xvii. c. ii. sect. 1.]\n\n[Footnote 118: _Qu\u00e6st. Peripat._ i. 1.]\n\n[Footnote 119: Tenneman, ix. 108.]\n\n[Footnote 120: _Hist. Ind. Sc._ b. v. c. iii. sect. 2.]\n\n[Footnote 121: Tenneman, ix. 420. \"Qu\u00e6cunque ab Aristotele dicta essent\ncommenticia esse.\" Freigius, _Vita Petri Rami_, p. 10.]\n\n[Footnote 122: Rami, _Animadv. Aristot._ i. iv.]\n\n[Footnote 123: See _Hist. Ind. Sc._ b. iv. c. iv. sect. 4.]\n\n[Footnote 124: Tenneman, ix. 230.]\n\n[Footnote 125: _Ibid._ 108.]\n\n[Footnote 126: Tenneman, ix. 246.]\n\n[Footnote 127: Melancthon, _De Anima_, p. 207, quoted in Tenneman, ix.\n121.]\n\n\n\n\nCHAPTER XIV.\n\nTHE PRACTICAL REFORMERS OF SCIENCE.\n\n\n1. _Character of the Practical Reformers._--We now come to a class\nof speculators who had perhaps a greater share in bringing about the\nchange from stationary to progressive knowledge, than those writers who\nso loudly announced the revolution. The mode in which the philosophers\nof whom we now speak produced their impressions on men's minds, was\nvery different from the procedure of the theoretical reformers. What\nthese talked of, they did; what these promised, they performed. While\nthe theorists concerning knowledge proclaimed that great advances\nwere to be made, the practical discoverers went steadily forwards.\nWhile one class spoke of a complete Reform of scientific Methods, the\nother, boasting little, and often thinking little of Method, proved\nthe novelty of their instrument by obtaining new results. While the\nmetaphysicians were exhorting men to consult experience and the senses,\nthe physicists were examining nature by such means with unparalleled\nsuccess. And while the former, even when they did for a moment refer\nto facts, soon rushed back into their own region of ideas, and tried\nat once to seize the widest generalizations, the latter, fastening\ntheir attention upon the phenomena, and trying to reduce them to\nlaws, were carried forwards by steps measured and gradual, such as no\nconjectural view of scientific method had suggested; but leading to\ntruths as profound and comprehensive as any which conjecture had dared\nto anticipate. The theoretical reformers were bold, self-confident,\nhasty, contemptuous of antiquity, ambitious of ruling all future\nspeculations, as they whom they sought to depose had ruled the past.\nThe practical reformers were cautious, modest, slow, despising no\nknowledge, whether borrowed from tradition or observation, confident in\nthe ultimate triumph of science, but impressed with the conviction that\neach single person could contribute a little only to its progress. Yet\nthough thus working rather than speculating,--dealing with particulars\nmore than with generals,--employed mainly in adding to knowledge, and\nnot in defining what knowledge is, or how additions are to be made\nto it,--these men, thoughtful, curious, and of comprehensive minds,\nwere constantly led to important views on the nature and methods of\nscience. And these views, thus suggested by reflections on their own\nmental activity, were gradually incorporated with the more abstract\ndoctrines of the metaphysicians, and had a most important influence\nin establishing an improved philosophy of science. The indications of\nsuch views we must now endeavour to collect from the writings of the\ndiscoverers of the times preceding the seventeenth century.\n\nSome of the earliest of these indications are to be found in those who\ndealt with Art rather than with Science. I have already endeavoured\nto show that the advance of the arts which give us a command over the\npowers of nature, is generally prior to the formation of exact and\nspeculative knowledge concerning those powers. But Art, which is thus\nthe predecessor of Science, is, among nations of acute and active\nintellects, usually its parent. There operates, in such a case, a\nspeculative spirit, leading men to seek for the reasons of that which\nthey find themselves able to do. How slowly, and with what repeated\ndeviations men follow this leading, when under the influence of a\npartial and dogmatical philosophy, the late birth and slow growth of\nsound physical theory shows. But at the period of which we now speak,\nwe find men, at length, proceeding in obedience to the impulse which\nthus drives them from practice to theory;--from an acquaintance with\nphenomena to a free and intelligent inquiry concerning their causes.\n\n\n2. _Leonardo da Vinci._--I have already noted, in the History of\nScience, that the Indistinctness of Ideas, which was long one main\nimpediment to the progress of science in the middle ages, was first\nremedied among architects and engineers. These men, so far at least as\nmechanical ideas were concerned, were compelled by their employments\nto judge rightly of the relations and properties of the materials with\nwhich they had to deal; and would have been chastised by the failure\nof their works, if they had violated the laws of mechanical truth. It\nwas not wonderful, therefore, that these laws became known to _them_\nfirst. We have seen, in the _History_, that Leonardo da Vinci, the\ncelebrated painter, who was also an engineer, is the first writer in\nwhom we find the true view of the laws of equilibrium of the lever in\nthe most general case. This artist, a man of a lively and discursive\nmind, is led to make some remarks[128] on the formation of our\nknowledge, which may show the opinions on that subject that already\noffered themselves at the beginning of the sixteenth century[129]. He\nexpresses himself as follows:--\"Theory is the general, Experiments are\nthe soldiers. The interpreter of the artifices of nature is Experience:\nshe is never deceived. Our judgment sometimes is deceived, because it\nexpects effects which Experience refuses to allow.\" And again, \"We\nmust consult Experience, and vary the circumstances till we have drawn\nfrom them general rules; for it is she who furnishes true rules. But\nof what use, you ask, are these rules; I reply, that they direct us in\nthe researches of nature and the operations of art. They prevent our\nimposing upon ourselves and others by promising ourselves results which\nwe cannot obtain.\n\n\"In the study of the sciences which depend on mathematics, those who do\nnot consult nature but authors, are not the children of nature, they\nare only her grandchildren. She is the true teacher of men of genius.\nBut see the absurdity of men! They turn up their noses at a man who\nprefers to learn from nature herself rather than from authors who are\nonly her clerks.\"\n\nIn another place, in reference to a particular case, he says, \"Nature\nbegins from the Reason and ends in Experience; but for all that, we\nmust take the opposite course; begin from the Experiment and try to\ndiscover the Reason.\"\n\nLeonardo was born forty-six years before Telesius; yet we have here\nan estimate of the value of experience far more just and substantial\nthan the Calabrian school ever reached. The expressions contained in\nthe above extracts, are well worthy our notice;--that experience is\nnever deceived;--that we must vary our experiments, and draw from them\ngeneral rules;--that nature is the original source of knowledge, and\nbooks only a derivative substitute;--with a lively image of the sons\nand grandsons of nature. Some of these assertions have been deemed,\nand not without reason, very similar to those made by Bacon a century\nlater. Yet it is probable that the import of such expressions, in\nLeonardo's mind, was less clear and definite than that which they\nacquired by the progress of sound philosophy. When he says that theory\nis the general and experiments the soldiers, he probably meant that\ntheory directs men what experiments to make; and had not in his mind\nthe notion of a theoretical Idea ordering and brigading the Facts. When\nhe says that Experience is the interpreter of Nature, we may recollect,\nthat in a more correct use of this image, Experience and Nature are the\nwriting, and the Intellect of man the interpreter. We may add, that\nthe clear apprehension of the importance of Experience led, in this as\nin other cases, to an unjust depreciation of the value of what science\nowed to books. Leonardo would have made little progress, if he had\nattempted to master a complex science, astronomy for instance, by means\nof observation alone, without the aid of books.\n\nBut in spite of such criticism, Leonardo's maxims show extraordinary\nsagacity and insight; and they appear to us the more remarkable, when\nwe see how rare such views are for a century after his time.\n\n\n3. _Copernicus._--For we by no means find, even in those practical\ndiscoverers to whom, in reality, the revolution in science, and\nconsequently in the philosophy of science, was due, this prompt and\nvigorous recognition of the supreme authority of observation as a\nground of belief; this bold estimate of the probable worthlessness\nof traditional knowledge; and this plain assertion of the reality of\ntheory founded upon experience. Among such discoverers, Copernicus must\never hold a most distinguished place. The heliocentric theory of the\nuniverse, established by him with vast labour and deep knowledge, was,\nfor the succeeding century, the field of discipline and exertion of all\nthe most active speculative minds. Men, during that time, proved their\nfreedom of thought, their hopeful spirit, and their comprehensive view,\nby adopting, inculcating, and following out the philosophy which this\ntheory suggested. But in the first promulgation of the theory, in the\nworks of Copernicus himself, we find a far more cautious and reserved\ntemper. He does not, indeed, give up the reality of his theory, but\nhe expresses himself so as to avoid shocking those who might (as some\nafterwards did) think it safe to speak of it as an _hypothesis_ rather\nthan a truth. In his preface addressed to the Pope[130], after speaking\nof the difficulties in the old and received doctrines, by which he\nwas led to his own theory, he says, \"Hence I began to think of the\nmobility of the earth; and although the opinion seemed absurd, yet\nbecause I knew that to others before me this liberty had been conceded,\nof imagining any kinds of circles in order to explain the phenomena\nof the stars, I thought it would also be readily granted me, that I\nmight try whether, by supposing the earth to be in motion, I might\nnot arrive at a better explanation than theirs, of the revolutions of\nthe celestial orbs.\" Nor does he anywhere assert that the seeming\nabsurdity had become a certain truth, or betray any feeling of triumph\nover the mistaken belief of his predecessors. And, as I have elsewhere\nshown, his disciples[131] indignantly and justly defended him from the\ncharge of disrespect towards Ptolemy and other ancient astronomers. Yet\nCopernicus is far from compromising the value or evidence of the great\ntruths which he introduced to general acceptance; and from sinking in\nhis exposition of his discoveries below the temper which had led to\nthem. His quotation from Ptolemy, that \"He who is to follow philosophy\nmust be a freeman in mind,\" is a grand and noble maxim, which it well\nbecame him to utter.\n\n\n4. _Fabricius._--In another of the great discoverers of this period,\nthough employed on a very different subject, we discern much of the\nsame temper. Fabricius of Acquapendente[132], the tutor and forerunner\nof our Harvey, and one of that illustrious series of Paduan professors\nwho were the fathers of anatomy[133], exhibits something of the same\nrespect for antiquity, in the midst of his original speculations.\nThus in a dissertation[134] _On the Action of the Joints_, he quotes\nAristotle's Mechanical Problems to prove that in all animal motion\nthere must be some quiescent fulcrum; and finds merit even in\nAristotle's ignorance. \"Aristotle,\" he says[135], \"did not know that\nmotion was produced by the muscle; and after staggering about from one\nsupposition to another, at last is compelled by the facts themselves\nto recur to an innate spirit, which, he conceives, is contrasted, and\nwhich pulls and pushes. And here we cannot help admiring the genius of\nAristotle, who, though ignorant of the muscle, invents something which\nproduces nearly the same effect as the muscle, namely, contraction and\npulling.\" He then, with great acuteness, points out the distinction\nbetween Aristotle's opinions, thus favourably interpreted, and those of\nGalen. In all this, we see something of the wish to find all truths in\nthe writings of the ancients, but nothing which materially interferes\nwith freedom of inquiry. The anatomists have in all ages and countries\nbeen practically employed in seeking knowledge from observation. Facts\nhave ever been to them a subject of careful and profitable study; while\nthe ideas which enter into the wider truths of the science, are, as we\nhave seen, even still involved in obscurity, doubt, and contest.\n\n\n5. _Maurolycus._--Francis Maurolycus of Messana, whose mathematical\nworks were published in 1575, was one of the great improvers of the\nscience of optics in his time. In his Preface to his Treatise on\nthe Spheres, he speaks of previous writers on the same subject; and\nobserves that as they have not superseded one another, they have not\nrendered it unfit for any one to treat the subject afresh. \"Yet,\" he\nsays, \"it is impossible to amend the errors of all who have preceded\nus. This would be a task too hard for Atlas, although he supports the\nheavens. Even Copernicus is tolerated, who makes the sun to be fixed,\nand the earth to move round it in a circle, and who is more worthy\nof a whip or a scourge than of a refutation.\" The mathematicians and\nastronomers of that time were not the persons most sensible of the\nprogress of physical knowledge; for the basis of their science, and\na great part of its substance, were contained in the writings of the\nancients; and till the time of Kepler, Ptolemy's work was, very justly,\nlooked upon as including all that was essential in the science.\n\n\n6. _Benedetti._--But the writers on Mechanics were naturally led to\npresent themselves as innovators and experimenters; for all that the\nancients had taught concerning the doctrine of motion was erroneous;\nwhile those who sought their knowledge from experiment, were constantly\nled to new truths. John Baptist Benedetti, a Venetian nobleman, in\n1599, published his _Speculationum Liber_, containing, among other\nmatter, a treatise on Mechanics, in which several of the Aristotelian\nerrors were refuted. In the Preface to this Treatise, he says, \"Many\nauthors have written much, and with great ability, on Mechanics; but\nsince nature is constantly bringing to light something either new,\nor before unnoticed, I too wished to put forth a few things hitherto\nunattempted, or not sufficiently explained.\" In the doctrine of motion\nhe distinctly and at some length condemns and argues against all the\nAristotelian doctrines concerning motion, weight, and many other\nfundamental principles of physics. Benedetti is also an adherent of\nthe Copernican doctrine. He states[136] the enormous velocity which\nthe heavenly bodies must have, if the earth be the centre of their\nmotions; and adds, \"which difficulty does not occur according to the\nbeautiful theory of the Samian Aristarchus, expounded in a divine\nmanner by Nicolas Copernicus; against which the reasons alleged by\nAristotle are of no weight.\" Benedetti throughout shows no want of the\ncourage or ability which were needed in order to rise in opposition\nagainst the dogmas of the Peripatetics. He does not, however, refer to\nexperiment in a very direct manner; indeed most of the facts on which\nthe elementary truths of mechanics rest, were known and admitted by the\nAristotelians; and therefore could not be adduced as novelties. On the\ncontrary, he begins with _\u00e0 priori_ maxims, which experience would not\nhave confirmed. \"Since,\" he says[137], \"we have undertaken the task\nof proving that Aristotle is wrong in his opinions concerning motion,\nthere are certain absolute truths, the objects of the intellect known\nof themselves, which we must lay down in the first place.\" And then, as\nan example of these truths, he states this: \"Any two bodies of equal\nsize and figure, but of different materials, will have their natural\nvelocities in the same proportion as their weights;\" where by their\nnatural velocities, he means the velocities with which they naturally\nfall downwards.\n\n\n7. _Gilbert._--The greatest of these practical reformers of science\nis our countryman, William Gilbert; if, indeed, in virtue of the\nclear views of the prospects which were then opening to science,\nand of the methods by which her future progress was to be secured,\nwhile he exemplified those views by physical discoveries, he does not\nrather deserve the still higher praise of being at the same time a\ntheoretical and a practical reformer. Gilbert's physical researches\nand speculations were employed principally upon subjects on which the\nancients had known little or nothing; and on which therefore it could\nnot be doubtful whether tradition or observation was the source of\nknowledge. Such was magnetism; for the ancients were barely acquainted\nwith the attractive property of the magnet. Its polarity, including\nrepulsion as well as attraction, its direction towards the north,\nits limited variation from this direction, its declination from the\nhorizontal position, were all modern discoveries. Gilbert's work[138]\non the magnet and on the magnetism of the earth, appeared in 1600;\nand in this, he repeatedly maintains the superiority of experimental\nknowledge over the physical philosophy of the ancients. His preface\nopens thus: \"Since in making discoveries and searching out the hidden\ncauses of things, stronger reasons are obtained from trustworthy\nexperiments and demonstrable arguments, than from probable conjectures\nand the dogmas of those who philosophize in the usual manner,\" he has,\nhe says, \"endeavoured to proceed from common magnetical experiments to\nthe inward constitution of the earth.\" As I have stated in the History\nof Magnetism[139], Gilbert's work contains all the fundamental facts\nof that science, so fully stated, that we have, at this day, little to\nadd to them. He is not, however, by the advance which he thus made,\nled to depreciate the ancients, but only to claim for himself the same\nliberty of philosophizing which they had enjoyed[140]. \"To those\nancient and first parents of philosophy, Aristotle, Theophrastus,\nPtolemy, Hippocrates, Galen, be all due honour; from them it was that\nthe stream of wisdom has been derived down to posterity. But our age\nhas discovered and brought to light many things which they, if they\nwere yet alive, would gladly embrace. Wherefore we also shall not\nhesitate to expound, by probable hypotheses, those things which by long\nexperience we have ascertained.\"\n\nIn this work the author not only adopts the Copernican doctrine of the\nearth's motion, but speaks[141] of the contrary supposition as utterly\nabsurd, founding his argument mainly on the vast velocities which such\na supposition requires us to ascribe to the celestial bodies. Dr.\nGilbert was physician to Queen Elizabeth and to James the First, and\ndied in 1603. Some time after his death the executors of his brother\npublished another work of his, _De Mundo nostro Sublunari Philosophia\nNova_, in which similar views are still more comprehensively presented.\nIn this he says, \"The two lords of philosophy, Aristotle and Galen,\nare held in worship like gods, and rule the schools;--the former by\nsome destiny obtained a sway and influence among philosophers, like\nthat of his pupil Alexander among the kings of the earth;--Galen, with\nlike success, holds his triumph among the physicians of Europe.\" This\ncomparison of Aristotle to Alexander was also taken hold of by Bacon.\nNor is Gilbert an unworthy precursor of Bacon in the view he gives of\nthe History of Science, which occupies the first three chapters of his\nPhilosophy. He traces this history from \"the simplicity and ignorance\nof the ancients,\" through \"the fabrication of the fable of the four\nelements,\" to Aristotle and Galen. He mentions with due disapproval the\nhost of commentators which succeeded, the alchemists, the \"shipwreck\nof science in the deluge of the Goths,\" and the revival of letters\nand genius in the time of \"our grandfathers.\" \"This later age,\" he\nsays, \"has exploded the Barbarians, and restored the Greeks and Latins\nto their pristine grace and honour. It remains, that if they have\nwritten aught in error, this should be remedied by better and more\nproductive processes (_frugiferis_ institutis), not to be contemned\nfor their novelty; (for nothing which is true is really new, but is\nperfect from eternity, though to weak man it may be unknown;) and that\nthus Philosophy may bear her fruit.\" The reader of Bacon will not fail\nto recognize, in these references to \"fruit-bearing\" knowledge, a\nsimilarity of expression with the _Novum Organon_.\n\nBacon does not appear to me to have done justice to his contemporary.\nHe nowhere recognizes in the labours of Gilbert a community of\npurpose and spirit with his own. On the other hand, he casts upon\nhim a reflection which he by no means deserves. In the _Advancement\nof Learning_[142], he says, \"Another error is, that men have used to\ninfect their meditations, opinions, and doctrines, with some conceits\nwhich they have most admired, or some sciences to which they have\nmost applied; and given all things else a tincture according to\nthem, utterly untrue and improper.... So have the alchemists made a\nphilosophy out of a few experiments of the furnace; and Gilbertus,\nour countryman, hath made a philosophy out of the observations of a\nloadstone,\" (in the Latin, philosophiam etiam e magnete elicuit).\nAnd in the same manner he mentions him in the _Novum Organon_[143],\nas affording an example of an empirical kind of philosophy, which\nappears to those daily conversant with the experiments, probable, but\nto other persons incredible and empty. But instead of blaming Gilbert\nfor disturbing and narrowing science by a too constant reference to\nmagnetical rules, we might rather censure Bacon, for not seeing how\nimportant in all natural philosophy are those laws of attraction\nand repulsion of which magnetical phenomena are the most obvious\nillustration. We may find ground for such a judgment in another passage\nin which Bacon speaks of Gilbert. In the Second Book[144] of the _Novum\nOrganon_, having classified motions, he gives, as one kind, what he\ncalls, in his figurative language, _motion for gain_, or _motion of\nneed_, by which a body shuns heterogeneous, and seeks cognate bodies.\nAnd he adds, \"The Electrical operation, concerning which Gilbert and\nothers since him have made up such a wonderful story, is nothing less\nthan the appetite of a body, which, excited by friction, does not well\ntolerate the air, and prefers another tangible body if it be found\nnear.\" Bacon's notion of an appetite in the body is certainly much\nless philosophical than Gilbert's, who speaks of light bodies as drawn\ntowards amber by certain material radii[145]; and we might perhaps\nventure to say that Bacon here manifests a want of clear mechanical\nideas. Bacon, too, showed his inferior aptitude for physical research\nin rejecting the Copernican doctrine which Gilbert adopted. In the\n_Advancement of Learning_[146], suggesting a history of the opinions\nof philosophers, he says that he would have inserted in it even recent\ntheories, as those of Paracelsus; of Telesius, who restored the\nphilosophy of Parmenides; or Patricius, who resublimed the fumes of\nPlatonism; or Gilbert, who brought back the dogmas of Philolaus. But\nBacon quotes[147] with pleasure Gilbert's ridicule of the Peripatetics'\ndefinition of heat. They had said, that heat is that which separates\nheterogeneous and unites homogeneous matter; which, said Gilbert, is\nas if any one were to define _man_ as that which sows wheat and plants\nvines.\n\nGalileo, another of Gilbert's distinguished contemporaries, had a\nhigher opinion of him. He says[148], \"I extremely admire and envy this\nauthor. I think him worthy of the greatest praise for the many new and\ntrue observations which he has made, to the disgrace of so many vain\nand fabling authors; who write, not from their own knowledge only,\nbut repeat everything they hear from the foolish and vulgar, without\nattempting to satisfy themselves of the same by experience; perhaps\nthat they may not diminish the size of their books.\"\n\n\n8. _Galileo._--Galileo was content with the active and successful\npractice of experimental inquiry; and did not demand that such\nresearches should be made expressly subservient to that wider and\nmore ambitious philosophy, on which the author of the _Novum Organon_\nemployed his powers. But still it now becomes our business to trace\nthose portions of Galileo's views which have reference to the theory,\nas well as the practice, of scientific investigation. On this subject,\nGalileo did not think more profoundly, perhaps, than several of his\ncontemporaries; but in the liveliness of expression and illustration\nwith which he recommended his opinions on such topics, he was\nunrivalled. Writing in the language of the people, in the attractive\nform of dialogue, with clearness, grace, and wit, he did far more than\nany of his predecessors had done to render the new methods, results,\nand prospects of science familiar to a wide circle of readers, first\nin Italy, and soon, all over Europe. The principal points inculcated\nby him were already becoming familiar to men of active and inquiring\nminds; such as,--that knowledge was to be sought from observation, and\nnot from books;--that it was absurd to adhere to, and debate about,\nthe physical tenets of Aristotle and the rest of the ancients. On\npersons who followed this latter course, Galileo fixed the epithet of\nPaper Philosophers[149]; because, as he wrote in a letter to Kepler,\nthis sort of men fancied that philosophy was to be studied like the\n_\u00c6neid_ or _Odyssey_, and that the true reading of nature was to be\ndetected by the collation of texts. Nothing so much shook the authority\nof the received system of Physics as the experimental discoveries,\ndirectly contradicting it, which Galileo made. By experiment, as I\nhave elsewhere stated[150], he disproved the Aristotelian doctrine that\nbodies fall quickly or slowly in proportion to their weight. And when\nhe had invented the telescope, a number of new discoveries of the most\nstriking kind (the inequalities of the moon's surface, the spots in\nthe sun, the moon-like phases of Venus, the satellites of Jupiter, the\nring of Saturn,) showed, by the evidence of the eyes, how inadequate\nwere the conceptions, and how erroneous the doctrines of the ancients,\nrespecting the constitution of the universe. How severe the blow was to\nthe disciples of the ancient schools, we may judge by the extraordinary\nforms of defence in which they tried to intrench themselves. They would\nnot look through Galileo's glasses; they maintained that what was seen\nwas an illusion of witchcraft; and they tried, as Galileo says[151],\nwith logical arguments, as if with magical incantations, to charm the\nnew planets out of the sky. No one could be better fitted than Galileo\nfor such a warfare. His great knowledge, clear intellect, gaiety, and\nlight irony, (with the advantage of being in the right,) enabled him to\nplay with his adversaries as he pleased. Thus when an Aristotelian[152]\nrejected the discovery of the irregularities in the moon's surface,\nbecause, according to the ancient doctrine, her form was a perfect\nsphere, and held that the apparent cavities were filled with an\ninvisible crystal substance, Galileo replied, that he had no objection\nto assent to this, but that then he should require his adversary in\nreturn to believe that there were on the same surface invisible crystal\nmountains ten times as high as those visible ones which he had actually\nobserved and measured.\n\nWe find in Galileo many thoughts which have since become established\nmaxims of modern philosophy. \"Philosophy,\" he says[153], \"is written\nin that great book, I mean the Universe, which is constantly open\nbefore our eyes; but it cannot be understood, unless we first know the\nlanguage and learn the characters in which it is written.\" With this\nthought he combines some other lively images. One of his interlocutors\nsays concerning another, \"Sarsi perhaps thinks that philosophy is\na book made up of the fancies of men, like the _Iliad_ or _Orlando\nFurioso_, in which the matter of least importance is, that what is\nwritten be true.\" And again, with regard to the system of authority, he\nsays, \"I think I discover in him a firm belief that, in philosophizing,\nit is necessary to lean upon the opinion of some celebrated author;\nas if our mind must necessarily remain unfruitful and barren till it\nbe married to another man's reason.\"--\"No,\" he says, \"the case is not\nso.--When we have the decrees of Nature, authority goes for nothing;\nreason is absolute[154].\"\n\nIn the course of Galileo's controversies, questions of the logic of\nscience came under discussion. Vincenzio di Grazia objected to a proof\nfrom induction which Galileo adduced, because _all_ the particulars\nwere not enumerated; to which the latter justly replies[155], that\nif induction were required to pass through all the cases, it would\nbe either useless or impossible;--impossible when the cases are\ninnumerable; useless when they have each already been verified, since\nthen the general proposition adds nothing to our knowledge.\n\nOne of the most novel of the characters which Science assumes in\nGalileo's hands is, that she becomes cautious. She not only proceeds\nleaning upon Experience, but she is content to proceed a little way\nat a time. She already begins to perceive that she must rise to the\nheights of knowledge by many small and separate steps. The philosopher\nis desirous to know much, but resigned to be ignorant for a time of\nthat which cannot yet be known. Thus when Galileo discovered the true\nlaw of the motion of a falling body[156], that the velocity increases\nproportionally to the time from the beginning of the fall, he did\nnot insist upon immediately assigning the cause of this law. \"The\ncause of the acceleration of the motions of falling bodies is not,\"\nhe says, \"a necessary part of the investigation.\" Yet the conception\nof this acceleration, as the result of the continued action of the\nforce of gravity upon the falling body, could hardly fail to suggest\nitself to one who had formed the idea of force. In like manner, the\ntruth that the velocities, acquired by bodies falling down planes of\nequal heights, are all equal, was known to Galileo and his disciples,\nlong before he accounted for it[157], by the principle, apparently\nso obvious, that the momentum generated is as the moving force which\ngenerates it. He was not tempted to rush at once, from an experimental\ntruth to a universal system. Science had learnt that she must move step\nby step; and the gravity of her pace already indicated her approaching\nmaturity and her consciousness of the long path which lay before her.\n\nBut besides the genuine philosophical prudence which thus withheld\nGalileo from leaping hastily from one inference to another, he had\nperhaps a preponderating inclination towards facts; and did not feel,\nso much as some other persons of his time, the need of reducing them to\nideas. He could bear to contemplate laws of motion without being urged\nby an uncontrollable desire to refer them to conceptions of force.\n\n\n9. _Kepler._--In this respect his friend Kepler differed from him;\nfor Kepler was restless and unsatisfied till he had reduced facts to\nlaws, and laws to causes; and never acquiesced in ignorance, though\nhe tested with the most rigorous scrutiny that which presented itself\nin the shape of knowledge to fill the void. It may be seen in the\nHistory of Astronomy[158] with what perseverance, energy, and fertility\nof invention, Kepler pursued his labours, (enlivened and relieved by\nthe most curious freaks of fancy,) with a view of discovering the\nrules which regulate the motions of the planet Mars. He represents\nthis employment under the image of a warfare; and describes[159] his\nobject to be \"to triumph over Mars, and to prepare for him, as for one\naltogether vanquished, tabular prisons and equated eccentric fetters;\"\nand when, \"the enemy, left at home a despised captive, had burst all\nthe chains of the equations, and broken forth of the prisons of the\ntables;\"--when \"it was buzzed here and there that the victory is vain,\nand that the war is raging anew as violently as before;\"--that is, when\nthe rules which he had proposed did not coincide with the facts;--he\nby no means desisted from his attempts, but \"suddenly sent into the\nfield a reserve of new physical reasonings on the rout and dispersion\nof the veterans,\" that is, tried new suppositions suggested by such\nviews as he then entertained of the celestial motions. His efforts\nto obtain the formal laws of the planetary motions resulted in some\nof the most important discoveries ever made in astronomy; and if his\nphysical reasonings were for the time fruitless, this arose only from\nthe want of that discipline in mechanical ideas which the minds of\nmathematicians had still to undergo; for the great discoveries of\nNewton in the next generation showed that, in reality, the next step\nof the advance was in this direction. Among all Kepler's fantastical\nexpressions, the fundamental thoughts were sound and true; namely,\nthat it was his business, as a physical investigator, to discover a\nmathematical rule which governed and included all the special facts;\nand that the rules of the motions of the planets must conform to some\nconception of causation.\n\nThe same characteristics,--the conviction of rule and cause,\nperseverance in seeking these, inventiveness in devising hypotheses,\nlove of truth in trying and rejecting them, and a lively Fancy playing\nwith the Reason without interrupting her,--appear also in his work\non Optics; in which he tried to discover the exact law of optical\nrefraction[160]. In this undertaking he did not succeed entirely;\nnor does he profess to have done so. He ends his numerous attempts by\nsaying, \"Now, reader, you and I have been detained sufficiently long\nwhile I have been attempting to _collect into one fagot_ the measures\nof different refractions.\"\n\nIn this and in other expressions, we see how clearly he apprehended\nthat _colligation of facts_ which is the main business of the practical\ndiscoverer. And by his peculiar endowments and habits, Kepler exhibits\nan essential portion of this process, which hardly appears at all in\nGalileo. In order to bind together facts, theory is requisite as well\nas observation,--the cord as well as the fagots. And the true theory\nis often, if not always, obtained by trying several and selecting the\nright. Now of this portion of the discoverer's exertions, Kepler is\na most conspicuous example. His fertility in devising suppositions,\nhis undaunted industry in calculating the results of them, his entire\nhonesty and candour in resigning them if these results disagreed with\nthe facts, are a very instructive spectacle; and are fortunately\nexhibited to us in the most lively manner in his own garrulous\nnarratives. Galileo urged men by precept as well as example to begin\ntheir philosophy from observation; Kepler taught them by his practice\nthat they must proceed from observation by means of hypotheses. The\none insisted upon facts; the other dealt no less copiously with ideas.\nIn the practical, as in the speculative portion of our history, this\nantithesis shows itself; although in the practical part we cannot have\nthe two elements separated, as in the speculative we sometimes have.\n\nIn the _History of Science_[161], I have devoted several pages to the\nintellectual character of Kepler, inasmuch as his habit of devising so\ngreat a multitude of hypotheses, so fancifully expressed, had led some\nwriters to look upon him as an inquirer who transgressed the most fixed\nrules of philosophical inquiry. This opinion has arisen, I conceive,\namong those who have forgotten the necessity of Ideas as well as Facts\nfor all theory; or who have overlooked the impossibility of selecting\nand explicating our ideas without a good deal of spontaneous play of\nthe mind. It must, however, always be recollected that Kepler's genius\nand fancy derived all their scientific value from his genuine and\nunmingled love of truth. These qualities appeared, not only in the\njudgment he passed upon hypotheses, but also in matters which more\nimmediately concerned his reputation. Thus when Galileo's discovery of\nthe telescope disproved several opinions which Kepler had published\nand strenuously maintained, he did not hesitate a moment to retract\nhis assertions and range himself by the side of Galileo, whom he\nvigorously supported in his warfare against those who were incapable of\nthus cheerfully acknowledging the triumph of new facts over their old\ntheories.\n\n\n10. _Tycho._--There remains one eminent astronomer, the friend and\nfellow-labourer of Kepler, whom we must not separate from him as one\nof the practical reformers of science. I speak of Tycho Brahe, who is,\nI think, not justly appreciated by the literary world in general, in\nconsequence of his having made a retrograde step in that portion of\nastronomical theory which is most familiar to the popular mind. Though\nhe adopted the Copernican view of the motion of the planets about the\nsun, he refused to acknowledge the annual and diurnal motion of the\nearth. But notwithstanding this mistake, into which he was led by his\ninterpretation of Scripture rather than of nature, Tycho must ever be\none of the greatest names in astronomy. In the philosophy of science\nalso, the influence of what he did is far from inconsiderable; and\nespecially its value in bringing into notice these two points:--that\nnot only are observations the beginning of science, but that the\nprogress of science may often depend upon the observer's pursuing his\ntask regularly and carefully for a long time, and with well devised\ninstruments; and again, that observed facts offer a _succession_ of\nlaws which we discover as our observations become better, and as our\ntheories are better adapted to the observations. With regard to the\nformer point, Tycho's observatory was far superior to all that had\npreceded it[162], not only in the optical, but in the mechanical\narrangements; a matter of almost equal consequence. And hence it was\nthat his observations inspired in Kepler that confidence which led him\nto all his labours and all his discoveries. \"Since,\" he says[163], \"the\ndivine goodness has given us in Tycho Brahe an exact observer, from\nwhose observations this error of eight minutes in the calculations of\nthe Ptolemaic hypothesis is detected, let us acknowledge and make use\nof this gift of God: and since this error cannot be neglected, these\neight minutes alone have prepared the way for an entire reform of\nAstronomy, and are to be the main subject of this work.\"\n\nWith regard to Tycho's discoveries respecting the moon, it is to be\nrecollected that besides the first inequality of the moon's motion,\n(the _equation of the centre_, arising from the elliptical form of her\norbit,) Ptolemy had discovered a second inequality, the _evection_,\nwhich, as we have observed in the History of this subject[164], might\nhave naturally suggested the suspicion that there were still other\ninequalities. In the middle ages, however, such suggestions, implying\na constant progress in science, were little attended to; and, we have\nseen, that when an Arabian astronomer[165] had really discovered\nanother inequality of the moon, it was soon forgotten, because it had\nno place in the established systems. Tycho not only rediscovered the\nlunar inequality, (the _variation_,) thus once before won and lost, but\nalso two other inequalities; namely[166], the _change of inclination_\nof the moon's orbit as the line of nodes moves round, and an inequality\nin the motion of the line of nodes. Thus, as I have elsewhere said,\nit appeared that the discovery of a rule is a step to the discovery\nof deviations from that rule, which require to be expressed in other\nrules. It became manifest to astronomers, and through them to all\nphilosophers, that in the application of theory to observation, we\nfind, not only the stated phenomena, for which the theory does account,\nbut also _residual phenomena_, which are unaccounted for, and remain\nover and above the calculation. And it was seen further, that these\nresidual phenomena might be, altogether or in part, exhausted by new\ntheories.\n\nThese were valuable lessons; and the more valuable inasmuch as men\nwere now trying to lay down maxims and methods for the conduct of\nscience. A revolution was not only at hand, but had really taken place,\nin the great body of real cultivators of science. The occasion now\nrequired that this revolution should be formally recognized;--that\nthe new intellectual power should be clothed with the forms of\ngovernment;--that the new philosophical republic should be acknowledged\nas a sister state by the ancient dynasties of Aristotle and Plato.\nThere was needed some great Theoretical Reformer, to speak in the name\nof the Experimental Philosophy; to lay before the world a declaration\nof its rights and a scheme of its laws. And thus our eyes are turned to\nFrancis Bacon, and others who like him attempted this great office. We\nquit those august and venerable names of discoverers, whose appearance\nwas the prelude and announcement of the new state of things then\nopening; and in doing so, we may apply to them the language which Bacon\napplies to himself[167]:--\n\n  \u03a7\u03b1\u03af\u03c1\u03b5\u03c4\u03b5 \u039a\u03ae\u03c1\u03c5\u03ba\u03b5\u03c2 \u0394\u03b9\u1f78 \u03c2 \u1f04\u03b3\u03b3\u03b5\u03bb\u03bf\u03b9 \u1f20\u03b4\u1f72 \u03ba\u03b1\u1f76 \u1f00\u03bd\u03b4\u03c1\u1ff6\u03bd.\n\n  Hail, Heralds, Messengers of Gods and Men!\n\n\nFOOTNOTES:\n\n[Footnote 128: His works have never been published, and exist in\nmanuscript in the library of the Institute at Paris. Some extracts were\npublished by Venturi, _Essai sur les Ouvrages de Leonard da Vinci_.\nParis, 1797.]\n\n[Footnote 129: Leonardo died in 1520, at the age of 78.]\n\n[Footnote 130: Paul III. in 1543.]\n\n[Footnote 131: _Hist. Ind. Sc._ b. v. c. ii.]\n\n[Footnote 132: Born 1537, died 1619.]\n\n[Footnote 133: _Hist. Ind. Sc._ b. xvii. c. ii. sect. 1.]\n\n[Footnote 134: Fabricius, _De Motu Locali_, p. 182.]\n\n[Footnote 135: p. 199.]\n\n[Footnote 136: _Speculationum Liber_, p. 195.]\n\n[Footnote 137: _Ibid._ p. 169.]\n\n[Footnote 138: Gulielmi Gilberti, _Colcestriensis, Medici Londinensis,\nDe Magnete, Magneticisque Corporibus, et de Magno Magnete Tellure,\nPhysiologia Nova, plurimis et Argumentis et Experimentis demonstrata_.]\n\n[Footnote 139: _Hist. Ind. Sc._ b. xii. c. i.]\n\n[Footnote 140: Pref.]\n\n[Footnote 141: _De Magnete_, lib. vi. c. 3, 4.]\n\n[Footnote 142: _Nov. Org._ b. i.]\n\n[Footnote 143: B. i. Aph. 64.]\n\n[Footnote 144: Vol. ix. 185.]\n\n[Footnote 145: _De Magnete_, p. 60.]\n\n[Footnote 146: B. iii. c. 4.]\n\n[Footnote 147: _Nov. Org._ b. ii. Aph. 48.]\n\n[Footnote 148: Drinkwater's _Life of Galileo_, p. 18.]\n\n[Footnote 149: _Life of Galileo_, p. 9.]\n\n[Footnote 150: _Hist. Ind. Sc._ b. vi. c. ii. sect. 5.]\n\n[Footnote 151: _Life of Galileo_, p. 29.]\n\n[Footnote 152: _Ibid._ p. 33.]\n\n[Footnote 153: _Il Saggiatore_, ii. 247.]\n\n[Footnote 154: _Il Saggiatore_, ii. 200.]\n\n[Footnote 155: _Ibid._ i. 501.]\n\n[Footnote 156: _Hist. Ind. Sc._ b. vi. c. ii. sect. 2.]\n\n[Footnote 157: _Hist. Ind. Sc._ b. vi. c. ii. sect. 4.]\n\n[Footnote 158: _Ibid._ b. v. c. iv. sect. 1.]\n\n[Footnote 159: _De Stell. Mart._ p. iv. c. 51 (1609); Drinkwater's\n_Kepler_, p. 33.]\n\n[Footnote 160: Published 1604. _Hist. Ind. Sc._ b. ix. c. ii.]\n\n[Footnote 161: _Hist. Ind. Sc._ b. v. c. iv. sect. 1.]\n\n[Footnote 162: _Hist. Ind. Sc._ b. vii. c. vi. sect 1.]\n\n[Footnote 163: _De Stell. Mart._ p. 11. c. 19.]\n\n[Footnote 164: _Hist. Ind. Sc._ b. ii. c. iv. sect. 6.]\n\n[Footnote 165: _Ibid._ sect. 8.]\n\n[Footnote 166: Montucla, i. 566.]\n\n[Footnote 167: _De Augm._ lib. iv. c. 1.]\n\n\n\n\nCHAPTER XV.\n\nFRANCIS BACON.\n\n\n(I.) 1. _General Remarks._--It is a matter of some difficulty to speak\nof the character and merits of this illustrious man, as regards his\nplace in that philosophical history with which we are here engaged.\nIf we were to content ourselves with estimating him according to the\noffice which, as we have just seen, he claims for himself[168], as\nmerely the harbinger and announcer of a sounder method of scientific\ninquiry than that which was recognized before him, the task would\nbe comparatively easy. For we might select from his writings those\npassages in which he has delivered opinions and pointed out processes,\nthen novel and strange, but since confirmed by the experience of\nactual discoverers, and by the judgments of the wisest of succeeding\nphilosophers; and we might pass by, without disrespect, but without\nnotice, maxims and proposals which have not been found available for\nuse;--views so indistinct and vague, that we are even yet unable to\npronounce upon their justice;--and boundless anticipations, dictated\nby the sanguine hopes of a noble and comprehensive intellect. But\nif we thus reduce the philosophy of Bacon to that portion which the\nsubsequent progress of science has rigorously verified, we shall\nhave to pass over many of those declarations which have excited\nmost notice in his writings, and shall lose sight of many of those\nstriking thoughts which his admirers most love to dwell upon. For he\nis usually spoken of, at least in this country, as a teacher who\nnot only commenced, but in a great measure completed, the Philosophy\nof Induction. He is considered, not only as having asserted some\ngeneral principles, but laid down the special rules of scientific\ninvestigation; as not only one of the Founders, but the supreme\nLegislator of the modern Republic of Science; not only the Hercules who\nslew the monsters that obstructed the earlier traveller, but the Solon\nwho established a constitution fitted for all future time.\n\n\n2. Nor is it our purpose to deny that of such praise he deserves\na share which, considering the period at which he lived, is truly\nastonishing. But it is necessary for us in this place to discriminate\nand select that portion of his system which, bearing upon _physical_\nscience, has since been confirmed by the actual history of science.\nMany of Bacon's most impressive and captivating passages contemplate\nthe extension of the new methods of discovering truth to intellectual,\nto moral, to political, as well as to physical science. And how far,\nand how, the advantages of the inductive method may be secured for\nthose important branches of speculation, it will at some future time\nbe a highly interesting task to examine. But our plan requires us at\npresent to omit the consideration of these; for our purpose is to learn\nwhat the genuine course of the formation of science is, by tracing it\nin those portions of human knowledge, which, by the confession of all,\nare most exact, most certain, most complete. Hence we must here deny\nourselves the dignity and interest which float about all speculations\nin which the great moral and political concerns of men are involved.\nIt cannot be doubted that the commanding position which Bacon occupies\nin men's estimation arises from his proclaiming a reform in philosophy\nof so comprehensive a nature;--a reform which was to infuse a new\nspirit into every part of knowledge. Physical Science has tranquilly\nand noiselessly adopted many of his suggestions; which were, indeed,\nher own natural impulses, not borrowed from him; and she is too deeply\nand satisfactorily absorbed in contemplating her results, to talk much\nabout the methods of obtaining them which she has thus instinctively\npursued. But the philosophy which deals with mind, with manners,\nwith morals, with polity, is conscious still of much obscurity and\nperplexity; and would gladly borrow aid from a system in which aid\nis so confidently promised. The aphorisms and phrases of the _Novum\nOrganon_ are far more frequently quoted by metaphysical, ethical, and\neven theological writers, than they are by the authors of works on\nphysics.\n\n\n3. Again, even as regards physics, Bacon's fame rests upon something\nbesides the novelty of the maxims which he promulgated. That a\nrevolution in the method of scientific research was going on, all\nthe greatest physical investigators of the sixteenth century were\nfully aware, as we have shown in the last chapter. But their writings\nconveyed this conviction to the public at large somewhat slowly. Men of\nletters, men of the world, men of rank, did not become familiar with\nthe abstruse works in which these views were published; and above all,\nthey did not, by such occasional glimpses as they took of the state of\nphysical science, become aware of the magnitude and consequences of\nthis change. But Bacon's lofty eloquence, wide learning, comprehensive\nviews, bold pictures of the coming state of things, were fitted to\nmake men turn a far more general and earnest gaze upon the passing\nchange. When a man of his acquirements, of his talents, of his rank and\nposition, of his gravity and caution, poured forth the strongest and\nloftiest expressions and images which his mind could supply, in order\nto depict the \"Great Instauration\" which he announced;--in order to\ncontrast the weakness, the blindness, the ignorance, the wretchedness,\nunder which men had laboured while they followed the long beaten track,\nwith the light, the power, the privileges, which they were to find in\nthe paths to which he pointed;--it was impossible that readers of all\nclasses should not have their attention arrested, their minds stirred,\ntheir hopes warmed; and should not listen with wonder and with pleasure\nto the strains of prophetic eloquence in which so great a subject\nwas presented. And when it was found that the prophecy was verified;\nwhen it appeared that an immense change in the methods of scientific\nresearch really _had_ occurred;--that vast additions to man's knowledge\nand power had been acquired, in modes like those which had been spoken\nof;--that further advances might be constantly looked for;--and that a\nprogress, seemingly boundless, was going on in the direction in which\nthe seer had thus pointed;--it was natural that men should hail him as\nthe leader of the revolution; that they should identify him with the\nevent which he was the first to announce; that they should look upon\nhim as the author of that which he had, as they perceived, so soon and\nso thoroughly comprehended.\n\n\n4. For we must remark, that although (as we have seen) he was not the\nonly, nor the earliest writer, who declared that the time was come\nfor such a change, he not only proclaimed it more emphatically, but\nunderstood it, in its general character, much more exactly, than any\nof his contemporaries. Among the maxims, suggestions and anticipations\nwhich he threw out, there were many of which the wisdom and the novelty\nwere alike striking to his immediate successors;--there are many\nwhich even now, from time to time, we find fresh reason to admire,\nfor their acuteness and justice. Bacon stands far above the herd of\nloose and visionary speculators who, before and about his time, spoke\nof the establishment of new philosophies. If we must select some one\nphilosopher as the Hero of the revolution in scientific method, beyond\nall doubt Francis Bacon must occupy the place of honour.\n\nWe shall, however, no longer dwell upon these general considerations,\nbut shall proceed to notice some of the more peculiar and\ncharacteristic features of Bacon's philosophy; and especially those\nviews, which, occurring for the first time in his writings, have been\nfully illustrated and confirmed by the subsequent progress of science,\nand have become a portion of the permanent philosophy of our times.\n\n\n(II.) 5. _A New Era announced._--The first great feature which\nstrikes us in Bacon's philosophical views is that which we have\nalready noticed;--his confident and emphatic announcement of a _New\nEra_ in the progress of science, compared with which the advances of\nformer times were poor and trifling. This was with Bacon no loose and\nshallow opinion, taken up on light grounds and involving only vague,\ngeneral notions. He had satisfied himself of the justice of such a\nview by a laborious course of research and reflection. In 1605, at the\nage of forty-four, he published his Treatise of the _Advancement of\nLearning_, in which he takes a comprehensive and spirited survey of\nthe condition of all branches of knowledge which had been cultivated\nup to that time. This work was composed with a view to that reform\nof the existing philosophy which Bacon always had before his eyes;\nand in the Latin edition of his works, forms the First Part of the\n_Instauratio Magna_. In the Second Part of the Instauratio, the _Novum\nOrganon_, published in 1620, he more explicitly and confidently states\nhis expectations on this subject. He points out how slightly and\nfeebly the examination of nature had been pursued up to his time, and\nwith what scanty fruit. He notes the indications of this in the very\nlimited knowledge of the Greeks who had till then been the teachers\nof Europe, in the complaints of authors concerning the subtilty and\nobscurity of the secrets of nature, in the dissensions of sects, in\nthe absence of useful inventions resulting from theory, in the fixed\nform which the sciences had retained for two thousand years. Nor, he\nadds[169], is this wonderful; for how little of his thought and labour\nhas man bestowed upon science! Out of twenty-five centuries scarce six\nhave been favourable to the progress of knowledge. And even in those\nfavoured times, natural philosophy received the smallest share of man's\nattention; while the portion so given was marred by controversy and\ndogmatism; and even those who have bestowed a little thought upon\nthis philosophy, have never made it their main study, but have used it\nas a passage or drawbridge to serve other objects. And thus, he says,\nthe great Mother of the Sciences is thrust down with indignity to the\noffices of a handmaid; is made to minister to the labours of medicine\nor mathematics, or to give the first preparatory tinge to the immature\nminds of youth. For these and similar considerations of the errors of\npast time, he draws hope for the future, employing the same argument\nwhich Demosthenes uses to the Athenians: \"That which is worst in the\nevents of the past, is the best as a ground of trust in the future.\nFor if you had done all that became you, and still had been in this\ncondition, your case might be desperate; but since your failure is the\nresult of your own mistakes, there is good hope that, correcting the\nerror of your course, you may reach a prosperity yet unknown to you.\"\n\n\n(III.) 6. _A change of existing Method._--All Bacon's hope of\nimprovement indeed was placed in an entire _change of the Method_ by\nwhich science was pursued; and the boldness, and at the same time (the\nthen existing state of science being considered), the definiteness of\nhis views of the change that was requisite, are truly remarkable.\n\nThat all knowledge must begin with observation, is one great principle\nof Bacon's philosophy; but I hardly think it necessary to notice the\ninculcation of this maxim as one of his main services to the cause of\nsound knowledge, since it had, as we have seen, been fully insisted\nupon by others before him, and was growing rapidly into general\nacceptance without his aid. But if he was not the first to tell men\nthat they must collect their knowledge from observation, he had no\nrival in his peculiar office of teaching them _how_ science must thus\nbe gathered from experience.\n\nIt appears to me that by far the most extraordinary parts of Bacon's\nworks are those in which, with extreme earnestness and clearness, he\ninsists upon a _graduated and successive induction_, as opposed to a\nhasty transit from special facts to the highest generalizations. The\nnineteenth Axiom of the First Book of the _Novum Organon_ contains a\nview of the nature of true science most exact and profound, and, so\nfar as I am aware, at the time perfectly new. \"There are two ways, and\ncan only be two, of seeking and finding truth. The one, from sense and\nparticulars, takes a flight to the most general axioms, and from those\nprinciples and their truth, settled once for all, invents and judges of\nintermediate axioms. The other method collects axioms from sense and\nparticulars, ascending _continuously and by degrees_, so that in the\nend it arrives at the most general axioms; this latter way is the true\none, but hitherto untried.\"\n\nIt is to be remarked, that in this passage Bacon employs the term\n_axioms_ to express any propositions collected from facts by induction,\nand thus fitted to become the starting-point of deductive reasonings.\nHow far propositions so obtained may approach to the character of\naxioms in the more rigorous sense of the term, we have already in some\nmeasure examined; but that question does not here immediately concern\nus. The truly remarkable circumstance is to find this recommendation\nof a continuous advance from observation, by limited steps, through\nsuccessive gradations of generality, given at a time when speculative\nmen in general had only just begun to perceive that they must begin\ntheir course from experience in some way or other. How exactly this\ndescription represents the general structure of the soundest and\nmost comprehensive physical theories, all persons who have studied\nthe progress of science up to modern times can bear testimony; but\nperhaps this structure of science cannot in any other way be made so\napparent as by those Tables of successive generalizations in which we\nhave exhibited the history and constitution of some of the principal\nphysical sciences, in the Chapter of a preceding work which treats of\nthe Logic of Induction. And the view which Bacon thus took of the true\nprogress of science was not only new, but, so far as I am aware, has\nnever been adequately illustrated up to the present day.\n\n\n7. It is true, as I observed in the last chapter, that Galileo had been\nled to see the necessity, not only of proceeding from experience in the\npursuit of knowledge, but of proceeding cautiously and gradually; and\nhe had exemplified this rule more than once, when, having made one step\nin discovery, he held back his foot, for a time, from the next step,\nhowever tempting. But Galileo had not reached this wide and commanding\nview of the successive subordination of many steps, all leading up at\nlast to some wide and simple general truth. In catching sight of this\nprinciple, and in ascribing to it its due importance, Bacon's sagacity,\nso far as I am aware, wrought unassisted and unrivalled.\n\n\n8. Nor is there any wavering or vagueness in Bacon's assertion of this\nimportant truth. He repeats it over and over again; illustrates it by\na great number of the most lively metaphors and emphatic expressions.\nThus he speaks of the successive _floors_ (_tabulata_) of induction;\nand speaks of each science as a _pyramid_[170] which has observation\nand experience for its basis. No images can better exhibit the relation\nof general and particular truths, as our own Inductive Tables may serve\nto show.\n\n\n(IV.) 9. _Comparison of the New and Old Method._ Again; not less\nremarkable is his contrasting this true Method of Science (while it was\nalmost, as he says, yet untried) with the ancient and _vicious Method_,\nwhich began, indeed, with facts of observation, but rushed at once\nand with no gradations, to the most general principles. For this was\nthe course which had been actually followed by all those speculative\nreformers who had talked so loudly of the necessity of beginning our\nphilosophy from experience. All these men, if they attempted to frame\nphysical doctrines at all, had caught up a few facts of observation,\nand had erected a universal theory upon the suggestions which these\noffered. This process of illicit generalization, or, as Bacon terms\nit, Anticipation of Nature (_anticipatio natur\u00e6_), in opposition to\nthe Interpretation of Nature, he depicts with singular acuteness, in\nits character and causes. \"These two ways,\" he says[171], \"both begin\nfrom sense and particulars; but their discrepancy is immense. The one\nmerely skims over experience and particulars in a cursory transit; the\nother deals with them in a due and orderly manner. The one, at its very\noutset, frames certain general abstract principles, but useless; the\nother gradually rises to those principles which have a real existence\nin nature.\"\n\n\"The former path,\" he adds[172], \"that of illicit and hasty\ngeneralization, is one which the intellect follows when abandoned to\nits own impulse; and this it does from the requisitions of logic. For\nthe mind has a yearning which makes it dart forth to generalities, that\nit may have something to rest in; and after a little dallying with\nexperience, becomes weary of it; and all these evils are augmented by\nlogic, which requires these generalities to make a show with in its\ndisputations.\"\n\n\"In a sober, patient, grave intellect,\" he further adds, \"the mind, by\nits own impulse, (and more especially if it be not impelled by the sway\nof established opinions) attempts in some measure that other and true\nway, of gradual generalization; but this it does with small profit;\nfor the intellect, except it be regulated and aided, is a faculty of\nunequal operation, and altogether unapt to master the obscurity of\nthings.\"\n\nThe profound and searching wisdom of these remarks appears more\nand more, as we apply them to the various attempts which men have\nmade to obtain knowledge; when they begin with the contemplation of\na few facts, and pursue their speculations, as upon most subjects\nthey have hitherto generally done; for almost all such attempts have\nled immediately to some process of illicit generalization, which\nintroduces an interminable course of controversy. In the physical\nsciences, however, we have the further inestimable advantage of seeing\nthe other side of the contrast exemplified: for many of them, as our\ninductive Tables show us, have gone on according to the most rigorous\nconditions of gradual and successive generalization; and in consequence\nof this circumstance in their constitution, possess, in each part of\ntheir structure, a solid truth, which is always ready to stand the\nseverest tests of reasoning and experiment.\n\nWe see how justly and clearly Bacon judged concerning the mode in which\nfacts are to be employed in the construction of science. This, indeed,\nhas ever been deemed his great merit: insomuch that many persons appear\nto apprehend the main substance of his doctrine to reside in the maxim\nthat facts of observation, and such facts alone, are the essential\nelements of all true science.\n\n\n(V.) 10. _Ideas are necessary._--Yet we have endeavoured to establish\nthe doctrine that facts are but one of two ingredients of knowledge\nboth equally necessary;--that _Ideas_ are no less indispensable than\nfacts themselves; and that except these be duly unfolded and applied,\nfacts are collected in vain. Has Bacon then neglected this great\nportion of his subject? Has he been led by some partiality of view, or\nsome peculiarity of circumstances, to leave this curious and essential\nelement of science in its pristine obscurity? Was he unaware of its\ninterest and importance?\n\nWe may reply that Bacon's philosophy, in its effect upon his readers\nin general, does _not_ give due weight or due attention to the ideal\nelement of our knowledge. He is considered as peculiarly and eminently\nthe asserter of the value of experiment and observation. He is always\nunderstood to belong to the experiential, as opposed to the ideal\nschool. He is held up in contrast to Plato and others who love to dwell\nupon that part of knowledge which has its origin in the intellect of\nman.\n\n\n11. Nor can it be denied that Bacon has, in the finished part of his\n_Novum Organon_, put prominently forwards the necessary dependence of\nall our knowledge upon Experience, and said little of its dependence,\nequally necessary, upon the Conceptions which the intellect itself\nsupplies. It will appear, however, on a close examination, that he\nwas by no means insensible or careless of this internal element of\nall connected speculation. He held the balance, with no partial or\nfeeble hand, between phenomena and ideas. He urged the Colligation of\nFacts, but he was not the less aware of the value of the Explication of\nConceptions.\n\n\n12. This appears plainly from some remarkable Aphorisms in the _Novum\nOrganon_. Thus, in noticing the causes of the little progress then\nmade by science[173], he states this:--\"In the current Notions, all is\nunsound, whether they be logical or physical. _Substance_, _quality_,\n_action_, _passion_, even _being_, are not good Conceptions; still less\nare _heavy_, _light_, _dense_, _rare_, _moist_, _dry_, _generation_,\n_corruption_, _attraction_, _repulsion_, _element_, _matter_, _form_,\nand others of that kind; all are fantastical and ill-defined.\" And in\nhis attempt to exemplify his own system, he hesitates[174] in accepting\nor rejecting the notions of _elementary_, _celestial_, _rare_, as\nbelonging to fire, since, as he says, they are vague and ill-defined\nnotions (_notiones vag\u00e6 nec bene terminat\u00e6_). In that part of his work\nwhich appears to be completed, there is not, so far as I have noticed,\nany attempt to fix and define any notions thus complained of as loose\nand obscure. But yet such an undertaking appears to have formed part\nof his plan; and in the _Abecedarium Natur\u00e6_[175], which consists of\nthe heads of various portions of his great scheme, marked by letters\nof the alphabet, we find the titles of a series of dissertations \"On\nthe Conditions of Being,\" which must have had for their object the\nelucidation of divers Notions essential to science, and which would\nhave been contributions to the Explication of Conceptions, such as\nwe have attempted in a former part of this work. Thus some of the\nsubjects of these dissertations are;--Of Much and Little;--Of Durable\nand Transitory;--Of Natural and Monstrous;--Of Natural and Artificial.\nWhen the philosopher of induction came to discuss these, considered as\n_conditions of existence_, he could not do otherwise than develope,\nlimit, methodize, and define the Ideas involved in these Notions,\nso as to make them consistent with themselves, and a fit basis of\ndemonstrative reasoning. His task would have been of the same nature\nas ours has been, in that part of this work which treats of the\nFundamental Ideas of the various classes of sciences.\n\n\n13. Thus Bacon, in his speculative philosophy, took firmly hold of\nboth the handles of science; and if he had completed his scheme, would\nprobably have given due attention to Ideas, no less than to Facts, as\nan element of our knowledge; while in his view of the general method\nof ascending from facts to principles, he displayed a sagacity truly\nwonderful. But we cannot be surprised, that in attempting to exemplify\nthe method which he recommended, he should have failed. For the method\ncould be exemplified only by some important discovery in physical\nscience; and great discoveries, even with the most perfect methods, do\nnot come at command. Moreover, although the general structure of his\nscheme was correct, the precise import of some of its details could\nhardly be understood, till the actual progress of science had made men\nsomewhat familiar with the kind of steps which it included.\n\n\n(VI.) 14. _Bacon's Example._--Accordingly, Bacon's _Inquisition into\nthe Nature of Heat_, which is given in the Second Book of the _Novum\nOrganon_ as an example of the mode of interrogating Nature, cannot be\nlooked upon otherwise than as a complete failure. This will be evident\nif we consider that, although the exact nature of heat is still an\nobscure and controverted matter, the science of Heat now consists of\nmany important truths; and that to none of these truths is there any\napproximation in Bacon's essay. From his process he arrives at this,\nas the \"forma or true definition\" of heat;--\"that it is an expansive,\nrestrained motion, modified in certain ways, and exerted in the\nsmaller particles of the body.\" But the steps by which the science of\nHeat really advanced were (as may be seen in the history[176] of the\nsubject) these;--The discovery of a _measure_ of heat or temperature\n(the thermometer); the establishment of the _laws_ of conduction\nand radiation; of the _laws_ of specific heat, latent heat, and the\nlike. Such steps have led to Amp\u00e8re's _hypothesis_[177], that heat\nconsists in the vibrations of an imponderable fluid; and to Laplace's\n_hypothesis_, that temperature consists in the internal radiation of\nsuch a fluid. These hypotheses cannot yet be said to be even probable;\nbut at least they are so modified as to include some of the preceding\nlaws which are firmly established; whereas Bacon's hypothetical motion\nincludes no laws of phenomena, explains no process, and is indeed\nitself an example of illicit generalization.\n\n\n15. One main ground of Bacon's ill fortune in this undertaking appears\nto be, that he was not aware of an important maxim of inductive\nscience, that we must first obtain the _measure_ and ascertain the\n_laws_ of phenomena, before we endeavour to discover their _causes_.\nThe whole history of thermotics up to the present time has been\noccupied with the _former_ step, and the task is not yet completed:\nit is no wonder, therefore, that Bacon failed entirely, when he so\nprematurely attempted the _second_. His sagacity had taught him that\nthe progress of science must be gradual; but it had not led him to\njudge adequately how gradual it must be, nor of what different kinds\nof inquiries, taken in due order, it must needs consist, in order to\nobtain success.\n\nAnother mistake, which could not fail to render it unlikely that Bacon\nshould really exemplify his precepts by any actual advance in science,\nwas, that he did not justly appreciate the sagacity, the inventive\ngenius, which all discovery requires. He conceived that he could\nsupersede the necessity of such peculiar endowments. \"Our method of\ndiscovery in science,\" he says[178], \"is of such a nature, that there\nis not much left to acuteness and strength of genius, but all degrees\nof genius and intellect are brought nearly to the same level.\" And he\nillustrates this by comparing his method to a pair of compasses, by\nmeans of which a person with no manual skill may draw a perfect circle.\nIn the same spirit he speaks of proceeding by _due rejections_; and\nappears to imagine that when we have obtained a collection of facts, if\nwe go on successively rejecting what is false, we shall at last find\nthat we have, left in our hands, that scientific truth which we seek.\nI need not observe how far this view is removed from the real state of\nthe case. The necessity of a _conception_ which must be furnished by\nthe mind in order to bind together the facts, could hardly have escaped\nthe eye of Bacon, if he had cultivated more carefully the ideal side\nof his own philosophy. And any attempts which he could have made to\nconstruct such conceptions by mere rule and method, must have ended\nin convincing him that nothing but a peculiar inventive talent could\nsupply that which was thus not contained in the facts, and yet was\nneeded for the discovery.\n\n\n(VII.) 16. _His Failure._--Since Bacon, with all his acuteness, had not\ndivined circumstances so important in the formation of science, it is\nnot wonderful that his attempt to reduce this process to a _Technical\nForm_ is of little value. In the first place, he says[179], we must\nprepare a natural and experimental history, good and sufficient; in the\nnext place, the instances thus collected are to be arranged in Tables\nin some orderly way; and then we must apply a legitimate and true\ninduction. And in his example[180], he first collects a great number\nof cases in which heat appears under various circumstances, which he\ncalls \"a Muster of Instances before the intellect,\" (_comparentia\ninstantiarum ad intellectum_,) or a _Table of the Presence_ of the\nthing sought. He then adds a _Table of its Absence_ in proximate cases,\ncontaining instances where heat does not appear; then a _Table of\nDegrees_, in which it appears with greater or less intensity. He then\nadds[181], that we must try to exclude several obvious suppositions,\nwhich he does by reference to some of the instances he has collected;\nand this step he calls the _Exclusive_, or the _Rejection of Natures_.\nHe then observes, (and justly,) that whereas truth emerges more easily\nfrom error than from confusion, we may, after this preparation, _give\nplay to the intellect_, (fiat permissio intellectus,) and make an\nattempt at induction, liable afterwards to be corrected; and by this\nstep, which he terms his _First Vindemiation_, or _Inchoate Induction_,\nhe is led to the proposition concerning heat, which we have stated\nabove.\n\n\n17. In all the details of his example he is unfortunate. By proposing\nto himself to examine at once into the _nature_ of heat, instead\nof the laws of special classes of phenomena, he makes, as we have\nsaid, a fundamental mistake; which is the less surprising since he\nhad before him so few examples of the right course in the previous\nhistory of science. But further, his collection of instances is very\nloosely brought together; for he includes in his list the _hot_ taste\nof aromatic plants, the _caustic_ effects of acids, and many other\nfacts which cannot be ascribed to heat without a studious laxity in\nthe use of the word. And when he comes to that point where he permits\nhis intellect its range, the conception of _motion_ upon which it at\nonce fastens, appears to be selected with little choice or skill, the\nsuggestion being taken from flame[182], boiling liquids, a blown fire,\nand some other cases. If from such examples we could imagine heat\nto be motion, we ought at least to have some gradation to cases of\nheat where no motion is visible, as in a red-hot iron. It would seem\nthat, after a large collection of instances had been looked at, the\nintellect, even in its first attempts, ought not to have dwelt upon\nsuch an hypothesis as this.\n\n\n18. After these steps, Bacon speaks of several classes of instances\nwhich, singling them out of the general and indiscriminate collection\nof facts, he terms _Instances with Prerogative_: and these he points\nout as peculiar aids and guides to the intellect in its task. These\nInstances with Prerogative have generally been much dwelt upon by those\nwho have commented on the _Novum Organon_. Yet, in reality, such a\nclassification, as has been observed by one of the ablest writers of\nthe present day[183], is of little service in the task of induction.\nFor the instances are, for the most part, classed, not according to\nthe ideas which they involve, or to any obvious circumstance in the\nfacts of which they consist, but according to the extent or manner of\ntheir influence upon the inquiry in which they are employed. Thus we\nhave Solitary Instances, Migrating Instances, Ostensive Instances,\nClandestine Instances, so termed according to the degree in which\nthey exhibit, or seem to exhibit, the property whose nature we would\nexamine. We have Guide-Post Instances, (_Instanti\u00e6 Crucis_,) Instances\nof the Parted Road, of the Doorway, of the Lamp, according to the\nguidance they supply to our advance. Such a classification is much of\nthe same nature as if, having to teach the art of building, we were to\ndescribe tools with reference to the amount and place of the work which\nthey must do, instead of pointing out their construction and use:--as\nif we were to inform the pupil that we must have tools for lifting a\nstone up, tools for moving it sideways, tools for laying it square,\ntools for cementing it firmly. Such an enumeration of ends would convey\nlittle instruction as to the means. Moreover, many of Bacon's classes\nof instances are vitiated by the assumption that the \"form,\" that is,\nthe general law and cause of the property which is the subject of\ninvestigation, is to be looked for directly in the instances; which, as\nwe have seen in his inquiry concerning heat, is a fundamental error.\n\n\n19. Yet his phraseology in some cases, as in the _instantia crucis_,\nserves well to mark the place which certain experiments hold in our\nreasonings: and many of the special examples which he gives are full\nof acuteness and sagacity. Thus he suggests swinging a pendulum in a\nmine, in order to determine whether the attraction of the earth arises\nfrom the attraction of its parts; and observing the tide at the same\nmoment in different parts of the world, in order to ascertain whether\nthe motion of the water is expansive or progressive; with other\ningenious proposals. These marks of genius may serve to counterbalance\nthe unfavourable judgment of Bacon's aptitude for physical science\nwhich we are sometimes tempted to form, in consequence of his false\nviews on other points; as his rejection of the Copernican system, and\nhis undervaluing Gilbert's magnetical speculations. Most of these\nerrors arose from a too ambitious habit of intellect, which would not\nbe contented with any except very wide and general truths; and from an\nindistinctness of mechanical, and perhaps, in general, of mathematical\nideas:--defects which Bacon's own philosophy was directed to remedy,\nand which, in the progress of time, it has remedied in others.\n\n\n(VIII.) 20. _His Idols._--Having thus freely given our judgment\nconcerning the most exact and definite portion of Bacon's precepts,\nit cannot be necessary for us to discuss at any length the value\nof those more vague and general _Warnings_ against prejudice and\npartiality, against intellectual indolence and presumption, with which\nhis works abound. His advice and exhortations of this kind are always\nexpressed with energy and point, often clothed in the happiest forms\nof imagery; and hence it has come to pass, that such passages are\nperhaps more familiar to the general reader than any other part of\nhis writings. Nor are Bacon's counsels without their importance, when\nwe have to do with those subjects in which prejudice and partiality\nexercise their peculiar sway. Questions of politics and morals,\nof manners, taste, or history, cannot be subjected to a scheme of\nrigorous induction; and though on such matters we venture to assert\ngeneral principles, these are commonly obtained with some degree of\ninsecurity, and depend upon special habits of thought, not upon mere\nlogical connexion. Here, therefore, the intellect may be perverted,\nby mixing, with the pure reason, our gregarious affections, or our\nindividual propensities; the false suggestions involved in language,\nor the imposing delusions of received theories. In these dim and\ncomplex labyrinths of human thought, _the Idol of the Tribe_, or _of\nthe Den_, _of the Forum_, or _of the Theatre_, may occupy men's minds\nwith delusive shapes, and may obscure or pervert their vision of truth.\nBut in that Natural Philosophy with which we are here concerned, there\nis little opportunity for such influences. As far as a physical theory\nis completed through all the steps of a just induction, there is a\nclear daylight diffused over it which leaves no lurking-place for\nprejudice. Each part can be examined separately and repeatedly; and\nthe theory is not to be deemed perfect till it will bear the scrutiny\nof all sound minds alike. Although, therefore, Bacon, by warning men\nagainst the idols of fallacious images above spoken of, may have\nguarded them from dangerous error, his precepts have little to do with\nNatural Philosophy: and we cannot agree with him when he says[184],\nthat the doctrine concerning these idols bears the same relation to\nthe interpretation of nature as the doctrine concerning sophistical\nparalogisms bears to common logic.\n\n\n(IX.) 21. _His Aim, Utility._--There is one very prominent feature in\nBacon's speculations which we must not omit to notice; it is a leading\nand constant object with him to apply his knowledge to _Use_. The\ninsight which he obtains into nature, he would employ in commanding\nnature for the service of man. He wishes to have not only principles\nbut works. The phrase which best describes the aim of his philosophy is\nhis own[185], \"Ascendendo ad _axiomata_, descendendo ad _opera_.\" This\ndisposition appears in the first aphorism of the _Novum Organon_, and\nruns through the work. \"Man, the _minister_ and interpreter of nature,\n_does_ and understands, so far as he has, in fact or in thought,\nobserved the course of nature; and he cannot know or _do_ more than\nthis.\" It is not necessary for us to dwell much upon this turn of mind;\nfor the whole of our present inquiry goes upon the supposition that an\nacquaintance with the laws of nature is worth our having for its own\nsake. It may be universally true, that Knowledge is Power; but we have\nto do with it not as Power, but as Knowledge. It is the formation of\nScience, not of Art, with which we are here concerned. It may give a\npeculiar interest to the history of science, to show how it constantly\ntends to provide better and better for the wants and comforts of the\nbody; but _that_ is not the interest which engages us in our present\ninquiry into the nature and course of philosophy. The consideration\nof the means which promote man's material well-being often appears to\nbe invested with a kind of dignity, by the discovery of general laws\nwhich it involves; and the satisfaction which rises in our minds at\nthe contemplation of such cases, men sometimes ascribe, with a false\ningenuity, to the love of mere bodily enjoyment. But it is never\ndifficult to see that this baser and coarser element is not the real\nsource of our admiration. Those who hold that it is the main business\nof science to construct instruments for the uses of life, appear\nsometimes to be willing to accept the consequence which follows from\nsuch a doctrine, that the first shoemaker was a philosopher worthy of\nthe highest admiration[186]. But those who maintain such paradoxes,\noften, by a happy inconsistency, make it their own aim, not to devise\nsome improved covering for the feet, but to delight the mind with acute\nspeculations, exhibited in all the graces of wit and fancy.\n\nIt has been said[187] that the key of the Baconian doctrine consists in\ntwo words, Utility and Progress. With regard to the latter point, we\nhave already seen that the hope and prospect of a boundless progress in\nhuman knowledge had sprung up in men's minds, even in the early times\nof imperial Rome; and were most emphatically expressed by that very\nSeneca who disdained to reckon the worth of knowledge by its value in\nfood and clothing. And when we say that Utility was the great business\nof Bacon's philosophy, we forget one-half of his characteristic phrase:\n\"Ascendendo ad aximomata,\" no less than \"descendendo ad opera,\" was,\nhe repeatedly declared, the scheme of his path. He constantly spoke,\nwe are told by his secretary[188], of two kinds of experiments,\n_experimenta fructifera_, and _experimenta lucifera_.\n\nAgain; when we are told by modern writers that Bacon merely recommended\nsuch induction as all men instinctively practise, we ought to recollect\nhis own earnest and incessant declarations to the contrary. The\ninduction hitherto practised is, he says, of no use for obtaining solid\nscience. There are two ways[189], \"h\u00e6c via in usu est,\" \"altera vera,\nsed intentata.\" Men have constantly been employed in _anticipation_;\nin illicit induction. The intellect left to itself rushes on in this\nroad[190]; the conclusions so obtained are persuasive[191]; far more\npersuasive than inductions made with due caution[192]. But still this\nmethod must be rejected if we would obtain true knowledge. We shall\nthen at length have ground of good hope for science when we proceed\nin another manner[193]. We must rise, not by a leap, but by small\nsteps, by successive advances, by a gradation of ascents, trying our\nfacts, and clearing our notions at every interval. The scheme of true\nphilosophy, according to Bacon, is not obvious and simple, but long and\ntechnical, requiring constant care and self-denial to follow it. And we\nhave seen that, in this opinion, his judgment is confirmed by the past\nhistory and present condition of science.\n\nAgain; it is by no means a just view of Bacon's character to place\nhim in contrast to Plato. Plato's philosophy was the philosophy of\nIdeas; but it was not left for Bacon to set up the philosophy of\nFacts in opposition to that of Ideas. That had been done fully by the\nspeculative reformers of the sixteenth century. Bacon had the merit of\nshowing that Facts and Ideas must be combined; and not only so, but of\ndivining many of the special rules and forms of this combination, when\nas yet there were no examples of them, with a sagacity hitherto quite\nunparalleled.\n\n\n(X.) 22. _His Perseverance._--With Bacon's unhappy political life we\nhave here nothing to do. But we cannot but notice with pleasure how\nfaithfully, how perseveringly, how energetically he discharged his\ngreat philosophical office of a Reformer of Methods. He had conceived\nthe purpose of making this his object at an early period. When\nmeditating the continuation of his _Novum Organon_, and speaking of\nhis reasons for trusting that his work will reach some completeness\nof effect, he says[194], \"I am by two arguments thus persuaded.\nFirst, I think thus from the zeal and constancy of my mind, which has\nnot waxed old in this design, nor, after so many years, grown cold\nand indifferent; I remember that about forty years ago I composed\na juvenile work about these things, which with great contrivance\nand a pompous title I called _temporis partum maximum_, or the most\nconsiderable birth of time; Next, that on account of its usefulness,\nit may hope the Divine blessing.\" In stating the grounds of hope for\nfuture progress in the sciences, he says[195]: \"Some hope may, we\nconceive, be ministered to men by our own example: and this we say, not\nfor the sake of boasting, but because it is useful to be said. If any\ndespond, let them look at me, a man among all others of my age most\noccupied with civil affairs, nor of very sound health, (which brings a\ngreat loss of time;) also in this attempt the first explorer, following\nthe footsteps of no man, nor communicating on these subjects with any\nmortal; yet, having steadily entered upon the true road and made my\nmind submit to things themselves, one who has, in this undertaking,\nmade, (as we think,) some progress.\" He then proceeds to speak of what\nmay be done by the combined and more prosperous labours of others,\nin that strain of noble hope and confidence, which rises again and\nagain, like a chorus, at intervals in every part of his writings. In\nthe _Advancement of Learning_ he had said, \"I could not be true and\nconstant to the argument I handle, if I were not willing to go beyond\nothers, but yet not more willing than to have others go beyond me\nagain.\" In the Preface to the _Instauratio Magna_, he had placed among\nhis postulates those expressions which have more than once warmed the\nbreast of a philosophical reformer[196]. \"Concerning ourselves we\nspeak not; but as touching the matter which we have in hand, this we\nask;--that men be of good hope, neither feign and imagine to themselves\nthis our Reform as something of infinite dimension and beyond the grasp\nof mortal man, when in truth it is the end and true limit of infinite\nerror; and is by no means unmindful of the condition of mortality and\nhumanity, not confiding that such a thing can be carried to its perfect\nclose in the space of a single age, but assigning it as a task to a\nsuccession of generations.\" In a later portion of the _Instauratio_ he\nsays: \"We bear the strongest love to the _human republic_ our common\ncountry; and we by no means abandon the hope that there will arise and\ncome forth some man among posterity, who will be able to receive and\ndigest all that is best in what we deliver; and whose care it will be\nto cultivate and perfect such things. Therefore, by the blessing of the\nDeity, to tend to this object, to open up the fountains, to discover\nthe useful, to gather guidance for the way, shall be our task; and from\nthis we shall never, while we remain in life, desist.\"\n\n\n(XI.) 23. _His Piety._--We may add, that the spirit of piety as well as\nof hope which is seen in this passage, appears to have been habitual\nto Bacon at all periods of his life. We find in his works several\ndrafts of portions of his great scheme, and several of them begin with\na prayer. One of these entitled, in the edition of his works, \"The\nStudent's Prayer,\" appears to me to belong probably to his early youth.\nAnother, entitled \"The Writer's Prayer,\" is inserted at the end of\nthe Preface of the _Instauratio_, as it was finally published. I will\nconclude my notice of this wonderful man by inserting here these two\nprayers.\n\n\"To God the Father, God the Word, God the Spirit, we pour forth most\nhumble and hearty supplications; that he, remembering the calamities\nof mankind, and the pilgrimage of this our life, in which we wear out\ndays few and evil, would please to open to us new refreshments out of\nthe fountains of his goodness for the alleviating of our miseries.\nThis also we humbly and earnestly beg, that human things may not\nprejudice such as are divine; neither that, from the unlocking of the\ngates of sense, and the kindling of a greater natural light, anything\nof incredulity, or intellectual night, may arise in our minds towards\ndivine mysteries. But rather, that by our mind thoroughly cleansed and\npurged from fancy and vanities, and yet subject and perfectly given up\nto the Divine oracles, there may be given unto faith the things that\nare faith's.\"\n\n\"Thou, O Father, who gavest the visible light as the first-born of\nthy creatures, and didst pour into man the intellectual light as the\ntop and consummation of thy workmanship, be pleased to protect and\ngovern this work, which coming from thy goodness, returneth to thy\nglory. Thou, after thou hadst reviewed the works which thy hands had\nmade, beheldest that everything was very good, and thou didst rest\nwith complacency in them. But man, reflecting on the works which he\nhad made, saw that all was vanity and vexation of spirit, and could by\nno means acquiesce in them. Wherefore, if we labour in thy works with\nthe sweat of our brows, thou wilt make us partakers of thy vision and\nthy Sabbath. We humbly beg that this mind may be steadfastly in us;\nand that thou, by our hands, and also by the hands of others on whom\nthou shalt bestow the same spirit, wilt please to convey a largess\nof new alms to thy family of mankind. These things we commend to thy\neverlasting love, by our Jesus, thy Christ, God with us. Amen.\"\n\n\nFOOTNOTES:\n\n[Footnote 168: And in other passages: thus, \"Ego enim buccinator tantum\npugnam non ineo.\" _Nov. Org._ lib. iv. c. i.]\n\n[Footnote 169: Lib. 1. Aphor. 78 _et seq._]\n\n[Footnote 170: _Aug. Sc._ Lib. iii. c. 4. p. 194. So in other places,\nas _Nov. Org._ i. Aph. 104. \"De scientiis tum demum bene sperandum est\nquando per scalam veram et per gradus continuos, et non intermissos aut\nhiulcos a particularibus ascendetur ad axiomata minora, et deinde ad\nmedia, alia aliis superiora, et postremo demum ad generalissima.\"]\n\n[Footnote 171: _Nov. Org._ 1. Aph. 22.]\n\n[Footnote 172: _Ib._ Aph. 20.]\n\n[Footnote 173: 1 Ax. 15.]\n\n[Footnote 174: _Nov. Org._ lib. ii. Aph. 19.]\n\n[Footnote 175: _Inst. Mag._ par. iii. (vol. viii. p. 244).]\n\n[Footnote 176: _Hist. Ind. Sc._ b. x. c. i.]\n\n[Footnote 177: _Ib._ c. iv.]\n\n[Footnote 178: _Nov. Org._ lib. i. Aph. 61.]\n\n[Footnote 179: _Nov. Org._ lib. ii. Aph. 10.]\n\n[Footnote 180: Aph. 11.]\n\n[Footnote 181: Aph. 15, p. 105.]\n\n[Footnote 182: Page 110.]\n\n[Footnote 183: Herschel, _On the Study of Nat. Phil._ Art. 192.]\n\n[Footnote 184: _Nov. Org._ lib. i. Aph. 40.]\n\n[Footnote 185: _Nov. Org._ lib. i. Ax. 103.]\n\n[Footnote 186: _Edinb. Rev._ No. cxxxii. p. 65.]\n\n[Footnote 187: _Ib._]\n\n[Footnote 188: Pref. to the _Nat. Hist._ i. 243.]\n\n[Footnote 189: _Nov. Org._ lib. i. Aph. 19.]\n\n[Footnote 190: _Ibid._ lib. i. Aph. 20.]\n\n[Footnote 191: Aph. 27.]\n\n[Footnote 192: _Ib._ 28.]\n\n[Footnote 193: Aph. 104. So Aph. 105. \"In constituendo axiomate forma\n_inductionis_ alia quam adhuc in usu fuit excogitanda est,\" &c.]\n\n[Footnote 194: _Ep. ad P. Fulgentium._ _Op._ x. 330.]\n\n[Footnote 195: _Nov. Org._ i. Aph. 113.]\n\n[Footnote 196: See the motto to Kant's _Kritik der Reinen Vernunft_.]\n\n\n\n\nCHAPTER XVI.\n\nADDITIONAL REMARKS ON FRANCIS BACON.\n\n\nFrancis Bacon and his works have recently been discussed and examined\nby various writers in France and Germany as well as England[197]. Not\nto mention smaller essays, M. Bouillet has published a valuable edition\nof his philosophical works; Count Joseph de Maistre wrote a severe\ncritique of his philosophy, which has been published since the death of\nthe author; M. Charles Remusat has written a lucid and discriminating\nEssay on the subject; and in England we have had a new edition of the\nworks published, with a careful and thoughtful examination of the\nphilosophy which they contain, written by one of the editors: a person\nespecially fitted for such an examination by an acute intellect, great\nacquaintance with philosophical literature, and a wide knowledge of\nmodern science. Robert Leslie Ellis, the editor of whom I speak, died\nduring the publication of the edition, and before he had done full\njustice to his powers; but he had already written various dissertations\non Bacon's philosophy, which accompany the different Treatises in the\nnew edition.\n\nMr. Ellis has given a more precise view than any of his predecessors\nhad done of the nature of Bacon's induction and of his philosophy of\ndiscovery. Bacon's object was to discover the 'natures' or essences\nof things, in order that he might reproduce these natures or essences\nat will; he conceived that these natures were limited in number, and\nmanifested in various combinations in the bodies which exist in the\nuniverse; so that by accumulating observations of them in a multitude\nof cases, we may learn by induction in what they do and in what\nthey do not consist; the _Induction_ which is to be used for this\npurpose consists in a great measure of _excluding_ the cases which\ndo not exhibit the 'nature' in question; and by such exclusion, duly\nrepeated, we have at last left in our hands the elements of which the\nproposed nature consists. And the knowledge which is thus obtained may\nbe applied to reproduce the things so analysed. As exhibiting this\nview clearly we may take a passage in the _Sylva Sylvarum_: \"Gold has\nthese natures: greatness of weight, closeness of parts, fixation,\npliantness or softness, immunity from rust, colour or tincture of\nyellow. Therefore the sure way, though most about, to make gold, is to\nknow the causes of the several natures before rehearsed, and the axioms\nconcerning the same. For if a man can make a metal, that hath all these\nproperties, let men dispute whether it be gold or no.\" He means that\nhowever they dispute, it is gold for all practical purposes.\n\nFor such an Induction as this, Bacon claims the merit both of\nbeing certain, and of being nearly independent of the ingenuity of\nthe inquirer. It is a method which enables all men to make exact\ndiscoveries, as a pair of compasses enables all men to draw an exact\ncircle.\n\nNow it is necessary for us, who are exploring the progress of the true\nphilosophy of discovery, to say plainly that this part of Bacon's\nspeculation is erroneous and valueless. No scientific discovery ever\nhas been made in this way. Men have not obtained truths concerning\nthe natural world by seeking for the natures of things, and by\nextracting them from phenomena by rejecting the cases in which they\nwere not. On the contrary, they have begun by ascertaining the _laws\nof the phenomena_; and have then gone on, not by a mechanical method\nwhich levels all intellect, but by special efforts of the brightest\nintellects to catch hold of the ideas by which these laws of phenomena\nmight be interpreted and expressed in more general terms. These two\nsteps, the finding the laws of phenomena, and finding the conceptions\nby which those laws can be expressed, are really the course of\ndiscovery, as the history of science exhibits it to us.\n\nBacon, therefore, according to the view now presented, was wrong both\nas to his object and as to his method. He was wrong in taking for his\nobject the essences of things,--the causes of abstract properties:\nfor these man cannot, or can very rarely discover; and all Bacon's\ningenuity in enumerating and classifying these essences and abstract\nproperties has led, and could lead, to no result. The vast results\nof modern science have been obtained, not by seeking and finding the\nessences of things, but by exploring the laws of phenomena and the\ncauses of those laws.\n\nAnd Bacon's method, as well as his object, is vitiated by a pervading\nerror:--the error of supposing that to be done by method which must\nbe done by mind;--that to be done by rule which must be done by a\nflight beyond rule;--that to be mainly negative which is eminently\npositive;--that to depend on other men which must depend on the\ndiscoverer himself;--that to be mere prose which must have a dash of\npoetry;--that to be a work of mere labour which must be also a work of\ngenius.\n\nMr. Ellis has seen very clearly and explained very candidly that this\nmethod thus recommended by Bacon has not led to discovery. \"It is,\" he\nsays, \"neither to the technical part of his method nor to the details\nof his view of the nature and progress of science, that his great fame\nis justly owing. His merits are of another kind. They belong to the\nspirit rather than to the positive precepts of his philosophy.\"\n\nAs the reader of the last chapter will see, this amounts to much the\nsame as the account which I had given of the positive results of\nBacon's method, and the real value of that portion of his philosophy\nwhich he himself valued most. But still there remain, as I have also\nnoted, portions of Bacon's speculations which have a great and enduring\nvalue, namely, his doctrine that Science is the Interpretation of\nNature, his distinction of this Interpretation of Nature from the\nvicious and premature Anticipation of Nature which had generally\nprevailed till then; and the recommendation of a graduated and\nsuccessive induction by which alone the highest and most general\ntruths were to be reached. These are points which he urges with great\nclearness and with great earnestness; and these are important points in\nthe true philosophy of discovery.\n\nI may add that Mr. Ellis agrees with me in noting the invention of\nthe conception by which the laws of phenomena are interpreted as\nsomething additional to _Induction_, both in the common and in the\nBaconian sense of the word. He says (General Preface, Art. 9), \"In\nall cases this process [scientific discovery] involves an element to\nwhich nothing corresponds in the Tables of Comparence and Exclusion;\nnamely the application to the facts of a _principle_ of arrangement,\nan _idea_, existing in the mind of the discoverer antecedently to the\nact of induction.\" It may be said that this principle or idea is aimed\nat in the Baconian analysis. \"And this is in one sense true: but it\nmust be added, that this _analysis_, if it be thought right to call it\nso, is of the essence of the discovery which results from it. To take\nfor granted that it has been already effected is simply a _petitio\nprincipii_. In most cases the mere act of induction follows as a matter\nof course as soon as the _appropriate idea_ has been introduced.\" And\nas an example he takes Kepler's invention of the ellipse, as the idea\nby which Mars's motions could be reduced to law; making the same use of\nthis example which we have repeatedly made of it.\n\nMr. Ellis may at first sight appear to express himself more favourably\nthan I have done, with regard to the value of Bacon's _Inquisitio in\nNaturam Calidi_ in the Second Book of the _Novum Organon_. He says of\none part of it[198]: \"Bacon here anticipates not merely the essential\ncharacter of the most recent theory of heat, but also the kind of\nevidence by which it has been established.... The merit of having\nperceived the true significance of the production of heat by friction\nbelongs of right to Bacon.\"\n\nBut notwithstanding this, Mr. Ellis's general judgment on this specimen\nof Bacon's application of his own method does not differ essentially\nfrom mine. He examines the _Inquisitio_ at some length, and finally\nsays: \"If it were affirmed that Bacon, after having had a glimpse of\nthe truth suggested by some obvious phenomena, had then recourse, as he\nhimself expresses it, to certain 'differenti\u00e6 inanes' in order to save\nthe phenomena, I think it would be hard to dispute the truth of the\ncensure.\"\n\n\nAnother of the Editors of this edition (Mr. Spedding) fixes his\nattention upon another of the features of the method of discovery\nproposed by Bacon, and is disposed to think that the proposed method\nhas never yet had justice done it, because it has not been tried in the\nway and on the scale that Bacon proposes[199]. Bacon recommended that\na great collection of facts should be at once made and accumulated,\nregarding every branch of human knowledge; and conceived that, when\nthis had been done by common observers, philosophers might extract\nscientific truths from this mass of facts by the application of a right\nmethod. This separation of the offices of the observer and discoverer,\nMr. Spedding thinks is shown to be possible by such practical examples\nas meteorological observations, made by ordinary observers, and\nreduced to tables and laws by a central calculator; by hydrographical\nobservations made by ships provided with proper instructions, and\nreduced to general laws by the man of science in his study; by\nmagnetical observations made by many persons in every part of the\nworld, and reduced into subservience to theory by mathematicians at\nhome.\n\nAnd to this our reply will be, in the terms which the history of\nall the Sciences has taught us, that such methods of procedure as\nthis do not belong to the _Epoch of Discovery_, but to the Period of\n_verification_ and _application_ of the discovery which follows. When a\ntheory has been established in its general form, our knowledge of the\ndistribution of its phenomena in time and space can be much promoted\nby ordinary observers scattered over the earth, and succeeding each\nother in time, provided they are furnished with instruments and methods\nof observation, duly constructed on the principles of science; but\nsuch observers cannot in any degree supersede the discoverer who is\nfirst to establish the theory, and to introduce into the facts a new\nprinciple of order. When the laws of nature have been caught sight\nof, much may be done, even by ordinary observers, in verifying and\nexactly determining them; but when a real discovery is to be made,\nthis separation of the observer and the theorist is not possible. In\nthose cases, the questioning temper, the busy suggestive mind, is\nneeded at every step, to direct the operating hand or the open gaze.\nNo possible accumulation of facts about mixture and heat, collected in\nthe way of blind trial, could have led to the doctrines of chemistry,\nor crystallography, or the atomic theory, or voltaic and chemical\nand magnetic polarity, or physiology, or any other science. Indeed\nnot only is an existing theory requisite to supply the observer with\ninstruments and methods, but without theory he cannot even describe his\nobservations. He says that he mixes an acid and an alkali; but what\nis an acid? What is an alkali? How does he know them? He classifies\ncrystals according to their forms: but till he has learnt what is\ndistinctive in the form of a crystal, he cannot distinguish a cube\nfrom a square prism, even if he had a goniometer and could use it. And\nthe like impossibility hangs over all the other subjects. To report\nfacts for scientific purposes without some aid from theory, is not only\nuseless, but impossible.\n\nWhen Mr. Spedding says, \"I could wish that men of science would apply\nthemselves earnestly to the solution of this practical problem:\nWhat measures are to be taken in order that the greatest variety of\njudicious observations of nature all over the world may be carried on\nin concert upon a common plan and brought to a common centre:\"--he is\nurging upon men of science to do what they have always done, so far\nas they have had any power, and in proportion as the state of science\nrendered such a procedure possible and profitable to science. In\nAstronomy, it has been done from the times of the Greeks and even of\nthe Chaldeans, having been begun _as soon as_ the heavens were reduced\nto law at all. In meteorology, it has been done extensively, though to\nlittle purpose, because the weather has _not yet_ been reduced to rule.\nMen of science have shown how barometers, thermometers, hygrometers,\nand the like, may be constructed; and these may be now read by any one\nas easily as a clock; but of ten thousand meteorological registers\nthus kept by ordinary observers, what good has come to science?\nAgain: The laws of the tides have been in a great measure determined\nby observations in all parts of the globe, _because_ theory pointed\nout what was to be observed. In like manner the facts of terrestrial\nmagnetism were ascertained with tolerable completeness by extended\nobservations, _then_, and then only, when a most recondite and profound\nbranch of mathematics had pointed out what was to be observed, and most\ningenious instruments had been devised by men of science for observing.\nAnd even with these, it requires an education to use the instruments.\nBut in many cases no education in the use of instruments devised by\nothers can supersede the necessity of a theoretical and suggestive\nspirit in the inquirer himself. He must devise his own instruments\nand his own methods, if he is to make any discovery. What chemist, or\ninquirer about polarities, or about optical laws yet undiscovered, can\nmake any progress by using another man's experiments and observations?\nHe must invent at every step of his observation; and the observer and\ntheorist can no more be dissevered, than the body and soul of the\ninquirer.\n\nThat persons of moderate philosophical powers may, when duly\neducated, make observations which may be used by greater discoverers\nthan themselves, is true. We have examples of such a subordination\nof scientific offices in astronomy, in geology, and in many other\ndepartments. But still, as I have said, a very considerable degree of\nscientific education is needed even for the subordinate labourers in\nscience; and the more considerable in proportion as science advances\nfurther and further; since every advance implies a knowledge of what\nhas already been done, and requires a new precision or generality in\nthe new points of inquiry.\n\n\nFOOTNOTES:\n\n[Footnote 197: _\u0152uvres Philosophiques de Bacon, &c._ par M. N.\nBouillet, 3 Tomes.\n\n_Examen de la Philosophie de Bacon_ (_\u0152uvres Posthumes_ du Comte J. de\nMaistre).\n\n_Bacon, sa Vie, son Temps, sa Philosophie_, par Charles de Remusat.\n\n_Histoire de la Vie et des Ouvrages de Fran\u00e7ois Bacon_, par J. B. de\nVaugelles.\n\n_Franz Baco von Verulam_, von Kuno Fischer.\n\n_The Works of Francis Bacon_, collected and edited by James Spedding,\nRobert Leslie Ellis, and Douglas Denon Heath.]\n\n[Footnote 198: Note to Aph. xviii.]\n\n[Footnote 199: Pref. to the _Parasceue_, Vol. i. p. 382.]\n\n\n\n\nCHAPTER XVII.\n\nFROM BACON TO NEWTON.\n\n\n1. _Harvey._--We have already seen that Bacon was by no means the\nfirst mover or principal author of the revolution in the method of\nphilosophizing which took place in his time; but only the writer who\nproclaimed in the most impressive and comprehensive manner, the scheme,\nthe profit, the dignity, and the prospects of the new philosophy.\nThose, therefore, who after him, took up the same views are not to be\nconsidered as his successors, but as his fellow-labourers; and the\nline of historical succession of opinions must be pursued without\nspecial reference to any one leading character, as the principal figure\nof the epoch. I resume this line, by noticing a contemporary and\nfellow-countryman of Bacon, Harvey, the discoverer of the circulation\nof the blood. This discovery was not published and generally accepted\ntill near the end of Bacon's life; but the anatomist's reflections\non the method of pursuing science, though strongly marked with the\ncharacter of the revolution that was taking place, belong to a very\ndifferent school from the Chancellor's. Harvey was a pupil of Fabricius\nof Acquapendente, whom we noticed among the practical reformers of the\nsixteenth century. He entertained, like his master, a strong reverence\nfor the great names which had ruled in philosophy up to that time,\nAristotle and Galen; and was disposed rather to recommend his own\nmethod by exhibiting it as the true interpretation of ancient wisdom,\nthan to boast of its novelty. It is true, that he assigns, as his\nreason for publishing some of his researches[200], \"that by revealing\nthe method I use in searching into things, I might propose to studious\nmen, a new and (if I mistake not) a surer path to the attainment of\nknowledge[201];\" but he soon proceeds to fortify himself with the\nauthority of Aristotle. In doing this, however, he has the very great\nmerit of giving a living and practical character to truths which exist\nin the Aristotelian works, but which had hitherto been barren and empty\nprofessions. We have seen that Aristotle had asserted the importance\nof experience as one root of knowledge; and in this had been followed\nby the schoolmen of the middle ages: but this assertion came with very\ndifferent force and effect from a man, the whole of whose life had been\nspent in obtaining, by means of experience, knowledge which no man had\npossessed before. In Harvey's general reflections, the necessity of\nboth the elements of knowledge, sensations and ideas, experience and\nreason, is fully brought into view, and rightly connected with the\nmetaphysics of Aristotle. He puts the antithesis of these two elements\nwith great clearness. \"Universals are chiefly known to us, for science\nis begot by reasoning from universals to particulars; yet that very\ncomprehension of universals in the understanding springs from the\nperception of singulars in our sense.\" Again, he quotes Aristotle's\napparently opposite assertions:--that made in his _Physics_[202],\n\"that we must advance from things which are first known to us, though\nconfusedly, to things more distinctly intelligible in themselves;\nfrom the whole to the part; from the universal to the particular;\"\nand that made in the _Analytics_[203]; that \"Singulars are more known\nto us and do first exist according to sense: for nothing is in the\nunderstanding which was not before in the sense.\" Both, he says, are\ntrue, though at first they seem to clash: for \"though in knowledge\nwe begin with sense, sensation itself is a universal thing.\" This he\nfurther illustrates; and quotes Seneca, who says, that \"Art itself is\nnothing but the _reason_ of the work, implanted in the Artist's mind:\"\nand adds, \"the same way by which we gain an Art, by the very same way\nwe attain any kind of science or knowledge whatever; for as Art is\na habit whose object is something to be done, so Science is a habit\nwhose object is something to be known; and as the former proceedeth\nfrom the imitation of examples, so this latter, from the knowledge of\nthings natural. The source of both is from sense and experience; since\n[but?] it is impossible that Art should be rightly purchased by the one\nor Science by the other without a direction from ideas.\" Without here\ndwelling on the relation of Art and Science, (very justly stated by\nHarvey, except that ideas exist in a very different form in the mind\nof the Artist and the Scientist) it will be seen that this doctrine,\nof science springing from experience with a direction from ideas, is\nexactly that which we have repeatedly urged, as the true view of the\nsubject. From this view, Harvey proceeds to infer the importance of a\nreference to sense in his own subject, not only for first discovering,\nbut for receiving knowledge: \"Without experience, not other men's but\nour own, no man is a proper disciple of any part of natural knowledge;\nwithout experimental skill in anatomy, he will no better apprehend\nwhat I shall deliver concerning generation, than a man born blind can\njudge of the nature and difference of colours, or one born deaf, of\nsounds.\" \"If we do otherwise, we may get a humid and floating opinion,\nbut never a solid and infallible knowledge: as is happenable to those\nwho see foreign countries only in maps, and the bowels of men falsely\ndescribed in anatomical tables. And hence it comes about, that in this\nrank age, we have many sophisters and bookwrights, but few wise men\nand philosophers.\" He had before declared \"how unsafe and degenerate a\nthing it is, to be tutored by other men's commentaries, without making\ntrial of the things themselves; especially since Nature's book is so\nopen and legible.\" We are here reminded of Galileo's condemnation\nof the \"paper philosophers.\" The train of thought thus expressed by\nthe practical discoverers, spread rapidly with the spread of the\nnew knowledge that had suggested it, and soon became general and\nunquestioned.\n\n\n2. _Descartes._--Such opinions are now among the most familiar and\npopular of those which are current among writers and speakers; but\nwe should err much if we were to imagine that after they were once\npropounded they were never resisted or contradicted. Indeed, even in\nour own time, not only are such maxims very often practically neglected\nor forgotten, but the opposite opinions, and views of science quite\ninconsistent with those we have been explaining, are often promulgated\nand widely accepted. The philosophy of pure ideas has its commonplaces,\nas well as the philosophy of experience. And at the time of which\nwe speak, the former philosophy, no less than the latter, had its\ngreat asserter and expounder; a man in his own time more admired than\nBacon, regarded with more deference by a large body of disciples all\nover Europe, and more powerful in stirring up men's minds to a new\nactivity of inquiry. I speak of Descartes, whose labours, considered\nas a philosophical system, were an endeavour to revive the method\nof obtaining knowledge by reasoning from our own ideas only, and to\nerect it in opposition to the method of observation and experiment.\nThe Cartesian philosophy contained an attempt at a counter-revolution.\nThus in this author's _Principia Philosophi\u00e6_[204], he says that \"he\nwill give a short account of the principal phenomena of the world,\nnot that he may use them as reasons to prove anything; for,\" adds he,\n\"we desire to deduce effects from causes, not causes from effects;\nbut only in order that out of the innumerable effects which we learn\nto be capable of resulting from the same causes, we may determine our\nmind to consider some rather than others.\" He had before said, \"The\nprinciples which we have obtained [by pure _\u00e0 priori_ reasoning] are so\nvast and so fruitful, that many more consequences follow from them than\nwe see contained in this visible world, and even many more than our\nmind can ever take a full survey of.\" And he professes to apply this\nmethod in detail. Thus in attempting to state the three fundamental\nlaws of motion, he employs only _\u00e0 priori_ reasonings, and is in fact\nled into error in the third law which he thus obtains[205]. And in\nhis _Dioptrics_[206] he pretends to deduce the laws of reflection\nand refraction of light from certain comparisons (which are, in\ntruth, arbitrary,) in which the radiation of light is represented\nby the motion of a ball impinging upon the reflecting or refracting\nbody. It might be represented as a curious instance of the caprice\nof fortune, which appears in scientific as in other history, that\nKepler, professing to derive all his knowledge from experience, and\nexerting himself with the greatest energy and perseverance, failed in\ndetecting the law of refraction; while Descartes, who professed to be\nable to despise experiment, obtained the true law of sines. But as we\nhave stated in the _History_[207], Descartes appears to have learnt\nthis law from Snell's papers. And whether this be so or not, it is\ncertain that notwithstanding the profession of independence which his\nphilosophy made, it was in reality constantly guided and instructed by\nexperience. Thus in explaining the Rainbow (in which his portion of\nthe discovery merits great praise) he speaks[208] of taking a globe\nof glass, allowing the sun to shine on one side of it, and noting the\ncolours produced by rays after two refractions and one reflection.\nAnd in many other instances, indeed in all that relates to physics,\nthe reasonings and explanations of Descartes and his followers were,\nconsciously or unconsciously, directed by the known facts, which they\nhad observed themselves or learnt from others.\n\nBut since Descartes thus, speculatively at least, set himself in\nopposition to the great reform of scientific method which was going\non in his time, how, it may be asked, did he acquire so strong an\ninfluence over the most active minds of his time? How is it that he\nbecame the founder of a large and distinguished school of philosophers?\nHow is it that he not only was mainly instrumental in deposing\nAristotle from his intellectual throne, but for a time appeared to have\nestablished himself with almost equal powers, and to have rendered the\nCartesian school as firm a body as the Peripatetic had been?\n\nThe causes to be assigned for this remarkable result are, I conceive,\nthe following. In the first place, the physicists of the Cartesian\nschool did, as I have just stated, found their philosophy upon\nexperiment, and did not practically, or indeed, most of them,\ntheoretically, assent to their master's boast of showing what the\nphenomena _must be_, instead of looking to see what they _are_. And\nas Descartes had really incorporated in his philosophy all the chief\nphysical discoveries of his own and preceding times, and had delivered,\nin a more general and systematic shape than any one before him, the\nprinciples which he thus established, the physical philosophy of his\nschool was in reality far the best then current; and was an immense\nimprovement upon the Aristotelian doctrines, which had not yet been\ndisplaced as a system. Another circumstance which gained him much\nfavour, was the bold and ostentatious manner in which he professed\nto begin his philosophy by liberating himself from all preconceived\nprejudice. The first sentence of his philosophy contains this\ncelebrated declaration: \"Since,\" he says, \"we begin life as infants,\nand have contracted various judgments concerning sensible things before\nwe possess the entire use of our reason, we are turned aside from the\nknowledge of truth by many prejudices: from which it does not appear\nthat we can be any otherwise delivered, than if once in our life we\nmake it our business to doubt of everything in which we discern the\nsmallest suspicion of uncertainty.\" In the face of this sweeping\nrejection or unhesitating scrutiny of all preconceived opinions,\nthe power of the ancient authorities and masters in philosophy must\nobviously shrink away; and thus Descartes came to be considered as\nthe great hero of the overthrow of the Aristotelian dogmatism. But\nin addition to these causes, and perhaps more powerful than all in\nprocuring the assent of men to his doctrines, came the deductive and\nsystematic character of his philosophy. For although all knowledge of\nthe external world is in reality only to be obtained from observation,\nby inductive steps,--minute, perhaps, and slow, and many, as Galileo\nand Bacon had already taught;--the human mind conforms to these\nconditions reluctantly and unsteadily, and is ever ready to rush to\ngeneral principles, and then to employ itself in deducing conclusions\nfrom these by synthetical reasonings; a task grateful, from the\ndistinctness and certainty of the result, and the accompanying feeling\nof our own sufficiency. Hence men readily overlooked the precarious\ncharacter of Descartes' fundamental assumptions, in their admiration\nof the skill with which a varied and complex Universe was evolved out\nof them. And the complete and systematic character of this philosophy\nattracted men no less than its logical connexion. I may quote here\nwhat a philosopher[209] of our own time has said of another writer:\n\"He owed his influence to various causes; at the head of which may be\nplaced that genius for system which, though it cramps the growth of\nknowledge, perhaps finally atones for that mischief by the zeal and\nactivity which it rouses among followers and opponents, who discover\ntruth by accident when in pursuit of weapons for their warfare. A\nsystem which attempts a task so hard as that of subjecting vast\nprovinces of human knowledge to one or two principles, if it presents\nsome striking instances of conformity to superficial appearances, is\nsure to delight the framer; and for a time to subdue and captivate the\nstudent too entirely for sober reflection and rigorous examination. In\nthe first instance consistency passes for truth. When principles in\nsome instances have proved sufficient to give an unexpected explanation\nof facts, the delighted reader is content to accept as true all other\ndeductions from the principles. Specious premises being assumed to be\ntrue, nothing more can be required than logical inference. Mathematical\nforms pass current as the equivalent of mathematical certainty. The\nunwary admirer is satisfied with the completeness and symmetry of the\nplan of his house, unmindful of the need of examining the firmness of\nthe foundation and the soundness of the materials. The system-maker,\nlike the conqueror, long dazzles and overawes the world; but when their\nsway is past, the vulgar herd, unable to measure their astonishing\nfaculties, take revenge by trampling on fallen greatness.\" Bacon\nshowed his wisdom in his reflections on this subject, when he said\nthat \"Method, carrying a show of total and perfect knowledge, hath a\ntendency to generate acquiescence.\"\n\nThe main value of Descartes' physical doctrines consisted in their\nbeing arrived at in a way inconsistent with his own professed method,\nnamely, by a reference to observation. But though he did in reality\nbegin from facts, his system was nevertheless a glaring example\nof that error which Bacon had called _Anticipation_; that illicit\ngeneralization which leaps at once from special facts to principles\nof the widest and remotest kind; such, for instance, as the Cartesian\ndoctrine, that the world is an absolute _plenum_, every part being\nfull of matter of some kind, and that all natural effects depend on\nthe laws of motion. Against this fault, to which the human mind is\nso prone, Bacon had lifted his warning voice in vain, so far as the\nCartesians were concerned; as indeed, to this day, one theorist after\nanother pursues his course, and turns a deaf ear to the Verulamian\ninjunctions; perhaps even complacently boasts that he founds his theory\nupon observation; and forgets that there are, as the aphorism of the\n_Novum Organon_ declares, two ways by which this may be done;--the one\nhitherto in use and suggested by our common tendencies, but barren and\nworthless; the other almost untried, to be pursued only with effort and\nself-denial, but alone capable of producing true knowledge.\n\n\n3. _Gassendi._--Thus the lessons which Bacon taught were far from being\ngenerally accepted and applied at first. The amount of the influence of\nthese two men, Bacon and Descartes, upon their age, has often been a\nsubject of discussion. The fortunes of the Cartesian school have been\nin some measure traced in the History of Science. But I may mention the\nnotice taken of these two philosophers by Gassendi, a contemporary and\ncountryman of Descartes. Gassendi, as I have elsewhere stated[210],\nwas associated with Descartes in public opinion, as an opponent of the\nAristotelian dogmatism; but was not in fact a follower or profound\nadmirer of that writer. In a Treatise on Logic, Gassendi gives an\naccount of the Logic of various sects and authors; treating, in order,\nof the Logic of Zeno (the Eleatic), of Euclid (the Megarean), of\nPlato, of Aristotle, of the Stoics, of Epicurus, of Lullius, of Ramus;\nand to these he adds the Logic of Verulam, and the Logic of Cartesius.\n\"We must not,\" he says, \"on account of the celebrity it has obtained,\npass over the Organon or Logic of Francis Bacon Lord Verulam, High\nChancellor of England, whose noble purpose in our time it has been, to\nmake an Instauration of the Sciences.\" He then gives a brief account\nof the _Novum Organon_, noticing the principal features in its rules,\nand especially the distinction between the vulgar induction which leaps\nat once from particular experiments to the more general axioms, and\nthe chastised and gradual induction, which the author of the _Organon_\nrecommends. In his account of the Cartesian Logic, he justly observes,\nthat \"He too imitated Verulam in this, that being about to build up a\nnew philosophy from the foundation, he wished in the first place to lay\naside all prejudice: and having then found some solid principle, to\nmake that the groundwork of his whole structure. But he proceeds by a\nvery different path from that which Verulam follows; for while Verulam\nseeks aid from things, to perfect the cogitation of the intellect,\nCartesius conceives, that when we have laid aside all knowledge of\nthings, there is, in our thoughts alone, such a resource, that the\nintellect may by its own power arrive at a perfect knowledge of all,\neven the most abstruse things.\"\n\nThe writings of Descartes have been most admired, and his method\nmost commended, by those authors who have employed themselves upon\nmetaphysical rather than physical subjects of inquiry. Perhaps we might\nsay that, in reference to such subjects, this method is not so vicious\nas at first, when contrasted with the Baconian induction, it seems to\nbe: for it might be urged that the _thoughts_ from which Descartes\nbegins his reasonings are, in reality, _experiments_ of the kind which\nthe subject requires us to consider: each such thought is a fact in\nthe intellectual world; and of such facts, the metaphysician seeks to\ndiscover the laws. I shall not here examine the validity of this plea;\nbut shall turn to the consideration of the actual progress of physical\nscience, and its effect on men's minds.\n\n\n4. _Actual progress in Science._--The practical discoverers were indeed\nvery active and very successful during the seventeenth century, which\nopened with Bacon's survey and exhortations. The laws of nature, of\nwhich men had begun to obtain a glimpse in the preceding century, were\ninvestigated with zeal and sagacity, and the consequence was that the\nfoundations of most of the modern physical sciences were laid. That\nmode of research by experiment and observation, which had, a little\ntime ago, been a strange, and to many, an unwelcome innovation, was now\nbecome the habitual course of philosophers. The revolution from the\nphilosophy of tradition to the philosophy of experience was completed.\nThe great discoveries of Kepler belonged to the preceding century.\nThey are not, I believe, noticed, either by Bacon or by Descartes; but\nthey gave a strong impulse to astronomical and mechanical speculators,\nby showing the necessity of a sound science of motion. Such a science\nGalileo had already begun to construct. At the time of which I speak,\nhis disciples[211] were still labouring at this task, and at other\nproblems which rapidly suggested themselves. They had already convinced\nthemselves that air had weight; in 1643 Torricelli proved this\npractically by the invention of the Barometer; in 1647 Pascal proved\nit still further by sending the Barometer to the top of a mountain.\nPascal and Boyle brought into clear view the fundamental laws of fluid\nequilibrium; Boyle and Mariotte determined the law of the compression\nof air as regulated by its elasticity. Otto Guericke invented the\nair-pump, and by his \"Madgeburg Experiments\" on a vacuum, illustrated\nstill further the effects of the air. Guericke pursued what Gilbert\nhad begun, the observation of electrical phenomena; and these two\nphysicists made an important step, by detecting repulsion as well as\nattraction in these phenomena. Gilbert had already laid the foundations\nof the science of Magnetism. The law of refraction, at which Kepler\nhad laboured in vain, was, as we have seen, discovered by Snell (about\n1621), and published by Descartes. Mersenne had discovered some of\nthe more important parts of the theory of Harmonics. In sciences of\na different kind, the same movement was visible. Chemical doctrines\ntended to assume a proper degree of generality, when Sylvius in 1679\ntaught the opposition of acid and alkali, and Stahl, soon after,\nthe phlogistic theory of combustion. Steno had remarked the most\nimportant law of crystallography in 1669, that the angles of the same\nkind of crystals are always equal. In the sciences of classification,\nabout 1680, Ray and Morison in England resumed the attempt to form a\nsystematic botany, which had been interrupted for a hundred years, from\nthe time of the memorable essay of C\u00e6salpinus. The grand discovery of\nthe circulation of the blood by Harvey about 1619, was followed in 1651\nby Pecquet's discovery of the course of the chyle. There could now no\nlonger be any question whether science was progressive, or whether\nobservation could lead to new truths.\n\nAmong these cultivators of science, such sentiments as have been\nalready quoted became very familiar;--that knowledge is to be sought\nfrom nature herself by observation and experiment;--that in such\nmatters tradition is of no force when opposed to experience, and that\nmere reasonings without facts cannot lead to solid knowledge. But I\ndo not know that we find in these writers any more special rules of\ninduction and scientific research which have since been confirmed\nand universally adopted. Perhaps too, as was natural in so great a\nrevolution, the writers of this time, especially the second-rate\nones, were somewhat too prone to disparage the labours and talents\nof Aristotle and the ancients in general, and to overlook the ideal\nelement of our knowledge, in their zealous study of phenomena. They\nurged, sometimes in an exaggerated manner, the superiority of modern\ntimes in all that regards science, and the supreme and sole importance\nof facts in scientific investigations. There prevailed among them also\na lofty and dignified tone of speaking of the condition and prospects\nof science, such as we are accustomed to admire in the Verulamian\nwritings; for this, in a less degree, is epidemic among those who a\nlittle after his time speak of the new philosophy.\n\n\n5. _Otto Guericke, &c._--I need not illustrate these characteristics\nat any great length. I may as an example notice Otto Guericke's\nPreface to his _Experimenta Magdeburgica_ (1670). He quotes a passage\nfrom Kircher's Treatise on the Magnetic Art, in which the author\nsays, \"Hence it appears how all philosophy, except it be supported by\nexperiments, is empty, fallacious, and useless; what monstrosities\nphilosophers, in other respects of the highest and subtlest genius,\nmay produce in philosophy by neglecting experiment. Thus Experience\nalone is the Dissolver of Doubts, the Reconciler of Difficulties, the\nsole Mistress of Truth, who holds a torch before us in obscurity,\nunties our knots, teaches us the true causes of things.\" Guericke\nhimself reiterates the same remark, adding that \"philosophers,\ninsisting upon their own thoughts and arguments merely, cannot come\nto any sound conclusion respecting the natural constitution of the\nworld.\" Nor were the Cartesians slow in taking up the same train of\nreflection. Thus Gilbert Clark who, in 1660, published[212] a defence\nof Descartes' doctrine of a _plenum_ in the universe, speaks in a\ntone which reminds us of Bacon, and indeed was very probably caught\nfrom him: \"Natural philosophy formerly consisted entirely of loose\nand most doubtful controversies, carried on in high-sounding words,\nfit rather to delude than to instruct men. But at last (by the favour\nof the Deity) there shone forth some more divine intellects, who\ntaking as their counsellors reason and experience together, exhibited\na new method of philosophizing. Hence has been conceived a strong hope\nthat philosophers may embrace, not a shadow or empty image of Truth,\nbut Truth herself: and that Physiology (Physics) scattering these\ncontroversies to the winds, will contract an alliance with Mathematics.\nYet this is hardly the work of one age; still less of one man. Yet let\nnot the mind despond, or doubt not that, one party of investigators\nafter another following the same method of philosophizing, at last,\nunder good auguries, the mysteries of nature being daily unlocked as\nfar as human feebleness will allow, Truth may at last appear in full,\nand these nuptial torches may be lighted.\"\n\nAs another instance of the same kind, I may quote the preface to the\nFirst volume of the Transactions of the Academy of Sciences at Paris:\n\"It is only since the present century,\" says the writer, \"that we can\nreckon the revival of Mathematics and Physics. M. Descartes and other\ngreat men have laboured at this work with so much success, that in this\ndepartment of literature, the whole face of things has been changed.\nMen have quitted a sterile system of physics, which for several\ngenerations had been always at the same point; the reign of words\nand terms is passed; men will have things; they establish principles\nwhich they understand, they follow those principles; and thus they\nmake progress. Authority has ceased to have more weight than Reason:\nthat which was received without contradiction because it had been\nlong received, is now examined, and often rejected: and philosophers\nhave made it their business to consult, respecting natural things,\nNature herself rather than the Ancients.\" These had now become the\ncommonplaces of those who spoke concerning the course and method of the\nSciences.\n\n\n6. _Hooke._--In England, as might be expected, the influence of\nFrancis Bacon was more directly visible. We find many writers, about\nthis time, repeating the truths which Bacon had proclaimed, and in\nalmost every case showing the same imperfections in their views\nwhich we have noticed in him. We may take as an example of this\nHooke's Essay, entitled \"A General Scheme or Idea of the present\nstate of Natural Philosophy, and how its defects may be remedied by\na Methodical proceeding in the making Experiments and collecting\nObservations; whereby to compile a Natural History as a solid basis\nfor the superstructure of true Philosophy.\" This Essay may be looked\nupon as an attempt to adapt the _Novum Organon_ to the age which\nsucceeded its publication. We have in this imitation, as in the\noriginal, an enumeration of various mistakes and impediments which had\nin preceding times prevented the progress of knowledge; exhortations\nto experiment and observation as the only solid basis of Science; very\ningenious suggestions of trains of inquiry, and modes of pursuing them;\nand a promise of obtaining scientific truths when facts have been\nduly accumulated. This last part of his scheme the author calls _a\nPhilosophical Algebra_; and he appears to have imagined that it might\nanswer the purpose of finding unknown causes from known facts, by means\nof certain regular processes, in the same manner as Common Algebra\nfinds unknown from known quantities. But this part of the plan appears\nto have remained unexecuted. The suggestion of such a method was a\nresult of the Baconian notion that invention in a discoverer might be\ndispensed with. We find Hooke adopting the phrases in which this notion\nis implied: thus he speaks of the understanding as \"being very prone to\nrun into the affirmative way of judging, and wanting patience to follow\nand prosecute the negative way of inquiry, by rejection of disagreeing\nnatures.\" And he follows Bacon also in the error of attempting at\nonce to obtain from the facts the discovery of a \"nature,\" instead of\ninvestigating first the measures and the laws of phenomena. I return to\nmore general notices of the course of men's thoughts on this subject.\n\n\n7. _Royal Society._--Those who associated themselves together for the\nprosecution of science quoted Bacon as their leader, and exulted in the\nprogress made by the philosophy which proceeded upon his principles.\nThus in Oldenburg's Dedication of the Transactions of the Royal Society\nof London for 1670, to Robert Boyle, he says; \"I am informed by such as\nwell remember the best and worst days of the famous Lord Bacon, that\nthough he wrote his _Advancement of Learning_ and his _Instauratio\nMagna_ in the time of his greatest power, yet his greatest reputation\nrebounded first from the most intelligent foreigners in many parts\nof Christendom:\" and after speaking of his practical talents and his\npublic employments, he adds, \"much more justly still may we wonder how,\nwithout any great skill in Chemistry, without much pretence to the\nMathematics or Mechanics, without optic aids or other engines of late\ninvention, he should so much transcend the philosophers then living,\nin judicious and clear instructions, in so many useful observations\nand discoveries, I think I may say beyond the records of many ages.\"\nAnd in the end of the Preface to the same volume, he speaks with\ngreat exultation of the advance of science all over Europe, referring\nundoubtedly to facts then familiar. \"And now let envy snarl, it\ncannot stop the wheels of active philosophy, in no part of the known\nworld;--not in France, either in Paris or in Caen;--not in Italy,\neither in Rome, Naples, Milan, Florence, Venice, Bononia or Padua;--in\nnone of the Universities either on this or on that side of the seas,\nMadrid and Lisbon, all the best spirits in Spain and Portugal, and\nthe spacious and remote dominions to them belonging;--the Imperial\nCourt and the Princes of Germany; the Northern Kings and their best\nluminaries; and even the frozen Muscovite and Russian have all taken\nthe operative ferment: and it works high and prevails every way, to the\nencouragement of all sincere lovers of knowledge and virtue.\"\n\nAgain, in the Preface for 1672, he pursues the same thought into\ndetail: \"We must grant that in the last age, when operative philosophy\nbegan to recover ground, and to tread on the heels of triumphant\nPhilology; emergent adventures and great successes were encountered by\ndangerous oppositions and strong obstructions. Galil\u00e6us and others in\nItaly suffered extremities for their celestial discoveries; and here\nin England Sir Walter Raleigh, when he was in his greatest lustrous,\nwas notoriously slandered to have erected a school of atheism, because\nhe gave countenance to chemistry, to practical arts, and to curious\nmechanical operations, and designed to form the best of them into\na college. And Queen Elizabeth's Gilbert was a long time esteemed\nextravagant for his magnetisms; and Harvey for his diligent researches\nin pursuance of the circulation of the blood. But when our renowned\nLord Bacon had demonstrated the methods for a perfect restoration\nof all parts of real knowledge; and the generous and philosophical\nPeireskius had, soon after, agitated in all parts to redeem the most\ninstructive antiquities, and to excite experimental essays and fresh\ndiscoveries; the success became on a sudden stupendous; and effective\nphilosophy began to sparkle, and even to flow into beams of shining\nlight all over the world.\"\n\nThe formation of the Royal Society of London and of the Academy\nof Sciences of Paris, from which proceeded the declamations just\nquoted, were among many indications, belonging to this period, of\nthe importance which states as well as individuals had by this time\nbegun to attach to the cultivation of science. The English Society was\nestablished almost immediately when the restoration of the monarchy\nappeared to give a promise of tranquillity to the nation (in 1660), and\nthe French Academy very soon afterwards (in 1666). These measures were\nvery soon followed by the establishment of the Observatories of Paris\nand Greenwich (in 1667 and 1675); which may be considered to be a kind\nof public recognition of the astronomy of observation, as an object\non which it was the advantage and the duty of nations to bestow their\nwealth.\n\n\n8. _Bacon's New Atalantis._--When philosophers had their attention\nturned to the boundless prospect of increase to the knowledge and\npowers and pleasures of man which the cultivation of experimental\nphilosophy seemed to promise, it was natural that they should think of\ndevising institutions and associations by which such benefits might be\nsecured. Bacon had drawn a picture of a society organized with a view\nto such purpose, in his fiction of the \"New Atalantis.\" The imaginary\nteacher who explains this institution to the inquiring traveller,\ndescribes it by the name of _Solomon's House_; and says[213], \"The end\nof our foundation is the knowledge of causes and secret motions of\nthings; and the enlarging the bounds of the human empire to effecting\nof things possible.\" And, as parts of this House, he describes caves\nand wells, chambers and towers, baths and gardens, parks and pools,\ndispensatories and furnaces, and many other contrivances, provided\nfor the purpose of making experiments of many kinds. He describes\nalso the various employments of the Fellows of this College, who take\na share in its researches. There are _merchants of light_, who bring\nbooks and inventions from foreign countries; _depredators_, who gather\nthe experiments which exist in books; _mystery-men_, who collect the\nexperiments of the mechanical arts; _pioneers_ or _miners_, who invent\nnew experiments; and _compilers_, \"who draw the experiments of the\nformer into titles and tables, to give the better light for the drawing\nof observations and axioms out of them.\" There are also _dowry-men_ or\n_benefactors_, that cast about how to draw out of the experiments of\ntheir fellows things of use and practice for man's life; _lamps_, that\ndirect new experiments of a more penetrating light than the former;\n_inoculators_, that execute the experiments so directed. Finally, there\nare the _interpreters of nature_, that raise the former discoveries by\nexperiments into greater observations (that is, more general truths),\naxioms and aphorisms. Upon this scheme we may remark, that fictitious\nas it undisguisedly is, it still serves to exhibit very clearly some of\nthe main features of the author's philosophy:--namely, his steady view\nof the necessity of ascending from facts to the most general truths\nby several stages;--an exaggerated opinion of the aid that could be\nderived in such a task from technical separation of the phenomena and a\ndistribution of them into tables;--a belief, probably incorrect, that\nthe offices of experimenter and interpreter may be entirely separated,\nand pursued by different persons with a certainty of obtaining\nsuccess!--and a strong determination to make knowledge constantly\nsubservient to the uses of life.\n\n\n9. _Cowley._--Another project of the same kind, less ambitious but\napparently more directed to practice, was published a little later\n(1657) by another eminent man of letters in this country. I speak of\nCowley's \"Proposition for the Advancement of Experimental Philosophy.\"\nHe suggests that a College should be established at a short distance\nfrom London, endowed with a revenue of four thousand pounds, and\nconsisting of twenty professors with other members. The objects of the\nlabours of these professors he describes to be, first, to examine all\nknowledge of nature delivered to us from former ages and to pronounce\nit sound or worthless; second, to recover the lost inventions of the\nancients; third, to improve all arts that we now have; lastly, to\ndiscover others that we yet have not. In this proposal we cannot help\nmarking the visible declension from Bacon's more philosophical view.\nFor we have here only a very vague indication of improving old arts\nand discovering new, instead of the two clear Verulamian antitheses,\nExperiments and Axioms deduced from them, on the one hand, and on the\nother an ascent to general Laws, and a derivation, from these, of Arts\nfor daily use. Moreover the prominent place which Cowley has assigned\nto the verifying the knowledge of former ages and recovering \"the lost\ninventions and drowned lands of the ancients,\" implies a disposition to\nthink too highly of traditionary knowledge; a weakness which Bacon's\nscheme shows _him_ to have fully overcome. And thus it has been up to\nthe present day, that with all Bacon's mistakes, in the philosophy of\nscientific method few have come up to him, and perhaps none have gone\nbeyond him.\n\nCowley exerted himself to do justice to the new philosophy in verse as\nwell as prose, and his Poem to the Royal Society expresses in a very\nnoble manner those views of the history and prospects of philosophy\nwhich prevailed among the men by whom the Royal Society was founded.\nThe fertility and ingenuity of comparison which characterize Cowley's\npoetry are well known; and these qualities are in this instance largely\nemployed for the embellishment of his subject. Many of the comparisons\nwhich he exhibits are apt and striking. Philosophy is a ward whose\nestate (human knowledge) is, in his nonage, kept from him by his\nguardians and tutors; (a case which the ancient rhetoricians were fond\nof taking as a subject of declamation;) and these wrong-doers retain\nhim in unjust tutelage and constraint for their own purposes; until\n\n      Bacon at last, a mighty man, arose,\n      (Whom a wise King, and Nature, chose\n      Lord Chancellor of both their laws,)\n    And boldly undertook the injured pupil's cause.\n\nAgain, Bacon is one who breaks a scarecrow Priapus which stands in the\ngarden of knowledge. Again, Bacon is one who, instead of a picture of\npainted grapes, gives us real grapes from which we press \"the thirsty\nsoul's refreshing wine.\" Again, Bacon is like Moses, who led the\nHebrews forth from the barren wilderness, and ascended Pisgah;--\n\n        Did on the very border stand\n        Of the blest promised land,\n    And from the mountain's top of his exalted wit\n    Saw it himself and showed us it.\n\nThe poet however adds, that Bacon discovered, but did not conquer\nthis new world; and that the men whom he addresses must subdue these\nregions. These \"champions\" are then ingeniously compared to Gideon's\nband:\n\n    Their old and empty pitchers first they brake,\n    And with their hands then lifted up the light.\n\nThere were still at this time some who sneered at or condemned the new\nphilosophy; but the tide of popular opinion was soon strongly in its\nfavour. I have elsewhere[214] noticed a pasquinade of the poet Boileau\nin 1682, directed against the Aristotelians. At this time, and indeed\nfor long afterwards, the philosophers of France were Cartesians. The\nEnglish men of science, although partially and for a time they accepted\nsome of Descartes' opinions, for the most part carried on the reform\nindependently, and in pursuance of their own views. And they very soon\nfound a much greater leader than Descartes to place at their head, and\nto take as their authority, so far as they acknowledged authority,\nin their speculations. I speak of Newton, whose influence upon the\nphilosophy of science I must now consider.\n\n\n10. _Barrow._--I will, however, first mention one other writer who may,\nin more than one way, be regarded as the predecessor of Newton. I speak\nof Isaac Barrow, whom Newton succeeded as Professor of Mathematics in\nthe University of Cambridge, and who in his mathematical speculations\napproached very near to Newton's method of Fluxions. He afterwards\n(in 1673) became Master of Trinity College, which office he held\ntill his death in 1677. But the passages which I shall quote belong\nto an earlier period, (when Barrow was about 22 years old,) and may\nbe regarded as expressions of the opinions which were then current\namong active-minded and studious young men. They manifest a complete\nfamiliarity with the writings both of Bacon and of Descartes, and a\nvery just appreciation of both. The discourse of which I speak is\nan academical exercise delivered in 1652, on the thesis _Cartesiana\nhypothesis haud satisfacit pr\u00e6cipuis natur\u00e6 ph\u00e6nomenis_. By the\n\"Cartesian hypothesis,\" he does not mean the hypothesis that the\nplanets are moved by vortices of etherial matter: I believe that this\nCartesian tenet never had any disciples in England; it certainly\nnever took any hold of Cambridge. By the Cartesian hypothesis, Barrow\nmeans the doctrine that all the phenomena of nature can be accounted\nfor by matter and motion; and allowing that the motions of the planets\nare to be so accounted for, (which is Newtonian as well as Cartesian\ndoctrine,) he denies that the Cartesian hypothesis accounts for \"the\ngenerations, properties, and specific operations of animals, plants,\nminerals, stones, and other natural bodies,\" in doing which he shows\na sound philosophical judgment. But among the parts of this discourse\nmost bearing on our present purpose are those where he mentions Bacon.\n\"Against Cartesius,\" he says, \"I pit the chymists and others, but\nespecially as the foremost champion of this battle, our Verulam, a man\nof great name and of great judgment, who condemned this philosophy\nbefore it was born.\" \"He,\" adds Barrow, \"several times in his\n_Organon_, warned men against all hypotheses of this kind, and noticed\nbeforehand that there was not much to be expected from those principles\nwhich are brought into being by violent efforts of argumentation from\nthe brains of particular men: for that, as upon the phenomena of the\nstars, various constructions of the heavens may be devised, so also\nupon the phenomena of the Universe, still more dogmas may be founded\nand constructed; and yet all such are mere inventions: and as many\nphilosophies of this kind as are or shall be extant, so many fictitious\nand theatrical worlds are made.\" The reference is doubtless to Aphorism\nLXII. of the First Book of the _Novum Organon_, in which Bacon is\nspeaking of his \"Idols of the Theatre.\" After making the remark which\nBarrow has adopted, Bacon adds, \"Such theatrical fables have also\nthis in common with those of dramatic poets, that the dramatic story\nis more regular and elegant than true histories are, and is made so\nas to be agreeable.\" Barrow, having this in his mind, goes on to say:\n\"And though Cartesius has dressed up the stage of his theatre more\nprettily than any other person, and made his drama more like history,\nstill he is not exempt from the like censure.\" And he then refers to\nCartesius's own declaration, that he did not learn his system from\nthings themselves, but tried to impose his own laws upon things; thus\ninverting the order of true philosophy.\n\nOther parts of Bacon's work to which Barrow refers are those where\nhe speaks of the Form, or Formal Cause of a body, and says that in\ncomparison with that, the Efficient Cause and the Material Cause are\nthings unimportant and superficial, and contribute little to true and\nactive science[215]. And again, his classification of the various\nkinds of motions[216],--the motus libertatis, motus nexus, motus\ncontinuitatis, motus ad lucrum, fug\u00e6, unionis, congregationis; and the\nexplanation of electrical attraction (about which Gilbert and others\nhad written) as _motus ad lucrum_.\n\nThese passages show that Barrow had read the _Novum Organon_ in a\ncareful and intelligent manner, and presumed his Cambridge hearers to\nbe acquainted with the work. Nor is his judgment of Descartes less wise\nand philosophical. He rejects, as we have seen, his system as a true\nscheme of the universe, and condemns altogether his _\u00e0 priori_ mode\nof philosophizing; but this does not prevent his accepting Descartes'\nreal discoveries, and admiring the boldness and vigour of his attempts\nto reform philosophy. There is, in Barrow's works, academic verse, as\nwell as prose, on the subject of the Cartesian hypothesis. In this,\nDescartes himself is highly praised, though his doctrines are very\npartially accepted. The writer says: \"Pardon us, great Cartesius, if\nthe Muse resists you. Pardon! We follow you, Inquiring Spirit that you\nare, while we reject your system. As you have taught us free thought,\nand broken down the rule of tyranny, we undauntedly speculate, even in\nopposition to you.\"\n\nDescartes is even yet spoken of, especially by French writers, as the\nperson who first asserted and established the freedom of inquiry which\nis the boast of modern philosophy; but this is said with reference to\nmetaphysics, not to physics. In physical philosophy, though he caught\nhold of some of the discoveries which were then coming into view, the\nmethod in which he reasoned or professed to reason was altogether\nvicious; and was, as I have already said, an attempt to undo what\nthe reformers, both theoretical and practical, had been doing:--to\ndiscredit the philosophy of experience, and to restore the reign of _\u00e0\npriori_ systems.\n\nIt was, however, now, too late to make any such attempt; and nothing\ncame of it to interrupt the progress of a better philosophy of\ndiscovery.\n\n\nFOOTNOTES:\n\n[Footnote 200: _Anatomical Exercitations concerning the Generation of\nLiving Creatures_, 1653. Preface.]\n\n[Footnote 201: He used similar expressions in conversation. George Ent,\nwho edited his _Generation of Animals_, visited him, \"at that time\nresiding not far from the city; and found him very intent upon the\nperscrutation of nature's works, and with a countenance as cheerful,\nas mind unperturbed; Democritus-like, chiefly searching into the cause\nof natural things.\" In the course of conversation the writer said, \"It\nhath always been your choice about the secrets of Nature, to consult\nNature herself.\" \"'Tis true,\" replied he; \"and I have constantly been\nof opinion that from thence we might acquire not only the knowledge\nof those less considerable secrets of Nature, but even a certain\nadmiration of that Supreme Essence, the Creator. And though I have\never been ready to acknowledge, that many things have been discovered\nby learned men of former times; yet do I still believe that the number\nof those which remain yet concealed in the darkness of impervestigable\nNature is much greater. Nay, I cannot forbear to wonder, and sometimes\nsmile at those, who persuade themselves, that all things were so\nconsummately and absolutely delivered by Aristotle, Galen, or some\nother great name, as that nothing was left to the superaddition of any\nthat succeeded.\"]\n\n[Footnote 202: Lib. i. c. 2, 3.]\n\n[Footnote 203: _Anal. Post._ ii.]\n\n[Footnote 204: Pars iii. p. 45.]\n\n[Footnote 205: See _Hist. Ind. Sc._ b. vi. c. ii.]\n\n[Footnote 206: Cap. i. ii.]\n\n[Footnote 207: _Hist. Ind. Sc._ b. ix. c. ii.]\n\n[Footnote 208: _Meteorum_, c. viii. p. 187.]\n\n[Footnote 209: Mackintosh, _Dissertation on Ethical Science_.]\n\n[Footnote 210: _Hist. Ind. Sc._ b. vii. c. i.]\n\n[Footnote 211: Castelli, Torricelli, Viviani, Baliani, Gassendi,\nMersenne, Borelli, Cavalleri.]\n\n[Footnote 212: _De Plenitudine Mundi, in qua defenditur Cartesiana\nPhilosophia contra sententias Francisci Baconi, Th. Hobbii et Sethi\nWardi._]\n\n[Footnote 213: Bacon's _Works_, vol. ii. 111.]\n\n[Footnote 214: _Hist. Ind. Sc._ b. vii. c. i.]\n\n[Footnote 215: _Nov. Org._ lib. ii. Aph. 2.]\n\n[Footnote 216: _Ib._ lib. ii. Aph. 45.]\n\n\n\n\nCHAPTER XVIII.\n\nNEWTON.\n\n\n1. Bold and extensive as had been the anticipations of those whose\nminds were excited by the promise of the new philosophy, the\ndiscoveries of Newton respecting the mechanics of the universe,\nbrought into view truths more general and profound than those earlier\nphilosophers had hoped or imagined. With these vast accessions to human\nknowledge, men's thoughts were again set in action; and philosophers\nmade earnest and various attempts to draw, from these extraordinary\nadvances in science, the true moral with regard to the conduct and\nlimits of the human understanding. They not only endeavoured to verify\nand illustrate, by these new portions of science, what had recently\nbeen taught concerning the methods of obtaining sound knowledge;\nbut they were also led to speculate concerning many new and more\ninteresting questions relating to this subject. They saw, for the first\ntime, or at least far more clearly than before, the distinction between\nthe inquiry into the _laws_, and into the _causes_ of phenomena. They\nwere tempted to ask, how far the discovery of causes could be carried;\nand whether it would soon reach, or clearly point to, the ultimate\ncause. They were driven to consider whether the properties which they\ndiscovered were essential properties of all matter, necessarily and\nprimarily involved in its essence, though revealed to us at a late\nperiod by their derivative effects. These questions even now agitate\nthe thoughts of speculative men. Some of them have already, in this\nwork, been discussed, or arranged in the places which our view of the\nphilosophy of these subjects assigns to them. But we must here notice\nthem as they occurred to Newton himself and his immediate followers.\n\n\n2. The general Baconian notion of the method of philosophizing,--that\nit consists in ascending from phenomena, through various stages of\ngeneralization, to truths of the highest order,--received, in Newton's\ndiscovery of the universal mutual gravitation of every particle of\nmatter, that pointed actual exemplification, for want of which it had\nhitherto been almost overlooked, or at least very vaguely understood.\nThat great truth, and the steps by which it was established, afford,\neven now, by far the best example of the successive ascent, from one\nscientific truth to another,--of the repeated transition from less to\nmore general propositions,--which we can yet produce; as may be seen\nin the Table which exhibits the relation of these steps in Book II. of\nthe _Novum Organon Renovatum_. Newton himself did not fail to recognize\nthis feature in the truths which he exhibited. Thus he says[217], \"By\nthe way of Analysis we proceed from compounds to ingredients, as from\nmotions to the forces producing them; and in general, from effects\nto their causes, and from particular causes to more general ones,\ntill the argument ends in the most general.\" And in like manner in\nanother Query[218]: \"The main business of natural philosophy is to\nargue from phenomena without feigning hypotheses, and to deduce causes\nfrom effects, till we come to the First Cause, which is certainly not\nmechanical.\"\n\n\n3. Newton appears to have had a horror of the term _hypothesis_,\nwhich probably arose from his acquaintance with the rash and illicit\ngeneral assumptions of Descartes. Thus in the passage just quoted,\nafter declaring that gravity must have some other cause than matter,\nhe says, \"Later philosophers banish the consideration of such a cause\nout of Natural Philosophy, feigning hypotheses for explaining all\nthings mechanically, and referring other causes to metaphysics.\" In the\ncelebrated Scholium at the end of the _Principia_ he says, \"Whatever\nis not deduced from the phenomena, is to be termed _hypothesis_;\nand hypotheses, whether metaphysical or physical, or occult causes,\nor mechanical, have no place in experimental philosophy. In this\nphilosophy, propositions are deduced from phenomena, and rendered\ngeneral by induction.\" And in another place, he arrests the course\nof his own suggestions, saying, \"Verum hypotheses non fingo.\" I have\nalready attempted to show that this is, in reality, a superstitious and\nself-destructive spirit of speculation. Some hypotheses are necessary,\nin order to connect the facts which are observed; some new principle\nof unity must be applied to the phenomena, before induction can be\nattempted. What is requisite is, that the hypothesis should be close\nto the facts, and not connected with them by the intermediation of\nother arbitrary and untried facts; and that the philosopher should be\nready to resign it as soon as the facts refuse to confirm it. We have\nseen in the _History_[219], that it was by such a use of hypotheses,\nthat both Newton himself, and Kepler, on whose discoveries those of\nNewton were based, made their discoveries. The suppositions of a force\ntending to the sun and varying inversely as the square of the distance;\nof a mutual force between all the bodies of the solar system; of the\nforce of each body arising from the attraction of all its parts; not to\nmention others, also propounded by Newton,--were all hypotheses before\nthey were verified as theories. It is related that when Newton was\nasked how it was that he saw into the laws of nature so much further\nthan other men, he replied, that if it were so, it resulted from his\nkeeping his thoughts steadily occupied upon the subject which was to be\nthus penetrated. But what is this occupation of the thoughts, if it be\nnot the process of keeping the phenomena clearly in view, and trying,\none after another, all the plausible hypotheses which seem likely to\nconnect them, till at last the true law is discovered? Hypotheses so\nused are a necessary element of discovery.\n\n\n4. With regard to the details of the process of discovery, Newton\nhas given us some of his views, which are well worthy of notice, on\naccount of their coming from him; and which are real additions to the\nphilosophy of this subject. He speaks repeatedly of the _analysis_\nand _synthesis_ of observed facts; and thus marks certain steps in\nscientific research, very important, and not, I think, clearly pointed\nout by his predecessors. Thus he says[220], \"As in Mathematics, so\nin Natural Philosophy, the investigation of difficult things by the\nmethod of analysis ought ever to precede the method of composition.\nThis analysis consists in making experiments and observations, and\nin drawing general conclusions from them by induction, and admitting\nof no objections against the conclusions, but such as are taken from\nexperiments or other certain truths. And although the arguing from\nexperiments and observations by induction be no demonstration of\ngeneral conclusions; yet it is the best way of arguing which the nature\nof things admits of, and may be looked upon as so much the stronger,\nby how much the induction is more general.\" And he then observes, as\nwe have quoted above, that by this way of analysis we proceed from\ncompounds to ingredients, from motions to forces, from effects to\ncauses, and from less to more general causes. The _analysis_ here\nspoken of includes the steps which in _our_ Novum Organon we call the\n_decomposition_ of facts, the exact _observation_ and _measurement_\nof the phenomena, and the _colligation_ of facts; the necessary\nintermediate step, the _selection_ and _explication_ of the appropriate\nconception, being passed over by Newton, in the fear of seeming to\nencourage the fabrication of hypotheses. The _synthesis_ of which\nNewton here speaks consists of those steps of _deductive reasoning_,\nproceeding from the conception once assumed, which are requisite for\nthe comparison of its consequences with the observed facts. This, his\nstatement of the process of research, is, as far as it goes, perfectly\nexact.\n\n\n5. In speaking of Newton's precepts on the subject, we are naturally\nled to the celebrated \"Rules of Philosophizing,\" inserted in the second\nedition of the _Principia_. These rules have generally been quoted and\ncommented on with an almost unquestioning reverence. Such Rules, coming\nfrom such an authority, cannot fail to be highly interesting to us; but\nat the same time, we cannot here evade the necessity of scrutinizing\ntheir truth and value, according to the principles which our survey of\nthis subject has brought into view. The Rules stand at the beginning of\nthat part of the _Principia_ (the Third Book) in which he infers the\nmutual gravitation of the sun, moon, planets, and all parts of each.\nThey are as follows:\n\n\"Rule I. We are not to admit other causes of natural things than such\nas both are true, and suffice for explaining their phenomena.\n\n\"Rule II. Natural effects of the same kind are to be referred to the\nsame causes, as far as can be done.\n\n\"Rule III. The qualities of bodies which cannot be increased or\ndiminished in intensity, and which belong to all bodies in which we\ncan institute experiments, are to be held for qualities of all bodies\nwhatever.\n\n\"Rule IV. In experimental philosophy, propositions collected from\nphenomena by induction, are to be held as true either accurately\nor approximately, notwithstanding contrary hypotheses; till other\nphenomena occur by which they may be rendered either more accurate or\nliable to exception.\"\n\nIn considering these Rules, we cannot help remarking, in the first\nplace, that they are constructed with an intentional adaptation to\nthe case with which Newton has to deal,--the induction of Universal\nGravitation; and are intended to protect the reasonings before which\nthey stand. Thus the first Rule is designed to strengthen the inference\nof gravitation from the celestial phenomena, by describing it as a\n_vera causa_, a true cause; the second Rule countenances the doctrine\nthat the planetary motions are governed by mechanical forces, as\nterrestrial motions are; the third rule appears intended to justify the\nassertion of gravitation, as a _universal_ quality of bodies; and the\nfourth contains, along with a general declaration of the authority of\ninduction, the author's usual protest against hypotheses, levelled at\nthe Cartesian hypotheses especially.\n\n\n6. _Of the First Rule._--We, however, must consider these Rules in\ntheir general application, in which point of view they have often been\nreferred to, and have had very great authority allowed them. One of the\npoints which has been most discussed, is that maxim which requires that\nthe causes of phenomena which we assign should be true causes, _ver\u00e6\ncaus\u00e6_. Of course this does not mean that they should be _the_ true\nor right cause; for although it is the philosopher's aim to discover\nsuch causes, he would be little aided in his search of truth, by being\ntold that it is truth which he is to seek. The rule has generally\nbeen understood to prescribe that in attempting to account for any\nclass of phenomena, we must assume such causes only, as _from other\nconsiderations_, we know to exist. Thus gravity, which was employed in\nexplaining the motions of the moon and planets, was already known to\nexist and operate at the earth's surface.\n\nNow the Rule thus interpreted is, I conceive, an injurious limitation\nof the field of induction. For it forbids us to look for a cause,\nexcept among the causes with which we are already familiar. But if we\nfollow this rule, how shall we ever become acquainted with any new\ncause? Or how do we know that the phenomena which we contemplate do\nreally arise from some cause which we already truly know? If they do\nnot, must we still insist upon making them depend upon some of our\nknown causes; or must we abandon the study of them altogether? Must we,\nfor example, resolve to refer the action of radiant heat to the air,\nrather than to any peculiar fluid or ether, because the former is known\nto exist, the latter is merely assumed for the purpose of explanation?\nBut why should we do this? Why should we not endeavour to learn the\ncause from the effects, even if it be not already known to us? We\ncan infer causes, which are new when we first become acquainted with\nthem. Chemical Forces, Optical Forces, Vital Forces, are known to us\nonly by chemical and optical and vital phenomena; must we, therefore,\nreject their existence or abandon their study? They do not conform to\nthe double condition, that they shall be sufficient and _also_ real:\nthey are true, only so far as they explain the facts, but are they,\ntherefore, unintelligible or useless? Are they not highly important\nand instructive subjects of speculation? And if the gravitation which\nrules the motions of the planets had not existed at the earth's\nsurface;--if it had been there masked and concealed by the superior\neffect of magnetism, or some other extraneous force,--might not Newton\nstill have inferred, from Kepler's laws, the tendency of the planets to\nthe sun; and from their perturbations, their tendency to each other?\nHis discoveries would still have been immense, if the cause which he\nassigned had not been a _vera causa_ in the sense now contemplated.\n\n\n7. But what do we mean by calling gravity a \"true cause\"? How do\nwe learn its reality? Of course, by its effects, with which we are\nfamiliar;--by the weight and fall of bodies about us. These strike even\nthe most careless observer. No one can fail to see that all bodies\nwhich we come in contact with are heavy;--that gravity acts in our\nneighbourhood here upon earth. Hence, it may be said, this cause is at\nany rate a true cause, whether it explains the celestial phenomena or\nnot.\n\nBut if this be what is meant by a _vera causa_, it appears strange to\nrequire that in all cases we should find such a one to account for\nall classes of phenomena. Is it reasonable or prudent to demand that\nwe shall reduce every set of phenomena, however minute, or abstruse,\nor complicated, to causes so obviously existing as to strike the most\nincurious, and to be familiar among men? How can we expect to find\n_such ver\u00e6 caus\u00e6_ for the delicate and recondite phenomena which\nan exact and skilful observer detects in chemical, or optical, or\nelectrical experiments? The facts themselves are too fine for vulgar\napprehension; their relations, their symmetries, their measures require\na previous discipline to understand them. How then can their causes be\nfound among those agencies with which the common unscientific herd of\nmankind are familiar? What likelihood is there that causes held for\nreal by such persons, shall explain facts which such persons cannot see\nor cannot understand?\n\nAgain: if we give authority to such a rule, and require that the causes\nby which science explains the facts which she notes and measures and\nanalyses, shall be causes which men, without any special study, have\nalready come to believe in, from the effects which they casually\nsee around them, what is this, except to make our first rude and\nunscientific persuasions the criterion and test of our most laborious\nand thoughtful inferences? What is it, but to give to ignorance and\nthoughtlessness the right of pronouncing upon the convictions of\nintense study and long-disciplined thought? \"Electrical atmospheres\"\nsurrounding electrized bodies, were at one time held to be a \"true\ncause\" of the effects which such bodies produce. These atmospheres, it\nwas said, are obvious to the senses; we feel them like a spider's web\non the hands and face. \u00c6pinus had to answer such persons, by proving\nthat there are no atmospheres, no effluvia, but only repulsion. He\nthus, for a _true cause_ in the vulgar sense of the term, substituted\nan _hypothesis_; yet who doubts that what he did was an advance in the\nscience of electricity?\n\n\n8. Perhaps some persons may be disposed to say, that Newton's Rule\ndoes not enjoin us to take those causes only which we clearly know, or\nsuppose we know, to be really existing and operating, but only causes\n_of such kinds_ as we have already satisfied ourselves do exist in\nnature. It may be urged that we are entitled to infer that the planets\nare governed in their motions by an attractive force, because we find,\nin the bodies immediately subject to observation and experiment,\nthat such motions are produced by attractive forces, for example, by\nthat of the earth. It may be said that we might on similar grounds\ninfer forces which unite particles of chemical compounds, or deflect\nparticles of light, because we see adhesion and deflection produced by\nforces.\n\nBut it is easy to show that the Rule, thus laxly understood, loses all\nsignificance. It prohibits no hypothesis; for all hypotheses suppose\ncauses _such as_, in some case or other, we have seen in action. No\none would think of explaining phenomena by referring them to forces\nand agencies altogether different from any which are known; for on\nthis supposition, how could he pretend to reason about the effects\nof the assumed causes, or undertake to prove that they would explain\nthe facts? Some close similarity with some known kind of cause is\nrequisite, in order that the hypothesis may have the appearance of\nan explanation. No forces, or virtues, or sympathies, or fluids, or\nethers, would be excluded by _this_ interpretation of _ver\u00e6 caus\u00e6_.\nLeast of all, would such an interpretation reject the Cartesian\nhypothesis of vortices; which undoubtedly, as I conceive, Newton\nintended to condemn by his Rule. For that _such_ a case as a whirling\nfluid, carrying bodies round a centre in orbits, does occur, is too\nobvious to require proof. Every eddying stream, or blast that twirls\nthe dust in the road, exhibits examples of such action, and would\njustify the assumption of the vortices which carry the planets in their\ncourses; as indeed, without doubt, such facts suggested the Cartesian\nexplanation of the solar system. The vortices, in this mode of\nconsidering the subject, are at the least as _real_ a cause of motion\nas gravity itself.\n\n\n9. Thus the Rule which enjoins \"true causes,\" is nugatory, if we take\n_ver\u00e6 caus\u00e6_ in the extended sense of any causes of a real _kind_,\nand unphilosophical, if we understand the term of _those very_ causes\nwhich we familiarly suppose to exist. But it may be said that we are to\ndesignate as \"true causes,\" not those which are collected in a loose,\nconfused and precarious manner, by undisciplined minds, from obvious\nphenomena, but those which are justly and rigorously inferred. Such\na cause, it may be added, gravity is; for the facts of the downward\npressures and downward motions of bodies at the earth's surface lead\nus, by the plainest and strictest induction, to the assertion of such\na force. Now to this interpretation of the Rule there is no objection;\nbut then, it must be observed, that on this view, terrestrial gravity\nis inferred by the same process as celestial gravitation; and the\ncause is no more entitled to be called \"true,\" because it is obtained\nfrom the former, than because it is obtained from the latter class of\nfacts. We thus obtain an intelligible and tenable explanation of a\n_vera causa_; but then, by this explanation, its _verity_ ceases to be\ndistinguishable from its other condition, that it \"suffices for the\nexplanation of the phenomena.\" The assumption of universal gravitation\naccounts for the fall of a stone; it also accounts for the revolutions\nof the Moon or of Saturn; but since both these explanations are of the\nsame kind, we cannot with justice make the one a criterion or condition\nof the admissibility of the other.\n\n\n10. But still, the Rule, so understood, is so far from being unmeaning\nor frivolous, that it expresses one of the most important tests which\ncan be given of a sound physical theory. It is true, the explanation of\none set of facts may be of the same nature as the explanation of the\nother class: but then, that the cause explains _both_ classes, gives it\na very different claim upon our attention and assent from that which\nit would have if it explained one class only. The very circumstance\nthat the two explanations coincide, is a most weighty presumption in\ntheir favour. It is the testimony of two witnesses in behalf of the\nhypothesis; and in proportion as these two witnesses are separate\nand independent, the conviction produced by their agreement is more\nand more complete. When the explanation of two kinds of phenomena,\ndistinct, and not apparently connected, leads us to the same cause,\nsuch a coincidence does give a reality to the cause, which it has\nnot while it merely accounts for those appearances which suggested\nthe supposition. This coincidence of propositions inferred from\nseparate classes of facts, is exactly what we noticed in the _Novum\nOrganon Renovatum_ (b. ii. c. 5, sect. 3), as one of the most decisive\ncharacteristics of a true theory, under the name of _Consilience of\nInductions_.\n\nThat Newton's First Rule of Philosophizing, so understood, authorizes\nthe inferences which he himself made, is really the ground on which\nthey are so firmly believed by philosophers. Thus when the doctrine\nof a gravity varying inversely as the square of the distance from\nthe body, accounted at the same time for the relations of times and\ndistances in the planetary orbits and for the amount of the moon's\ndeflection from the tangent of her orbit, such a doctrine became most\nconvincing: or again, when the doctrine of the universal gravitation of\nall parts of matter, which explained so admirably the inequalities of\nthe moon's motions, also gave a satisfactory account of a phenomenon\nutterly different, the precession of the equinoxes. And of the same\nkind is the evidence in favour of the undulatory theory of light, when\nthe assumption of the length of an undulation, to which we are led by\nthe colours of thin plates, is found to be identical with that length\nwhich explains the phenomena of diffraction; or when the hypothesis of\ntransverse vibrations, suggested by the facts of polarization, explains\nalso the laws of double refraction. When such a convergence of two\ntrains of induction points to the same spot, we can no longer suspect\nthat we are wrong. Such an accumulation of proof really persuades us\nthat we have to do with a _vera causa_. And if this kind of proof be\nmultiplied;--if we again find other facts of a sort uncontemplated in\nframing our hypothesis, but yet clearly accounted for when we have\nadopted the supposition;--we are still further confirmed in our belief;\nand by such accumulation of proof we may be so far satisfied, as to\nbelieve without conceiving it possible to doubt. In this case, when the\nvalidity of the opinion adopted by us has been repeatedly confirmed by\nits sufficiency in unforeseen cases, so that all doubt is removed and\nforgotten, the theoretical cause takes its place among the realities\nof the world, and becomes _a true cause_.\n\n\n11. Newton's Rule then, to avoid mistakes, might be thus expressed:\nThat \"we may, provisorily, assume such hypothetical cause as will\naccount for any given class of natural phenomena; but that when two\ndifferent classes of facts lead us to the same hypothesis, we may hold\nit to be a _true cause_.\" And this Rule will rarely or never mislead\nus. There are no instances, in which a doctrine recommended in this\nmanner has afterwards been discovered to be false. There have been\nhypotheses which have explained many phenomena, and kept their ground\nlong, and have afterwards been rejected. But these have been hypotheses\nwhich explained only one class of phenomena; and their fall took place\nwhen another kind of facts was examined and brought into conflict with\nthe former. Thus the system of eccentrics and epicycles accounted\nfor all the observed _motions_ of the planets, and was the means of\nexpressing and transmitting all astronomical knowledge for two thousand\nyears. But then, how was it overthrown? By considering the _distances_\nas well as motions of the heavenly bodies. Here was a second class of\nfacts; and when the system was adjusted so as to agree with the one\nclass, it was at variance with the other. These cycles and epicycles\ncould not be true, because they could not be made a just representation\nof the facts. But if the measures of distance as well as of position\nhad conspired in pointing out the cycles and epicycles, as the paths of\nthe planets, the paths so determined could not have been otherwise than\ntheir real paths; and the epicyclical theory would have been, at least\ngeometrically, true.\n\n\n12. _Of the Second Rule._--Newton's Second Rule directs that \"natural\nevents of the _same kind_ are to be referred to the _same causes_, so\nfar as can be done.\" Such a precept at first appears to help us but\nlittle; for all systems, however little solid, profess to conform to\nsuch a rule. When any theorist undertakes to explain a class of facts,\nhe assigns causes which, according to him, will by their natural\naction, as seen in other cases, produce the effects in question. The\nevents which he accounts for by his hypothetical cause, are, he holds,\nof the same kind as those which such a cause is known to produce.\nKepler, in ascribing the planetary motions to magnetism, Descartes, in\nexplaining them by means of vortices, held that they were referring\ncelestial motions to the causes which give rise to terrestrial motions\nof the same kind. The question is, _Are_ the effects of the same kind?\nThis once settled, there will be no question about the propriety of\nassigning them to the same cause. But the difficulty is, to determine\n_when_ events are of the same kind. Are the motions of the planets of\nthe same kind with the motion of a body moving freely in a curvilinear\npath, or do they not rather resemble the motion of a floating body\nswept round by a whirling current? The Newtonian and the Cartesian\nanswered this question differently. How then can we apply this Rule\nwith any advantage?\n\n\n13. To this we reply, that there is no way of escaping this uncertainty\nand ambiguity, but by obtaining a clear possession of the ideas which\nour hypothesis involves, and by reasoning rigorously from them. Newton\nasserts that the planets move in free paths, acted on by certain\nforces. The most exact calculation gives the closest agreement of\nthe results of this hypothesis with the facts. Descartes asserts\nthat the planets are carried round by a fluid. The more rigorously\nthe conceptions of force and the laws of motion are applied to this\nhypothesis, the more signal is its failure in reconciling the facts\nto one another. Without such calculation, we can come to no decision\nbetween the two hypotheses. If the Newtonian hold that the motions\nof the planets are _evidently_ of the _same kind_ as those of a body\ndescribing a curve in free space, and therefore, like that, to be\nexplained by a force acting upon the body; the Cartesian denies that\nthe planets do move in free space. They are, he maintains, immersed\nin a plenum. It is only when it appears that comets pass through this\nplenum in all directions with no impediment, and that no possible form\nand motion of its whirlpools can explain the forces and motions which\nare observed in the solar system, that he is compelled to allow the\nNewtonian's classification of events of the _same kind_.\n\nThus it does not appear that this Rule of Newton can be interpreted in\nany distinct and positive manner, otherwise than as enjoining that, in\nthe task of induction, we employ clear ideas, rigorous reasoning, and\nclose and fair comparison of the results of the hypothesis with the\nfacts. These are, no doubt, important and fundamental conditions of a\njust induction; but in this injunction we find no peculiar or technical\ncriterion by which we may satisfy ourselves that we are right, or\ndetect our errors. Still, of such general prudential rules, none can be\nmore wise than one which thus, in the task of connecting facts by means\nof ideas, recommends that the ideas be clear, the facts, correct, and\nthe chain of reasoning which connects them, without a flaw.\n\n\n14. _Of the Third Rule._--The Third Rule, that \"qualities which are\nobserved without exception be held to be universal,\" as I have already\nsaid, seems to be intended to authorize the assertion of gravitation\nas a universal attribute of matter. We formerly stated, in treating of\nMechanical Ideas[221], that this application of such a Rule appears\nto be a mode of reasoning far from conclusive. The assertion of the\nuniversality of any property of bodies must be grounded upon the\nreason of the case, and not upon any arbitrary maxim. Is it intended\nby this Rule to prohibit any further examination how far gravity is\nan original property of matter, and how far it may be resolved into\nthe result of other agencies? We know perfectly well that this was not\nNewton's intention; since the cause of gravity was a point which he\nproposed to himself as a subject of inquiry. It would certainly be very\nunphilosophical to pretend, by this Rule of Philosophizing, to prejudge\nthe question of such hypotheses as that of Mosotti, That gravity is\nthe excess of the electrical attraction over electrical repulsion, and\nyet to adopt this hypothesis, would be to suppose electrical forces\nmore truly universal than gravity; for according to the hypothesis,\ngravity, being the inequality of the attraction and repulsion, is only\nan accidental and partial relation of these forces. Nor would it be\nallowable to urge this Rule as a reason of assuming that double stars\nare attracted to each other by a force varying according to the inverse\nsquare of the distance; without examining, as Herschel and others have\ndone, the orbits which they really describe. But if the Rule is not\navailable in such cases, what is its real value and authority? and in\nwhat cases are they exemplified?\n\n\n15. In a former work[222], it was shown that the fundamental laws of\nmotion, and the properties of matter which these involve, are, after a\nfull consideration of the subject, unavoidably assumed as universally\ntrue. It was further shown, that although our knowledge of these laws\nand properties be gathered from experience, we are strongly impelled,\n(some philosophers think, authorized,) to look upon these as not only\nuniversally, but necessarily true. It was also stated, that the law\nof gravitation, though its universality may be deemed probable, does\nnot apparently involve the same necessity as the fundamental laws of\nmotion. But it was pointed out that these are some of the most abstruse\nand difficult questions of the whole of philosophy; involving the\nprofound, perhaps insoluble, problem of the identity or diversity of\nIdeas and Things. It cannot, therefore, be deemed philosophical to\ncut these Gordian knots by peremptory maxims, which encourage us to\ndecide without rendering a reason. Moreover, it appears clear that\nthe reason which is rendered for this Rule by the Newtonians is quite\nuntenable; namely, that we know extension, hardness, and inertia, to\nbe universal qualities of bodies by experience alone, and that we have\nthe same evidence of experience for the universality of gravitation.\nWe have already observed that we cannot, with any propriety, say that\nwe _find_ by experience all bodies are extended. This could not be a\njust assertion, unless we conceive the possibility of our finding the\ncontrary. But who can conceive our finding by experience some bodies\nwhich are not extended? It appears, then, that the reason given for\nthe Third Rule of Newton involves a mistake respecting the nature and\nauthority of experience. And the Rule itself cannot be applied without\nattempting to decide, by the casual limits of observation, questions\nwhich necessarily depend upon the relations of ideas.\n\n\n16. _Of the Fourth Rule._--Newton's Fourth Rule is, that \"Propositions\ncollected from phenomena by induction, shall be held to be true,\nnotwithstanding contrary hypotheses; but shall be liable to be rendered\nmore accurate, or to have their exceptions pointed out, by additional\nstudy of phenomena.\" This Rule contains little more than a general\nassertion of the authority of induction, accompanied by Newton's usual\nprotest against hypotheses.\n\nThe really valuable part of the Fourth Rule is that which implies\nthat a constant verification, and, if necessary, rectification,\nof truths discovered by induction, should go on in the scientific\nworld. Even when the law is, or appears to be, most certainly exact\nand universal, it should be constantly exhibited to us afresh in the\nform of experience and observation. This is necessary, in order to\ndiscover exceptions and modifications if such exist: and if the law be\nrigorously true, the contemplation of it, as exemplified in the world\nof phenomena, will best give us that clear apprehension of its bearings\nwhich may lead us to see the ground of its truth.\n\nThe concluding clause of this Fourth Rule appears, at first, to\nimply that all inductive propositions are to be considered as merely\nprovisional and limited, and never secure from exception. But to judge\nthus would be to underrate the stability and generality of scientific\ntruths; for what man of science can suppose that we shall hereafter\ndiscover exceptions to the universal gravitation of all parts of the\nsolar system? And it is plain that the author did not intend the\nrestriction to be applied so rigorously; for in the Third Rule, as\nwe have just seen, he authorizes us to infer universal properties of\nmatter from observation, and carries the liberty of inductive inference\nto its full extent. The Third Rule appears to encourage us to assert a\nlaw to be universal, even in cases in which it has not been tried; the\nFourth Rule seems to warn us that the law may be inaccurate, even in\ncases in which it has been tried. Nor is either of these suggestions\nerroneous; but both the universality and the rigorous accuracy of our\nlaws are proved by reference to Ideas rather than to Experience; a\ntruth, which, perhaps, the philosophers of Newton's time were somewhat\ndisposed to overlook.\n\n\n17. The disposition to ascribe all our knowledge to Experience, appears\nin Newton and the Newtonians by other indications; for instance, it\nis seen in their extreme dislike to the ancient expressions by which\nthe principles and causes of phenomena were described, as the _occult\ncauses_ of the Schoolmen, and the _forms_ of the Aristotelians, which\nhad been adopted by Bacon. Newton says[223], that the particles of\nmatter not only possess inertia, but also active principles, as\ngravity, fermentation, cohesion; he adds, \"These principles I consider\nnot as Occult Qualities, supposed to result from the Specific Forms of\nthings, but as General Laws of Nature, by which the things themselves\nare formed: their truth appearing to us by phenomena, though their\ncauses be not yet discovered. For these are manifest qualities, and\ntheir causes only are occult. And the Aristotelians gave the name of\n_occult qualities_, not to manifest qualities, but to such qualities\nonly as they supposed to lie hid in bodies, and to the unknown causes\nof manifest effects: such as would be the causes of gravity, and of\nmagnetick and electrick attractions, and of fermentations, if we\nshould suppose that these forces or actions arose from qualities\nunknown to us, and incapable of being discovered and made manifest.\nSuch occult qualities put a stop to the improvement of Natural\nPhilosophy, and therefore of late years have been rejected. To tell\nus that every species of things is endowed with an occult specific\nquality by which it acts and produces manifest effects, is to tell us\nnothing: but to derive two or three general principles of motion from\nphenomena, and afterwards to tell us how the properties and actions\nof all corporeal things follow from these manifest principles, would\nbe a great step in philosophy, though the causes of those principles\nwere not yet discovered: and therefore I scruple not to propose the\nprinciples of motion above maintained, they being of very general\nextent, and leave their causes to be found out.\"\n\n\n18. All that is here said is highly philosophical and valuable; but we\nmay observe that the investigation of _specific forms_ in the sense in\nwhich some writers had used the phrase, was by no means a frivolous\nor unmeaning object of inquiry. Bacon and others had used _form_ as\nequivalent to _law_[224]. If we could ascertain that arrangement of\nthe particles of a crystal from which its external crystalline form\nand other properties arise, this arrangement would be the _internal\nform_ of the crystal. If the undulatory theory be true, the _form_ of\nlight is transverse vibrations: if the emission theory be maintained,\nthe _form_ of light is particles moving in straight lines, and\ndeflected by various forces. Both the terms, _form_ and _law_, imply\nan ideal connexion of sensible phenomena; form supposes matter which\nis moulded to the form; law supposes objects which are governed by\nthe law. The former term refers more precisely to existences, the\nlatter to occurrences. The latter term is now the more familiar, and\nis, perhaps, the better metaphor: but the former also contains the\nessential antithesis which belongs to the subject, and might be used in\nexpressing the same conclusions.\n\nBut occult causes, employed in the way in which Newton describes,\nhad certainly been very prejudicial to the progress of knowledge, by\nstopping inquiry with a mere word. The absurdity of such pretended\nexplanations had not escaped ridicule. The pretended physician in the\ncomedy gives an example of an occult cause or virtue.\n\n        Mihi demandatur\n        A doctissimo Doctore\n      _Quare_ Opium facit dormire:\n        Et ego respondeo,\n        _Quia_ est in eo\n        _Virtus dormitiva_,\n    Cujus natura est sensus assoupire.\n\n\n19. But the most valuable part of the view presented to us in\nthe quotation just given from Newton is the distinct separation,\nalready noticed as peculiarly brought into prominence by him, of the\ndetermination of the _laws_ of phenomena, and the investigation of\ntheir _causes_. The maxim, that the former inquiry must precede the\nlatter, and that if the general laws of facts be discovered, the result\nis highly valuable, although the causes remain unknown, is extremely\nimportant; and had not, I think, ever been so strongly and clearly\nstated, till Newton both repeatedly promulgated the precept, and added\nto it the weight of the most striking examples.\n\nWe have seen that Newton, along with views the most just and important\nconcerning the nature and methods of science, had something of the\ntendency, prevalent in his time, to suspect or reject, at least\nspeculatively, all elements of knowledge except observation. This\ntendency was, however, in him so corrected and restrained by his own\nwonderful sagacity and mathematical habits, that it scarcely led to\nany opinion which we might not safely adopt. But we must now consider\nthe cases in which this tendency operated in a more unbalanced manner,\nand led to the assertion of doctrines which, if consistently followed,\nwould destroy the very foundations of all general and certain knowledge.\n\n\nFOOTNOTES:\n\n[Footnote 217: _Optics_, qu. 31, near the end.]\n\n[Footnote 218: Qu. 28.]\n\n[Footnote 219: _Hist. Ind. Sc._ b. v. and b. vii.]\n\n[Footnote 220: _Optics_, qu. 31.]\n\n[Footnote 221: _History of Ideas_, b. iii. c. x.]\n\n[Footnote 222: _Ibid._ b. iii. c. ix. x. xi.]\n\n[Footnote 223: _Opticks_, qu. 31.]\n\n[Footnote 224: _Nov. Org._ l. ii. Aph. 2. \"Licet enim in natura nihil\nexistet pr\u00e6ter corpora individua, edentia actus puros individuos\nex lege; in doctrinis tamen illa ipsa lex, ejusque inquisitio, et\ninventio, et explicatio, pro fundamento est tam ad sciendum quam ad\noperandum. Eam autem _legem_, ejusque _paragraphos, formarum_ nomine\nintelligimus; pr\u00e6sertim cum hoc vocabulum invaluerit, et familiariter\noccurrat.\"\n\nAph. 17. \"Eadem res est _forma_ calidi vel _forma_ luminis, et _lex_\ncalidi aut _lex_ luminis.\"]\n\n\n\n\nCHAPTER XIX.\n\nLOCKE AND HIS FRENCH FOLLOWERS.\n\n\n1. In the constant opposition and struggle of the schools of\nphilosophy, which consider our Senses and our Ideas respectively,\nas the principal sources of our knowledge, we have seen that at the\nperiod of which we now treat, the tendency was to exalt the external\nand disparage the internal element. The disposition to ascribe our\nknowledge to observation alone, had already, in Bacon's time, led him\nto dwell to a disproportionate degree upon that half of his subject;\nand had tinged Newton's expressions, though it had not biassed his\npractice. But this partiality soon assumed a more prominent shape,\nbecoming extreme in Locke, and extravagant in those who professed to\nfollow him.\n\nIndeed Locke appears to owe his popularity and influence as a popular\nwriter mainly to his being one of the first to express, in a plain and\nunhesitating manner, opinions which had for some time been ripening\nin the minds of a large portion of the cultivated public. Hobbes had\nalready promulgated the main doctrines which Locke afterwards urged, on\nthe subject of the origin and nature of our knowledge: but in him these\ndoctrines were combined with offensive opinions on points of morals,\ngovernment, and religion, so that their access to general favour was\nimpeded: and it was to Locke that they were indebted for the extensive\ninfluence which they soon after obtained. Locke owed this authority\nmainly to the intellectual circumstances of the time. Although a writer\nof great merit, he by no means possesses such metaphysical acuteness or\nsuch philosophical largeness of view, or such a charm of writing, as\nmust necessarily give him the high place he has held in the literature\nof Europe. But he came at a period when the reign of Ideas was\ntottering to its fall. All the most active and ambitious spirits had\ngone over to the new opinions, and were prepared to follow the fortunes\nof the Philosophy of Experiment, then in the most prosperous and\nbrilliant condition, and full of still brighter promise. There were,\nindeed, a few learned and thoughtful men who still remained faithful\nto the empire of Ideas; partly, it may be, from a too fond attachment\nto ancient systems; but partly, also, because they knew that there\nwere subjects of vast importance, in which experience did not form the\nwhole foundation of our knowledge. They knew, too, that many of the\nplausible tenets of the new philosophy were revivals of fallacies which\nhad been discussed and refuted in ancient times. But the advocates of\nmere experience came on with a vast store of weighty truth among their\nartillery, and with the energy which the advance usually bestows. The\nideal system of philosophy could, for the present, make no effectual\nresistance; Locke, by putting himself at the head of the assault,\nbecame the hero of his day: and his name has been used as the watchword\nof those who adhere to the philosophy of the senses up to our own times.\n\n\n2. Locke himself did not assert the exclusive authority of the senses\nin the extreme unmitigated manner in which some who call themselves\nhis disciples have done. But this is the common lot of the leaders\nof revolutions, for they are usually bound by some ties of affection\nand habit to the previous state of things, and would not destroy all\ntraces of that condition: while their followers attend, not to their\ninconsistent wishes, but to the meaning of the revolution itself;\nand carry out, to their genuine and complete results, the principles\nwhich won the victory, and which have been brought out more sharp from\nthe conflict. Thus Locke himself does not assert that all our ideas\nare derived from Sensation, but from Sensation _and Reflection_. But\nit was easily seen that, in this assertion, two very heterogeneous\nelements were conjoined: that while to pronounce Sensation the origin\nof ideas, is a clear decided tenet, the acceptance or rejection of\nwhich determines the general character of our philosophy; to make the\nsame declaration concerning Reflection, is in the highest degree vague\nand ambiguous; since reflection may either be resolved into a mere\nmodification of sensation, as was done by one school, or may mean all\nthat the opposite school opposes to sensation, under the name of Ideas.\nHence the clear and strong impression which fastened upon men's minds,\nand which does in fact represent all the systematic and consistent part\nof Locke's philosophy, was, that in it all our ideas are represented as\nderived from Sensation.\n\n\n3. We need not spend much time in pointing out the inconsistencies into\nwhich Locke fell; as all must fall into inconsistencies who recognize\nno source of knowledge except the senses. Thus he maintains that our\nIdea of Space is derived from the senses of sight and touch; our Idea\nof Solidity from the touch alone. Our Notion of Substance is an unknown\nsupport of unknown qualities, and is illustrated by the Indian fable\nof the tortoise which supports the elephant, which supports the world.\nOur Notion of Power or Cause is in like manner got from the senses.\nAnd yet, though these ideas are thus mere fragments of our experience,\nLocke does not hesitate to ascribe to them necessity and universality\nwhen they occur in propositions. Thus he maintains the necessary truth\nof geometrical properties: he asserts that the resistance arising from\nsolidity is absolutely insurmountable[225]; he conceives that nothing\nshort of Omnipotence can annihilate a particle of matter[226]; and he\nhas no misgivings in arguing upon the axiom that Every thing must have\na cause. He does not perceive that, upon his own account of the origin\nof our knowledge, we can have no right to make any of these assertions.\nIf our knowledge of the truths which concern the external world were\nwholly derived from experience, all that we could venture to say would\nbe,--that geometrical properties of figures are true _as far as we have\ntried them_;--that we have seen _no example_ of a solid body being\nreduced to occupy less space by pressure, or of a material substance\nannihilated by natural means;--and that _wherever we have examined_,\nwe have found that every change has had a cause. Experience can never\nentitle us to declare that what she has not seen is impossible; still\nless, that things which she can not see are certain. Locke himself\nintended to throw no doubt upon the certainty of either human or\ndivine knowledge; but his principles, when men discarded the temper in\nwhich he applied them, and the checks to their misapplication which\nhe conceived that he had provided, easily led to a very comprehensive\nskepticism. His doctrines tended to dislodge from their true bases the\nmost indisputable parts of knowledge; as, for example, pure and mixed\nmathematics. It may well be supposed, therefore, that they shook the\nfoundations of many other parts of knowledge in the minds of common\nthinkers.\n\nIt was not long before these consequences of the overthrow of\nideas showed themselves in the speculative world. I have already\nin a previous work[227] mentioned Hume's skeptical inferences from\nLocke's maxim, that we have no ideas except those which we acquire\nby experience; and the doctrines set up in opposition to this by\nthe metaphysicians of Germany. I might trace the progress of the\nsensational opinions in Britain till the reaction took place here\nalso: but they were so much more clearly and decidedly followed out in\nFrance, that I shall pursue their history in that country.\n\n\n4. _The French Followers of Locke, Condillac, &c._--Most of the\nFrench writers who adopted Locke's leading doctrines, rejected the\n\"Reflection,\" which formed an anomalous part of his philosophy, and\ndeclared that Sensation alone was the source of ideas. Among these\nwriters, Condillac was the most distinguished. He expressed the leading\ntenet of their school in a clear and pointed manner by saying that \"All\nideas are transformed sensations.\" We have already considered this\nphrase[228], and need not here dwell upon it.\n\nOpinions such as these tend to annihilate, as we have seen, one of the\ntwo co-ordinate elements of our knowledge. Yet they were far from being\nso prejudicial to the progress of science, or even of the philosophy\nof science, as might have been anticipated. One reason of this was,\nthat they were practically corrected, especially among the cultivators\nof Natural Philosophy, by the study of mathematics; for that study did\nreally supply all that was requisite on the ideal side of science, so\nfar as the ideas of space, time, and number, were concerned, and partly\nalso with regard to the idea of cause and some others. And the methods\nof discovery, though the philosophy of them made no material advance,\nwere practically employed with so much activity, and in so many various\nsubjects, that a certain kind of prudence and skill in this employment\nwas very widely diffused.\n\n\n5. _Importance of Language._--In one respect this school of\nmetaphysicians rendered a very valuable service to the philosophy of\nscience. They brought into prominent notice the great importance of\n_words_ and _terms_ in the formation and progress of knowledge, and\npointed out that the office of language is not only to convey and\npreserve our thoughts, but to perform the analysis in which reasoning\nconsists. They were led to this train of speculation, in a great\nmeasure, by taking pure mathematical science as their standard example\nof substantial knowledge. Condillac, rejecting, as we have said, almost\nall those ideas on which universal and demonstrable truths must be\nbased, was still not at all disposed to question the reality of human\nknowledge; but was, on the contrary, a zealous admirer of the evidence\nand connexion which appear in those sciences which have the ideas of\nspace and number for their foundation, especially the latter. He looked\nfor the grounds of the certainty and reality of the knowledge which\nthese sciences contain; and found them, as he conceived, in the nature\nof the _language_ which they employ. The _Signs_ which are used in\narithmetic and algebra enable us to keep steadily in view the identity\nof the same quantity under all the forms which, by composition and\ndecomposition, it may be made to assume; and these Signs also not only\nexpress the operations which are performed, but suggest the extension\nof the operations according to analogy. Algebra, according to him,\nis only a very perfect language; and language answers its purpose of\nleading us to truth, by possessing the characteristics of algebra.\nWords are the symbols of certain groups of impressions or facts; they\nare so selected and applied as to exhibit the analogies which prevail\namong these facts; and these analogies are the truths of which our\nknowledge consists. \"Every language is an analytical method; every\nanalytical method is a language[229];\" these were the truths \"alike new\nand simple,\" as he held, which he conceived that he had demonstrated.\n\"The art of speaking, the art of writing, the art of reasoning, the\nart of thinking, are only, at bottom, one and the same art[230].\" Each\nof these operations consists in a succession of analytical operations;\nand words are the marks by which we are able to fix our minds upon the\nsteps of this analysis.\n\n\n6. The analysis of our impressions and notions does in reality lead\nto truth, not only in virtue of the identity of the whole with its\nparts, as Condillac held, but also in virtue of certain Ideas which\ngovern the synthesis of our sensations, and which contain the elements\nof universal truths, as we have all along endeavoured to show. But\nalthough Condillac overlooked or rejected this doctrine, the importance\nof words, as marking the successive steps of this synthesis and\nanalysis, is not less than he represented it to be. Every truth, once\nestablished by induction from facts, when it is become familiar under\na brief and precise form of expression, becomes itself a fact; and is\ncapable of being employed, along with other facts of a like kind, as\nthe materials of fresh inductions. In this successive process, the\nterm, like the cord of a fagot, both binds together the facts which it\nincludes, and makes it possible to manage the assemblage as a single\nthing. On occasion of most discoveries in science, the selection of a\ntechnical term is an essential part of the proceeding. In the _History\nof Science_, we have had numerous opportunities of remarking this; and\nthe List of technical terms given as an Index to that work, refers us,\nby almost every word, to one such occasion. And these terms, which\nthus have had so large a share in the formation of science, and which\nconstitute its language, do also offer the means of analyzing its\ntruths, each into its constituent truths; and these into facts more\nspecial, till the original foundations of our most general propositions\nare clearly exhibited. The relations of general and particular truths\nare most evidently represented by the Inductive Tables given in\nBook II. of the _Novum Organon Renovatum_. But each step in each of\nthese Tables has its proper form of expression, familiar among the\ncultivators of science; and the analysis which our Tables display, is\ncommonly performed in men's minds, when it becomes necessary, by fixing\nthe attention successively upon a series of words, not upon the lines\nof a Table. Language offers to the mind such a scale or ladder as the\nTable offers to the eye; and since such Tables present to us, as we\nhave said, the Logic of Induction, that is, the formal conditions of\nthe soundness of our reasoning from facts, we may with propriety say\nthat a just analysis of the meaning of words is an essential portion of\nInductive Logic.\n\nIn saying this, we must not forget that a decomposition of general\ntruths into ideas, as well as into facts, belongs to our philosophy;\nbut the point we have here to remark, is the essential importance of\nwords to the latter of these processes. And this point had not ever\nhad its due weight assigned to it till the time of Condillac and other\nfollowers of Locke, who pursued their speculations in the spirit I have\njust described. The doctrine of the importance of terms is the most\nconsiderable addition to the philosophy of science which has been made\nsince the time of Bacon[231].\n\n\n7. _The French Encyclopedists._--The French _Encyclop\u00e9die_, published\nin 1751, of which Diderot and Dalembert were the editors, may be\nconsidered as representing the leading characters of European\nphilosophy during the greater part of the eighteenth century. The\nwriters in this work belong for the most part to the school of Locke\nand Condillac; and we may make a few remarks upon them, in order to\nbring into view one or two points in addition to what we have already\nsaid of that school. The _Discours Pr\u00e9liminaire_, written by Dalembert,\nis celebrated as containing a view of the origin of our knowledge, and\nthe connexion and classification of the sciences.\n\nA tendency of the speculations of the Encyclopedists, as of the School\nof Locke in general, is to reject all ideal principles of connexion\namong facts, as something which experience, the only source of true\nknowledge, does not give. Hence all certain knowledge consists only\nin the recognition of the same thing under different aspects, or\ndifferent forms of expression. Axioms are not the result of an original\nrelation of ideas, but of the use, or it may be the abuse[232], of\nwords. In like manner, the propositions of Geometry are a series of\nmodifications,--of distortions, so to speak,--of one original truth;\nmuch as if the proposition were stated in the successive forms of\nexpression presented by a language which was constantly growing more\nand more artificial. Several of the sciences which rest upon physical\nprinciples, that is, (says the writer,) truths of experience or simple\nhypotheses, have only an experimental or hypothetical certainty.\nImpenetrability added to the idea of extent is a mystery in addition:\nthe nature of motion is a riddle for philosophers: the metaphysical\nprinciple of the laws of percussion is equally concealed from them. The\nmore profoundly they study the idea of matter and of the properties\nwhich represent it, the more obscure this idea becomes; the more\ncompletely does it escape them.\n\n\n8. This is a very common style of reflection, even down to our own\ntimes. I have endeavoured to show that concerning the Fundamental Ideas\nof space, of force and resistance, of substance, external quality, and\nthe like, we know enough to make these Ideas the grounds of certain\nand universal truths;--enough to supply us with axioms from which we\ncan demonstratively reason. If men wish for any other knowledge of\nthe nature of matter than that which ideas, and facts conformable to\nideas, give them, undoubtedly their desire will be frustrated, and\nthey will be left in a mysterious vacancy; for it does not appear\nhow such knowledge as they ask for could be knowledge at all. But in\nreality, this complaint of our ignorance of the real nature of things\nproceeds from the rejection of ideas, and the assumption of the senses\nalone as the ground of knowledge. \"Observation and calculation are\nthe only sources of truth:\" this is the motto of the school of which\nwe now speak. And its import amounts to this:--that they reject all\nideas except the idea of number, and recognize the modifications which\nparts undergo by addition and subtraction as the only modes in which\ntrue propositions are generated. The laws of nature are assemblages of\nfacts: the truths of science are assertions of the identity of things\nwhich are the same. \"By the avowal of almost all philosophers,\" says\na writer of this school[233], \"the most sublime truths, when once\nsimplified and reduced to their lowest terms, are converted into facts,\nand thenceforth present to the mind only this proposition; the white is\nwhite, the black is black.\"\n\nThese statements are true in what they positively assert, but they\ninvolve error in the denial which by implication they convey. It\nis true that observation and demonstration are the only sources of\nscientific truth; but then, demonstration may be founded on other\ngrounds besides the elementary properties of number. It is true that\nthe theory of gravitation is but the assertion of a general fact; but\nthis is so, not because a sound theory does not involve ideas, but\nbecause our apprehension of a fact does.\n\n\n9. Another characteristic indication of the temper of the\nEncyclopedists and of the age to which they belong, is the importance\nby them assigned to those practical _Arts_ which minister to man's\ncomfort and convenience. Not only, in the body of the Encyclopedia, are\nthe Mechanical Arts placed side by side with the Sciences, and treated\nat great length; but in the Preliminary Discourse, the preference\nassigned to the liberal over the mechanical Arts is treated as a\nprejudice[234], and the value of science is spoken of as measured\nby its utility. \"The discovery of the Mariner's Compass is not less\nadvantageous to the human race than the explanation of its properties\nwould be to physics.--Why should we not esteem those to whom we owe\nthe fusee and the escapement of watches as much as the inventors of\nAlgebra?\" And in the classification of sciences which accompanies the\nDiscourse, the labours of artisans of all kinds have a place.\n\nThis classification of the various branches of science contained\nin the Dissertation is often spoken of. It has for its basis the\nclassification proposed by Bacon, in which the parts of human knowledge\nare arranged according to the faculties of the mind in which they\noriginate; and these faculties are taken, both by Bacon and by\nDalembert, as Memory, Reason, and Imagination. The insufficiency of\nBacon's arrangement as a scientific classification is so glaring, that\nthe adoption of it, with only superficial modifications, at the period\nof the Encyclopedia, is a remarkable proof of the want of original\nthought and real philosophy at the time of which we speak.\n\n\n10. We need not trace further the opinion which derives all our\nknowledge from the senses in its application to the philosophy of\nScience. Its declared aim is to reduce all knowledge to the knowledge\nof Facts; and it rejects all inquiries which involve the Idea of Cause,\nand similar Ideas, describing them as \"metaphysical,\" or in some other\ndamnatory way. It professes, indeed, to discard all Ideas; but, as we\nhave long ago seen, some Ideas or other are inevitably included even\nin the simplest Facts. Accordingly the speculations of this school\nare compelled to retain the relations of Position, Succession, Number\nand Resemblance, which are rigorously ideal relations. The philosophy\nof Sensation, in order to be consistent, ought to reject these Ideas\nalong with the rest, and to deny altogether the possibility of general\nknowledge.\n\nWhen the opinions of the Sensational School had gone to an extreme\nlength, a Reaction naturally began to take place in men's minds. Such\nhave been the alternations of opinion, from the earliest ages of human\nspeculation. Man may perhaps have existed in an original condition in\nwhich he was only aware of the impressions of Sense; but his first\nattempts to analyse his perceptions brought under his notice Ideas as\na separate element, essential to the existence of knowledge. Ideas\nwere thenceforth almost the sole subject of the study of philosophers;\nof Plato and his disciples, professedly; of Aristotle, and still more\nof the followers and commentators of Aristotle, practically. And this\ncontinued till the time of Galileo, when the authority of the Senses\nagain began to be asserted; for it was shown by the great discoveries\nwhich were then made, that the Senses had at least some share in\nthe promotion of knowledge. As discoveries more numerous and more\nstriking were supplied by Observation, the world gradually passed\nover to the opinion that the share which had been ascribed to Ideas in\nthe formation of real knowledge was altogether a delusion, and that\nSensation alone was true. But when this was asserted as a general\ndoctrine, both its manifest falsity and its alarming consequences\nroused men's minds, and made them recoil from the extreme point to\nwhich they were approaching. Philosophy again oscillated back towards\nIdeas; and over a great part of Europe, in the clearest and most\ncomprehensive minds, this regression from the dogmas of the Sensational\nSchool is at present the prevailing movement. We shall conclude our\nreview by noticing a few indications of this state of things.\n\n\nFOOTNOTES:\n\n[Footnote 225: _Essay_, b. xi. c. iv. sect. 3.]\n\n[Footnote 226: _Ibid._ c. xiii. sect. 22.]\n\n[Footnote 227: _History of Ideas_, b. iii. c. iii. Modern Opinions\nrespecting the Idea of Cause.]\n\n[Footnote 228: _Ibid._ b. i. c. iv.]\n\n[Footnote 229: _Langue des Calculs_, p. 1.]\n\n[Footnote 230: _Grammaire_, p. xxxvi.]\n\n[Footnote 231: Since the selection and construction of terms is thus\na matter of so much consequence in the formation of science, it is\nproper that systematic rules, founded upon sound principles, should be\nlaid down for the performance of this operation. Some such rules are\naccordingly suggested in b. iv. of the _Nov. Org. Ren._]\n\n[Footnote 232: _Disc. Pr\u00e9lim._ p. viii.]\n\n[Footnote 233: Helvetius _Sur l'Homme_, c. xxiii.]\n\n[Footnote 234: P. xiii.]\n\n\n\n\nCHAPTER XX.\n\nTHE REACTION AGAINST THE SENSATIONAL SCHOOL.\n\n\n1. When Locke's _Essay_ appeared, it was easily seen that its tendency\nwas to urge, in a much more rigorous sense than had previously been\nusual, the ancient maxim of Aristotle, adopted by the schoolmen of\nthe middle ages, that \"nothing exists in the intellect but what has\nentered by the senses.\" Leibnitz expressed in a pointed manner the\nlimitation with which this doctrine had always been understood. \"Nihil\nest in intellectu quod non prius fuerit in sensu;--_nempe_,\" he added,\n\"_nisi intellectus ipse_.\" To this it has been objected[235], that we\ncannot say that the intellect is _in_ the intellect. But this remark\nis obviously frivolous; for the faculties of the understanding (which\nare what the argument against the Sensational School requires us to\nreserve) may be said to be _in_ the understanding, with as much justice\nas we may assert there are _in_ it the impressions derived from sense.\nAnd when we take account of these faculties, and of the Ideas to which,\nby their operation, we necessarily subordinate our apprehension of\nphenomena, we are led to a refutation of the philosophy which makes\nphenomena, unconnected by Ideas, the source of all knowledge. The\nsucceeding opponents of the Lockian school insisted upon and developed\nin various ways this remark of Leibnitz, or some equivalent view.\n\n\n2. It was by inquiries into the foundations of Morals that English\nphilosophers were led to question the truth of Locke's theory. Dr.\nPrice, in his _Review of the Principal Questions in Morals_, first\npublished in 1757, maintained that we cannot with propriety assert\nall our ideas to be derived from sensation and reflection. He pointed\nout, very steadily, the other source. \"The power, I assert, that\n_understands_, or the faculty within us that discerns _truth_, and that\ncompares all the objects of thought and _judges_ of them, is a spring\nof new ideas[236].\" And he exhibits the antithesis in various forms.\n\"Were not _sense_ and _knowledge_ entirely different, we should rest\nsatisfied with sensible impressions, such as light, colours and sounds,\nand inquire no further about them, at least when the impressions are\nstrong and vigorous: whereas, on the contrary, we necessarily desire\nsome further acquaintance with them, and can never be satisfied\ntill we have subjected them to the survey of reason. Sense presents\n_particular_ forms to the mind, but cannot rise to any _general_ ideas.\nIt is the intellect that examines and compares the presented forms,\nthat rises above individuals to universal and abstract ideas; and\nthus looks downward upon objects, takes in at one view an infinity of\nparticulars, and is capable of discovering general truths. Sense sees\nonly the outside of things, reason acquaints itself with their natures.\nSensation is only a mode of feeling in the mind; but knowledge implies\nan active and vital energy in the mind[237].\"\n\n\n3. The necessity of refuting Hume's inferences from the mere sensation\nsystem led other writers to limit, in various ways, their assent to\nLocke. Especially was this the case with a number of intelligent\nmetaphysicians in Scotland, as Reid, Beattie, Dugald Stewart, and\nThomas Brown. Thus Reid asserts[238], \"that the account which Mr.\nLocke himself gives of the Idea of Power cannot be reconciled to\nhis favourite doctrine, that all our simple ideas have their origin\nfrom sensation or reflection.\" Reid remarks, that our memory and our\nreasoning power come in for a share in the origin of this idea: and\nin speaking of reasoning, he obviously assumes the axiom that every\nevent must have a cause. By succeeding writers of this school, the\nassumption of the fundamental principles, to which our nature in such\ncases irresistibly directs us, is more clearly pointed out. Thus\nStewart defends the form of expression used by Price[239]: \"A variety\nof intuitive judgments might be mentioned, involving simple ideas,\nwhich it is impossible to trace to any origin but to the power which\nenables us to form these judgments. Thus it is surely an intuitive\ntruth that the sensations of which I am conscious, and all those I\nremember, belong to one and the same being, which I call _myself_. Here\nis an intuitive judgment involving the simple idea of _Identity_. In\nlike manner, the changes which I perceive in the universe impress me\nwith a conviction that some cause must have operated to produce them.\nHere is an intuitive judgment involving the simple Idea of _Causation_.\nWhen we consider the adjacent angles made by a straight line standing\nupon another, and perceive that their sum is equal to two right angles,\nthe judgment we form involves a simple idea of _Equality_. To say,\ntherefore, that the Reason or the Understanding is a source of new\nideas, is not so exceptionable a mode of speaking as has been sometimes\nsupposed. According to Locke, _Sense_ furnishes our ideas, and Reason\nperceives their agreements and disagreements. But the truth is, that\nthese agreements and disagreements are in many instances, simple\nideas, of which no analysis can be given; and of which the origin must\ntherefore be referred to Reason, according to Locke's own doctrine.\"\nThis view, according to which the Reason or Understanding is the source\nof certain simple ideas, such as Identity, Causation, Equality, which\nideas are necessarily involved in the intuitive judgments which we\nform, when we recognize fundamental truths of science, approaches very\nnear in effect to the doctrine which in several works I have presented,\nof Fundamental Ideas belonging to each science, and manifesting\nthemselves in the axioms of the science. It may be observed, however,\nthat by attempting to enumerate these ideas and axioms, so as to\nlay the foundations of the whole body of physical science, and by\nendeavouring, as far as possible, to simplify and connect each group\nof such Ideas, I have at least given a more systematic form to this\ndoctrine. I have, moreover, traced it into many consequences to which\nit necessarily leads, but which do not appear to have been contemplated\nby the metaphysicians of the Scotch school. But I gladly acknowledge\nmy obligations to the writers of that school; and I trust that in the\nnear agreement of my views on such points with theirs, there is ground\nfor believing the system of philosophy which I have presented, to be\nthat to which the minds of thoughtful men, who have meditated on such\nsubjects, are generally tending.\n\n\n4. As a further instance that such a tendency is at work, I may make\na quotation from an eminent English philosophical writer of another\nschool. \"If you will be at the pains,\" says Archbishop Whately[240],\n\"carefully to analyze the simplest description you hear of any\ntransaction or state of things, you will find that the process which\nalmost invariably takes place is, in logical language, this: that each\nindividual _has in his mind_ certain major premises or principles\nrelative to the subject in question;--that observation of what actually\npresents itself to the senses, supplies minor premises; and that\nthe statement given (and which is reported as a thing experienced)\nconsists, in fact, of the _conclusions_ drawn from the combinations of\nthese premises.\" The major premises here spoken of are the Fundamental\nIdeas, and the Axioms and Propositions to which they lead; and whatever\nis regarded as a fact of observation is necessarily a conclusion in\nwhich these propositions are assumed; for these contain, as we have\nsaid, the conditions of our experience. Our experience conforms to\nthese axioms and their consequences, whether or not the connexion be\nstated in a logical manner, by means of premises and a conclusion.\n\n\n5. The same persuasion is also suggested by the course which the study\nof metaphysics has taken of late years in France. In that country,\nas we have seen, the Sensational System, which was considered as the\nnecessary consequence of the revolution begun by Locke, obtained a more\ncomplete ascendancy than it did in England; and in that country too,\nthe reaction, among metaphysical and moral writers, when its time came,\nwas more decided and rapid than it was among Locke's own countrymen.\nIt would appear that M. Laromigui\u00e8re was one of the first to give\nexpression to this feeling, of the necessity of a modification of the\nsensational philosophy. He began by professing himself the disciple\nof Condillac, even while he was almost unconsciously subverting the\nfundamental principles of that writer. And thus, as M. Cousin justly\nobserves[241], his opinions had the more powerful effect from being\npresented, not as thwarting and contradicting, but as sharing and\nfollowing out the spirit of his age. M. Laromigui\u00e8re's work, entitled\n_Essai sur les Facult\u00e9s de l'Ame_, consists of lectures given to the\nFaculty of Letters of the Academy of Paris, in the years 1811, 1812\nand 1813. In the views which these lectures present, there is much\nwhich the author has in common with Condillac. But he is led by his\ninvestigation to assert[242], that it is not true that sensation is\nthe sole fundamental element of our thoughts and our understanding.\n_Attention_ also is requisite: and here we have an element of quite\nanother kind. For sensation is passive; attention is active. Attention\ndoes not spring out of sensation; the passive principle is not the\nreason of the active principle. Activity and passivity are two facts\nentirely different. Nor can this activity be defined or derived; being,\nas the author says, a fundamental idea. The distinction is manifest\nby its own nature; and we may find evidence of it in the very forms of\nlanguage. To _look_ is more than to _see_; to _hearken_ is more than\nto _hear_. The French language marks this distinction with respect to\nother senses also. \"On _voit_, et l'on _regarde_; on _entend_, et l'on\n_\u00e9coute_; on _sent_, et l'on _flaire_; on _go\u00fbte_, et l'on _savoure_.\"\nAnd thus the mere sensation, or capacity of feeling, is only the\noccasion on which the attention is exercised; while the attention is\nthe foundation of all the operations of the understanding.\n\nThe reader of my works will have seen how much I have insisted upon the\nactivity of the mind, as the necessary basis of all knowledge. In all\nobservation and experience, the mind is active, and by its activity\napprehends all sensations in subordination to its own ideas; and thus\nit becomes capable of collecting knowledge from phenomena, since\nideas involve general relations and connexions, which sensations of\nthemselves cannot involve. And thus we see that, in this respect also,\nour philosophy stands at that point to which the speculations of the\nmost reflecting men have of late constantly been verging.\n\n\n6. M. Cousin himself, from whom we have quoted the above account\nof Laromigui\u00e8re, shares in this tendency, and has argued very\nenergetically and successfully against the doctrines of the Sensational\nSchool. He has made it his office once more to bring into notice among\nhis countrymen, the doctrine of ideas as the sources of knowledge; and\nhas revived the study of Plato, who may still be considered as one of\nthe great leaders of the ideal school. But the larger portion of M.\nCousin's works refers to questions out of the reach of our present\nreview, and it would be unsuitable to dwell longer upon them in this\nplace.\n\n\n7. We turn to speculations more closely connected with our present\nsubject. M. Amp\u00e8re, a French man of science, well entitled by his\nextensive knowledge, and large and profound views, to deal with the\nphilosophy of the sciences, published in 1834, his _Essai sur la\nPhilosophie des Sciences, ou Exposition analytique d'une Classification\nNaturelle de toutes les Connaissances Humaines_. In this remarkable\nwork we see strong evidence of the progress of the reaction against\nthe system which derives our knowledge from sensation only. The\nauthor starts from a maxim, that in classing the sciences, we must\nnot only regard the nature of the objects about which each science is\nconcerned, but also the point of view under which it considers them:\nthat is, the _ideas_ which each science involves. M. Amp\u00e8re also gives\nbriefly his views of the intellectual constitution of man; a subject\non which he had long and sedulously employed his thoughts; and these\nviews are far from belonging to the Sensational School. Human thought,\nhe says, is composed of phenomena and of conceptions. Phenomena are\nexternal, or _sensitive_; and internal, or _active_. Conceptions are\nof four kinds; _primitive_, as space and motion, duration and cause;\n_objective_, as our idea of matter and substance; _onomatic_, or those\nwhich we associate with the general terms which language presents to\nus; and _explicative_, by which we ascend to causes after a comparative\nstudy of phenomena. He teaches further, that in deriving ideas from\nsensation, the mind is not passive; but exerts an action which, when\nvoluntary, is called _attention_, but when it is, as it often is,\ninvoluntary, may be termed _reaction_.\n\nI shall not dwell upon the examination of these opinions[243]; but I\nmay remark, that both in the recognition of conceptions as an original\nand essential element of the mind, and in giving a prominent place to\nthe active function of the mind, in the origin of our knowledge, this\nview approaches to that which I have presented in preceding works;\nalthough undoubtedly with considerable differences.\n\n\n8. The classification of the sciences which M. Amp\u00e8re proposes, is\nfounded upon a consideration of the sciences themselves; and is,\nthe author conceives, in accordance with the conditions of natural\nclassifications, as exhibited in Botany and other sciences. It is of\na more symmetrical kind, and exhibits more steps of subordination,\nthan that to which I have been led; it includes also practical Art as\nwell as theoretical Science; and it is extended to moral and political\nas well as physical Sciences. It will not be necessary for me here\nto examine it in detail: but I may remark, that it is throughout a\n_dichotomous_ division, each higher member being subdivided into two\nlower ones, and so on. In this way, M. Amp\u00e8re obtains sciences of\nthe First Order, each of which is divided into two sciences of the\nSecond, and four of the Third Order. Thus Mechanics is divided into\n_Cinematics_, _Statics_, _Dynamics_, and _Molecular Mechanics_; Physics\nis divided into _Experimental Physics_, _Chemistry_, _Stereometry_,\nand _Atomology_; Geology is divided into _Physical Geography_,\n_Mineralogy_, _Geonomy_, and _Theory of the Earth_. Without here\ncriticizing these divisions or their principle, I may observe that\n_Cinematics_, the doctrine of motion without reference to the force\nwhich produces it, is a portion of knowledge which our investigation\nhas led us also to see the necessity of erecting into a separate\nscience; and which we have termed _Pure Mechanism_. Of the divisions of\nGeology, _Physical Geography_, especially as explained by M. Amp\u00e8re, is\ncertainly a part of the subject, both important and tolerably distinct\nfrom the rest. _Geonomy_ contains what we have termed in the History,\n_Descriptive Geology_;--the exhibition of the facts separate from the\ninquiry into their causes; while our _Physical Geology_ agrees with M.\nAmp\u00e8re's _Theory of the Earth_. _Mineralogy_ appears to be placed by\nhim in a different place from that which it occupies in our scheme:\nbut in fact, he uses the term for a different science; he applies\nit to the classification not of _simple minerals_, but of _rocks_,\nwhich is a science auxiliary to geology, and which has sometimes been\ncalled _Petralogy_. What we have termed _Mineralogy_, M. Amp\u00e8re unites\nwith _Chemistry_. \"It belongs,\" he says[244], \"to Chemistry, and not\nto Mineralogy, to inquire how many atoms of silicium and of oxygen\ncompose silica; to tell us that its primitive form is a rhombohedron of\ncertain angles, that it is called _quartz_, &c.; leaving, on one hand,\nto Molecular Geometry the task of explaining the different secondary\nforms which may result from the primitive form; and on the other hand,\nleaving to Mineralogy the office of describing the different varieties\nof quartz, and the rocks in which they occur, according as the quartz\nis crystallized, transparent, coloured, amorphous, solid, or in sand.\"\nBut we may remark, that by adopting this arrangement, we separate from\nMineralogy almost all the knowledge, and absolutely all the general\nknowledge, which books professing to treat of that science have\nusually contained. The consideration of Mineralogical Classifications,\nwhich, as may be seen in the _History of Science_, is so curious and\ninstructive, is forced into the domain of Chemistry, although many of\nthe persons who figure in it were not at all properly chemists. And we\nlose, in this way, the advantage of that peculiar office which, in our\narrangement, Mineralogy fills; of forming a rigorous transition from\nthe sciences of classification to those which consider the mathematical\nproperties of bodies; and connecting the external characters and the\ninternal constitution of bodies by means of a system of important\ngeneral truths. I conceive, therefore, that our disposition of this\nscience, and our mode of applying the name, are far more convenient\nthan those of M. Amp\u00e8re.\n\n\n9. We have seen the reaction against the pure sensational doctrines\noperating very powerfully in England and in France. But it was in\nGermany that these doctrines were most decidedly rejected; and systems\nin extreme opposition to these put forth with confidence, and received\nwith applause. Of the authors who gave this impulse to opinions in that\ncountry, Kant was the first, and by far the most important. I have in\nthe _History of Ideas_ (b. iii. c. 3), endeavoured to explain how he\nwas aroused, by the skepticism of Hume, to examine wherein the fallacy\nlay which appeared to invalidate all reasonings from effect to cause;\nand how this inquiry terminated in a conviction that the foundations\nof our reasonings on this and similar points were to be sought in\nthe mind, and not in the phenomena;--in the _subject_, and not in\nthe _object_. The revolution in the customary mode of contemplating\nhuman knowledge which Kant's opinions involved, was most complete.\nHe himself, with no small justice, compares[245] it with the change\nproduced by Copernicus's theory of the solar system. \"Hitherto,\" he\nsays, \"men have assumed that all our knowledge must be regulated by\nthe objects of it; yet all attempts to make out anything concerning\nobjects _\u00e0 priori_ by means of our conceptions,\" (as for instance their\ngeometrical properties) \"must, on this foundation, be unavailing. Let\nus then try whether we cannot make out something more in the problems\nof metaphysics, by assuming that objects must be regulated by our\nknowledge, since this agrees better with that supposition, which we are\nprompted to make, that we can know something of them _\u00e0 priori_. This\nthought is like that of Copernicus, who, when he found that nothing\nwas to be made of the phenomena of the heavens so long as everything\nwas supposed to turn about the spectator, tried whether the matter\nmight not be better explained if he made the spectator turn, and left\nthe stars at rest. We may make the same essay in metaphysics, as to\nwhat concerns our intuitive knowledge respecting objects. If our\napprehension of objects must be regulated by the properties of the\nobjects, I cannot comprehend how we can possibly know anything about\nthem _\u00e0 priori_. But if the object, as apprehended by us, be regulated\nby the constitution of our faculties of apprehension, I can readily\nconceive this possibility.\" From this he infers that our experience\nmust be regulated by our conceptions.\n\n\n10. This view of the nature of knowledge soon superseded entirely\nthe doctrines of the Sensational School among the metaphysicians of\nGermany. These philosophers did not gradually modify and reject the\ndogmas of Locke and Condillac, as was done in England and France[246];\nnor did they endeavour to ascertain the extent of the empire of Ideas\nby a careful survey of its several provinces, as we have been doing in\nthis series of works. The German metaphysicians saw at once that Ideas\nand Things, the Subjective and the Objective elements of our knowledge,\nwere, by Kant's system, brought into opposition and correlation, as\nequally real and equally indispensable. Seeing this, they rushed at\nonce to the highest and most difficult problem of philosophy,--to\ndetermine what this correlation is;--to discover how Ideas and Things\nare at the same time opposite and identical;--how the world, while it\nis distinct from and independent of us, is yet, as an object of our\nknowledge, governed by the conditions of our thoughts. The attempts\nto solve this problem, taken in the widest sense, including the forms\nwhich it assumes in Morals, Politics, the Arts, and Religion, as well\nas in the Material Sciences, have, since that time, occupied the most\nprofound speculators of Germany; and have given rise to a number of\nsystems, which, rapidly succeeding each other, have, each in its day,\nbeen looked upon as a complete solution of the problem. To trace the\ncharacters of these various systems, does not belong to the business of\nthe present chapter: my task is ended when I have shown, as I have now\ndone, how the progress of thought in the philosophical world, followed\nfrom the earliest up to the present time, has led to that recognition\nof the co-existence and joint necessity of the two opposite elements\nof our knowledge; and when I have pointed out processes adapted to\nthe extension of our knowledge, which a true view of its nature has\nsuggested or may suggest.\n\nThe latter portion of this task occupies the Third Book of the _Novum\nOrganon Renovatum_. With regard to the recent succession of German\nsystems of philosophy, I shall add something in a subsequent chapter:\nand I shall also venture to trace further than I have yet done, the\nbearing of the philosophy of science upon the theological view of the\nuniverse and the moral and religious condition of man.\n\n\nFOOTNOTES:\n\n[Footnote 235: See Mr. Sharpe's _Essays_.]\n\n[Footnote 236: Price's _Essays_, p. 16.]\n\n[Footnote 237: P. 18.]\n\n[Footnote 238: Reid, _Essays on the Powers of the Human Mind_, iii. 31.]\n\n[Footnote 239: Stewart, _Outlines of Moral Phil._ p. 138.]\n\n[Footnote 240: Whately, _Polit. Econ._ p. 76.]\n\n[Footnote 241: Cousin, _Fragmens Philosophiques_, i. 53.]\n\n[Footnote 242: _Ibid._ i. 67.]\n\n[Footnote 243: See also the vigorous critique of Locke's _Essay_, by\nLemaistre, _Soir\u00e9es de St. Petersbourg_.]\n\n[Footnote 244: Amp\u00e8re, _Essai_, p. 210.]\n\n[Footnote 245: _Kritik der Reinen Vernunft_, Pref. p. xv.]\n\n[Footnote 246: The sensational system never acquired in Germany the\nascendancy which it obtained in England and France; but I am compelled\nhere to pass over the history of philosophy in Germany, except so far\nas it affects ourselves.]\n\n\n\n\nCHAPTER XXI.\n\nFURTHER ADVANCE OF THE SENSATIONAL SCHOOL.\n\nM. AUGUSTE COMTE.\n\n\nI shall now take the liberty of noticing the views published by a\ncontemporary writer; not that it forms part of my design to offer\nany criticism upon the writings of all those who have treated of\nthose subjects on which we are now employed; but because we can\nmore distinctly in this manner point out the contrasts and ultimate\ntendencies of the several systems of opinion which have come under\nour survey: and since from among these systems we have endeavoured to\nextract and secure the portion of truth which remains in each, and\nto reject the rest, we are led to point out the errors on which our\nattention is thus fixed, in recent as well as older writers.\n\nM. Auguste Comte published in 1830 the first, and in 1835 the second\nvolume of his _Cours de Philosophie Positive_; of which the aim is not\nmuch different from that of the present work, since as he states (p.\nviii.) such a title as the _Philosophy of the Sciences_ would describe\na part of his object, and would be inappropriate only by excluding that\nportion (not yet published) which refers to speculations concerning\nsocial relations.\n\n\n1. _M. Comte on Three States of Science._--By employing the term\n_Philosophie Positive_, he wishes to distinguish the philosophy\ninvolved in the present state of our sciences from the previous forms\nof human knowledge. For according to him, each branch of knowledge\npasses, in the course of man's history, through three different states;\nit is first _theological_, then _metaphysical_, then _positive_. By\nthe latter term he implies a state which includes nothing but general\nrepresentations of facts;--phenomena _arranged according_ to relations\nof succession and resemblance. This \"positive philosophy\" rejects all\ninquiry after causes, which inquiry he holds to be void of sense[247]\nand inaccessible. All such conceptions belong to the \"metaphysical\"\nstate of science which deals with abstract forces, real entities,\nand the like. Still more completely does he reject, as altogether\nantiquated and absurd, the \"theological\" view of phenomena. Indeed he\nconceives[248] that any one's own consciousness of what passes within\nhimself is sufficient to convince him of the truth of the law of the\nthree phases through which knowledge must pass. \"Does not each of us,\"\nhe says, \"in contemplating his own history, recollect that he has been\nsuccessively a _theologian_ in his infancy, a _metaphysician_ in his\nyouth, and a _physicist_ in his ripe age? This may easily be verified\nfor all men who are up to the level of their time.\"\n\nIt is plain from such statements, and from the whole course of his\nwork, that M. Comte holds, in their most rigorous form, the doctrines\nto which the speculations of Locke and his successors led; and which\ntended, as we have seen, to the exclusion of all ideas except those\nof number and resemblance. As M. Comte refuses to admit into his\nphilosophy the fundamental idea of Cause, he of course excludes most of\nthe other ideas, which are, as we endeavoured to show, the foundations\nof science; such as the ideas of Media by which secondary qualities are\nmade known to us; the ideas of Chemical Attraction, of Polar Forces,\nand the like. He would reduce all science to the mere expression of\nlaws of phenomena, expressed in formul\u00e6 of space, time, and number; and\nwould condemn as unmeaning, and as belonging to an obsolete state of\nscience, all endeavours to determine the causes of phenomena, or even\nto refer them to any of the other ideas just mentioned.\n\n\n2. _M. Comte rejects the Search of Causes._--In a previous work[249]\nI have shown, I trust decisively, that it is the genuine office\nof science to inquire into the causes as well as the laws of\nphenomena;--that such an inquiry cannot be avoided; and that it has\nbeen the source of almost all the science we possess. I need not here\nrepeat the arguments there urged; but I may make a remark or two upon\nM. Comte's hypothesis, that all science is first \"metaphysical\" and\nthen \"positive;\" since it is in virtue of this hypothesis that he\nrejects the investigation of causes, as worthy only of the infancy\nof science. All discussions concerning ideas, M. Comte would condemn\nas \"metaphysical,\" and would consider as mere preludes to positive\nphilosophy. Now I venture to assert, on the contrary, that discussions\nconcerning ideas, and real discoveries, have in every science gone\nhand in hand. There is no science in which the pretended order of\nthings can be pointed out. There is no science in which the discoveries\nof the laws of phenomena, when once begun, have been carried on\nindependently of discussions concerning ideas. There is no science\nin which the expression of the laws of phenomena can at this time\ndispense with ideas which have acquired their place in science in\nvirtue of metaphysical considerations. There is no science in which\nthe most active disquisitions concerning ideas did not come _after_,\nnot _before_, the first discovery of laws of phenomena. In Astronomy,\nthe discovery of the phenomenal laws of the epicyclical motions of the\nheavens led to assumptions of the metaphysical principle of equable\ncircular motions: Kepler's discoveries would never have been made\nbut for his metaphysical notions. These discoveries of the laws of\nphenomena did not lead immediately to Newton's theory, _because_ a\ncentury of metaphysical discussions was requisite as a preparation.\nNewton then discovered, not merely a law of phenomena, but a _cause_;\nand _therefore_ he was the greatest of discoverers. The same is the\ncase in Optics; the ancients possessed some share of our knowledge\nof facts; but meddled little with the metaphysical reasonings of the\nsubject. In modern times when men began to inquire into the _nature_\nof light, they soon extended their knowledge of its _laws_. When this\nseries of discoveries had come to a pause, a new series of brilliant\ndiscoveries of laws of phenomena went on, inseparably connected with a\nnew series of views of the nature and cause of light. In like manner,\nthe most modern discoveries in chemistry involve indispensably the idea\nof polar forces. The metaphysics (in M. Comte's sense) of each subject\nadvances in a parallel line with the knowledge of physical laws. The\nExplication of Conceptions must go on, as we have already shown, at the\nsame rate as the Colligation of Facts.\n\nM. Comte will say[250] that Newton's discovery of gravitation only\nconsists in exhibiting the astronomical phenomena of the universe\nas one single fact under different points of view. But this _fact_\ninvolves the idea of _force_, that is, of _cause_. And that this idea\nis not a mere modification of the ideas of time and space, we have\nshown: if it were so, how could it lead to the axiom that attraction\nis mutual, an indispensable part of the Newtonian theory? M. Comte\nsays[251] that we do not know what attraction is, since we can only\ndefine it by identical phrases: but this is just as true of space,\nor time, or motion; and is in fact exactly the characteristic of a\nfundamental idea. We do not obtain such ideas from definitions, but we\npossess them not the less truly because we cannot define them.\n\nThat M. Comte's hypothesis is historically false, is obvious by such\nexamples as I have mentioned. Metaphysical discussions have been\nessential steps in the progress of each science. If we arbitrarily\nreject all these portions of scientific history as useless trifling,\nbelonging to the first rude attempts at knowledge, we shall not only\ndistort the progress of things, but pervert the plainest facts. Of\nthis we have an example in M. Comte's account of Kepler's mechanical\nspeculations. We have seen, in the History of Physical Astronomy, that\nKepler's second law, (that the planets describe areas about the sun\nproportional to the times,) was proved by him, by means of calculations\nfounded on the observations of Tycho; but that the mechanical reason\nof it was not assigned till a later period, when it appeared as the\nfirst proposition of Newton's _Principia_. It is plain from the\nwritings of Kepler, that it was impossible for him to show how this\nlaw resulted from the forces which were in action; since the forces\nwhich he considered were not those tending to the centre, which really\ndetermine the property in question, but forces exerted by the sun _in\nthe direction of the planet's motion_, without which forces Kepler\nconceived that the motion could not go on. In short, the state of\nmechanical science in Kepler's time was such that no demonstration of\nthe law could be given. The terms in which such a demonstration must\nbe expressed had not at that time acquired a precise significance; and\nit was in virtue of many subsequent _metaphysical_ discussions (as M.\nComte would term them) that these terms became capable of expressing\nsound mechanical reasoning. Kepler did indeed pretend to assign what\nhe called a \"physical proof\" of his law, depending upon this, that the\nsun's force is less at greater distances; a condition which does not\nat all influence the result. Thus Kepler's reason for his law proves\nnothing but the confusion of thought in which he was involved on such\nsubjects. Yet M. Comte assigns to Kepler the credit of having proved\nthis law by sound mechanical reasoning, as well as established it as\na matter of fact[252]. \"This discovery by Kepler,\" he adds, \"is the\nmore remarkable, inasmuch as it occurred before the science of dynamics\nhad really been created by Galileo.\" We may remark that inasmuch as M.\nComte perceived this incongruity in the facts as he stated them, it is\nthe more remarkable that he did not examine them more carefully.\n\n\n3. _Causes in Physics._--The condemnation of the inquiry into causes\nwhich is conveyed in M. Comte's notion of the three stages of Science,\nhe again expresses more in detail, in stating[253] what he calls his\n_Fundamental theory of hypotheses_. This \"theory\" is, that we may\nemploy hypotheses in our natural philosophy, but these hypotheses\nmust always be such as admit of a positive verification. We must have\nno suppositions concerning the agents by which effects are produced.\nAll such suppositions have an anti-scientific character, and can only\nimpede the real progress of physics. There can be no use in the ethers\nand imaginary fluids to which some persons refer the phenomena of heat,\nlight, electricity and magnetism. And in agreement with this doctrine,\nM. Comte in his account[254] of the Science of Optics, condemns, as\nutterly unphilosophical and absurd, both the theory of emission and\nthat of undulation.\n\nTo this we reply, that theory of one kind or other is indispensable\nto the expression of the phenomena; and that when the laws are\nexpressed, and apparently explained, by means of a theory, to forbid\nus to inquire whether it be really true or false, is a pedantic and\ncapricious limitation of our knowledge, to which the intellect of man\nneither can nor should submit. If any one holds the adoption of one or\nother of these theories to be indifferent, let him express the _laws\nof phenomena_ of diffraction in terms of the theory of emission[255].\nIf any one rejects the doctrine of undulation, let him point out some\nother way of connecting double refraction with polarization. And\nsurely no man of science will contend that the beautiful branch of\nscience which refers to that connexion is not a portion of our positive\nknowledge.\n\nM. Comte's contempt for the speculations of the undulationists seems\nto have prevented his acquainting himself with their reasonings, and\neven with the laws of phenomena on which they have reasoned, although\nthese form by far the most striking and beautiful addition which\nScience has received in modern times. He adduces, as an insuperable\nobjection to the undulatory theory, a difficulty which is fully\nremoved by calculation in every work on the subject:--the existence\nof shadow[256]. He barely mentions the subject of diffraction, and\nYoung's law of interferences;--speaks of Fresnel as having applied this\nprinciple to the phenomena of coloured rings, \"on which the ingenious\nlabours of Newton left much to desire;\" as if Fresnel's labours on\nthis subject had been the supplement of those of Newton: and after\nregretting that \"this principle of interferences has not yet been\ndistinctly disentangled from chemical conceptions on the nature of\nlight,\" concludes his chapter. He does not even mention the phenomena\nof dipolarization, of circular and elliptical polarization, or of the\noptical properties of crystals; discoveries of laws of phenomena quite\nas remarkable as any which can be mentioned.\n\nM. Comte's favourite example of physical research is Thermotics, and\nespecially Fourier's researches with regard to heat. It is shown[257]\nin the History of Thermotics, that the general phenomena of radiation\nrequired the assumption of a fluid to express them; as appears in the\n_theory of exchanges_[258]. And the explanation of the principal laws\nof radiation, which Fourier gives, depends upon the conception of\nmaterial molecular radiation. The _flux_ of caloric, of which Fourier\nspeaks, cannot be conceived otherwise than as implying a material\nflow. M. Comte apologizes[259] for this expression, as too figurative,\nand says that it merely indicates a _fact_. But what is the flow of a\ncurrent of fluid except a fact? And is it not evident that without such\nexpressions, and the ideas corresponding to them, Fourier could neither\nhave conveyed nor conceived his theory?\n\nIn concluding this discussion it must be recollected, that though\nit is a most narrow and untenable rule to say that we will admit no\nagency of ethers and fluids into philosophy; yet the reality of such\nagents is only to be held in the way, and to the extent, which the laws\nof phenomena indicate. It is not only allowable, but inevitable to\nassume, as the vehicle of heat and light, a medium possessing some of\nthe properties of more familiar kinds of matter. But the idea of such\na medium, which we possess, and on which we cannot but reason, can be\nfully developed only by an assiduous study of the cases in which it is\napplicable. It may be, that as science advances, all our knowledge may\nconverge to one general and single aspect of the universe. We abandon\nand reject this hope, if we refuse to admit those ideas which must\nbe our stepping-stones in advancing to such a point: and we no less\nfrustrate such an expectation, if we allow ourselves to imagine that\nfrom our present position we can stride at once to the summit.\n\n\n4. _Causes in other Sciences._--But if it is, in the sciences just\nmentioned, impracticable to reduce our knowledge to laws of phenomena\nalone, without referring to causes, media, and other agencies; how much\nmore plainly is it impossible to confine our thoughts to phenomena,\nand to laws of succession and resemblance, in other sciences, as\nchemistry, physiology, and geology? Who shall forbid us, or why should\nwe be forbidden, to inquire whether chemical and galvanic forces are\nidentical; whether irritability is a peculiar vital power; whether\ngeological causes have been uniform or paroxysmal? To exclude such\ninquiries, would be to secure ourselves from the poison of error by\nabstaining from the banquet of truth:--it would be to attempt to feed\nour minds with the meagre diet of space and number, because we may find\ntoo delightful a relish in such matters as cause and end, symmetry and\naffinity, organization and development.\n\nThus M. Comte's arrangement of the progress of science as successively\nmetaphysical and positive, is contrary to history in fact, and contrary\nto sound philosophy in principle. Nor is there any better foundation\nfor his statement that theological views are to be found only in the\nrude infantine condition of human knowledge, and vanish as science\nadvances. Even in material sciences this is not the case. We have\nshown in the chapter on Final Causes, that physiologists have been\ndirected in their remarks by the conviction of a purpose in every\npart of the structure of animals; and that this idea, which had its\nrise _after_ the first observations, has gone on constantly gaining\nstrength and clearness, so that it is now the basis of a large portion\nof the science. We have seen, too, in the Book on the pal\u00e6tiological\nsciences, that the researches of that class do by no means lead us to\nreject an origin of the series of events, nor to suppose this origin\nto be included in the series of natural laws. Science has not at all\nshown any reason for denying either the creation or the purpose of the\nuniverse.\n\nThis is true of those aspects of the universe which have become the\nsubjects of rigorous science: but how small a portion of the whole do\nthey form! Especially how minute a proportion does our knowledge bear\nto our ignorance, if we admit into science, as M. Comte advises, only\nthe laws of phenomena! Even in the best explored fields of science, how\nfew such laws do we know! Meteorology, climate, terrestrial magnetism,\nthe colours and other properties of bodies, the conditions of musical\nand articulate sound, and a thousand other facts of physics, are not\ndefined by any known laws. In physiology we may readily convince\nourselves how little we know of laws, since we can hardly study one\nspecies without discovering some unguessed property, or apply the\nmicroscope without seeing some new structure in the best known organs.\nAnd when we go on to social and moral and political matters, we may\nwell doubt whether any one single rigorous rule of phenomena has ever\nbeen stated, although on such subjects man's ideas have been busily\nand eagerly working ever since his origin. What a wanton and baseless\nassumption it would be, then, to reject those suggestions of a Governor\nof the universe which we derive from man's moral and spiritual nature,\nand from the institutions of society, because we fancy we see in the\nsmall field of our existing \"positive knowledge\" a tendency to exclude\n\"theological views!\" Because we can explain the motion of the stars by\na general Law which seems to imply no hyperphysical agency, and can\ntrace a few more limited laws in other properties of matter, we are\nexhorted to reject convictions irresistibly suggested to us by our\nbodies and our souls, by history and antiquities, by conscience and\nhuman law.\n\n\n5. _M. Comte's practical philosophy._--It is not merely as a\nspeculative doctrine that M. Comte urges the necessity of our thus\nfollowing the guidance of \"positive philosophy.\" The fevered and\nrevolutionary condition of human society at present arises, according\nto him[260], from the simultaneous employment of three kinds of\nphilosophy radically incompatible;--theological, metaphysical, and\npositive philosophy. The remedy for the evil is to reject the two\nformer, and to refer everything to that positive philosophy, of which\nthe destined triumph cannot be doubtful. In like manner, our European\neducation[261], still essentially theological, metaphysical, and\nliterary, must be replaced by a _positive_ education, suited to the\nspirit of our epoch.\n\nWith these practical consequences of M. Comte's philosophy we are not\nhere concerned: but the notice of them may serve to show how entirely\nthe rejection of the theological view pervades his system; and how\nclosely this rejection is connected with the principles which lead\nhim also to reject the fundamental ideas of the sciences as we have\npresented them.\n\n\n6. _M. Comte on Hypotheses._--In the detail of M. Comte's work, I do\nnot find any peculiar or novel remarks on the induction by which the\nsciences are formed; except we may notice, as such, his permission of\nhypotheses to the inquirer, already referred to. \"There can only be,\"\nhe says[262], \"two general modes fitted to reveal to us, in a direct\nand entirely rational manner, the true law of any phenomenon;--either\nthe immediate analysis of this phenomenon, or its exact and evident\nrelation to some more extended law, previously established;--in a word,\n_induction_, or _deduction_. But both these ways would certainly be\ninsufficient, even with regard to the simplest phenomenon, in the eyes\nof any one who fully comprehends the essential difficulties of the\nintimate study of nature, if we did not often begin by anticipating\nthe result, and making a provisory supposition, at first essentially\nconjectural, even with respect to some of the notions which constitute\nthe final object of inquiry. Hence the introduction, which is strictly\nindispensable, of hypotheses in natural philosophy.\" We have already\nseen that the \"permissio intellectus\" had been noticed as a requisite\nstep in discovery, as long before as the time of Bacon.\n\n\n7. _M. Comte's Classification of Sciences._--I do not think it\nnecessary to examine in detail M. Comte's views of the philosophy of\nthe different sciences; but it may illustrate the object of the present\nwork, to make a remark upon his attempt to establish a distinction\nbetween physical and chemical science. This distinction he makes to\nconsist in three points[263];--that Physics considers general and\nChemistry special properties;--that Physics considers masses and\nChemistry molecules;--that in Physics the mode of arrangement of\nthe molecules remains constant, while in Chemistry this arrangement\nis necessarily altered. M. Comte however allows that these lines\nof distinction are vague and insecure; for, among many others,\nmagnetism, a special property, belongs to physics, and breaks down\nhis first criterion; and molecular attractions are a constant subject\nof speculation in physics, so that the second distinction cannot be\ninsisted on. To which we may add that the greater portion of chemistry\ndoes not attend at all to the arrangement of the molecules, so that\nthe third character is quite erroneous. The real distinction of\nthese branches of science is, as we have seen, the fundamental ideas\nwhich they employ. Physics deals with relations of space, time, and\nnumber, media, and scales of qualities, according to intensity and\nother differences; while chemistry has for its subject elements and\nattractions as shown in composition; and polarity, though in different\nsenses, belongs to both. The failure of this attempt of M. Comte at\ndistinguishing these provinces of science by their objects, may be\nlooked upon as an illustration of the impossibility of establishing a\nphilosophy of the sciences on any other ground than the ideas which\nthey involve.\n\nWe have thus traced to its extreme point, so far as the nature\nof science is concerned, one of those two antagonistic opinions,\nof which the struggle began in the outset of philosophy, and has\ncontinued during the whole of her progress;--namely, the opinions\nwhich respectively make our sensations and our ideas the origin of our\nknowledge. The former, if it be consistent with itself, must consider\nall knowledge of causes as impossible, since no sensation can give us\nthe idea of cause. And when this opinion is applied to science, it\nreduces it to the mere investigation of laws of phenomena, according\nto relations of space, time, and number. I purposely abstain, as far\nas possible, from the consideration of the other consequences, not\nstrictly belonging to the physical sciences, which were drawn from\nthe doctrine that all our ideas are only transformed sensations. The\nmaterialism, the atheism, the sensualist morality, the anarchical\npolity, which some of the disciples of the Sensational School erected\nupon the fundamental dogmas of their sect, do not belong to our\npresent subject, and are matters too weighty to be treated of as mere\naccessories.\n\n       *       *       *       *       *\n\nThe above Remarks were written before I had seen the third volume of M.\nComte's work, or the subsequent volumes. But I do not find, in anything\nwhich those volumes contain, any ground for altering what I have\nwritten. Indeed they are occupied altogether with subjects which do not\ncome within the field of my present speculations.\n\n\nFOOTNOTES:\n\n[Footnote 247: i. p. 14.]\n\n[Footnote 248: i. p. 7.]\n\n[Footnote 249: _Hist. Ind. Sc._ b. xi. c. vii.]\n\n[Footnote 250: P. 15.]\n\n[Footnote 251: P. 16.]\n\n[Footnote 252: M. Comte's statement is so entirely at variance with the\nfact that I must quote it here. (_Phil. Pos._ vol. i. p. 705.)\n\n\"Le second th\u00e9or\u00e8me g\u00e9n\u00e9ral de dynamique consiste dans le c\u00e9l\u00e8bre et\nimportant _principe des aires_, dont le premi\u00e8re id\u00e9e est due \u00e0 Kepler,\nqui d\u00e9couvrit et d\u00e9montra forte simplement cette propri\u00e9t\u00e9 pour le cas\ndu mouvement d'une molecule unique, ou en d'autres terms, d'un corps\ndont tous les points se meuvent identiquement. Kepler \u00e9tablit, par les\nconsid\u00e9rations les plus \u00e9l\u00e9mentaires, qui si la force acc\u00e9l\u00e9ratrice\ntotale dont une molecule est anim\u00e9e tend constamment vers un point\nfix\u00e9, le rayon vecteur du mobile d\u00e9crit autour de ce point des aires\n\u00e9gales en temps egaux, de telle sorte que l'aire d\u00e9crite au bout d'un\ntemps quelconque cro\u00eet proportionellement \u00e0 ce temps. Il fit voir en\noutre que r\u00e9ciproquement, si une semblable relation a \u00e9t\u00e9 v\u00e9rifi\u00e9e\ndans le mouvement d'un corps par rapport \u00e0 un certain point, c'est une\npreuve suffisante de l'action sur le corps d'un force dirig\u00e9e sans\ncesse vers ce point.\"\n\nThere is not a trace of the above propositions in the work _De Stell\u00e2\nMartis_, which contains Kepler's discovery of his law, nor, I am\nconvinced, in any other of Kepler's works. He is everywhere constant to\nhis conceptions of the _magnetic_ virtue residing in the sun, by means\nof which the sun, revolving on his axis, carries the planets round with\nhim. M. Comte's statement so exactly expresses _Newton's_ propositions,\nthat one is led to suspect some extraordinary mistake, by which what\nshould have been said of the one was transferred to the other.]\n\n[Footnote 253: Vol. ii. p. 433.]\n\n[Footnote 254: Vol. ii. 640.]\n\n[Footnote 255: I venture to offer this problem;--to express the\n_laws of the phenomena_ of diffraction without the hypothesis of\nundulations;--as a challenge to any one who holds such hypothesis to be\nunphilosophical.]\n\n[Footnote 256: ii. p. 641.]\n\n[Footnote 257: ii. p. 673.]\n\n[Footnote 258: _Hist. Ind. Sc._ ii. 489, b. x. c. i.]\n\n[Footnote 259: ii. p. 561.]\n\n[Footnote 260: i. 50.]\n\n[Footnote 261: i. 41.]\n\n[Footnote 262: ii. 433.]\n\n[Footnote 263: _Phil. Pos._ ii. 392-398.]\n\n\n\n\nCHAPTER XXII.\n\nMR. MILL'S LOGIC[264].\n\n\nThe _History of the Inductive Sciences_ was published in 1837, and\nthe _Philosophy of the Inductive Sciences_ in 1840. In 1843 Mr. Mill\npublished his _System of Logic_, in which he states that without the\naid derived from the facts and ideas in my volumes, the corresponding\nportion of his own would most probably not have been written, and\nquotes parts of what I have said with commendation. He also, however,\ndissents from me on several important and fundamental points, and\nargues against what I have said thereon. I conceive that it may tend\nto bring into a clearer light the doctrines which I have tried to\nestablish, and the truth of them, if I discuss some of the differences\nbetween us, which I shall proceed to do[265].\n\nMr. Mill's work has had, for a work of its abstruse character, a\ncirculation so extensive, and admirers so numerous and so fervent, that\nit needs no commendation of mine. But if my main concern at present\nhad not been with the points in which Mr. Mill _differs_ from me, I\nshould have had great pleasure in pointing out passages, of which there\nare many, in which Mr. Mill appears to me to have been very happy in\npromoting or in expressing philosophical truth.\n\nThere is one portion of his work indeed which tends to give it an\ninterest of a wider kind than belongs to that merely scientific truth\nto which I purposely and resolutely confined my speculations in the\nworks to which I have referred. Mr. Mill has introduced into his work\na direct and extensive consideration of the modes of dealing with\nmoral and political as well as physical questions; and I have no doubt\nthat this part of his book has, for many of his readers, a more lively\ninterest than any other. Such a comprehensive scheme seems to give to\ndoctrines respecting science a value and a purpose which they cannot\nhave, so long as they are restricted to mere material sciences. I still\nretain the opinion, however, upon which I formerly acted, that the\nphilosophy of science is to be extracted from the portions of science\nwhich are universally allowed to be most certainly established, and\nthat those are the physical sciences. I am very far from saying, or\nthinking, that there is no such thing as Moral and Political Science,\nor that no method can be suggested for its promotion; but I think that\nby attempting at present to include the Moral Sciences in the same\nformul\u00e6 with the Physical, we open far more controversies than we\nclose; and that in the moral as in the physical sciences, the first\nstep towards showing how truth is to be discovered, is to study some\nportion of it which is assented to so as to be beyond controversy.\n\n\n1. _What is Induction?_--1. Confining myself, then, to the material\nsciences, I shall proceed to offer my remarks on Induction with\nespecial reference to Mr. Mill's work. And in order that we may, as\nI have said, proceed as intelligibly as possible, let us begin by\nconsidering what we mean by _Induction_, as a mode of obtaining truth;\nand let us note whether there is any difference between Mr. Mill and me\non this subject.\n\n\"For the purposes of the present inquiry,\" Mr. Mill says (i. 347[266]),\n\"Induction may be defined the operation of discovering and forming\ngeneral propositions:\" meaning, as appears by the context, the\ndiscovery of them from particular facts. He elsewhere (i. 370) terms\nit \"generalization from experience:\" and again he speaks of it with\ngreater precision as the inference of a more general proposition from\nless general ones.\n\n2. Now to these definitions and descriptions I assent as far as they\ngo; though, as I shall have to remark, they appear to me to leave\nunnoticed a feature which is very important, and which occurs in all\ncases of Induction, so far as we are concerned with it. Science, then,\nconsists of general propositions, inferred from particular facts, or\nfrom less general propositions, by Induction; and it is our object to\ndiscern the nature and laws of _Induction_ in this sense. That the\npropositions are general, or are more general than the facts from which\nthey are inferred, is an indispensable part of the notion of Induction,\nand is essential to any discussion of the process, as the mode of\narriving at Science, that is, at a body of general truths.\n\n3. I am obliged therefore to dissent from Mr. Mill when he includes, in\nhis notion of Induction, the process by which we arrive _at individual\nfacts_ from other facts _of the same order of particularity_.\n\nSuch inference is, at any rate, not Induction _alone_; if it be\nInduction at all, it is Induction applied to an example.\n\nFor instance, it is a general law, obtained by Induction from\nparticular facts, that a body falling vertically downwards from rest,\ndescribes spaces proportional to the squares of the times. But that a\nparticular body will fall through 16 feet in one second and 64 feet in\ntwo seconds, is not an induction simply, it is a result obtained by\napplying the inductive law to a particular case.\n\nBut further, such a process is often not induction _at all_. That a\nball striking another ball directly will communicate to it as much\nmomentum as the striking ball itself loses, is a law established\nby induction: but if, from habit or practical skill, I make one\nbilliard-ball strike another, so as to produce the velocity which\nI wish, without knowing or thinking of the general law, the term\n_Induction_ cannot then be rightly applied. If I _know the law_ and\nact upon it, I have in my mind both the general induction and its\nparticular application. But if I act by the ordinary billiard-player's\nskill, without thinking of momentum or law, there is no Induction in\nthe case.\n\n4. This distinction becomes of importance, in reference to Mr. Mill's\ndoctrine, because he has extended his use of the term _Induction_, not\nonly to the cases in which the general induction is consciously applied\nto a particular instance; but to the cases in which the particular\ninstance is dealt with by means of experience, in that rude sense in\nwhich _experience_ can be asserted of brutes; and in which, of course,\nwe can in no way imagine that the law is possessed or understood, as a\ngeneral proposition. He has thus, as I conceive, overlooked the broad\nand essential difference between speculative knowledge and practical\naction; and has introduced cases which are quite foreign to the idea\nof science, alongside with cases from which we may hope to obtain some\nviews of the nature of science and the processes by which it must be\nformed.\n\n5. Thus (ii. 232) he says, \"This inference of one particular fact from\nanother is a case of induction. It is of this sort of induction that\nbrutes are capable.\" And to the same purpose he had previously said (i.\n251), \"He [the burnt child who shuns the fire] is not generalizing:\nhe is inferring a particular from particulars. In the same way also,\nbrutes reason ... not only the burnt child, but the burnt dog, dreads\nthe fire.\"\n\n6. This confusion, (for such it seems to me,) of knowledge with\npractical tendencies, is expressed more in detail in other places. Thus\nhe says (i. 118), \"I cannot dig the ground unless I have an idea of the\nground and of a spade, and of all the other things I am operating upon.\"\n\n7. This appears to me to be a use of words which can only tend to\nconfuse our idea of knowledge by obliterating all that is distinctive\nin _human_ knowledge. It seems to me quite false to say that I cannot\ndig the ground, unless I have an idea of the ground and of my spade.\nAre we to say that we cannot _walk_ the ground, unless we have an idea\nof the ground, and of our feet, and of our shoes, and of the muscles of\nour legs? Are we to say that a mole cannot dig the ground, unless he\nhas an idea of the ground and of the snout and paws with which he digs\nit? Are we to say that a pholas cannot perforate a rock, unless he have\nan idea of the rock, and of the acid with which he corrodes it?\n\n8. This appears to me, as I have said, to be a line of speculation\nwhich can lead to nothing but confusion. The knowledge concerning which\nI wish to inquire is _human_ knowledge. And in order that I may have\nany chance of success in the inquiry, I find it necessary to single\nout that kind of knowledge which is especially and distinctively\nhuman. Hence, I pass by, in this part of my investigation, all the\n_knowledge_, if it is to be so called, which man has in no other way\nthan brutes have it;--all that merely shows itself in action. For\nthough action may be modified by habit, and habit by experience, in\nanimals as well as in men, such experience, so long as it retains\nthat merely practical form, is no part of the materials of science.\nKnowledge in a _general_ form, is alone knowledge for that purpose;\nand to _that_, therefore, I must confine my attention; at least till\nI have made some progress in ascertaining its nature and laws, and am\nthus prepared to compare such knowledge,--_human knowledge_ properly so\ncalled,--with mere animal tendencies to action; or even with practical\nskill which does not include, as for the most part practical skill does\nnot include, speculative knowledge.\n\n9. And thus, I accept Mr. Mill's definition of Induction only in its\nfirst and largest form; and reject, as useless and mischievous for our\npurposes, his extension of the term to the practical influence which\nexperience of one fact exercises upon a creature dealing with similar\nfacts. Such influence cannot be resolved into _ideas_ and _induction_,\nwithout, as I conceive, making all our subsequent investigation vague\nand heterogeneous, indefinite and inconclusive. If we must speak of\nanimals as _learning_ from experience, we may at least abstain from\napplying to them terms which imply that they learn, in the same way\nin which men learn astronomy from the stars, and chemistry from the\neffects of mixture and heat. And the same may be said of the language\nwhich is to be used concerning what _men_ learn, when their _learning_\nmerely shows itself in action, and does not exist as a general thought.\n_Induction_ must not be applied to such cases. _Induction_ must be\nconfined to cases where we have in our minds general propositions, in\norder that the sciences, which are our most instructive examples of the\nprocess we have to consider, may be, in any definite and proper sense,\n_Inductive_ Sciences.\n\n10. Perhaps some persons may be inclined to say that this difference\nof opinion, as to the extent of meaning which is to be given to the\nterm _Induction_, is a question merely of words; a matter of definition\nonly. This is a mode in which men in our time often seem inclined to\ndispose of philosophical questions; thus evading the task of forming\nan opinion upon such questions, while they retain the air of looking\nat the subject from a more comprehensive point of view. But as I have\nelsewhere said, such questions of definition are never questions\nof definition merely. A proposition is always implied along with\nthe definition; and the truth of the proposition depends upon the\nsettlement of the definition. This is the case in the present instance.\nWe are speaking of _Induction_, and we mean that kind of Induction\nby which the sciences now existing among men have been constructed.\nOn this account it is, that we cannot include, in the meaning of the\nterm, mere practical tendencies or practical habits; for science is not\nconstructed of these. No accumulation of these would make up any of the\nacknowledged sciences. The elements of such sciences are something of a\nkind different from practical habits. The elements of such sciences are\nprinciples which we _know_; truths which can be contemplated as being\n_true_. Practical habits, practical skill, instincts and the like,\nappear in action, and in action only. Such endowments or acquirements\nshow themselves when the occasion for action arrives, and then, show\nthemselves in the act; without being put, or being capable of being\nput, in the form of truths contemplated by the intellect. But the\nelements and materials of Science are necessary truths contemplated by\nthe intellect. It is by consisting of such elements and such materials,\nthat Science _is_ Science. Hence a use of the term _Induction_ which\nrequires us to obliterate this distinction, must make it impossible for\nus to arrive at any consistent and intelligible view of the nature of\nScience, and of the mental process by which Sciences come into being.\nWe must, for the purpose which Mr. Mill and I have in common, retain\nhis larger and more philosophical definition of Induction,--that it is\nthe inference of a more general proposition from less general ones.\n\n11. Perhaps, again, some persons may say, that practical skill and\npractical experience _lead_ to science, and may therefore be included\nin the term _Induction_, which describes the formation of science. But\nto this we reply, that these things lead to science as occasions only,\nand do not form part of science; and that science begins then only\nwhen we look at the facts in a general point of view. This distinction\nis essential to the philosophy of science. The rope-dancer may, by\nhis performances, suggest, to himself or to others, properties of\nthe center of gravity; but this is so, because man has a tendency to\nspeculate and to think of general truths, as well as a tendency to\ndance on a rope on special occasions, and to acquire skill in such\ndancing by practice. The rope-dancer does not dance by Induction,\nany more than the dancing dog does. To apply the terms Science and\nInduction to such cases, carries us into the regions of metaphor;\nas when we call birds of passage \"wise meteorologists,\" or the bee\n\"a natural chemist, who turns the flower-dust into honey.\" This is\nvery well in poetry: but for our purposes we must avoid recognizing\nthese cases as really belonging to the sciences of meteorology and\nchemistry,--as really cases of Induction. Induction for us is general\npropositions, _contemplated as such_, derived from particulars.\n\nScience may result _from_ experience and observation _by_ Induction;\nbut Induction is not therefore the same thing as experience and\nobservation. Induction is experience or observation _consciously_\nlooked at in a _general_ form. This consciousness and generality are\nnecessary parts of that knowledge which is science. And accordingly,\non the other hand, science cannot result from mere Instinct, as\ndistinguished from Reason; because Instinct by its nature is not\nconscious and general, but operates blindly and unconsciously in\nparticular cases, the actor not seeing or thinking of the rule which he\nobeys.\n\n12. A little further on I shall endeavour to show that not only a\ngeneral _thought_, but a general _word_ or phrase is a requisite\nelement in Induction. This doctrine, of course, still more decidedly\nexcludes the case of animals, and of mere practical knowledge in man.\nA burnt child dreads the fire; but reason must be unfolded, before the\nchild learns to understand the words \"fire will hurt you.\" The burnt\ndog never thus learns to understand words. And this difference points\nto an entirely different state of thought in the two cases: or rather,\nto a difference between a state of rational thought on the one hand,\nand of mere practical instinct on the other.\n\n13. Besides this difference of speculative thought and practical\ninstinct which thus are, as appears to me, confounded in Mr. Mill's\nphilosophy, in such a way as tends to destroy all coherent views of\nhuman knowledge, there is another set of cases to which Mr. Mill\napplies the term _Induction_, and to which it appears to me to be\naltogether inapplicable. He employs it to describe the mode in which\nsuperstitious men, in ignorant ages, were led to the opinion that\nstriking natural events presaged or accompanied calamities. Thus he\nsays (i. 389), \"The opinion so long prevalent that a comet or any\nother unusual appearance in the heavenly regions was the precursor of\ncalamities to mankind, or at least to those who witnessed it; the\nbelief in the oracles of Delphi and Dodona; the reliance on astrology,\nor on the weather-prophecies in almanacs; were doubtless inductions\nsupposed to be grounded on experience;\" and he speaks of these\ninsufficient inductions being extinguished by the stronger inductions\nsubsequently obtained by scientific inquiry. And in like manner,\nhe says in another place (i. 367), \"Let us now compare different\npredictions: the first, that eclipses will occur whenever one planet\nor satellite is so situated as to cast its shadow upon another: the\nsecond, that they will occur whenever some great calamity is impending\nover mankind.\"\n\n14. Now I cannot see how anything but confusion can arise from\napplying the term _Induction_ to superstitious fancies like those\nhere mentioned. They are not imperfect truths, but entire falsehoods.\nOf that, Mr. Mill and I are agreed: how then can they exemplify the\nprogress towards truth? They were not collected from the facts by\nseeking a law of their occurrence; but were suggested by an imagination\nof the anger of superior powers shown by such deviations from the\nordinary course of nature. If we are to speak of _inductions_ to any\npurpose, they must be such inductions as represent the facts, in some\ndegree at least. It is not meant, I presume, that these opinions are in\nany degree true: to what purpose then are they adduced? If I were to\nhold that my dreams predict or conform to the motions of the stars or\nof the clouds, would this be an induction? It would be so, as much one\nas those here so denominated: yet what but confusion could arise from\nclassing it among scientific truths? Mr. Mill himself has explained\n(ii. 389) the way in which such delusions as the prophecies of\nalmanac-makers, and the like, obtain credence; namely, by the greater\neffect which the positive instances produce on ordinary minds in\ncomparison with the negative, when the rule has once taken possession\nof their thoughts. And this being, as he says, the recognized\nexplanation of such cases, why should we not leave them to their due\nplace, and not confound and perplex the whole of our investigation by\nelevating them to the rank of \"inductions\"? The very condemnation of\nsuch opinions is that they are not at all inductive. When we have made\nany progress in our investigation of the nature of science, to attempt\nto drive us back to the wearisome discussion of such elementary points\nas these, is to make progress hopeless.\n\n\nII. _Induction or Description?_--15. In the cases hitherto noticed, Mr.\nMill extends the term _Induction_, as I think, too widely, and applies\nit to cases to which it is not rightly applicable. I have now to notice\na case of an opposite kind, in which he does not apply it where I do,\nand condemns me for using it in such a case. I had spoken of Kepler's\ndiscovery of the Law, that the planets move round the sun in ellipses,\nas an example of Induction. The separate facts of any planet (Mars, for\ninstance,) being in certain places at certain times, are all included\nin the general proposition which Kepler discovered, that Mars describes\nan ellipse of a certain form and position. This appears to me a very\nsimple but a very distinct example of the operation of discovering\ngeneral propositions; general, that is, with reference to particular\nfacts; which operation Mr. Mill, as well as myself, says is Induction.\nBut Mr. Mill denies this operation in this case to be Induction at\nall (i. 357). I should not have been prepared for this denial by the\nprevious parts of Mr. Mill's book, for he had said just before (i.\n350), \"such facts as the magnitudes of the bodies of the solar system,\ntheir distances from each other, the figure of the earth and its\nrotation ... are proved indirectly, by the aid of inductions founded\non other facts which we can more easily reach.\" If the figure of the\nearth and its rotation are proved by Induction, it seems very strange,\nand is to me quite incomprehensible, how the figure of the earth's\norbit and its revolution (and of course, of the figure of Mars's orbit\nand his revolution in like manner,) are not also proved by Induction.\nNo, says Mr. Mill, Kepler, in putting together a number of places of\nthe planet into one figure, only performed an act of _description_.\n\"This descriptive operation,\" he adds (i. 359), \"Mr. Whewell, by an\naptly chosen expression, has termed Colligation of Facts.\" He goes on\nto commend my observations concerning this process, but says that,\naccording to the old and received meaning of the term, it is not\nInduction at all.\n\n16. Now I have already shown that Mr. Mill himself, a few pages\nearlier, had applied the term _Induction_ to cases undistinguishable\nfrom this in any essential circumstance. And even in this case, he\nallows that Kepler did really perform an act of Induction (i. 358),\n\"namely, in concluding that, because the observed places of Mars were\ncorrectly represented by points in an imaginary ellipse, therefore Mars\nwould continue to revolve in that same ellipse; and even in concluding\nthat the position of the planet during the time which had intervened\nbetween the two observations must have coincided with the intermediate\npoints of the curve.\" Of course, in Kepler's Induction, of which I\nspeak, I include all this; all this is included in speaking of the\n_orbit_ of Mars: a continuous line, a periodical motion, are implied\nin the term _orbit_. I am unable to see what would remain of Kepler's\ndiscovery, if we take from it these conditions. It would not only not\nbe an induction, but it would not be a description, for it would not\nrecognize that Mars moved in an orbit. Are particular positions to be\nconceived as points in a curve, without thinking of the intermediate\npositions as belonging to the same curve? If so, there is no law at\nall, and the facts are not bound together by any intelligible tie.\n\nIn another place (ii. 209) Mr. Mill returns to his distinction of\nDescription and Induction; but without throwing any additional light\nupon it, so far as I can see.\n\n17. The only meaning which I can discover in this attempted distinction\nof Description and Induction is, that when particular facts are bound\ntogether by their relation in _space_, Mr. Mill calls the discovery\nof the connexion _Description_, but when they are connected by other\ngeneral relations, as time, cause and the like, Mr. Mill terms the\ndiscovery of the connexion _Induction_. And this way of making a\ndistinction, would fall in with the doctrine of other parts of Mr.\nMill's book, in which he ascribes very peculiar attributes to space\nand its relations, in comparison with other Ideas, (as I should call\nthem). But I cannot see any ground for this distinction, of connexion\naccording to space and other connexions of facts.\n\nTo stand upon such a distinction, appears to me to be the way to miss\nthe general laws of the formation of science. For example: The ancients\ndiscovered that the planets revolved in recurring periods, and thus\nconnected the observations of their motions according to the Idea of\n_Time_. Kepler discovered that they revolved in ellipses, and thus\nconnected the observations according to the Idea of _Space_. Newton\ndiscovered that they revolved in virtue of the Sun's attraction, and\nthus connected the motions according to the Idea of _Force_. The first\nand third of these discoveries are recognized on all hands as processes\nof Induction. Why is the second to be called by a different name? or\nwhat but confusion and perplexity can arise from refusing to class it\nwith the other two? It is, you say, Description. But such Description\nis a kind of Induction, and must be spoken of as Induction, if we are\nto speak of Induction as the process by which Science is formed: for\nthe three steps are all, the second in the same sense as the first\nand third, in co-ordination with them, steps in the formation of\nastronomical science.\n\n18. But, says Mr. Mill (i. 363), \"it is a fact surely that the planet\ndoes describe an ellipse, and a fact which we could see if we had\nadequate visual organs and a suitable position.\" To this I should\nreply: \"Let it be so; and it is a fact, surely, that the planet does\nmove periodically: it is a fact, surely, that the planet is attracted\nby the sun. Still, therefore, the asserted distinction fails to find a\nground.\" Perhaps Mr. Mill would remind us that the elliptical form of\nthe orbit is a fact which we could see if we had adequate visual organs\nand a suitable position: but that force is a thing which we cannot\nsee. But this distinction also will not bear handling. Can we not see\na tree blown down by a storm, or a rock blown up by gunpowder? Do we\nnot here see force:--see it, that is, by its effects, the only way in\nwhich we need to see it in the case of a planet, for the purposes of\nour argument? Are not such operations of force, Facts which may be the\nobjects of sense? and is not the operation of the sun's Force a Fact\nof the same kind, just as much as the elliptical form of orbit which\nresults from the action? If the latter be \"surely a Fact,\" the former\nis a Fact no less surely.\n\n19. In truth, as I have repeatedly had occasion to remark, all attempts\nto frame an argument by the exclusive or emphatic appropriation of\nthe term _Fact_ to particular cases, are necessarily illusory and\ninconclusive. There is no definite and stable distinction between Facts\nand Theories; Facts and Laws; Facts and Inductions. Inductions, Laws,\nTheories, which are true, _are_ Facts. Facts involve Inductions. It is\na fact that the moon is attracted by the earth, just as much as it is a\nFact that an apple falls from a tree. That the former fact is collected\nby a more distinct and conscious Induction, does not make it the less\na Fact. That the orbit of Mars is a Fact--a true Description of the\npath--does not make it the less a case of Induction.\n\n20. There is another argument which Mr. Mill employs in order to\nshow that there is a difference between mere colligation which is\ndescription, and induction in the more proper sense of the term. He\nnotices with commendation a remark which I had made (i. 364), that\nat different stages of the progress of science the facts had been\nsuccessfully connected by means of very different conceptions, while\nyet the later conceptions have not contradicted, but included, so far\nas they were true, the earlier: thus the ancient Greek representation\nof the motions of the planets by means of epicycles and eccentrics,\nwas to a certain degree of accuracy true, and is not negatived, though\nsuperseded, by the modern representation of the planets as describing\nellipses round the sun. And he then reasons that this, which is thus\ntrue of Descriptions, cannot be true of Inductions. He says (i. 367),\n\"Different descriptions therefore may be all true: but surely not\ndifferent explanations.\" He then notices the various explanations of\nthe motions of the planets--the ancient doctrine that they are moved\nby an inherent virtue; the Cartesian doctrine that they are moved by\nimpulse and by vortices; the Newtonian doctrine that they are governed\nby a central force; and he adds, \"Can it be said of these, as was said\nof the different descriptions, that they are all true as far as they\ngo? Is it not true that one only can be true in any degree, and that\nthe other two must be altogether false?\"\n\n21. And to this questioning, the history of science compels me to reply\nvery distinctly and positively, in the way which Mr. Mill appears to\nthink extravagant and absurd. I am obliged to say, Undoubtedly, all\nthese explanations _may_ be true and consistent with each other, and\nwould be so if each had been followed out so as to show in what manner\nit could be made consistent with the facts. And this was, in reality,\nin a great measure done[267]. The doctrine that the heavenly bodies\nwere moved by vortices was successively modified, so that it came to\ncoincide in its results with the doctrine of an inverse-quadratic\ncentripetal force, as I have remarked in the _History_[268]. When this\npoint was reached, the vortex was merely a machinery, well or ill\ndevised, for producing such a centripetal force, and therefore did not\ncontradict the doctrine of a centripetal force. Newton himself does\nnot appear to have been averse to explaining gravity by impulse. So\nlittle is it true that if the one theory be true the other must be\nfalse. The attempt to explain gravity by the impulse of streams of\nparticles flowing through the universe in all directions, which I have\nmentioned in the _Philosophy_[269] so far from being inconsistent\nwith the Newtonian theory, that it is founded entirely upon it. And\neven with regard to the doctrine, that the heavenly bodies move by\nan inherent virtue; if this doctrine had been maintained in any such\nway that it was brought to agree with the facts, the inherent virtue\nmust have had its laws determined; and then, it would have been found\nthat the virtue had a reference to the central body; and so, the\n\"inherent virtue\" must have coincided in its effect with the Newtonian\nforce; and then, the two explanations would agree, except so far as\nthe word \"inherent\" was concerned. And if such a part of an earlier\ntheory as this word _inherent_ indicates, is found to be untenable,\nit is of course rejected in the transition to later and more exact\ntheories, in Inductions of this kind, as well as in what Mr. Mill calls\nDescriptions. There is therefore still no validity discoverable in the\ndistinction which Mr. Mill attempts to draw between \"descriptions\" like\nKepler's law of elliptical orbits, and other examples of induction.\n\n22. When Mr. Mill goes on to compare what he calls different\npredictions--the first, the true explanation of eclipses by the shadows\nwhich the planets and satellites cast upon one another, and the\nother, the belief that they will occur whenever some great calamity\nis impending over mankind, I must reply, as I have stated already,\n(Art. 17), that to class such superstitions as the last with cases of\nInduction, appears to me to confound all use of words, and to prevent,\nas far as it goes, all profitable exercise of thought. What possible\nadvantage can result from comparing (as if they were alike) the\nrelation of two descriptions of a phenomenon, each to a certain extent\ntrue, and therefore both consistent, with the relation of a scientific\ntruth to a false and baseless superstition?\n\n23. But I may make another remark on this example, so strangely\nintroduced. If, under the influence of fear and superstition, men\nmay make such mistakes with regard to laws of nature, as to imagine\nthat eclipses portend calamities, are they quite secure from mistakes\nin _description_? Do not the very persons who tell us how eclipses\npredict disasters, also describe to us fiery swords seen in the air,\nand armies fighting in the sky? So that even in this extreme case,\nat the very limit of the rational exercise of human powers, there is\nnothing to distinguish Description from Induction.\n\nI shall now leave the reader to judge whether this feature in the\nhistory of science,--that several views which appear at first quite\ndifferent are yet all true,--which Mr. Mill calls a curious and\ninteresting remark of mine, and which he allows to be \"strikingly true\"\nof the Inductions which he calls _Descriptions_, (i. 364) is, as he\nsays, \"unequivocally false\" of other Inductions. And I shall confide\nin having general assent with me, when I continue to speak of Kepler's\n_Induction_ of the elliptical orbits.\n\nI now proceed to another remark.\n\n\nIII. _In Discovery a new Conception is introduced._--\n\n24. There is a difference between Mr. Mill and me in our view of the\nessential elements of this Induction of Kepler, which affects all other\ncases of Induction, and which is, I think, the most extensive and\nimportant of the differences between us. I must therefore venture to\ndwell upon it a little in detail.\n\nI conceive that Kepler, in discovering the law of Mars's motion,\nand in asserting that the planet moved in an ellipse, did this;--he\nbound together particular observations of separate places of Mars\nby the notion, or, as I have called it, the _conception_, of an\n_ellipse_, which was supplied by his own mind. Other persons, and he\ntoo, before he made this discovery, had present to their minds the\nfacts of such separate successive positions of the planet; but could\nnot bind them together rightly, because they did not apply to them\nthis conception of an _ellipse_. To supply this conception, required\na special preparation, and a special activity in the mind of the\ndiscoverer. He, and others before him, tried other ways of connecting\nthe special facts, none of which fully succeeded. To discover such\na connexion, the mind must be conversant with certain relations of\nspace, and with certain kinds of figures. To discover the right figure\nwas a matter requiring research, invention, resource. To hit upon\nthe right conception is a difficult step; and when this step is once\nmade, the facts assume a different aspect from what they had before:\nthat done, they are seen in a new point of view; and the catching\nthis point of view, is a special mental operation, requiring special\nendowments and habits of thought. Before this, the facts are seen as\ndetached, separate, lawless; afterwards, they are seen as connected,\nsimple, regular; as parts of one general fact, and thereby possessing\ninnumerable new relations before unseen. Kepler, then, I say, bound\ntogether the facts by superinducing upon them the _conception_ of an\n_ellipse_; and this was an essential element in his Induction.\n\n25. And there is the same essential element in all Inductive\ndiscoveries. In all cases, facts, before detached and lawless, are\nbound together by a new thought. They are reduced to law, by being\nseen in a new point of view. To catch this new point of view, is an\nact of the mind, springing from its previous preparation and habits.\nThe facts, in other discoveries, are brought together according to\nother relations, or, as I have called them, _Ideas_;--the Ideas of\nTime, of Force, of Number, of Resemblance, of Elementary Composition,\nof Polarity, and the like. But in all cases, the mind performs the\noperation by an apprehension of some such relations; by singling out\nthe one true relation; by combining the apprehension of the true\nrelation with the facts; by applying to them the Conception of such a\nrelation.\n\n26. In previous writings, I have not only stated this view generally,\nbut I have followed it into detail, exemplifying it in the greater part\nof the History of the principal Inductive Sciences in succession. I\nhave pointed out what are the Conceptions which have been introduced in\nevery prominent discovery in those sciences; and have noted to which of\nthe above Ideas, or of the like Ideas, each belongs. The performance\nof this task is the office of the greater part of my _Philosophy\nof the Inductive Sciences_. For that work is, in reality, no less\nhistorical than the _History_ which preceded it. The _History of the\nInductive Sciences_ is the history of the discoveries, mainly so far\nas concerns the _Facts_ which were brought together to form sciences.\nThe _Philosophy_ is, in the first ten Books, the history of the _Ideas_\nand _Conceptions_, by means of which the facts were connected, so as\nto give rise to scientific truths. It would be easy for me to give a\nlong list of the Ideas and Conceptions thus brought into view, but\nI may refer any reader who wishes to see such a list, to the Tables\nof Contents of the _History_, and of the first ten Books of the\n_Philosophy_.\n\n27. That these Ideas and Conceptions are really distinct elements of\nthe scientific truths thus obtained, I conceive to be proved beyond\ndoubt, not only by considering that the discoveries never were made,\nnor could be made, till the right Conception was obtained, and by\nseeing how difficult it often was to obtain this element; but also, by\nseeing that the Idea and the Conception itself, as distinct from the\nFacts, was, in almost every science, the subject of long and obstinate\ncontroversies;--controversies which turned upon the possible relations\nof Ideas, much more than upon the actual relations of Facts. The first\nten Books of the _Philosophy_ to which I have referred, contain the\nhistory of a great number of these controversies. These controversies\nmake up a large portion of the history of each science; a portion quite\nas important as the study of the facts; and a portion, at every stage\nof the science, quite as essential to the progress of truth. Men, in\nseeking and obtaining scientific knowledge, have always shown that they\nfound the formation of right conceptions in their own minds to be an\nessential part of the process.\n\n28. Moreover, the presence of a Conception of the mind as a special\nelement of the inductive process, and as the tie by which the\nparticular facts are bound together, is further indicated, by there\nbeing some special new _term_ or _phrase_ introduced in every\ninduction; or at least some term or phrase thenceforth steadily\napplied to the facts, which had not been applied to them before; as\nwhen Kepler asserted that Mars moved round the sun in an _elliptical\norbit_, or when Newton asserted that the planets _gravitate_ towards\nthe sun; these new terms, _elliptical orbit_, and _gravitate_, mark\nthe new conceptions on which the inductions depend. I have in the\n_Philosophy_[270] further illustrated this application of \"technical\nterms,\" that is, fixed and settled terms, in every inductive discovery;\nand have spoken of their use in enabling men to proceed from each such\ndiscovery to other discoveries more general. But I notice these terms\nhere, for the purpose of showing the existence of a conception in the\ndiscoverer's mind, corresponding to the term thus introduced; which\nconception, the term is intended to convey to the minds of those to\nwhom the discovery is communicated.\n\n29. But this element of discovery,--right conceptions supplied by\nthe mind in order to bind the facts together,--Mr. Mill denies to be\nan element at all. He says, of Kepler's discovery of the elliptical\norbit (i. 363), \"It superadded nothing to the particular facts\nwhich it served to bind together;\" yet he adds, \"except indeed the\nknowledge that a resemblance existed between the planetary orbit\nand other ellipses;\" that is, except the knowledge that it _was_ an\nellipse;--precisely the circumstance in which the discovery consisted.\nKepler, he says, \"asserted as a fact that the planet moved in an\nellipse. But this fact, which Kepler did not add to, but found in the\nmotion of the planet ... was the very fact, the separate parts of\nwhich had been separately observed; it was the sum of the different\nobservations.\"\n\n30. That the fact of the elliptical motion was not merely the _sum_ of\nthe different observations, is plain from this, that other persons, and\nKepler himself before his discovery, did not find it by adding together\nthe observations. The fact of the elliptical orbit was not the sum of\nthe observations _merely_; it was the sum of the observations, _seen\nunder a new point of view_, which point of view Kepler's mind supplied.\nKepler found it in the facts, because it was there, no doubt, for one\nreason; but also, for another, because he had, in his mind, those\nrelations of thought which enabled him to find it. We may illustrate\nthis by a familiar analogy. We too find the law in Kepler's book; but\nif we did not understand Latin, we should not find it there. We must\nlearn Latin in order to find the law in the book. In like manner, a\ndiscoverer must know the language of science, as well as look at the\nbook of nature, in order to find scientific truth. All the discussions\nand controversies respecting Ideas and Conceptions of which I have\nspoken, may be looked upon as discussions and controversies respecting\nthe grammar of the language in which nature speaks to the scientific\nmind. Man is the _Interpreter_ of Nature; not the Spectator merely,\nbut the Interpreter. The study of the language, as well as the mere\nsight of the characters, is requisite in order that we may read the\ninscriptions which are written on the face of the world. And this\nstudy of the language of nature, that is, of the necessary coherencies\nand derivations of the relations of phenomena, is to be pursued by\nexamining Ideas, as well as mere phenomena;--by tracing the formation\nof Conceptions, as well as the accumulation of Facts. And this is what\nI have tried to do in the books already referred to.\n\n31. Mr. Mill has not noticed, in any considerable degree, what I have\nsaid of the formation of the Conceptions which enter into the various\nsciences; but he has, in general terms, denied that the Conception is\nanything different from the facts themselves. \"If,\" he says (i. 301),\n\"the facts are rightly classed under the conceptions, it is because\nthere is in the facts themselves, something of which the conception\nis a copy.\" But it is a copy which cannot be made by a person without\npeculiar endowments; just as a person cannot copy an ill-written\ninscription, so as to make it convey sense, unless he understand the\nlanguage. \"Conceptions,\" Mr. Mill says (ii. 217), \"do not develope\nthemselves from within, but are impressed from without.\" But what comes\nfrom without is not enough: they must have both origins, or they cannot\nmake knowledge. \"The conception,\" he says again (ii. 221), \"is not\nfurnished _by_ the mind till it has been furnished _to_ the mind.\" But\nit is furnished to the mind by its own activity, operating according to\nits own laws. No doubt, the conception may be formed, and in cases of\ndiscovery, must be formed, by the suggestion and excitement which the\nfacts themselves produce; and must be so moulded as to agree with the\nfacts. But this does not make it superfluous to examine, out of what\n_materials_ such conceptions are formed, and _how_ they are capable of\nbeing moulded so as to express laws of nature; especially, when we see\nhow large a share this part of discovery--the examination how our ideas\ncan be modified so as to agree with nature,--holds, in the history of\nscience.\n\n32. I have already (Art. 28) given, as evidence that the conception\nenters as an element in every induction, the constant introduction\nin such cases, of a new fixed term or phrase. Mr. Mill (ii. 282)\nnotices this introduction of a new phrase in such cases as important,\nthough he does not appear willing to allow that it is necessary. Yet\nthe necessity of the conception at least, appears to result from the\nconsiderations which he puts forward. \"What darkness,\" he says, \"would\nhave been spread over geometrical demonstration, if wherever the word\n_circle_ is used, the definition of a circle was inserted instead of\nit.\" \"If we want to make a particular combination of ideas permanent\nin the mind, there is nothing which clenches it like a name specially\ndevoted to express it.\" In my view, the new conception is the _nail_\nwhich connects the previous notions, and the name, as Mr. Mill says,\n_clenches_ the junction.\n\n33. I have above (Art. 30) referred to the difficulty of getting\nhold of the right conception, as a proof that induction is not a\nmere juxtaposition of facts. Mr. Mill does not dispute that it is\noften difficult to hit upon the right conception. He says (i. 360),\n\"that a conception of the mind is introduced, is indeed most certain,\nand Mr. Whewell has rightly stated elsewhere, that to hit upon the\nright conception is often a far more difficult, and more meritorious\nachievement, than to prove its applicability when obtained. But,\" he\nadds, \"a conception implies and corresponds to something conceived; and\nalthough the conception itself is not in the facts, but in our mind, it\nmust be a conception of something which really is in the facts.\" But to\nthis I reply, that its being really in the facts, does not help us at\nall towards knowledge, if we cannot see it there. As the poet says,\n\n    It is the mind that sees: the outward eyes\n    Present the object, but the mind descries.\n\nAnd this is true of the sight which produces knowledge, as well as of\nthe sight which produces pleasure and pain, which is referred to in the\nTale.\n\n34. Mr. Mill puts his view, as opposed to mine, in various ways, but,\nas will easily be understood, the answers which I have to offer are\nin all cases nearly to the same effect. Thus, he says (ii. 216), \"the\ntardy development of several of the physical sciences, for example,\nof Optics, Electricity, Magnetism, and the higher generalizations of\nChemistry, Mr. Whewell ascribes to the fact that mankind had not yet\npossessed themselves of the idea of Polarity, that is, of opposite\nproperties in opposite directions. But what was there to suggest such\nan idea, until by a separate examination of several of these different\nbranches of knowledge it was shown that the facts of each of them did\npresent, in some instances at least, the curious phenomena of opposite\nproperties in opposite directions?\" But on this I observe, that these\nfacts did not, nor do yet, present this conception to ordinary minds.\nThe opposition of properties, and even the opposition of directions,\nwhich are thus apprehended by profound cultivators of science, are\nof an abstruse and recondite kind; and to conceive any one kind of\npolarity in its proper generality, is a process which few persons\nhitherto appear to have mastered; still less, have men in general\ncome to conceive of them all as modifications of a general notion of\nPolarity. The description which I have given of Polarity in general,\n\"opposite properties in opposite directions,\" is of itself a very\nimperfect account of the manner in which corresponding antitheses are\ninvolved in the portions of science into which Polar relations enter.\nIn excuse of its imperfection, I may say, that I believe it is the\nfirst attempt to define Polarity in general; but yet, the conception\nof Polarity has certainly been strongly and effectively present in the\nminds of many of the sagacious men who have discovered and unravelled\npolar phenomena. They attempted to convey this conception, each in his\nown subject, sometimes by various and peculiar expressions, sometimes\nby imaginary mechanism by which the antithetical results were produced;\ntheir mode of expressing themselves being often defective or imperfect,\noften containing what was superfluous; and their meaning was commonly\nvery imperfectly apprehended by most of their hearers and readers.\nBut still, the conception was there, gradually working itself into\nclearness and distinctness, and in the mean time, directing their\nexperiments, and forming an essential element of their discoveries. So\nfar would it be from a sufficient statement of the case to say, that\nthey conceived polarity because they saw it;--that they saw it as soon\nas it came into view;--and that they described it as they saw it.\n\n35. The way in which such conceptions acquire clearness and\ndistinctness is often by means of Discussions of Definitions. To define\nwell a thought which already enters into trains of discovery, is often\na difficult matter. The business of such definition is a part of the\nbusiness of discovery. These, and other remarks connected with these,\nwhich I had made in the _Philosophy_, Mr. Mill has quoted and adopted\n(ii. 242). They appear to me to point very distinctly to the doctrine\nto which he refuses his assent,--that there is a special process in the\nmind, in addition to the mere observation of facts, which is necessary\nat every step in the progress of knowledge. The Conception must be\n_formed_ before it can be _defined_. The Definition gives the last\nstamp of distinctness to the Conception; and enables us to express, in\na compact and lucid form, the new scientific propositions into which\nthe new Conception enters.\n\n36. Since Mr. Mill assents to so much of what has been said in the\n_Philosophy_, with regard to the process of scientific discovery, how,\nit may be asked, would he express these doctrines so as to exclude that\nwhich he thinks erroneous? If he objects to our saying that when we\nobtain a new inductive truth, we connect phenomena by applying to them\na new Conception which fits them, in what terms would he describe the\nprocess? If he will not agree to say, that in order to discover the law\nof the facts, we must find an appropriate Conception, what language\nwould he use instead of this? This is a natural question; and the\nanswer cannot fail to throw light on the relation in which his views\nand mine stand to each other.\n\nMr. Mill would say, I believe, that when we obtain a new inductive law\nof facts, we find something in which the facts _resemble each other_;\nand that the business of making such discoveries is the business of\ndiscovering such resemblances. Thus, he says (of me,) (ii. 211),\n\"his Colligation of Facts by means of appropriate Conceptions, is\nbut the ordinary process of finding by a comparison of phenomena, in\nwhat consists their agreement or resemblance.\" And the Methods of\nexperimental Inquiry which he gives (i. 450, &c.), proceed upon the\nsupposition that the business of discovery may be thus more properly\ndescribed.\n\n37. There is no doubt that when we discover a law of nature by\ninduction, we find some point in which all the particular facts agree.\nAll the orbits of the planets agree in being ellipses, as Kepler\ndiscovered; all falling bodies agree in being acted on by a uniform\nforce, as Galileo discovered; all refracted rays agree in having\nthe sines of incidence and refraction in a constant ratio, as Snell\ndiscovered; all the bodies in the universe agree in attracting each\nother, as Newton discovered; all chemical compounds agree in being\nconstituted of elements in definite proportions, as Dalton discovered.\nBut it appears to me a most scanty, vague, and incomplete account of\nthese steps in science, to say that the authors of them discovered\nsomething in which the facts in each case agreed. The point in which\nthe cases agree, is of the most diverse kind in the different cases--in\nsome, a relation of space, in others, the action of a force, in others,\nthe mode of composition of a substance;--and the point of agreement,\nvisible to the discoverer alone, does not come even into his sight,\ntill after the facts have been connected by thoughts of his own, and\nregarded in points of view in which he, by his mental acts, places\nthem. It would seem to me not much more inappropriate to say, that an\nofficer, who disciplines his men till they move together at the word of\ncommand, does so by finding something in which they agree. If the power\nof consentaneous motion did not exist in the individuals, he could not\ncreate it: but that power being there, he finds it and uses it. Of\ncourse I am aware that the parallel of the two cases is not exact; but\nin the one case, as in the other, that in which the particular things\nare found to agree, is something formed in the mind of him who brings\nthe agreement into view.\n\n\nIV. _Mr. Mill's Four Methods of Inquiry._--38. Mr. Mill has not only\nthus described the business of scientific discovery; he has also given\nrules for it, founded on this description. It may be expected that we\nshould bestow some attention upon the methods of inquiry which he thus\nproposes. I presume that they are regarded by his admirers as among the\nmost valuable parts of his book; as certainly they cannot fail to be,\nif they describe methods of scientific inquiry in such a manner as to\nbe of use to the inquirer.\n\nMr. Mill enjoins four methods of experimental inquiry, which he calls\n_the Method of Agreement_, _the Method of Difference_, _the Method\nof Residues_, and _the Method of Concomitant Variations_[271]. They\nare all described by formul\u00e6 of this kind:--Let there be, in the\nobserved facts, combinations of antecedents, _ABC_, _BC_, _ADE_, &c.\nand combinations of corresponding consequents, _abc_, _bc_, _ade_, &c.;\nand let the object of inquiry be, the consequence of some cause _A_, or\nthe cause of some consequence _a_. The Method of Agreement teaches us,\nthat when we find by experiment such facts as _abc_ the consequent of\n_ABC_, and _ade_ the consequent of _ADE_, then _a_ is the consequent of\n_A_. The Method of Difference teaches us that when we find such facts\nas _abc_ the consequent of _ABC_, and _bc_ the consequent of _BC_, then\n_a_ is the consequent of _A_. The Method of Residues teaches us, that\nif _abc_ be the consequent of _ABC_, and if we have already ascertained\nthat the effect of _A_ is _a_, and the effect of _B_ is _b_, then we\nmay infer that the effect of _C_ is _c_. The Method of Concomitant\nVariations teaches us, that if a phenomenon _a_ varies according as\nanother phenomenon _A_ varies, there is some connexion of causation\ndirect or indirect, between _A_ and _a_.\n\n39. Upon these methods, the obvious thing to remark is, that they take\nfor granted the very thing which is most difficult to discover, the\nreduction of the phenomena to formul\u00e6 such as are here presented to\nus. When we have any set of complex facts offered to us; for instance,\nthose which were offered in the cases of discovery which I have\nmentioned,--the facts of the planetary paths, of falling bodies, of\nrefracted rays, of cosmical motions, of chemical analysis; and when, in\nany of these cases, we would discover the law of nature which governs\nthem, or, if any one chooses so to term it, the feature in which all\nthe cases agree, where are we to look for our _A_, _B_, _C_ and _a_,\n_b_, _c_? Nature does not present to us the cases in this form; and\nhow are we to reduce them to this form? You say, _when_ we find the\ncombination of _ABC_ with _abc_ and _ABD_ with _abd_, then we may\ndraw our inference. Granted: but when and where are we to find such\ncombinations? Even now that the discoveries are made, who will point\nout to us what are the _A_, _B_, _C_ and _a_, _b_, _c_ elements of the\ncases which have just been enumerated? Who will tell us which of the\nmethods of inquiry those historically real and successful inquiries\nexemplify? Who will carry these formul\u00e6 through the history of the\nsciences, as they have really grown up; and show us that these four\nmethods have been operative in their formation; or that any light is\nthrown upon the steps of their progress by reference to these formul\u00e6?\n\n40. Mr. Mill's four methods have a great resemblance to Bacon's\n\"Prerogatives of Instances;\" for example, the Method of Agreement to\nthe _Instanti\u00e6 Ostensiv\u00e6_; the Method of Differences to the _Instanti\u00e6\nAbsenti\u00e6 in Proximo_, and the _Instanti\u00e6 Crucis_; the Method of\nConcomitant Variations to the _Instanti\u00e6 Migrantes_. And with regard to\nthe value of such methods, I believe all study of science will convince\nus more and more of the wisdom of the remarks which Sir John Herschel\nhas made upon them[272].\n\n\"It has always appeared to us, we must confess, that the help which\nthe classification of instances under their different titles of\nprerogative, affords to inductions, however just such classification\nmay be in itself, is yet more apparent than real. The force of the\ninstance must be felt in the mind before it can be referred to\nits place in the system; and before it can be either referred or\nappreciated it must be known; and when it _is_ appreciated, we are\nready enough to weave our web of induction, without greatly troubling\nourselves whence it derives the weight we acknowledge it to have in our\ndecisions.... No doubt such instances as these are highly instructive;\nbut the difficulty in physics is to find such, not to perceive their\nforce when found.\"\n\n\nV. _His Examples._--41. If Mr. Mill's four methods had been applied by\nhim in his book to a large body of conspicuous and undoubted examples\nof discovery, well selected and well analysed, extending along the\nwhole history of science, we should have been better able to estimate\nthe value of these methods. Mr. Mill has certainly offered a number\nof examples of his methods; but I hope I may say, without offence,\nthat they appear to me to be wanting in the conditions which I have\nmentioned. As I have to justify myself for rejecting Mr. Mill's\ncriticism of doctrines which I have put forward, and examples which I\nhave adduced, I may, I trust, be allowed to offer some critical remarks\nin return, bearing upon the examples which he has given, in order to\nillustrate his doctrines and precepts.\n\n42. The first remark which I have to make is, that a large proportion\nof his examples (i. 480, &c.) is taken from one favourite author;\nwho, however great his merit may be, is too recent a writer to have\nhad his discoveries confirmed by the corresponding investigations and\nsearching criticisms of other labourers in the same field, and placed\nin their proper and permanent relation to established truths; these\nalleged discoveries being, at the same time, principally such as deal\nwith the most complex and slippery portions of science, the laws of\nvital action. Thus Mr. Mill has adduced, as examples of discoveries,\nProf. Liebig's doctrine--that death is produced by certain metallic\npoisons through their forming indecomposable compounds; that the effect\nof respiration upon the blood consists in the conversion of peroxide\nof iron into protoxide--that the antiseptic power of salt arises from\nits attraction for moisture--that chemical action is contagious; and\nothers. Now supposing that we have no doubt of the truth of these\ndiscoveries, we must still observe that they cannot wisely be cited,\nin order to exemplify the nature of the progress of knowledge, till\nthey have been verified by other chemists, and worked into their places\nin the general scheme of chemistry; especially, since it is tolerably\ncertain that in the process of verification, they will be modified and\nmore precisely defined. Nor can I think it judicious to take so large\na proportion of our examples from a region of science in which, of all\nparts of our material knowledge, the conceptions both of ordinary\npersons, and even of men of science themselves, are most loose and\nobscure, and the genuine principles most contested; which is the case\nin physiology. It would be easy, I think, to point out the vague and\nindeterminate character of many of the expressions in which the above\nexamples are propounded, as well as their doubtful position in the\nscale of chemical generalization; but I have said enough to show why I\ncannot give much weight to these, as cardinal examples of the method\nof discovery; and therefore I shall not examine in detail how far they\nsupport Mr. Mill's methods of inquiry.\n\n43. Mr. Liebig supplies the first and the majority of Mr. Mill's\nexamples in chapter IX. of his Book on Induction. The second is\nan example for which Mr. Mill states himself to be indebted to\nMr. Alexander Bain; the law established being this, that (i. 487)\nelectricity cannot exist in one body without the simultaneous\nexcitement of the opposite electricity in some neighbouring body, which\nMr. Mill also confirms by reference to Mr. Faraday's experiments on\nvoltaic wires.\n\nI confess I am quite at a loss to understand what there is in the\ndoctrine here ascribed to Mr. Bain which was not known to the\nelectricians who, from the time of Franklin, explained the phenomena of\nthe Leyden vial. I may observe also that the mention of an \"electrified\natmosphere\" implies a hypothesis long obsolete. The essential point in\nall those explanations was, that each electricity produced by induction\nthe opposite electricity in neighbouring bodies, as I have tried to\nmake apparent in the _History_[273]. Faraday has, more recently,\nillustrated this universal co-existence of opposite electricities with\nhis usual felicity.\n\nBut the conjunction of this fact with voltaic phenomena, implies a\nnon-recognition of some of the simplest doctrines of the subject.\n\"Since,\" it is said (i. 488), \"common or machine electricity, and\nvoltaic electricity may be considered for the present purpose to be\nidentical, Faraday wished to know, &c.\" I think Mr. Faraday would be\nmuch astonished to learn that he considered electricity in equilibrium,\nand electricity in the form of a voltaic current, to be, for any\npurpose, identical. Nor do I conceive that he would assent to the\nexpression in the next page, that \"from the nature of a voltaic charge,\nthe two opposite currents necessary to the existence of each other are\nboth accommodated in one wire.\" Mr. Faraday has, as it appears to me,\nstudiously avoided assenting to this hypothesis.\n\n44. The next example is the one already so copiously dwelt upon by Sir\nJohn Herschel, Dr. Wells's researches on the production of Dew. I have\nalready said[274] that \"this investigation, although it has sometimes\nbeen praised as an original discovery, was in fact only resolving the\nphenomenon into principles already discovered namely, the doctrine of a\n_constituent temperature_ of vapour, the different conducting power of\ndifferent bodies, and the like. And this agrees in substance with what\nMr. Mill says (i. 497); that the discovery, when made, was corroborated\nby deduction from the known laws of aqueous vapour, of conduction, and\nthe like. Dr. Wells's researches on Dew tended much in this country\nto draw attention to the general principles of Atmology; and we may\nsee, in this and in other examples which Mr. Mill adduces, that the\nexplanation of special phenomena by means of general principles,\nalready established, has, for common minds, a greater charm, and\nis more complacently dwelt on, than the discovery of the general\nprinciples themselves.\n\n45. The next example, (i. 502) is given in order to illustrate the\nMethod of Residues, and is the discovery by M. Arago that a disk\nof copper affects the vibrations of the magnetic needle. But this\napparently detached fact affords little instruction compared with the\nsingularly sagacious researches by which Mr. Faraday discovered the\ncause of this effect to reside in the voltaic currents which the motion\nof the magnetic needle developed in the copper. I have spoken of this\ndiscovery in the _History_[275]. Mr. Mill however is quoting Sir John\nHerschel in thus illustrating the Method of Residues. He rightly gives\nthe Perturbations of the Planets and Satellites as better examples of\nthe method[276].\n\n46. In the next chapter (c. x.) Mr. Mill speaks of Plurality of causes\nand of the Intermixture of effects, and gives examples of such cases.\nHe here teaches (i. 517) that chemical synthesis and analysis, (as when\noxygen and hydrogen compose water, and when water is resolved into\noxygen and hydrogen,) is properly _transformation_, but that because we\nfind that the weight of the compound is equal to the sum of the weights\nof the elements, we take up the notion of chemical _composition_. I\nhave endeavoured to show[277] that the maxim, that the sum of the\nweights of the elements is equal to the weight of the compound, was,\nhistorically, not _proved_ from experiment, but _assumed_ in the\nreasonings upon experiments.\n\n47. I have now made my remarks upon nearly all the examples which Mr.\nMill gives of scientific inquiry, so far as they consist of knowledge\nwhich has really been obtained. I may mention, as points which\nappear to me to interfere with the value of Mr. Mill's references to\nexamples, expressions which I cannot reconcile with just conceptions\nof scientific truth; as when he says (i. 523), \"some other force which\n_impinges on_ the first force;\" and very frequently indeed, of the\n\"tangential _force_,\" as co-ordinate with the centripetal force.\n\nWhen he speaks (ii. 20, Note) of \"the doctrine now universally received\nthat the earth is a great natural magnet with two poles,\" he does not\nrecognize the recent theory of Gauss, so remarkably coincident with a\nvast body of facts[278]. Indeed in his statement, he rejects no less\nthe earlier views proposed by Halley, theorized by Euler, and confirmed\nby Hansteen, which show that we are compelled to assume at least _four_\npoles of terrestrial magnetism; which I had given an account of in the\nfirst edition of the _History_.\n\nThere are several other cases which he puts, in which, the knowledge\nspoken of not having been yet acquired, he tells us how he would\nset about acquiring it; for instance, if the question were (i. 526)\nwhether mercury be a cure for a given disease; or whether the brain be\na voltaic pile (ii. 21); or whether the moon be inhabited (ii. 100);\nor whether all crows are black (ii. 124); I confess that I have no\nexpectation of any advantage to philosophy from discussions of this\nkind.\n\n48. I will add also, that I do not think any light can be thrown upon\nscientific methods, at present, by grouping along with such physical\ninquiries as I have been speaking of, speculations concerning the\nhuman mind, its qualities and operations. Thus he speaks (i. 508) of\nhuman characters, as exemplifying the effect of plurality of causes;\nof (i. 518) the phenomena of our mental nature, which are analogous to\nchemical rather than to dynamical phenomena; of (i. 518) the reason why\nsusceptible persons are imaginative; to which I may add, the passage\nwhere he says (i. 444), \"let us take as an example of a phenomenon\nwhich we have no means of fabricating artificially, a human mind.\"\nThese, and other like examples, occur in the part of his work in which\nhe is speaking of scientific inquiry in general, not in the Book on the\nLogic of the Moral Sciences; and are, I think, examples more likely to\nlead us astray than to help our progress, in discovering the laws of\nScientific Inquiry, in the ordinary sense of the term.\n\n\nVI. _Mr. Mill against Hypothesis._--49. I will now pass from Mr. Mill's\nmethods, illustrated by such examples as those which I have been\nconsidering, to the views respecting the conditions of Scientific\nInduction to which I have been led, by such a survey as I could\nmake, of the whole history of the principal Inductive Sciences; and\nespecially, to those views to which Mr. Mill offers his objections[279].\n\nMr. Mill thinks that I have been too favourable to the employment\nof hypotheses, as means of discovering scientific truth; and that\nI have countenanced a laxness of method, in allowing hypotheses to\nbe established, merely in virtue of the accordance of their results\nwith the phenomena. I believe I should be as cautious as Mr. Mill, in\naccepting mere hypothetical explanations of phenomena, in any case in\nwhich we had the phenomena, and their relations, placed before both of\nus in an equally clear light. I have not accepted the Undulatory theory\nof Heat, though recommended by so many coincidences and analogies[280].\nBut I see some grave reasons for not giving any great weight to Mr.\nMill's admonitions;--reasons drawn from the language which he uses on\nthe subject, and which appears to me inconsistent with the conditions\nof the cases to which he applies it. Thus, when he says (ii. 22) that\nthe condition of a hypothesis accounting for all the known phenomena\nis \"often fulfilled equally well by two conflicting hypotheses,\" I can\nonly say that I know of no such case in the history of Science, where\nthe phenomena are at all numerous and complicated; and that if such\na case were to occur, one of the hypotheses might always be resolved\ninto the other. When he says, that \"this evidence (the agreement of the\nresults of the hypothesis with the phenomena) cannot be of the smallest\nvalue, because we cannot have in the case of such an hypothesis the\nassurance that if the hypothesis be false it must lead to results at\nvariance with the true facts,\" we must reply, with due submission, that\nwe have, in the case spoken of, the most complete evidence of this;\nfor any change in the hypothesis would make it incapable of accounting\nfor the facts. When he says that \"if we give ourselves the license\nof inventing the causes as well as their laws, a person of fertile\nimagination might devise a hundred modes of accounting for any given\nfact;\" I reply, that the question is about accounting for a large and\ncomplex series of facts, of which the laws have been ascertained: and\nas a test of Mr. Mill's assertion, I would propose as a challenge to\nany person of fertile imagination to devise any _one_ other hypothesis\nto account for the perturbations of the moon, or the coloured fringes\nof shadows, besides the hypothesis by which they have actually been\nexplained with such curious completeness. This challenge has been\nrepeatedly offered, but never in any degree accepted; and I entertain\nno apprehension that Mr. Mill's supposition will ever be verified by\nsuch a performance.\n\n50. I see additional reason for mistrusting the precision of Mr. Mill's\nviews of that accordance of phenomena with the results of a hypothesis,\nin several others of the expressions which he uses (ii. 23). He speaks\nof a hypothesis being a \"_plausible_ explanation of all or most of the\nphenomena;\" but the case which we have to consider is where it gives an\n_exact_ representation of all the phenomena in which its results can be\ntraced. He speaks of its being certain that the laws of the phenomena\nare \"_in some measure analogous_\" to those given by the hypothesis; the\ncase to be dealt with being, that they are in every way identical. He\nspeaks of this analogy being certain, from the fact that the hypothesis\ncan be \"for a moment _tenable_;\" as if any one had recommended a\nhypothesis which is tenable only while a small part of the facts\nare considered, when it is inconsistent with others which a fuller\nexamination of the case discloses. I have nothing to say, and have said\nnothing, in favour of hypotheses which are _not_ tenable. He says there\nare many such \"_harmonies_ running through the laws of phenomena in\nother respects radically distinct;\" and he gives as an instance, the\nlaws of light and heat. I have never alleged such harmonies as grounds\nof theory, unless they should amount to identities; and if they should\ndo this, I have no doubt that the most sober thinkers will suppose\nthe causes to be of the same kind in the two harmonizing instances.\nIf chlorine, iodine and brome, or sulphur and phosphorus, have, as\nMr. Mill says, analogous properties, I should call these substances\n_analogous_: but I can see no temptation to frame an hypothesis that\nthey are _identical_ (which he seems to fear), so long as Chemistry\nproves them distinct. But any hypothesis of an analogy in the\nconstitution of these elements (suppose, for instance, a resemblance\nin their atomic form or composition) would seem to me to have a fair\nclaim to trial; and to be capable of being elevated from one degree of\nprobability to another by the number, variety, and exactitude of the\nexplanations of phenomena which it should furnish.\n\n\nVII. _Against prediction of Facts._--51. These expressions of Mr.\nMill have reference to a way in which hypotheses may be corroborated,\nin estimating the value of which, it appears that he and I differ.\n\"It seems to be thought,\" he says (ii. 23), \"that an hypothesis of\nthe sort in question is entitled to a more favourable reception, if,\nbesides accounting for the facts previously known, it has led to the\nanticipation and prediction of others which experience afterwards\nverified.\" And he adds, \"Such predictions and their fulfilment are\nindeed well calculated to strike the ignorant vulgar;\" but it is\nstrange, he says, that any considerable stress should be laid upon such\na coincidence by scientific thinkers. However strange it may seem to\nhim, there is no doubt that the most scientific thinkers, far more than\nthe ignorant vulgar, have allowed the coincidence of results predicted\nby theory with fact afterwards observed, to produce the strongest\neffects upon their conviction; and that all the best-established\ntheories have obtained their permanent place in general acceptance\nin virtue of such coincidences, more than of any other evidence. It\nwas not the ignorant vulgar alone, who were struck by the return of\nHalley's comet, as an evidence of the Newtonian theory. Nor was it the\nignorant vulgar, who were struck with those facts which did so much\nstrike men of science, as curiously felicitous proofs of the undulatory\ntheory of light,--the production of darkness by two luminous rays\ninterfering in a special manner; the refraction of a single ray of\nlight into a conical pencil; and other complex yet precise results,\npredicted by the theory and verified by experiment. It must, one would\nthink, strike all persons in proportion to their thoughtfulness, that\nwhen Nature thus does our bidding, she acknowledges that we have learnt\nher true language. If we can predict new facts which we have not seen,\nas well as explain those which we have seen, it must be because our\nexplanation is not a mere formula of observed facts, but a truth of a\ndeeper kind. Mr. Mill says, \"If the laws of the propagation of light\nagree with those of the vibrations of an elastic fluid in so many\nrespects as is necessary to make the hypothesis a plausible explanation\nof all or most of the phenomena known at the time, it is nothing\nstrange that they should accord with each other in one respect more.\"\nNothing strange, if the theory be true; but quite unaccountable,\nif it be not. If I copy a long series of letters of which the last\nhalf-dozen are concealed, and if I guess those aright, as is found to\nbe the case when they are afterwards uncovered, this must be because\nI have made out the import of the inscription. To say, that because I\nhave copied all that I could see, it is nothing strange that I should\nguess those which I cannot see, would be absurd, without supposing such\na ground for guessing. The notion that the discovery of the laws and\ncauses of phenomena is a loose haphazard sort of guessing, which gives\n\"plausible\" explanations, accidental coincidences, casual \"harmonies,\"\nlaws, \"in some measure analogous\" to the true ones, suppositions\n\"tenable\" for a time, appears to me to be a misapprehension of the\nwhole nature of science; as it certainly is inapplicable to the case to\nwhich it is principally applied by Mr. Mill.\n\n52. There is another kind of evidence of theories, very closely\napproaching to the verification of untried predictions, and to which,\napparently, Mr. Mill does not attach much importance, since he has\nborrowed the term by which I have described it, _Consilience_, but\nhas applied it in a different manner (ii. 530, 563, 590). I have\nspoken, in the _Philosophy_[281], of the _Consilience of Inductions_,\nas one of the _Tests of Hypotheses_, and have exemplified it by many\ninstances; for example, the theory of universal gravitation, obtained\nby induction from the motions of the planets, was found to explain\nalso that peculiar motion of the spheroidal earth which produces the\nPrecession of the Equinoxes. This, I have said, was a striking and\nsurprising coincidence which gave the theory a stamp of truth beyond\nthe power of ingenuity to counterfeit. I may compare such occurrences\nto a case of interpreting an unknown character, in which two different\ninscriptions, deciphered by different persons, had given the same\nalphabet. We should, in such a case, believe with great confidence\nthat the alphabet was the true one; and I will add, that I believe the\nhistory of science offers no example in which a theory supported by\nsuch consiliences, had been afterwards proved to be false.\n\n53. Mr. Mill accepts (ii. 21) a rule of M. Comte's, that we may apply\nhypotheses, provided they are capable of being afterwards verified as\nfacts. I have a much higher respect for Mr. Mill's opinion than for\nM. Comte's[282]; but I do not think that this rule will be found of\nany value. It appears to me to be tainted with the vice which I have\nalready noted, of throwing the whole burthen of explanation upon the\nunexplained word _fact_--unexplained in any permanent and definite\nopposition to theory. As I have said, the Newtonian theory _is_ a\nfact. Every true theory is a fact. Nor does the distinction become\nmore clear by Mr. Mill's examples. \"The vortices of Descartes would\nhave been,\" he says, \"a perfectly legitimate hypothesis, if it had\nbeen possible by any mode of explanation which we could entertain\nthe hope of possessing, to bring the question whether such vortices\nexist or not, within the reach of our observing faculties.\" But this\nwas possible, and was done. The free passage of comets through the\nspaces in which these vortices should have been, convinced men that\nthese vortices did not exist. In like manner Mr. Mill rejects the\nhypothesis of a luminiferous ether, \"because it can neither be seen,\nheard, smelt, tasted, or touched.\" It is a strange complaint to make of\nthe vehicle of light, that it cannot be heard, smelt, or tasted. Its\nvibrations _can_ be seen. The fringes of shadows for instance, show its\nvibrations, just as the visible lines of waves near the shore show the\nundulations of the sea. Whether this can be touched, that is, whether\nit resists motion, is hardly yet clear. I am far from saying there are\nnot difficulties on this point, with regard to _all_ theories which\nsuppose a _medium_. But there are no more difficulties of this kind in\nthe undulatory theory of light, than there are in Fourier's theory of\nheat, which M. Comte adopts as a model of scientific investigation; or\nin the theory of voltaic _currents_, about which Mr. Mill appears to\nhave no doubt; or of electric _atmospheres_, which, though generally\nobsolete, Mr. Mill appears to favour; for though it had been said that\nwe _feel_ such atmospheres, no one had said that they have the other\nattributes of matter.\n\n\nVIII. _Newton's Vera Causa._--54. Mr. Mill conceives (ii. 17) that his\nown rule concerning hypotheses coincides with Newton's Rule, that the\ncause assumed must be a _vera causa_. But he allows that \"Mr. Whewell\n... has had little difficulty in showing that his (Newton's) conception\nwas neither precise nor consistent with itself.\" He also allows that\n\"Mr. Whewell is clearly right in denying it to be necessary that the\ncause assigned should be a cause already known; else how could we ever\nbecome acquainted with new causes?\" These points being agreed upon, I\nthink that a little further consideration will lead to the conviction\nthat Newton's Rule of philosophizing will best become a valuable guide,\nif we understand it as asserting that when the explanation of two or\nmore different kinds of phenomena (as the revolutions of the planets,\nthe fall of a stone, and the precession of the equinoxes,) lead us to\n_the same_ cause, such a coincidence gives a reality to the cause. We\nhave, in fact, in such a case, a Consilience of Inductions.\n\n55. When Mr. Mill condemns me (ii. 24) (using, however, expressions of\ncivility which I gladly acknowledge,) for having recognized no mode of\nInduction except that of trying hypothesis after hypothesis until one\nis found which fits the phenomena, I must beg to remind the readers of\nour works, that Mr. Mill himself allows (i. 363) that the process of\nfinding a conception which binds together observed facts \"is tentative,\nthat it consists of a succession of guesses, many being rejected until\none at last occurs fit to be chosen.\" I must remind them also that I\nhave given a Section upon the _Tests of Hypotheses_, to which I have\njust referred,--that I have given various methods of Induction, as\nthe _Method of Gradation_, the _Method of Natural Classification_,\nthe _Method of Curves_, the _Method of Means_, the _Method of Least\nSquares_, the _Method of Residues_: all which I have illustrated by\nconspicuous examples from the History of Science; besides which, I\nconceive that what I have said of the Ideas belonging to each science,\nand of the construction and explication of conceptions, will point\nout in each case, in what region we are to look for the Inductive\nElement in order to make new discoveries. I have already ventured to\nsay, elsewhere, that the methods which I have given, are as definite\nand practical as any others which have been proposed, with the\ngreat additional advantage of being the methods by which all great\ndiscoveries in science have really been made.\n\n\nIX. _Successive Generalizations._--56. There is one feature in the\nconstruction of science which Mr. Mill notices, but to which he does\nnot ascribe, as I conceive, its due importance: I mean, that process by\nwhich we not only ascend from particular facts to a general law, but\nwhen this is done, ascend from the first general law to others more\ngeneral; and so on, proceeding to the highest point of generalization.\nThis character of the scientific process was first clearly pointed\nout by Bacon, and is one of the most noticeable instances of his\nphilosophical sagacity. \"There are,\" he says, \"two ways, and can\nbe only two, of seeking and finding truth. The one from sense and\nparticulars, takes a flight to the most general axioms, and from these\nprinciples and their truth, settled once for all, invents and judges of\nintermediate axioms. The other method collects axioms from sense and\nparticulars, ascending _continuously and by degrees_, so that in the\nend it arrives at the most general axioms:\" meaning by _axioms_, laws\nor principles. The structure of the most complete sciences consists\nof several such steps,--_floors_, as Bacon calls them, of successive\ngeneralization; and thus this structure may be exhibited as a kind\nof scientific pyramid. I have constructed this pyramid in the case\nof the science of Astronomy[283]: and I am gratified to find that\nthe illustrious Humboldt approves of the design, and speaks of it as\nexecuted with complete success[284]. The capability of being exhibited\nin this form of successive generalizations, arising from particulars\nupward to some very general law, is the condition of all tolerably\nperfect sciences; and the steps of the successive generalizations are\ncommonly the most important events in the history of the science.\n\n57. Mr. Mill does not reject this process of generalization; but he\ngives it no conspicuous place, making it only one of three modes of\nreducing a law of causation into other laws. \"There is,\" he says (i.\n555), \"the _subsumption_ of one law under another; ... the gathering up\nof several laws into one more general law which includes them all. He\nadds afterwards, that the general law is the _sum_ of the partial ones\n(i. 557), an expression which appears to me inadequate, for reasons\nwhich I have already stated. The general law is not the mere sum of\nthe particular laws. It is, as I have already said, their amount _in a\nnew point of view_. A new conception is introduced; thus, Newton did\nnot merely add together the laws of the motions of the moon and of the\nplanets, and of the satellites, and of the earth; he looked at them\naltogether as the result of a universal force of mutual gravitation;\nand therein consisted his generalization. And the like might be pointed\nout in other cases.\n\n58. I am the more led to speak of Mr. Mill as not having given due\nimportance to this process of successive generalization, by the way in\nwhich he speaks in another place (ii. 525) of this doctrine of Bacon.\nHe conceives Bacon \"to have been radically wrong when he enunciates,\nas a universal rule, that induction should proceed from the lowest to\nthe middle principles, and from those to the highest, never reversing\nthat order, and consequently, leaving no room for the discovery of new\nprinciples by way of deduction[285] at all.\"\n\n59. I conceive that the Inductive Table of Astronomy, to which I have\nalready referred, shows that in that science,--the most complete which\nhas yet existed,--the history of the science has gone on, as to its\ngeneral movement, in accordance with the view which Bacon's sagacity\nenjoined. The successive generalizations, _so far as they were true_,\nwere made by successive generations. I conceive also that the Inductive\nTable of Optics shows the same thing; and this, without taking for\ngranted the truth of the Undulatory Theory; for with regard to all the\nsteps of the progress of the science, lower than that highest one,\nthere is, I conceive, no controversy.\n\n60. Also, the Science of Mechanics, although Mr. Mill more especially\nrefers to it, as a case in which the highest generalizations (for\nexample the Laws of Motion) were those earliest ascertained with any\nscientific exactness, will, I think, on a more careful examination of\nits history, be found remarkably to confirm Bacon's view. For, in that\nscience, we have, in the first place, very conspicuous examples of the\nvice of the method pursued by the ancients in flying to the highest\ngeneralizations first; as when they made their false distinctions of\nthe laws of _natural_ and _violent_ motions, and of _terrestrial_\nand _celestial_ motions. Many erroneous laws of motion were asserted\nthrough neglect of facts or want of experiments. And when Galileo and\nhis school had in some measure succeeded in discovering some of the\ntrue laws of the motions of terrestrial bodies, they did not at once\nassert them as general: for they did not at all apply those laws to\nthe celestial motions. As I have remarked, all Kepler's speculations\nrespecting the causes of the motions of the planets, went upon the\nsupposition that the First Law of terrestrial Motion did not apply to\ncelestial bodies; but that, on the contrary, some continual force was\nrequisite to keep up, as well as to originate, the planetary motions.\nNor did Descartes, though he enunciated the Laws of Motion with more\ngenerality than his predecessors, (but not with exactness,) venture\nto trust the planets to those laws; on the contrary, he invented his\nmachinery of Vortices in order to keep up the motions of the heavenly\nbodies. Newton was the first who extended the laws of terrestrial\nmotion to the celestial spaces; and in doing so, he used all the laws\nof the celestial motions which had previously been discovered by\nmore limited inductions. To these instances, I may add the gradual\ngeneralization of the Third Law of motion by Huyghens, the Bernoullis,\nand Herman, which I have described in the _History_[286] as preceding\nthat Period of Deduction, to which the succeeding narrative[287] is\nappropriated. In Mechanics, then, we have a cardinal example of the\nhistorically gradual and successive ascent of science from particulars\nto the most general laws.\n\n61. The Science of Hydrostatics may appear to offer a more favourable\nexample of the ascent to the most general laws, without going through\nthe intermediate particular laws; and it is true, with reference\nto this science, as I have observed[288], that it does exhibit the\n_peculiarity_ of our possessing the most general principles on which\nthe phenomena depend, and from which many cases of special facts are\nexplained by deduction; while other cases cannot be so explained,\nfrom the want of principles intermediate between the highest and the\nlowest. And I have assigned, as the reason of this peculiarity, that\nthe general principles of the Mechanics of Fluids were not obtained\nwith reference to the science itself, but by extension from the sister\nscience of the Mechanics of Solids. The two sciences are parts of the\nsame Inductive Pyramid; and having reached the summit of this Pyramid\non one side, we are tempted to descend on the other from the highest\ngenerality to more narrow laws. Yet even in this science, the best\npart of our knowledge is mainly composed of inductive laws, obtained\nby inductive examination of particular classes of facts. The mere\nmathematical investigations of the laws of waves, for instance, have\nnot led to any results so valuable as the experimental researches of\nBremontier, Emy, the Webers, and Mr. Scott Russell. And in like manner\nin Acoustics, the Mechanics of Elastic Fluids[289], the deductions of\nmathematicians made on general principles have not done so much for\nour knowledge, as the cases of vibrations of plates and pipes examined\nexperimentally by Chladni, Savart, Mr. Wheatstone and Mr. Willis. We\nsee therefore, even in these sciences, no reason to slight the wisdom\nwhich exhorts us to ascend from particulars to intermediate laws,\nrather than to hope to deduce these latter better from the more general\nlaws obtained once for all.\n\n62. Mr. Mill himself indeed, notwithstanding that he slights Bacon's\ninjunction to seek knowledge by proceeding from less general to more\ngeneral laws, has given a very good reason why this is commonly\nnecessary and wise. He says (ii. 526), \"Before we attempt to explain\ndeductively, from more general laws, any new class of phenomena, it is\ndesirable to have gone as far as is practicable in ascertaining the\nempirical laws of these phenomena; so as to compare the results of\ndeduction, not with one individual instance after another, but with\ngeneral propositions expressive of the points of agreement which have\nbeen found among many instances. For,\" he adds with great justice,\n\"if Newton had been obliged to verify the theory of gravitation, not\nby deducing from it Kepler's laws, but by deducing all the observed\nplanetary positions which had served Kepler to establish those laws,\nthe Newtonian theory would probably never have emerged from the state\nof an hypothesis.\" To which we may add, that it is certain, from the\nhistory of the subject, that in that case the hypothesis would never\nhave been framed at all.\n\n\nX. _Mr. Mill's Hope from Deduction._--63. Mr. Mill expresses a hope\nof the efficacy of Deduction, rather than Induction, in promoting\nthe future progress of Science; which hope, so far as the physical\nsciences are concerned, appears to me at variance with all the lessons\nof the history of those sciences. He says (i. 579), \"that the advances\nhenceforth to be expected even in physical, and still more in mental\nand social science, will be chiefly the result of deduction, is evident\nfrom the general considerations already adduced:\" these considerations\nbeing, that the phenomena to be considered are very complex, and are\nthe result of many known causes, of which we have to disentangle the\nresults.\n\n64. I cannot but take a very different view from this. I think that\nany one, looking at the state of physical science, will see that there\nare still a vast mass of cases, in which we do not at all know the\ncauses, at least, in their full generality; and that the knowledge of\nnew causes, and the generalization of the laws of those already known,\ncan only be obtained by new _inductive_ discoveries. Except by new\nInductions, equal, in their efficacy for grouping together phenomena\nin new points of view, to any which have yet been performed in the\nhistory of science, how are we to solve such questions as those which,\nin the survey of what we already know, force themselves upon our minds?\nSuch as, to take only a few of the most obvious examples--What is the\nnature of the connexion of heat and light? How does heat produce the\nexpansion, liquefaction and vaporization of bodies? What is the nature\nof the connexion between the optical and the chemical properties of\nlight? What is the relation between optical, crystalline and chemical\npolarity? What is the connexion between the atomic constitution and\nthe physical qualities of bodies? What is the tenable definition of a\nmineral species? What is the true relation of the apparently different\ntypes of vegetable life (monocotyledons, dicotyledons, and cryptogamous\nplants)? What is the relation of the various types of animal life\n(vertebrates, articulates, radiates, &c.)? What is the number, and\nwhat are the distinctions of the Vital Powers? What is the internal\nconstitution of the earth? These, and many other questions of equal\ninterest, no one, I suppose, expects to see solved by deduction from\nprinciples already known. But we can, in many of them, see good hope of\nprogress by a large use of induction; including, of course, copious and\ncareful experiments and observations.\n\n65. With such questions before us, as have now been suggested, I\ncan see nothing but a most mischievous narrowing of the field and\nenfeebling of the spirit of scientific exertion, in the doctrine that\n\"Deduction is the great scientific work of the present and of future\nages;\" and that \"A revolution is peaceably and progressively effecting\nitself in philosophy the reverse of that to which Bacon has attached\nhis name.\" I trust, on the contrary, that we have many new laws of\nnature still to discover; and that our race is destined to obtain a\nsight of wider truths than any we yet discern, including, as cases, the\ngeneral laws we now know, and obtained from these known laws as they\nmust be, by Induction.\n\n66. I can see, however, reasons for the comparatively greater favour\nwith which Mr. Mill looks upon Deduction, in the views to which he has\nmainly directed his attention. The explanation of remarkable phenomena\nby known laws of Nature, has, as I have already said, a greater charm\nfor many minds than the discovery of the laws themselves. In the case\nof such explanations, the problem proposed is more definite, and the\nsolution more obviously complete. For the process of induction includes\na mysterious step, by which we pass from particulars to generals,\nof which step the reason always seems to be inadequately rendered\nby any words which we can use; and this step to most minds is not\ndemonstrative, as to few is it given to perform it on a great scale.\nBut the process of explanation of facts by known laws is deductive,\nand has at every step a force like that of demonstration, producing\na feeling peculiarly gratifying to the clear intellects which are\nmost capable of following the process. We may often see instances in\nwhich this admiration for deductive skill appears in an extravagant\nmeasure; as when men compare Laplace with Newton. Nor should I think\nit my business to argue against such a preference, unless it were\nlikely to leave us too well satisfied with what we know already, to\nchill our hope of scientific progress, and to prevent our making any\nfurther strenuous efforts to ascend, higher than we have yet done, the\nmountain-chain which limits human knowledge.\n\n67. But there is another reason which, I conceive, operates in leading\nMr. Mill to look to Deduction as the principal means of future progress\nin knowledge, and which is a reason of considerable weight in the\nsubjects of research which, as I conceive, he mainly has in view. In\nthe study of our own minds and of the laws which govern the history of\nsociety, I do not think that it is very likely that we shall hereafter\narrive at any wider principles than those of which we already possess\nsome considerable knowledge; and this, for a special reason; namely,\nthat our knowledge in such cases is not gathered by mere external\nobservation of a collection of external facts; but acquired by\nattention to internal facts, our own emotions, thoughts, and springs of\naction; facts are connected by ties existing in our own consciousness,\nand not in mere observed juxtaposition, succession, or similitude.\nHow the character, for instance, is influenced by various causes, (an\nexample to which Mr. Mill repeatedly refers, ii. 518, &c.), is an\ninquiry which may perhaps be best conducted by considering what we know\nof the influence of education and habit, government and occupation,\nhope and fear, vanity and pride, and the like, upon men's characters,\nand by tracing the various effects of the intermixture of such\ninfluences. Yet even here, there seems to be room for the discovery\nof laws in the way of experimental inquiry: for instance, what share\nrace or family has in the formation of character; a question which can\nhardly be solved to any purpose in any other way than by collecting\nand classing instances. And in the same way, many of the principles\nwhich regulate the material wealth of states, are obtained, if not\nexclusively, at least most clearly and securely, by induction from\nlarge surveys of facts. Still, however, I am quite ready to admit that\nin Mental and Social Science, we are much less likely than in Physical\nScience, to obtain new truths by any process which can be distinctively\ntermed _Induction_; and that in those sciences, what may be called\n_Deductions_ from principles of thought and action of which we are\nalready conscious, or to which we assent when they are felicitously\npicked out of our thoughts and put into words, must have a large share;\nand I may add, that this observation of Mr. Mill appears to me to be\nimportant, and, in its present connexion, new.\n\n\nXI. _Fundamental opposition of our doctrines._--68. I have made nearly\nall the remarks which I now think it of any consequence to make upon\nMr. Mill's _Logic_, so far as it bears upon the doctrines contained\nin my _History_ and _Philosophy_. And yet there remains still\nuntouched one great question, involving probably the widest of all the\ndifferences between him and me. I mean the question whether geometrical\naxioms, (and, as similar in their evidence to these, _all_ axioms,) be\ntruths derived from experience, or be necessary truths in some deeper\nsense. This is one of the fundamental questions of philosophy; and all\npersons who take an interest in metaphysical discussions, know that the\ntwo opposite opinions have been maintained with great zeal in all ages\nof speculation. To me it appears that there are _two_ distinct elements\nin our knowledge, Experience, without, and the Mind, within. Mr. Mill\nderives all our knowledge from Experience _alone_. In a question thus\ngoing to the root of all knowledge, the opposite arguments must needs\ncut deep on both sides. Mr. Mill cannot deny that our knowledge of\ngeometrical axioms and the like, _seems_ to be _necessary_. I cannot\ndeny that our knowledge, axiomatic as well as other, _never is_\nacquired _without experience_.\n\n69. Perhaps ordinary readers may despair of following our reasonings,\nwhen they find that they can only be made intelligible by supposing,\non the one hand, a person who thinks distinctly and yet has never seen\nor felt any external object; and on the other hand, a person who is\ntransferred, as Mr. Mill supposes (ii. 117), to \"distant parts of the\nstellar regions where the phenomena may be entirely unlike those with\nwhich we are acquainted,\" and where even the axiom, that every effect\nmust have a cause, does not hold good. Nor, in truth, do I think it\nnecessary here to spend many words on this subject. Probably, for those\nwho take an interest in this discussion, most of the arguments on each\nside have already been put forwards with sufficient repetition. I have,\nin an \"Essay on the Fundamental Antithesis of Philosophy,\" and in some\naccompanying \"Remarks,\" printed[290] at the end of the second edition\nof my _Philosophy_, given my reply to what has been said on this\nsubject, both by Mr. Mill, and by the author of a very able critique on\nmy _History_ and _Philosophy_ which appeared in the _Quarterly Review_\nin 1841: and I will not here attempt to revive the general discussion.\n\n70. Perhaps I may be allowed to notice, that in one part of Mr. Mill's\nwork where this subject is treated, there is the appearance of one of\nthe parties to the controversy pronouncing judgment in his own cause.\nThis indeed is a temptation which it is especially difficult for an\nauthor to resist, who writes a treatise upon _Fallacies_, the subject\nof Mr. Mill's fifth Book. In such a treatise, the writer has an easy\nway of disposing of adverse opinions by classing them as \"Fallacies,\"\nand putting them side by side with opinions universally acknowledged to\nbe false. In this way, Mr. Mill has dealt with several points which are\nstill, as I conceive, matters of controversy (ii. 357, &c.).\n\n71. But undoubtedly, Mr. Mill has given his argument against my\nopinions with great distinctness in another place (i. 319). In order\nto show that it is merely habitual association which gives to an\nexperimental truth the character of a necessary truth, he quotes\nthe case of the laws of motion, which were really discovered from\nexperiment, but are now looked upon as the only conceivable laws; and\nespecially, what he conceives as \"the _reductio ad absurdum_ of the\ntheory of inconceivableness,\" an opinion which I had ventured to throw\nout, that if we could conceive the Composition of bodies distinctly,\nwe might be able to see that it is necessary that the modes of their\ncomposition should be definite. I do not think that readers in general\nwill see anything absurd in the opinion, that the laws of Mechanics,\nand even the laws of the Chemical Composition of bodies, may depend\nupon principles as necessary as the properties of space and number; and\nthat this necessity, though not at all perceived by persons who have\nonly the ordinary obscure and confused notions on such subjects, may\nbe evident to a mind which has, by effort and discipline, rendered its\nideas of Mechanical Causation, Elementary Composition and Difference of\nKind, clear and precise. It may easily be, I conceive, that while such\nnecessary principles are perceived to be necessary only by a few minds\nof highly cultivated insight, such principles as the axioms of Geometry\nand Arithmetic may be perceived to be necessary by _all_ minds which\nhave any habit of abstract thought at all: and I conceive also, that\nthough these axioms are brought into distinct view by a certain degree\nof intellectual cultivation, they may still be much better described\nas conditions of experience, than as results of experience:--as laws\nof the mind and of its activity, rather than as facts impressed upon a\nmind merely passive.\n\n\nXII. _Absurdities in Mr. Mill's Logic._--72. I will not pursue the\nsubject further: only, as the question has arisen respecting the\nabsurdities to which each of the opposite doctrines leads, I will point\nout opinions connected with this subject, which Mr. Mill has stated in\nvarious parts of his book.\n\nHe holds (i. 317) that it is merely from habit that we are unable to\nconceive the _last point_ of space or the _last instant_ of time.\nHe holds (ii. 360) that it is strange that any one should rely upon\nthe _\u00e0 priori_ evidence that space or extension is infinite, or that\nnothing can be made of nothing. He holds (i. 304) that the first law\nof _motion_ is _rigorously true_, but that the axioms respecting\nthe _lever_ are only _approximately_ true. He holds (ii. 110) that\nthere may be sidereal firmaments in which events succeed each other\nat random, without obeying any laws of causation; although one might\nsuppose that even if space and cause are both to have their limits,\nstill they might terminate together: and then, even on this bold\nsupposition, we should no _where_ have a world in which events were\n_casual_. He holds (ii. 111) that the axiom, that every event must\nhave a cause, is established by means of an \"induction by simple\nenumeration:\" and in like manner, that the principles of number and\nof geometry are proved by this method of simple enumeration alone. He\nascribes the proof (i. 162) of the axiom, \"things which are equal to\nthe same are equal to each other,\" to the fact that this proposition\nhas been perpetually _found_ true and never false. He holds (i. 338)\nthat \"In all propositions concerning numbers, a condition is implied,\nwithout which none of them would be true; and that condition is an\nassumption which _may be false_. _The condition is that_ 1 = 1.\"\n\n73. Mr. Mill further holds (i. 309), that it is a characteristic\nproperty of geometrical forms, that they are capable of being painted\nin the imagination with a distinctness equal to reality:--that our\nideas of forms exactly resemble our sensations: which, it is implied,\nis not the case with regard to any other class of our ideas;--that we\nthus may have mental pictures of all possible combinations of lines\nand angles, which are as fit subjects of geometrical experimentation\nas the realities themselves. He says, that \"we know that the imaginary\nlines exactly resemble real ones;\" and that we obtain this knowledge\nrespecting the characteristic property of the idea of space by\nexperience; though it does not appear _how_ we can compare our _ideas_\nwith the _realities_, since we know the realities only _by_ our ideas;\nor why this property of their resemblance should be confined to _one\nclass_ of ideas alone.\n\n74. I have now made such remarks as appear to me to be necessary, on\nthe most important parts of Mr. Mill's criticism of my _Philosophy_. I\nhope I have avoided urging any thing in a contentious manner; as I have\ncertainly written with no desire of controversy, but only with a view\nto offer to those who may be willing to receive it, some explanation of\nportions of my previous writings. I have already said, that if this had\nnot have been my especial object, I could with pleasure have noted the\npassages of Mr. Mill's _Logic_ which I admire, rather than the points\nin which we differ. I will in a very few words refer to some of these\npoints, as the most agreeable way of taking leave of the dispute.\n\nI say then that Mr. Mill appears to me especially instructive in\nhis discussion of the nature of the proof which is conveyed by the\nsyllogism; and that his doctrine, that the force of the syllogism\nconsists in an _inductive assertion, with an interpretation added\nto it_, solves very happily the difficulties which baffle the\nother theories of this subject. I think that this doctrine of his\nis made still more instructive, by his excepting from it the cases\nof Scriptural Theology and of Positive Law (i. 260), as cases in\nwhich general propositions, not particular facts, are our original\ndata. I consider also that the recognition of _Kinds_ (i. 166) as\nclasses in which we have, not a finite but an _inexhaustible_ body of\nresemblances among individuals, and as groups made by nature, not by\nmere definition, is very valuable, as stopping the inroad to an endless\ntrain of false philosophy. I conceive that he takes the right ground\nin his answer to Hume's argument against miracles (ii. 183): and I\nadmire the acuteness with which he has criticized Laplace's tenets on\nthe Doctrine of Chances, and the candour with which he has, in the\nsecond edition, acknowledged oversights on this subject made in the\nfirst. I think that much, I may almost say all, which he says on the\nsubject of Language, is very philosophical; for instance, what he says\n(ii. 238) of the way in which words acquire their meaning in common\nuse. I especially admire the acuteness and force with which he has\nshown (ii. 255) how moral principles expressed in words degenerate into\nformulas, and yet how the formula cannot be rejected without a moral\nloss. This \"perpetual oscillation in spiritual truths,\" as he happily\nterms it, has never, I think, been noted in the same broad manner,\nand is a subject of most instructive contemplation. And though I have\nmyself refrained from associating moral and political with physical\nscience in my study of the subject, I see a great deal which is full of\npromise for the future progress of moral and political knowledge in Mr.\nMill's sixth Book, \"On the Logic of the Moral and Political Sciences.\"\nEven his arrangement of the various methods which have been or may\nbe followed in \"the Social Science,\"--\"the Chemical or Experimental\nMethod,\" \"the Geometrical or Abstract Method,\" \"the Physical or\nConcrete Deductive Method,\" \"the Inverse Deductive or Historical\nMethod,\" though in some degree fanciful and forced, abounds with\nvaluable suggestions; and his estimate of \"the interesting philosophy\nof the Bentham school,\" the main example of \"the geometrical method,\"\nis interesting and philosophical. On some future occasion, I may,\nperhaps, venture into the region of which Mr. Mill has thus essayed\nto map the highways: for it is from no despair either of the great\nprogress to be made in such truth as that here referred to, or of the\neffect of philosophical method in arriving at such truth, that I have,\nin what I have now written, confined myself to the less captivating but\nmore definite part of the subject.\n\n\nFOOTNOTES:\n\n[Footnote 264: [_A System of Logic, Ratiocinative and Inductive, being\na connected view of the Principles of Evidence, and of the Methods of\nScientific Investigation._ By John Stuart Mill.]]\n\n[Footnote 265: These Remarks were published in 1849, under the title\n_Of Induction, with especial reference to Mr. J. S. Mill's System of\nLogic_.]\n\n[Footnote 266: My references are throughout (except when otherwise\nexpressed) to the volume and the page of Mr. Mill's first edition of\nhis _Logic_.]\n\n[Footnote 267: On this subject see an Essay _On the Transformation of\nHypotheses_, given in the Appendix.]\n\n[Footnote 268: B. vii. c. iii. sect. 3.]\n\n[Footnote 269: B. iii. c. ix. art. 7.]\n\n[Footnote 270: B. i. c. iii.]\n\n[Footnote 271: B. iii. c. viii.]\n\n[Footnote 272: _Discourse_, Art. 192.]\n\n[Footnote 273: B. xi. c. xi.]\n\n[Footnote 274: _Phil._ b. xiii. c. ix. art. 7.]\n\n[Footnote 275: B. xiii. c. viii.]\n\n[Footnote 276: Given also in the _Phil. Ind. Sc._ b. xiii. c. vii.\nsect. 17.]\n\n[Footnote 277: _Ibid._ b. vi. c. iv.]\n\n[Footnote 278: See _Hist. Ind. Sc._ b. xii. note D, in the second\nedition.]\n\n[Footnote 279: There are some points in my doctrines on the subject\nof the Classificatory Sciences to which Mr. Mill objects, (ii. 314,\n&c.), but there is nothing which I think it necessary to remark here,\nexcept one point. After speaking of Classification of organized beings\nin general, Mr. Mill notices (ii. 321) as an additional subject, the\narrangement of natural groups into a Natural Series; and he says, that\n\"all who have attempted a theory of natural arrangement, including\namong the rest Mr. Whewell, have stopped short of this: all except M.\nComte.\" On this I have to observe, that I stopped short of, or rather\npassed by, the doctrine of a Series of organized beings, because I\nthought it bad and narrow philosophy: and that I sufficiently indicated\nthat I did this. In the _History_ (b. xvi. c. vi.) I have spoken of the\ndoctrine of Circular Progression propounded by Mr. Macleay, and have\nsaid, \"so far as this view _negatives_ a mere _linear_ progression in\nnature, which would place each genus in contact with the preceding and\nsucceeding ones, and so far as it requires us to attend to the more\nvaried and ramified resemblances, there can be no doubt that it is\nsupported by the result of all the attempts to form natural systems.\"\nAnd with regard to the difference between Cuvier and M. de Blainville,\nto which Mr. Mill refers (ii. 321), I certainly cannot think that M.\nComte's suffrage can add any weight to the opinion of either of those\ngreat naturalists.]\n\n[Footnote 280: _Hist. Ind. Sc._ b. x. note (VA) in the second edition.]\n\n[Footnote 281: B. xi. c. v. art. 11.]\n\n[Footnote 282: I have given elsewhere (see last chapter) reasons why I\ncannot assign to M. Comte's _Philosophie Positive_ any great value as a\ncontribution to the philosophy of science. In this judgment I conceive\nthat I am supported by the best philosophers of our time. M. Comte\nowes, I think, much of the notice which has been given to him to his\nincluding, as Mr. Mill does, the science of society and of human nature\nin his scheme, and to his boldness in dealing with these. He appears\nto have been received with deference as a mathematician: but Sir John\nHerschel has shown that a supposed astronomical discovery of his is a\nmere assumption. I conceive that I have shown that his representation\nof the history of science is erroneous, both in its details and in its\ngeneralities. His distinction of the three stages of sciences, the\ntheological, metaphysical, and positive, is not at all supported by the\nfacts of scientific history. Real discoveries always involve what he\ncalls _metaphysics_; and the doctrine of final causes in physiology,\nthe main element of science which can properly be called _theological_,\nis retained at the end, as well as the beginning of the science, by all\nexcept a peculiar school.]\n\n[Footnote 283: I have also, in the same place, given the Inductive\nPyramid for the science of Optics. These Pyramids are necessarily\ninverted in their form, in order that, in reading in the ordinary way,\nwe may proceed _to_ the vertex. _Phil. Ind. Sc._ b. xi. c. vi.]\n\n[Footnote 284: _Cosmos_, vol. ii. note 35.]\n\n[Footnote 285: The reader will probably recollect that as _Induction_\nmeans the inference of general propositions from particular cases,\n_Deduction_ means the inference by the application of general\npropositions to particular cases, and by combining such applications;\nas when from the most general principles of Geometry or of Mechanics,\nwe prove some less general theorem; for instance, the number of the\npossible regular solids, or the principle of _vis viva_.]\n\n[Footnote 286: B. vi. c. v.]\n\n[Footnote 287: c. vi.]\n\n[Footnote 288: _Hist._ b. vi. c. vi. sect. 13.]\n\n[Footnote 289: _Hist. Ind. Sc._ b. viii.]\n\n[Footnote 290: Reprinted in the Appendix to this volume.]\n\n\n\n\nCHAPTER XXIII.\n\nPOLITICAL ECONOMY AS AN INDUCTIVE SCIENCE.\n\n\n(_Moral Sciences._)--1. Both M. Comte and Mr. Mill, in speaking of the\nmethods of advancing science, aim, as I have said, at the extension of\ntheir methods to moral subjects, and aspire to suggest means for the\naugmentation of our knowledge of ethical, political, and social truths.\nI have not here ventured upon a like extension of my conclusions,\nbecause I wished to confine my views of the philosophy of discovery\nto the cases in which all allow that solid and permanent discoveries\nhave been made. Moreover in the case of moral speculations, we have\nto consider not only observed external facts and the ideas by which\nthey are colligated, but also internal facts, in which the instrument\nof observation is consciousness, and in which observations and ideas\nare mingled together, and act and react in a peculiar manner. It may\ntherefore be doubted whether the methods which have been effectual\nin the discovery of physical theories will not require to be greatly\nmodified, or replaced by processes altogether different, when we would\nmake advances in ethical, political, or social knowledge. In ethics, at\nleast, it seems plain that we must take our starting-point not without\nbut within us. Our mental powers, our affections, our reason, and any\nother faculties which we have, must be the basis of our convictions.\nAnd in this field of knowledge, the very form of our highest\npropositions is different from what it is in the physical sciences. In\nPhysics we examine what _is_, in a form more or less general: in Ethics\nwe seek to determine what OUGHT _to be_, as the highest rule, which is\nsupreme over all others. In this case we cannot expect the methods of\nphysical discovery to aid us.\n\nBut others of the subjects which I have mentioned, though strongly\nmarked and influenced by this ethical element, are still of a mixed\ncharacter, and require also observation of external facts of human,\nindividual, and social conduct, and generalizations derived from\nsuch observations. The facts of political constitutions and social\nrelations in communities of men, and the histories of such communities,\nafford large bodies of materials for political and social science;\nand it seems not at all unlikely that such science may be governed,\nin its formation and progress, by laws like those which govern the\nphysical sciences, and may be steered clear of errors and directed\ntowards truths by an attention to the forms which error and truth have\nassumed in the most stable and certain sciences. The different forms\nof society, and the principal motives which operate upon men regarded\nin masses, may be classified as facts; and though our consciousness of\nwhat we ourselves are and the affections which we ourselves feel are\nalways at work in our interpretations of such facts, yet the knowledge\nwhich we thus obtain may lead us to bodies of knowledge which we may\ncall _Sciences_, and compare with the other sciences as to their form\nand maxims.\n\n\n(_Political Economy._)--2. Among such bodies of knowledge, I may notice\nas a specimen, the science of _Political Economy_, and may compare it\nwith other sciences in the respects which have been referred to.\n\nM. Comte has given a few pages to the discussion of this science of\nPolitical Economy[291]; but what he has said amounts only to a few\nvague remarks on Adam Smith and Destutt de Tracy; his main object\nbeing, it would seem, to introduce his usual formula, and to condemn\nall that has hitherto been done (with which there is no evidence that\nhe is adequately acquainted) as worthless, because it is \"theological,\"\n\"metaphysical,\" \"literary,\" and not \"_positive_.\"\n\nMr. Mill has much more distinctly characterized the plan and form\nof Political Economy in his system[292]. He regards this science as\nthat which deals with the results which take place in human society\nin consequence of the desire of wealth. He explains, however, that\nit is only for the sake of convenience that one of the motives which\noperate upon man is thus insulated and treated as if it were the only\none:--that there are other principles, for instance, the principles on\nwhich the progress of population depends, which co-operate with the\nmain principle, and materially modify its results: and he gives reasons\nwhy this mode of simplifying the study of social phenomena tends to\npromote the progress of systematic knowledge.\n\nInstead of discussing these reasons, I will notice the way in which the\nspeculations of political economists have exemplified tendencies to\nerror, and corrections of those tendencies, of the same nature as those\nwhich we have already noticed in speaking of other sciences.\n\n\n(_Wages, Profits, and Rent._)--3. We may regard as one of the first\nimportant steps in this science, Adam Smith's remark, that the value\nor price of any article bought and sold consists of three elements,\n_Wages_, _Profits_, and _Rent_. Some of the most important of\nsubsequent speculations were attempts to determine the laws of each of\nthese three elements. At first it might be supposed that there ought to\nbe added to them a fourth element, _Materials_. But upon consideration\nit will be seen that materials, as an element of price, resolves itself\ninto wages and rent; for all materials derive their value from the\nlabour which is bestowed upon them. The iron of the ploughshare costs\njust what it costs to sink the mine, dig up and smelt the iron. The\nwood of the frame costs what it costs to cut down the tree, together\nwith the rent of the ground on which it grows.\n\n\n(_Premature Generalizations._)--4. But what determines Wages?--The\namount of persons seeking work, that is, speaking loosely, the\npopulation; and the amount of money which is devoted to the payment of\nwages. And what determines the population? It was replied,--the means\nof subsistence. And how does the population tend to increase?--In a\ngeometrical ratio. And how does the subsistence tend to increase?--At\nmost in an arithmetical ratio. And hence it was inferred that the\npopulation tends constantly to run beyond the means of subsistence,\nand will be limited by a threatened deficiency of these means. And\nthe wages paid must be such as to form this limit. And therefore the\nwages paid will always be such as just to keep up the population in its\nordinary state of progress. Here was one general proposition which was\ngathered from summary observations of society.\n\nAgain: as to Rent: Adam Smith had treated Rent as if it were a monopoly\nprice--the result of a monopoly of the land by the landowners. But\nsubsequent writers acutely remarked that land is of various degrees of\nfertility, and there is some land which barely pays the cultivator, if\ncultivating it he pay no rent. And rent can be afforded for other land\nonly in so far as it is better than this bad land. And thus, there was\nobtained another general proposition; that the Rent of good land was\njust equal to the excess of its produce over the worst cultivable land.\n\nNow these two propositions are examples of a hasty and premature\ngeneralization, like that from which the sweeping physical systems\nof antiquity were derived. They were examples of that process which\nFrancis Bacon calls _anticipation_; in which we leap at once from a few\nfacts to propositions of the highest generality; and supposing these\nto be securely established, proceed to draw a body of conclusions from\nthem, and thus frame a system.\n\nAnd what is the sounder and wiser mode of proceeding in order to obtain\na science of such things? We must classify the facts which we observe,\nand take care that we do not ascribe to the facts in our immediate\nneighbourhood or specially under our notice, a generality of prevalence\nwhich does not belong to them. We must proceed by the ladder of\nInduction, and be sure we have obtained the narrower generalizations,\nbefore we aspire to the widest.\n\n\n(_Correction of them by Induction. Rent._)--5. For instance; in the\ncase of the latter of the above two propositions--that Rent is the\nexcess of the produce of good soils over the worst--that is the case\nin England and Scotland; but is it the case in other countries? Let us\nsee. Why is it the case in England? Because if the rent demanded for\ngood land were _more_ than the excess of the produce over bad land, the\nfarmer would prefer the bad land as more gainful. If the rent demanded\nfor good land were _less_ than the excess, the bad land would be\nabandoned by the farmer.\n\nBut all this goes upon the supposition that the farmer can remove from\ngood land to bad, or from bad to good, or apply his capital in some\nother way than farming, according as it is more gainful. This is true\nin England; but is it true all over the world?\n\nBy no means. It is true in scarcely any other part of the world. In\nalmost every other part of the world the cultivator is bound to the\nland, so that he cannot remove himself and his capital from it; and\ncannot, because he is not satisfied with his position upon it, seek and\nfind a position and a subsistence elsewhere. On the contrary, he is\nbound by the laws and customs of the country, by constitution, history\nand character, so that he cannot, or can only with great difficulty,\nchange his plan and mode of life. And thus over great part of the world\nthe fundamental supposition on which rests the above generalization\nrespecting Rent is altogether false.\n\nAn able political economist[293] has taken the step, which as we have\nsaid, sound philosophy would have prescribed: he has classified the\nstates of society which exist or have existed on the earth, as they\nbear on this point, the amount of Rent. He has classified the modes\nin which the produce is, in different countries and different stages\nof society, divided between the cultivator and the proprietor: and he\nfinds that the natural divisions are these:--_Serf Rents_, that is,\nlabour rents paid by the Cultivator to the Landowner, as in Russia:\n_M\u00e9tayer Rents_, where the produce is divided between the Cultivator\nand the Landowner, as in Central Europe: _Ryot Rents_, where a portion\nof the produce is paid to the Sovereign as Landlord, as in India:\n_Cottier Rents_, where a money-rent is paid by a Cultivator who raises\nhis own subsistence from the soil; and _Farmers' Rents_, where a\ncovenanted Rent is paid by a person employing labourers. In this last\ncase alone is it true that the Rent is equal to the excess of good over\nbad soils.\n\nThe error of the conclusion, in this case, arises from assuming the\nmobility of capital and labour in cases in which it is not moveable:\nwhich is much as if mechanicians had reasoned respecting rigid bodies,\nsupposing them to be fluid bodies.\n\nBut the error of method was in not classifying the facts of societies\nbefore jumping to a conclusion which was to be applicable to all\nsocieties.\n\n\n(_Wages._)--6. And in like manner there is an error of the same kind\nin the assertion of the other general principles:--that wages are\ndetermined by the capital which is forthcoming for the payment of\nwages; and that population is determined in its progress by wages. For\nthere is a vast mass of population on the surface of the earth which\ndoes not live upon wages: and though in England the greater part of the\npeople lives upon wages, in the rest of the world the part that does so\nis small. And in this case, as in the other, we must class these facts\nas they exist in different nations, before we can make assertions of\nany wide generality.\n\nMr. Jones[294] classed the condition of labourers in different\ncountries in the same inductive manner in which he classed the tenure\nof land. He pointed out that there are three broad distinct classes\nof them: _Unhired Labourers_, who cultivate the ground which they\noccupy, and live on _self-produced wages_; _Paid Dependants_, who are\npaid out of the _revenue_ or income of their employers, as the military\nretainers and domestic artizans of feudal times in Europe, and the\ngreater part of the people of Asia at the present day; and _Hired\nLabourers_, who are paid wages from _capital_.\n\nThis last class, though taken as belonging to the normal condition of\nsociety by many political economists, is really the exceptional case,\ntaking the world at large; and no propositions concerning the structure\nand relations of ranks in society can have any wide generality which\nare founded on a consideration of this case alone.\n\n\n(_Population._)--7. And again: with regard to the proposition that\nthe progress of population depends merely on the rate of wages, a\nvery little observation of different communities, and of the same\ncommunities at different times, will show that this is a very rash and\nhasty generalization. When wages rise, whether or not population shall\nundergo a corresponding increase depends upon many other circumstances\nbesides this single fact of the increase of wages. The effect of a\nrise of wages upon population is affected by the form of the wages,\nthe time occupied by the change, the institutions of the society\nunder consideration, and other causes: and a due classification of\nthe conditions of the society according to these circumstances, is\nrequisite in order to obtain any general proposition concerning the\neffect of a rise or fall of wages upon the progress of the population.\n\nAnd thus those precepts of the philosophy of discovery which we have\nrepeated so often, which are so simple, and which seem so obvious,\nhave been neglected or violated in the outset of Political Economy as\nin so many other sciences:--namely, the precepts that we must classify\nour facts before we generalize, and seek for narrower generalizations\nand inductions before we aim at the widest. If these maxims had been\nobeyed, they would have saved the earlier speculators on this subject\nfrom some splendid errors; but, on the other hand, it may be said, that\nif these earlier speculators had not been thus bold, the science could\nnot so soon have assumed that large and striking form which made it so\nattractive, and to which it probably owes a large part of its progress.\n\n\nFOOTNOTES:\n\n[Footnote 291: _Phil. Pos._ t. iv. p. 264.]\n\n[Footnote 292: _Logic_, b. vi. c. 3.]\n\n[Footnote 293: Jones, _On Rent_, 1833.]\n\n[Footnote 294: _Literary Remains_, 1859.]\n\n\n\n\nCHAPTER XXIV.\n\nMODERN GERMAN PHILOSOPHY[295].\n\n\nI. _Science is the Idealization of Facts._\n\n1. I have spoken, a few chapters back, of the Reaction against the\ndoctrines of the Sensational School in England and France. In Germany\nalso there was a Reaction against these doctrines;--but there, this\nmovement took a direction different from its direction in other\ncountries. Omitting many other names, Kant, Fichte, Schelling and Hegel\nmay be regarded as the writers who mark, in a prominent manner, this\nGermanic line of speculation. The problem of philosophy, in the way in\nwhich they conceived it, may best be explained by reference to that\nFundamental Antithesis of which I had occasion to speak in the _History\nof Scientific Ideas_[296]. And in order to characterize the steps taken\nby these modern German philosophers, I must return to what I have said\nconcerning the Fundamental Antithesis.\n\nThis Antithesis, as I have there remarked, is stated in various\nways:--as the Antithesis of Thoughts and Things; of Ideas and\nSensations; of Theory and Facts; of Necessary Truth and Experience; of\nthe Subjective and Objective elements of our knowledge; and in other\nphrases. I have further remarked that the elements thus spoken of,\nthough opposed, are inseparable. We cannot have the one without the\nother. We cannot have thoughts without thinking of Things: we cannot\nhave things before us without thinking of them.\n\nFurther, it has been shown, I conceive, that our knowledge derives\nfrom the former of these two elements, namely our Ideas, its form\nand character of knowledge; our ideas being the necessary _Forms_ of\nknowledge, while the _Matter_ of our knowledge in each case is supplied\nby the appropriate perception or outward experience.\n\nThus our Ideas of Space and Time are the necessary Forms of our\ngeometrical and arithmetical knowledge; and no sensations or experience\nare needed as the matter of such knowledge, except in so far as\nsensation and experience are needed to evoke our Ideas in any degree.\nAnd hence these sciences are sometimes called _Formal_ sciences. All\nother Sciences involve, along with the experience and observation\nappropriate to each, a development of the ideal conditions of knowledge\nexisting in our minds; and I have given the history, both of this\ndevelopment of ideas and of the matter derived from experience, in two\nformer works, the _History of Scientific Ideas_, and the _History of\nthe Inductive Sciences_. I have there traced this history through the\nwhole body of the physical sciences.\n\nBut though Ideas and Perceptions are thus separate elements in our\nphilosophy, they cannot in fact be distinguished and separated, but are\ndifferent aspects of the same thing. And the only way in which we can\napproach to truth is by gradually and successively, in one instance\nafter another, advancing from the perception to the idea; from the fact\nto the theory.\n\n2. I would now further observe, that in this progression from fact\nto theory, we advance (when the theory is complete and completely\npossessed by the mind) from the apprehension of truths as _actual_ to\nthe apprehension of them as _necessary_; and thus Facts which were\noriginally observed merely as Facts become the consequences of theory,\nand are thus brought within the domain of Ideas. That which was a part\nof the objective world becomes also a part of the subjective world; a\nnecessary part of the thoughts of the theorist. And in this way the\nprogress of true theory is the _Idealization of Facts_.\n\nThus the Progress of Science consists in a perpetual reduction of Facts\nto Ideas. Portions are perpetually transferred from one side to another\nof the Fundamental Antithesis: namely, from the Objective to the\nSubjective side. The Centre or Fulcrum of the Antithesis is shifted by\nevery movement which is made in the advance of science, and is shifted\nso that the ideal side gains something from the real side.\n\n3. I will proceed to illustrate this Proposition a little further.\nNecessary Truths belong to the Subjective, Observed Facts to the\nObjective side of our knowledge. Now in the progress of that exact\nspeculative knowledge which we call Science, Facts which were at a\nprevious period merely Observed Facts, come to be known as Necessary\nTruths; and the attempts at new advances in science generally introduce\nthe representation of known truths of fact, as included in higher and\nwider truths, and therefore, so far, necessary.\n\nWe may exemplify this progress in the history of the science of\nMechanics. Thus the property of the lever, the inverse proportion of\nthe weights and arms, was known as a fact before the time of Aristotle,\nand known as no more; for he gives many fantastical and inapplicable\nreasons for the fact. But in the writings of Archimedes we find this\nfact brought within the domain of necessary truth. It was there\ntransferred from the empirical to the ideal side of the Fundamental\nAntithesis; and thus a progressive step was made in science. In like\nmanner, it was at first taken by Galileo as a mere fact of experience,\nthat in a falling body, the velocity increases in proportion to the\ntime; but his followers have seen in this the necessary effect of the\nuniform force of gravity. In like manner, Kepler's empirical Laws were\nshown by Newton to be necessary results of a central force attracting\ninversely as the square of the distance. And if it be still, even at\npresent, doubtful whether this is the _necessary_ law of a central\nforce, as some philosophers have maintained that it is, we cannot doubt\nthat if now or hereafter, those philosophers could establish their\ndoctrine as certain, they would make an important step in science, in\naddition to those already made.\n\nAnd thus, such steps in science are made, whenever empirical facts\nare discerned to be necessary laws; or, if I may be allowed to use a\nbriefer expression, whenever _facts are idealized_.\n\n4. In order to show how widely this statement is applicable, I will\nexemplify it in some of the other sciences.\n\nIn Chemistry, not to speak of earlier steps in the science, which\nmight be presented as instances of the same general process, we may\nremark that the analyses of various compounds into their elements,\naccording to the quantity of the elements, form a vast multitude of\nfacts, which were previously empirical only, but which are reduced\nto a law, and therefore to a certain kind of ideal necessity, by the\ndiscovery of their being compounded according to definite and multiple\nproportions. And again, this very law of definite proportions, which\nmay at first be taken as a law given by experience only, it has been\nattempted to make into a necessary truth, by asserting that bodies\nmust necessarily consist of atoms, and atoms must necessarily combine\nin definite small numbers. And however doubtful this Atomic Theory may\nat present be, it will not be questioned that any chemical philosopher\nwho could establish it, or any other Theory which would produce an\nequivalent change in the aspect of the science, would make a great\nscientific advance. And thus, in this Science also, the Progress of\nScience consists in the transfer of facts from the empirical to the\nnecessary side of the antithesis; or, as it was before expressed, in\nthe idealization of facts.\n\n5. We may illustrate the same process in the Natural History\nSciences. The discovery of the principle of Morphology in plants\nwas the reduction of a vast mass of Facts to an _Idea_; as Schiller\nsaid to G\u00f6the when he explained the discovery; although the latter,\ncherishing a horror of the term _Idea_, which perhaps is quite as\ncommon in England as in Germany, was extremely vexed at being told\nthat he possessed such furniture in his mind. The applications of this\nPrinciple to special cases, for instance, to Euphorbia by Brown, to\nReseda by Lindley, have been attempts to idealize the facts of these\nspecial cases.\n\n6. We may apply the same view to steps in Science which are still\nunder discussion;--the question being, whether an advance has really\nbeen made in science or not. For instance, in Astronomy, the Nebular\nHypothesis has been propounded, as an explanation of many of the\nobserved phenomena of the Universe. If this Hypothesis could be\nconceived ever to be established as a true Theory, this must be done\nby its taking into itself, as necessary parts of the whole Idea, many\nFacts which have already been observed; such as the various form of\nnebul\u00e6;--many Facts which it must require a long course of years to\nobserve, such as the changes of nebul\u00e6 from one form to another;--and\nmany facts which, so far as we can at present judge, are utterly\nat variance with the Idea, such as the motions of satellites, the\nrelations of the material elements of planets, the existence of\nvegetable and animal life upon their surfaces. But if all these Facts,\nwhen fully studied, should appear to be included in the general Idea\nof Nebular Condensation according to the Laws of Nature, the Facts\nso idealized would undoubtedly constitute a very remarkable advance\nin science. But then, we are to recollect that we are not to suppose\nthat the Facts will agree with the Idea, merely because the Idea,\nconsidered by itself, and without carefully attending to the Facts,\nis a large and striking Idea. And we are also to recollect that the\nFacts may be compared with another Idea, no less large and striking;\nand that if we take into our account, (as, in forming an Idea of the\nCourse of the Universe, we must do,) not only vegetable and animal,\nbut also _human_ life, this other Idea appears likely to take into it\na far larger portion of the known Facts, than the Idea of the Nebular\nHypothesis. The other Idea which I speak of is the Idea of Man as the\nprincipal Object in the Creation; to whose sustenance and development\nthe other parts of the Universe are subservient as means to an end; and\nalthough, in our attempts to include all known Facts in this Idea, we\nagain meet with many difficulties, and find many trains of Facts which\nhave no apparent congruity with the Idea; yet we may say that, taking\ninto account the Facts of man's intellectual and moral condition, and\nhis history, as well as the mere Facts of the material world, the\ndifficulties and apparent incongruities are far less when we attempt\nto idealize the Facts by reference to this Idea, of Man as the End of\nCreation, than according to the other Idea, of the World as the result\nof Nebular Condensation, without any conceivable End or Purpose. I am\nnow, of course, merely comparing these two views of the Universe, as\nsupposed steps in science, according to the general notion which I\nhave just been endeavouring to explain, that a step in science is some\nIdealization of Facts.\n\n7. Perhaps it will be objected, that what I have said of the\nIdealization of Facts, as the manner in which the progress of science\ngoes on, amounts to no more than the usual expressions, that the\nprogress of science consists in reducing Facts to Theories. And to this\nI reply, that the advantage at which I aim, by the expression which\nI have used, is this, to remind the reader, that Fact and Theory, in\nevery subject, are not marked by separate and prominent features of\ndifference, but only by their present opposition, which is a transient\nrelation. They are related to each other no otherwise than as the poles\nof the fundamental antithesis: the point which separates those poles\nshifts with every advance of science; and then, what was Theory becomes\nFact. As I have already said elsewhere, a true Theory is a Fact; a Fact\nis a familiar Theory. If we bear this in mind, we express the view\non which I am now insisting when we say that the progress of science\nconsists in reducing Facts to Theories. But I think that speaking of\n_Ideas_ as opposed to Facts, we express more pointedly the original\nAntithesis, and the subsequent identification of the Facts with the\nIdea. The expression appears to be simple and apt, when we say, for\ninstance, that the Facts of Geography are identified with the Idea\nof globular Earth; the Facts of Planetary Astronomy with the Idea of\nthe Heliocentric system; and ultimately, with the Idea of Universal\nGravitation.\n\n8. We may further remark, that though by successive steps in science,\nsuccessive Facts are reduced to Ideas, this process can never be\ncomplete. However the point may shift which separates the two poles,\nthe two poles will always remain. However, far the ideal element may\nextend, there will always be something beyond it. However far the\nphenomena may be idealized, there will always remain some which are\nnot idealized, and which are mere phenomena. This also is implied\nby making our expressions refer to the fundamental antithesis: for\nbecause the antithesis _is_ fundamental, its two elements will always\nbe present; the objective as well as the subjective. And thus, in the\ncontemplation of the universe, however much we understand, there must\nalways be something which we do not understand; however far we may\ntrace necessary truths, there must always be things which are to our\napprehension arbitrary: however far we may extend the sphere of our\ninternal world, in which we feel power and see light, it must always\nbe surrounded by our external world, in which we see no light, and\nonly feel resistance. Our subjective being is inclosed in an objective\nshell, which, though it seems to yield to our efforts, continues entire\nand impenetrable beyond our reach, and even enlarges in its extent\nwhile it appears to give up to us a portion of its substance.\n\n\nII. _Successive German Philosophies._\n\n9. The doctrine of the Fundamental Antithesis of two elements of which\nthe union is involved in all knowledge, and of which the separation\nis the task of all philosophy, affords us a special and distinct mode\nof criticizing the philosophies which have succeeded each other in the\nworld; and we may apply it to the German Philosophies of which we have\nspoken.\n\nThe doctrine of the Fundamental Antithesis is briefly this:\n\n_That in every act of knowledge (1) there are two opposite elements\nwhich we may call Ideas and Perceptions; but of which the opposition\nappears in various other antitheses; as Thoughts and Things, Theories\nand Facts, Necessary Truths and Experiential Truths; and the like: (2)\nthat our knowledge derives from the former of these elements, namely\nour Ideas, its form and character as knowledge, our Ideas of space\nand time being the necessary forms, for instance, of our geometrical\nand arithmetical knowledge; (3) and in like manner, all our other\nknowledge involving a development of the ideal conditions of knowledge\nexisting in our minds: (4) but that though ideas and perceptions are\nthus separate elements in our philosophy, they cannot, in fact, be\ndistinguished and separated, but are different aspects of the same\nthing; (5) that the only way in which we can approach to truth is by\ngradually and successively, in one instance after another, advancing\nfrom the perception to the idea; from the fact to the theory; from\nthe apprehension of truths as actual to the apprehension of them as\nnecessary. (6) This successive and various progress from fact to theory\nconstitutes the history of science; (7) and this progress, though\nalways leading us nearer to that central unity of which both the idea\nand the fact are emanations, can never lead us to that point, nor to\nany measurable proximity to it, or definite comprehension of its place\nand nature._\n\n10. Now the doctrine being thus stated, successive sentences of the\nstatement contain successive steps of German philosophy, as it has\nappeared in the series of celebrated authors whom I have named.\n\nIdeas, and Perceptions or Sensations, being regarded as the two\nelements of our knowledge, Locke, or at least the successors of\nLocke, had rejected the former element, Ideas, and professed to\nresolve all our knowledge into Sensation. After this philosophy had\nprevailed for a time, Kant exposed, to the entire conviction of the\ngreat body of German speculators, the untenable nature of this account\nof our knowledge. He taught (one of the first sentences of the above\nstatement) that (2) _Our knowledge derives from our Ideas its form\nand character as knowledge; our Ideas of space and time being, for\ninstance, the necessary forms of our geometrical and arithmetical\nknowledge_. Fichte carried still further this view of our knowledge,\nas derived from our Ideas, or from its nature as knowledge; and held\nthat (3) _all our knowledge is a development of the ideal conditions of\nknowledge existing in our minds_ (one of our next following sentences).\nBut when the ideal element of our knowledge was thus exclusively\ndwelt upon, it was soon seen that this ideal system no more gave a\ncomplete explanation of the real nature of knowledge, than the old\nsensational doctrine had done. Both elements, Ideas and Sensations,\nmust be taken into account. And this was attempted by Schelling, who,\nin his earlier works, taught (as we have also stated above) that (4)\n_Ideas and Facts are different aspects of the same thing_:--this thing,\nthe central basis of truth in which both elements are involved and\nidentified, being, in Schelling's language, the _Absolute_, while each\nof the separate elements is subjected to _conditions_ arising from\ntheir union. But this Absolute, being a point inaccessible to us, and\ninconceivable by us, as _our_ philosophy teaches (as above), cannot\nto any purpose be made the basis of our philosophy: and accordingly\nthis _Philosophy of the Absolute_ has not been more permanent than\nits predecessors. Yet the philosophy of Hegel, which still has a wide\nand powerful sway in Germany, is, in the main, a development of the\nsame principle as that of Schelling;--the identity of the idea and the\nfact; and Hegel's _Identity-System_, is rather a more methodical and\ntechnical exposition of Schelling's Philosophy of the Absolute than\na new system. But Hegel traces the manifestation of the identity of\nthe idea and fact in the _progress_ of human knowledge; and thus in\nsome measure approaches to our doctrine (above stated), that (5) _the\nway in which we approach to truth is by gradually and successively, in\none instance after another_, that is, _historically, advancing from\nthe perception to the idea, from the fact to the theory_: while at the\nsame time Hegel has not carried out this view in any comprehensive or\ncomplete manner, so as to show that (6) _this process constitutes the\nhistory of science_: and as with Schelling, his system shows an entire\nwant of the conviction (above expressed as part of our doctrine),\n(7) that _we can never, in our speculations reach or approach to the\ncentral unity of which both idea and fact are emanations_.\n\n11. This view of the relation of the Sensational School, of the Schools\nof Kant, Fichte, Schelling, and Hegel, and of the fundamental defects\nof all, may be further illustrated. It will, of course, be understood\nthat our illustration is given only as a slight and imperfect sketch of\nthese philosophies; but their relation may perhaps become more apparent\nby the very brevity with which it is stated; and the object of the\npresent chapter is not the detailed criticism of systems, but this very\nrelation of systems to each other.\n\nThe actual and the ideal, the external and the internal elements\nof knowledge, were called by the Germans the _objective_ and the\n_subjective_ elements respectively. The forms of knowledge and\nespecially space and time, were pronounced by Kant to be essentially\n_subjective_; and this view of the nature of knowledge, more fully\nunfolded and extended to all knowledge, became the _subjective\nideality_ of Fichte. But the subjective and the objective are, as\nwe have said, in their ultimate and supreme form, one; and hence\nwe are told of the _subjective-objective_, a phrase which has also\nbeen employed by Mr. Coleridge. Fichte had spoken of the subjective\nelement as the _Me_, (das Ich); and of the objective element as the\n_Not-me_, (das Nicht-Ich); and has deduced the _Not-me_ from the _Me_.\nSchelling, on the contrary, laboured with great subtlety to deduce\nthe _Me_ from the _Absolute_ which includes both. And this Absolute,\nor Subjective-objective, is spoken of by Schelling as unfolding itself\ninto endless other antitheses. It was held that from the assumption of\nsuch a principle might be deduced and explained the oppositions which,\nin the contemplation of nature, present themselves at every step, as\nleading points of general philosophy:--for example, the opposition\nof matter as _passive_ and _active_, as _dead_ and _organized_,\nas _unconscious_ or _conscious_; the opposition of _individual_\nand _species_, of _will_ and _moral rule_. And this antithetical\ndevelopment was carried further by Hegel, who taught that the Absolute\nIdea developes itself so as to assume qualities, limitations, and\nseeming oppositions, and then completes the cycle of its development by\nreturning into unity.\n\n12. That there is, in the history of Science, much which easily lends\nitself to such a formula, the views which I have endeavoured to\nexpound, show and exemplify in detail. But yet the attempts to carry\nthis view into detail by conjecture--by a sort of divination--with\nlittle or no attention to the historical progress and actual\ncondition of knowledge, (and such are those which have been made by\nthe philosophers whom I have mentioned,) have led to arbitrary and\nbaseless views of almost every branch of knowledge. Such oppositions\nand differences as are found to exist in nature, are assumed as the\nrepresentatives of the elements of necessary antitheses, in a manner\nin which scientific truth and inductive reasoning are altogether\nslighted. Thus, this peculiar and necessary antithetical character is\nassumed to be displayed in attraction and repulsion, in centripetal and\ncentrifugal forces, in a supposed positive and negative electricity,\nin a supposed positive and negative magnetism; in still more doubtful\npositive and negative elements of light and heat; in the different\nelements of the atmosphere, which are, quite groundlessly, assumed to\nhave a peculiar antithetical character: in animal and vegetable life:\nin the two sexes; in gravity and light. These and many others, are\ngiven by Schelling, as instances of the radical opposition of forces\nand elements which necessarily pervades all nature. I conceive that the\nheterogeneous and erroneous principles involved in these views of the\nmaterial world show us how unsafe and misleading is the philosophical\nassumption on which they rest. And the Triads of Hegel, consisting of\nThesis, Antithesis, and Union, are still more at variance with all\nsound science. Thus we are told that matter and motion are determined\nas _inertia_, _impulsion_, _fall_; that Absolute Mechanics determines\nitself as _centripetal force_, _centrifugal force_, _universal\ngravitation_. Light, it is taught, is a secondary determination of\nmatter. Light is the most intimate element of nature, and might be\ncalled _the Me_ of nature: it is limited by what we may call negative\nlight, which is darkness.\n\n13. In these rash and blind attempts to construct physical science\n_\u00e0 priori_, we may see how imperfect the Hegelian doctrines are as\na complete philosophy. In the views of moral and political subjects\nthe results of such a scheme are naturally less obviously absurd, and\nmay often be for a moment striking and attractive, as is usually the\ncase with attempts to reduce history to a formula. Thus we are told\nthat _the State_ appears under the following determinations:--first\nas one, substantial, self-included: next, varied, individual, active,\ndisengaging itself from the substantial and motionless unity: next,\nas two principles, altogether distinct, and placed front to front in\na marked and active opposition: then, arising out of the ruins of the\npreceding, the idea appears afresh, one, identical, harmonious. And the\nEast, Greece, Rome, Germany, are declared to be the historical forms\nof these successive determinations. Whatever amount of real historical\ncolour there may be for this representation, it will hardly, I think,\nbe accepted as evidence of a profound political philosophy; but on such\nparts of the subject I shall not here dwell.\n\n14. I may observe that in the series of philosophical systems now\ndescribed, the two elements of the Fundamental Antithesis are\nalternately dwelt upon in an exaggerated degree, and then confounded.\nThe Sensational School could see in human knowledge nothing but\nfacts: Kant and Fichte fixed their attention almost entirely upon\nideas: Schelling and Hegel assume the identity of the two, (a point\nwe never can reach,) as the origin of their philosophy. The external\nworld in Locke's school was all in all. In the speculations of\nKant this external world became a dim and unknown region. Things\nwere acknowledged to be _something_ in themselves, but _what_, the\nphilosopher could not tell. Besides the _ph\u00e6nomenon_ which we see, Kant\nacknowledged a _noumenon_ which we think of; but this assumption, for\nsuch it is, exercises no influence upon his philosophy.\n\n15. We may for the sake of illustration imagine to ourselves each\nsystem of philosophy as a Drama in which _Things_ are the _Dramatis\nPerson\u00e6_ and the _Idea_ which governs the system is the _Plot_ of the\ndrama. In Kant's Drama, Things in themselves are merely a kind of 'Mute\nPersonages,' \u03ba\u03c9\u03c6\u1f70 \u03c0\u03c1\u03cc\u03c3\u03c9\u03c0\u03b1, which stand on the stage to be pointed at\nand talked about, but which do not tell us anything, or enter into the\naction of the piece. Fichte carries this further, and if we go on with\nthe same illustration, we may say that he makes the whole drama into\na kind of Monologue; in which the author tells the story, and merely\nnames the persons who appear. If we would still carry on the image,\nwe may say that Schelling, going upon the principle that the whole of\nthe drama is merely a progress to the Denouement, which denouement\ncontains the result of all the preceding scenes and events, starts\nwith the last scene of the piece; and bringing all the characters on\nthe stage in their final attitudes, would elicit the story from this.\nWhile the true mode of proceeding is, to follow the drama Scene by\nScene, learning as much as we can of the Action and the Characters,\nbut knowing that we shall not be allowed to see the Denouement, and\nthat to do so is probably not the lot of our species on earth. So far\nas any philosopher has thus followed the historical progress of the\ngrand spectacle offered to the eyes of speculative man, in which the\nPhenomena of Nature are the Scenes, and the Theory of them the Plot, he\nhas taken the course by which knowledge really has made its advances.\nBut those who have partially done this, have often, like Hegel, assumed\nthat they had divined the whole course and end of the story, and have\nthus criticised the scenes and the characters in a spirit quite at\nvariance with that by which any real insight into the import of the\nrepresentation can be obtained.\n\nIf it be asked which position we can assign, in this dramatic\nillustration, to those who hold that all our knowledge is derived from\nfacts only, and who reject the supposition of ideas; we may say that\nthey look on with a belief that the drama has _no_ plot, and that these\nscenes are improvised without connexion or purpose.\n\n16. I will only offer one more illustration of the relative position\nof these successive philosophies. Kant compares the change which he\nintroduced into philosophy to the change which Copernicus introduced\ninto astronomical theory. When Copernicus found that nothing could be\nmade of the phenomena of the heavens so long as everything was made\nto turn round the spectator, he tried whether the matter might not be\nbetter explained if he made the spectator turn, and left the stars\nat rest. So Kant conceives that our experience is regulated by our\nown faculties, as the phenomena of the heavens are regulated by our\nown motions. But accepting and carrying out this illustration, we may\nsay that Kant, in explaining the phenomena of the heavens by means\nof the motions of the earth, has almost forgotten that the planets\nhave their own proper motions, and has given us a system which hardly\nexplains anything besides broadest appearances, such as the annual and\ndaily motions of the sun; and that Fichte appears as if he wished to\ndeduce all the motions of the planets, as well as of the sun, from the\nconditions of the spectator;--while Schelling goes to the origin of\nthe system, like Descartes, and is not content to show how the bodies\nmove, without also proving that from some assumed original condition,\nall the movements and relations of the system must necessarily be what\nthey are. It may be that a theory which explains how the planets,\nwith their orbits and accompaniments, have come into being, may offer\nitself to bold speculators, like those who have framed and produced\nthe nebular hypothesis. But I need not remind my readers either how\nprecarious such a hypothesis is; or, that if it be capable of being\nconsidered probable, its proofs must gradually dawn upon us, step by\nstep, age after age: and that a system of doctrine which assumes such\na scheme as a certain and fundamental truth, and deduces the whole of\nastronomy from it, must needs be arbitrary, and liable to the gravest\nerror at every step. Such a precarious and premature philosophy, at\nbest, is that of Schelling and Hegel; especially as applied to those\nsciences in which, by the past progress of all sure knowledge, we are\ntaught what the real cause and progress of knowledge is: while at the\nsame time we may allow that all these forms of philosophy, since they\ndo recognize the condition and motion of the spectator, as a necessary\nelement in the explanation of the phenomena, are a large advance upon\nthe Ptolemaic scheme--the view of those who appeal to phenomena alone\nas the source of our knowledge, and say that the sun, the moon, and\nthe planets move as we see them move, and that all further theory is\nimaginary and fantastical.\n\n\nFOOTNOTES:\n\n[Footnote 295: The substance of this and the next chapter was printed\nas a communication to the Cambridge Phil. Soc. in 1840.]\n\n[Footnote 296: Or in the earlier editions, in the _Philosophy of the\nInductive Sciences_.]\n\n\n\n\nCHAPTER XXV.\n\nTHE FUNDAMENTAL ANTITHESIS AS IT EXISTS IN THE MORAL WORLD.\n\n\n1. We have hitherto spoken of the Fundamental Antithesis as the ground\nof our speculations concerning the material world, at least mainly.\nWe have indeed been led by the physical sciences, and especially by\nBiology, to the borders of Psychology. We have had to consider not only\nthe mechanical effects of muscular contraction, but the sensations\nwhich the nerves receive and convey:--the way in which sensations\nbecome perceptions; the way in which perceptions determine actions. In\nthis manner we have been led to the subject of volition or will[297],\nand this brings us to a new field of speculation, the moral nature of\nman; and this moral nature is a matter not only of speculative but\nof practical interest. On this subject I shall make only a few brief\nremarks.\n\n2. Even in the most purely speculative view, the moral aspect of man's\nnature differs from the aspect of the material universe, in this\nrespect, that in the moral world, external events are governed in\nsome measure by the human will. When we speculate concerning the laws\nof material nature, we suppose that the phenomena of nature follow a\ncourse and order which we may perhaps, in some measure, discover and\nunderstand, but which we cannot change or control. But when we consider\nman as an agent, we suppose him able to determine some at least of the\nevents of the external world; and thus, able to determine the actions\nof other men, and to lay down laws for them. He cannot alter the\nproperties of fire and metals, stones and fluids, air and light; but he\ncan use fire and steel so as to compel other men's actions; stone-walls\nand ocean-shores so as to control other men's motions; gold and gems\nso as to have a hold on other men's desires; articulate sounds and\nintelligible symbols so as to direct other men's thoughts and move\ntheir will. There is an external world of Facts; and in this, the Facts\nare such as he makes them by his Acts.\n\n3. But besides this, there is also, standing over against this external\nworld of Facts, an internal world of Ideas. The Moral Acts without are\nthe results of Moral Ideas within. Men have an Idea of Justice, for\ninstance, according to which they are led to external acts, as to use\nforce, to make a promise, to perform a contract, as individuals; or to\nmake war and peace, to enact laws and to execute them, as a nation.\n\n4. Some such internal moral Idea necessarily exists, along with\nall properly human actions. Man feels not only pain and anger, but\nindignation and the sentiment of wrong, which feelings imply a moral\nidea of right and wrong. Again, what he thinks of as wrong, he tries to\nprevent; what he deems right, he attempts to realize. The Idea gives\na character to the Act; the Act embodies the Idea. In the moral world\nas in the natural world, the Antithesis is universal and inseparable.\nIt is an Antithesis of inseparable elements. In human action, there is\never involved the Idea of what is right, and the external Act in which\nthis idea is in some measure embodied.\n\n5. But the moral Ideas, such as that of Justice, of Rightness, and\nthe like, are always embodied incompletely in the world of external\naction. Although men's actions are to a great extent governed by the\nIdeas of Justice, Rightness and the like; (for it must be recollected\nthat we include in their actions, laws, and the enforcement of laws;)\nyet there is a large portion of human actions which is not governed by\nsuch ideas: (actions which result from mere desire, and violations of\nlaw). There is a perpetual Antithesis of Ideas and Facts, which is the\nfundamental basis of moral as of natural philosophy. In the former as\nin the latter subject, besides what is ideal, there is an Actual which\nthe ideal does not include. This Actual is the region in which the\nresults of mere desire, of caprice, of apparent accident, are found. It\nis the region of history, as opposed to justice; it is the region of\nwhat _is_, as distinct from what _ought_ to be.\n\n6. Now what I especially wish here to remark, is this;--that the\nprogress of man as a moral being consists in a constant extension of\nthe Idea into the region of Facts. This progress consists in making\nhuman actions conform more and more to the moral Ideas of Justice,\nRightness, and the like; including in human actions, as we have said,\nLaws, the enforcement of Laws, and other collective acts of bodies of\nmen. The History of Man _as_ Man consists in this extension of moral\nIdeas into the region of Facts. It is not that the actual history of\nwhat men do has always consisted in such an extension of moral Ideas;\nfor there has ever been, in the actual doings of men, a large portion\nof facts which had no moral character; acts of desire, deeds of\nviolence, transgressions of acknowledged law, and the like. But such\nevents are not a part of the genuine progress of humanity. They do\nnot belong to the history of man as man, but to the history of man as\nbrute. On the other hand, there are events which belong to the history\nof man as man, events which belong to the genuine progress of humanity;\nsuch as the establishment of just laws; their enforcement; their\nimprovement by introducing into them a fuller measure of moral Ideas.\nBy such means there is a constant progress of man as a moral being.\nBy this _realization of moral Ideas_ there is a constant progress of\nHumanity.\n\n7. I have made this reflection, because it appears to me to bring\ninto view an analogy between the Progress of Science and the Progress\nof Man, or of Humanity, in the sense in which I have used the term.\nIn both these lines of Progress, Facts are more and more identified\nwith Ideas. In both, there is a fundamental Antithesis of Ideas\nand Facts, and progress consists in a constant advance of the point\nwhich separates the two elements of this Antithesis. In both, Facts\nare constantly won over to the domain of Ideas. But still, there is\na difference in the two cases; for in the one case the Facts are\nbeyond our control. We cannot make them other than they are; and all\nthat we can do, if we can do that, is to shape our Ideas so that they\nshall coincide with the Facts, and still have the manifest connexion\nwhich belongs to them as Ideas. In the other case, the Facts are, to\na certain extent, in our power. They are what we make them, for they\nare what we do. In this case, the Facts ought to come towards the\nIdeas, rather than the Ideas towards the Facts. As we called the former\nprocess the Idealization of Facts, we may call this the Realization of\nIdeas; and the analogy which I have here wished to bring into view may\nbe expressed by saying, that the Progress of Physical Science consists\nin a constant successive Idealization of Physical Facts; and the\nProgress of man's Moral Being is a constant successive Realization of\nMoral Ideas.\n\n8. Thus the necessary co-existence of an objective and a subjective\nelement belongs not only to human knowledge, as was before explained,\nbut also to human action. The objective and the subjective element are\ninseparable in this case as in the other. We have always the Fact of\nPositive Law, along with the Idea of Absolute Justice; the Facts of\nGain or Loss, along with the Idea of Rights. The Idea of Justice is\ninseparable from historical facts, for justice gives to each his own,\nand history determines what that is. We cannot even conceive justice\nwithout society, or society without law, and thus in the moral and in\nthe natural world the fundamental antithesis is inseparable, even in\nthought. The two elements must always subsist; for however far the\nmoral ideas be realized in the world, there will always remain much in\nthe world which is not conformable to moral ideas, even if it were only\nthrough its necessary dependence on an unmoral and immoral past. As\nin the physical world so in the moral, however much the ideal sphere\nexpands, it is surrounded by a region which is not conformable to the\nidea, although in one case the expansion takes place by educing ideas\nout of facts, in the other, by producing facts from ideas.\n\nI shall hereafter venture to pursue further this train of speculation,\nbut at present I shall make some remarks on writers who may be regarded\nas the successors amongst ourselves of these German schools of\nPhilosophy.\n\n\nFOOTNOTES:\n\n[Footnote 297: _Phil. of Biol._ c. v.]\n\n\n\n\nCHAPTER XXVI.\n\nOF THE \"PHILOSOPHY OF THE INFINITE.\"\n\n\nIn the last Chapter but one I stated that Schelling propounded a\nPhilosophy of the Absolute, the Absolute being the original basis\nof truth in which the two opposite elements, Ideas and Facts, are\nidentified, and that Hegel also founded his philosophy on the Identity\nof these two elements. These German philosophies appear to me, as I\nhave ventured to intimate, of small or no value in their bearing on\nthe history of actual science. I have in the history of the sciences\nnoted instances in which these writers seem to me to misconceive\naltogether the nature and meaning of the facts of scientific history;\nas where[298] Schelling condemns Newton's Opticks as a fabric of\nfallacies: and where[299] Hegel says that the glory due to Kepler has\nbeen unjustly transferred to Newton. As it appears to me important that\nEnglish philosophers should form a just estimate of Hegel's capacity of\njudging and pronouncing on this subject, I will print in the Appendix a\nspecial discussion of what he has said respecting Newton's discovery of\nthe law of gravitation.\n\nRecently attempts have been made to explain to English readers\nthese systems of German philosophy, and in these attempts there are\nsome points which may deserve our notice as to their bearing on the\nphilosophy of science. I find some difficulty in discussing these\nattempts, for they deal much with phrases which appear to me to\noffer no grasp to man's power of reason. What, for instance, is the\n_Absolute_, which occupies a prominent place in these expositions? It\nis, as I have stated, in Schelling, the central basis of truth in which\nthings and thoughts are united and identified. To attempt to reason\nabout such an \"Absolute\" appears to me to be an entire misapprehension\nof the power of reason. Again; one of the most eminent of the\nexpositors has spoken of each system of this kind as a _Philosophy of\nthe Unconditioned_[300]. But what, we must ask, is the _Unconditioned_?\nThat which is subject to no conditions, is subject to no conditions\nwhich distinguish it from any thing else, and so, cannot be a matter of\nthought. But again; this _Absolute_ or _Unconditioned_ is (if I rightly\nunderstand) said to be described also by various other names; _unity_,\n_identity_, _substance_, _absolute cause_, the _infinite_, _pure\nthought_, &c. As each of these terms expresses some condition on which\nthe name fixes our thoughts, I cannot understand why they should any of\nthem be called the _Unconditioned_; and as they express very different\nthoughts, I cannot understand why they should be called by the same\nname. From speculations starting from such a point, I can expect\nnothing but confusion and perplexity; nor can I find that anything else\nhas come of them. They appear to me more barren, and more certain to be\nbarren, of any results which have any place in our real knowledge, than\nthe most barren speculations of the schoolmen of the middle ages: which\nindeed they much resemble in all their features--their acuteness, their\nlearning, their ambitious aim, and their actual failure.\n\n2. But leaving the Absolute and the Unconditioned, as notions which\ncannot be dealt with by our reason without being something entirely\ndifferent from their definitions, we may turn for a moment to another\nnotion which is combined with them by the expositors of whom I speak,\nand which has some bearing upon our positive science, because it enters\ninto the reasonings of mathematics: I mean the notion of _Infinite_.\nSome of those who hold that we can know nothing concerning the\nAbsolute and the Unconditioned, (which they pretend to prove, though\nconcerning such words I do not conceive that anything can be true or\nfalse,) hold also that the Infinite is in the same condition;--that we\ncan know nothing concerning what is Infinite;--therefore, I presume,\nnothing concerning infinite space, infinite time, infinite number, or\ninfinite degrees.\n\nTo disprove this doctrine, it might be sufficient to point out that\nthere is a vast mass of mathematical science which includes the notion\nof infinites, and leads to a great body of propositions concerning\nInfinites. The whole of the infinitesimal calculus depends upon\nconceiving finite magnitudes divided into an infinite number of parts:\nthese parts are infinitely small, and of these parts there are other\ninfinitesimal parts infinitely smaller still, and so on, as far as we\nplease to go. And even those methods which shun the term _infinite_, as\nNewton's method of Ultimate Ratios, the method of Indivisibles, and the\nmethod of Exhaustions of the ancient geometers, do really involve the\nnotion of infinite; for they imply a process continued without limit.\n\n3. But perhaps it will be more useful to point out the fallacies of\nthe pretended proofs that we can know nothing concerning Infinity and\ninfinite things.\n\nThe argument offered is, that of infinity we have no notion but the\nnegation of a limit, and that from this negative notion no positive\nresult can be deduced.\n\nBut to this I reply: It is not at all true that our notion of what is\ninfinite is merely that it is _that_ which has no limit. We must ask\nfurther that _what_? that space? that time? that number?--And if that\nspace, that what kind of space? That line? that surface? that solid\nspace?--And if that line, that line bounded at one end, or not? If that\nsurface, that surface bounded on one, or on two, or on three sides?\nor on none? However any of these questions are answered, we may still\nhave an infinite space. Till they are answered, we can assert nothing\nabout the space; not because we can assert nothing about infinites; but\nbecause we are not told what _kind_ of infinite we are talking of.\n\nIn reality the definition of an Infinite Quantity is not negative\nmerely, but contains a positive part as well. We assume a quantity\nof a certain kind which may be augmented by carrying onward its\nlimits in one or more directions: this is a finite quantity of a\ngiven kind. We _then_--when we have thus positively determined the\nkind of the quantity--suppose the limit in one or more directions to\nbe annihilated, and thus we have an infinite quantity. But in this\ninfinite quantity there remain the positive properties from which we\nbegan, as well as the negative property, the negation of a limit; and\nthe positive properties joined with the negative property may and do\nsupply grounds of reasoning respecting the infinite quantity.\n\n4. This is lore so elementary to mathematicians that it appears almost\npuerile to dwell upon it; but this seems to have been overlooked, in\nthe proof that we can have no knowledge concerning infinites. In such\nproof it is assumed as quite evident, that all infinites are equal.\nYet, as we have seen, infinites may differ infinitely among themselves,\nboth in quantity and in kind. A German writer is quoted[301] for an\n\"ingenious\" proof of this kind. In his writings, the opponent is\nsupposed to urge that a line _BAC_ may be made infinite by carrying\nthe extremity _C_ infinitely to the right, and again infinite by\ncarrying the extremity _B_ infinitely to the left; and thus the line\ninfinitely extended both ways would be double of the line infinite on\none side only. The supposed reply to this is, that it cannot be so,\nbecause one infinite is equal to another: and moreover that what is\nbounded at one end _A_, cannot be infinite: both which assumptions are\nwithout the smallest ground. That one infinite quantity may be double\nof another, is just as clear and certain as that one finite quantity\nmay. For instance, if one leaf of the book which the reader has before\nhim were produced infinitely upwards it would be an infinite space,\nthough bounded at the bottom and at both sides. If the other leaf were\nin like manner produced infinitely upwards it would in like manner be\ninfinite; and the two together, though each infinite, would be double\nof either of them.\n\n5. As I have said, infinite quantities are conceived by conceiving\nfinite quantities increased by the transfer of a certain limit, and\nthen by negativing this limit altogether. And thus an infinite number\nis conceived by assuming the series 1, 2, 3, 4, and so on, up to a\nlimit, and then removing this limit altogether. And this shows the\nbaselessness of another argument quoted from Werenfels. The opponent\nasks, Are there in the infinite line an infinite number of feet?\nThen in the double line there must be twice as many; and thus the\nformer infinite number did not contain all the (possible) unities;\n(numerus infinitus non omnes habet unitates, sed pr\u00e6ter eum concipi\npossunt totidem unitates, quibus ille careat, eique possunt addi).\nTo which I reply, that the definition of an infinite number is not\nthat it contains all possible unities: but this--that the progress of\nnumeration being begun according to a certain law, goes on without\nlimit. And accordingly it is easy to conceive how one infinite number\nmay be larger than another infinite number, in any proportion. If, for\ninstance, we take, instead of the progression of the natural numbers 1,\n2, 3, 4, &c. and the progression of the square numbers 1, 4, 9, 16, &c.\nany term of the latter series will be greater than the corresponding\nterm of the other series in a ratio constantly increasing, and the\ninfinite term of the one, infinitely greater than the corresponding\ninfinite term of the other.\n\n6. In the same manner we form a conception of infinite time, by\nsupposing time to begin now, and to go on, after the nature of time,\nwithout limit; or by going back in thought from the present to a past\ntime, and by continuing this retrogression without limit. And thus we\nhave time infinite _a parte ante_ and _a parte post_, as the phrase\nused to run; and time infinite both ways includes both, and is the most\ncomplete notion of eternity.\n\n7. Perhaps those who thus maintain that we cannot conceive anything\ninfinite, mean that we cannot form to ourselves a definite image of\nanything infinite. And this of course is true. We cannot form to\nourselves an image of anything of which one of the characteristics is\nthat it is, in a certain way, unlimited. But this impossibility does\nnot prevent our reasoning about infinite quantities; combining as\nelements of our reasoning, the absence of a limit with other positive\ncharacters.\n\n8. One of the consequences which is drawn by the assertors of the\ndoctrine that we cannot know anything about Infinity, is that we cannot\nobtain from science any knowledge concerning God: And I have been the\nmore desirous to show the absence of proof of this doctrine, because I\nconceive that science _does_ give us some knowledge, though it be very\nlittle, of the nature of God: as I shall endeavour to show hereafter.\n\nFor instance, I conceive that when we say that God is an _eternal_\nBeing, this phraseology is not empty and unmeaning. It has been used\nby the wisest and most thoughtful men in all ages, and, as I conceive,\nmay be used with undiminished, or with increased propriety, after\nall the light which science and philosophy have thrown upon such\ndeclarations. The reader of Newton will recollect how emphatically he\nuses this expression along with others of a cognate character[302]:\n\"God is eternal and infinite, ... that is, He endures from eternity\nto eternity, and is present from infinity to infinity.... He is not\neternity and infinity, but eternal and infinite. He is not duration and\nspace, but He endures and is present. He endures always, and is present\neverywhere, and by existing always and everywhere He constitutes\nduration and space.\" We shall see shortly that the view to which we are\nled may be very fitly expressed by this language.\n\nBut I will first notice some other aspects of this philosophy.\n\n\nFOOTNOTES:\n\n[Footnote 298: _Hist. Ind. Sc._ b. ix. c. iii.]\n\n[Footnote 299: _Ibid._ b. vii. c. ii.]\n\n[Footnote 300: Sir W. Hamilton's Note on the _Philosophy of the\nUnconditioned_.]\n\n[Footnote 301: Werenfels in Mr. Mansel's _Bampton Lectures_, lect. ii.\nNote 15.]\n\n[Footnote 302: _Scholium Generale_ at the end of the _Principia_.]\n\n\n\n\nCHAPTER XXVII.\n\nSIR WILLIAM HAMILTON ON INERTIA AND WEIGHT.\n\n\nIn a preceding chapter I have spoken of Sir William Hamilton as the\nexpositor, to English readers, of modern German systems, and especially\nof the so-called \"Philosophy of the Unconditioned.\" But the same writer\nis also noticeable as a continuator of the speculations of English and\nScottish philosophers concerning primary and secondary qualities; and\nthese speculations bear so far upon the philosophy of science that it\nis proper to notice them here.\n\n\n1. In our survey of the sciences, we have spoken of a class which we\nhave termed the Secondary Mechanical Sciences; these being the sciences\nwhich explain certain sensible phenomena, as sound, light, and heat, by\nmeans of a medium interposed between external bodies and our organs of\nsense. In these cases, we ascribe to bodies certain qualities: we call\nthem resonant, bright, red or green, hot or cold. But in the sciences\nwhich relate to these subjects, we explain these qualities by the\nfigure, size and motions of the parts of the medium which intervenes\nbetween the object and the ear, eye, or other sensible organ. And those\nformer qualities, sound, warmth and colour, are called _secondary\nqualities_ of the bodies; while the latter, figure, size and motion,\nare called the _primary qualities_ of body.\n\n\n2. This distinction, in its substance, is of great antiquity. The\natomic theory which was set up at an early period of Greek philosophy\nwas an attempt to account for the secondary qualities of bodies by\nmeans of their primary qualities. And this is really the scientific\nground of the distinction. _Those_ are primary qualities or attributes\nof body by means of which we, in a scientific view, explain and derive\ntheir other qualities. But the explanation of the sensible qualities\nof bodies by means of their operation through a medium has till now\nbeen very defective, and is so still. We have to a certain extent\ntheories of Sound, Light and Heat, which reduce these qualities to\nscales and standards, and in some measure account mechanically for\ntheir differences and gradations. But we have as yet no similar theory\nof Smells and Tastes. Still, we do not doubt that fragrance and flavour\nare perceived by means of an aerial medium in which odours float, and\na fluid medium in which sapid matters are dissolved. And the special\nodour and flavour which are thus perceived must depend upon the size,\nfigure, motion, number, &c. of the particles thus conveyed to the\norgans of taste and smell: that is, _those_ secondary qualities, as\nwell as the others, must depend upon the primary qualities of the parts\nof the medium.\n\n\n3. In this way the distinction of primary and secondary qualities is\ndefinite and precise. But when men attempt to draw the distinction\nby guess, without any scientific principle, the separation of\nthe two classes is vague and various. I have, in the _History of\nScientific Ideas_[303], pointed out some of the variations which\nare to be found on this subject in the writings of philosophers.\nSir William Hamilton[304] has given an account of many more which\nhe has compared and analysed with great acuteness. He has shown how\nthis distinction is treated, among others, by the ancient atomists,\nLeucippus and Democritus, by Aristotle, Galen, Galileo, Descartes,\nBoyle, Malebranche, Locke, Reid, Stewart, Royer-Collard. He then\nproceeds to give his own view; which is, that we may most properly\ndivide the qualities of bodies into _three_ classes, which he calls\n_Primary_, _Secundo-primary_, and _Secondary_. The former he enumerates\nas 1, Extension; 2, Divisibility; 3, Size; 4, Density or Rarity; 5,\nFigure; 6, Incompressibility absolute; 7, Mobility; 8, Situation.\nThe Secundo-primary are Gravity, Cohesion, Inertia, Repulsion. The\nSecondary are those commonly so called, Colour, Sound, Flavour,\nSavour, and Tactical Sensation; to which he says may be added the\nmuscular and cutaneous sensation which accompany the perception of the\nSecundo-primary qualities. \"Such, though less directly the result of\nforeign causes, are Titillation, Sneezing, Horripilation, Shuddering,\nthe feeling of what is called Setting-the-teeth-on-edge, &c.\"\n\nThe Secundo-primary qualities Sir William Hamilton traces in further\ndetail. He explains that with reference to Gravity, bodies are _heavy_\nor _light_. With reference to Cohesion, there are many coordinate\npairs, of which he enumerates these:--_hard_ and _soft_; _firm_\nand _fluid_,--the fluid being subdivided into _thick_ and _thin_;\n_viscid_ and _friable_; _tough_ and _brittle_; _rigid_ and _flexible_;\n_fissile_ and _infissile_; _ductile_ and _inductile_; _retractile_\nand _irretractile_; _rough_ and _smooth_; _slippery_ and _tenacious_.\nWith reference to Repulsion he gives these qualities:--_compressible_\nand _incompressible_; _elastic_ and _inelastic_. And with reference to\nInertia he mentions only _moveable_ and _immoveable_.\n\nI do not see what advantage is gained to philosophy by such an\nenumeration of qualities as this, which, after all, does not pretend\nto completeness; nor do I see anything either precise or fundamental\nin such distinctions as that of elasticity, a mode of cohesion, and\nelasticity, a mode of repulsion. But a question in which our philosophy\nis really concerned is how far any of these qualities are _universal_\nqualities of matter. Sir W. Hamilton holds that they are none of them\nnecessary qualities of matter, and therefore of course not universal,\nand argues this point at some length. With regard to one of his\nSecundo-primary qualities, I will make some remarks.\n\n\n4. _Inertia._--In discussing the Ideas which enter into the Mechanical\nSciences[305], I have stated that the Idea of Force and Resistance to\nForce, that is, of _Force_ and _Matter_, are the necessary foundations\nof those sciences. Force cannot act without matter to act on; Matter\ncannot exist without Force to keep its parts together and to keep it in\nits place. But Force acting upon matter may either be Force producing\nrest, or Force producing motion. If we consider Force producing motion,\nthe motion produced, that is, the velocity produced, must depend upon\nthe quantity of matter moved. It cannot be that the same power, acting\nin the same way, shall produce the same velocity by pushing a small\npebble and a large rock. If this were so, we could have no science on\nsuch matters. It must needs be that the same force produces a smaller\nvelocity in the larger body; and this according to some measure of\nits largeness. The measure of the degree in which the body thus\nresists this communication of motion is _inertia_. And the inertia is\nnecessarily supposed to be proportional to the quantity of matter,\nbecause it is by this inertia that this existence and quantity of the\nmatter is measured. If therefore any Science concerning Force and\nMatter is to exist, matter must have inertia, and the inertia must be\nproportional to the quantity of matter.\n\n\n5. Sir W. Hamilton, in opposition to this, says, that we can conceive\na body occupying space, and yet without attraction or repulsion for\nanother body, and wholly indifferent to this or that position, in\nspace, to motion and to rest. He infers thence that inertia is not a\nnecessary quality of bodies.\n\nTo this I reply, that even if we can conceive such bodies, (which in\nfact man, living in a world of matter cannot conceive,) at any rate\nwe cannot conceive any _science_ about such bodies. If bodies were\nindifferent to motion and rest, Forces could not be measured by their\neffects; nor could be measured or known in any way. Such bodies might\nfloat about like clouds, visible to the eye, but intangible, and\ngoverned by no laws of motion. But if we have any science about bodies,\nthey must be tangible, and governed by laws of motion. Not, then, from\nany observed properties of bodies, but from the possibility of any\nscience about bodies, does it follow that all bodies have inertia.\n\n\n6. _Gravity._--Reasoning of the same kind may be employed about weight.\nWe can conceive, it is urged, matter without weight. But I reply,\nwe cannot conceive a _science_ which deals with matter that has no\nweight:--a science, I mean, which deals with the quantity of matter of\nbodies, as arising from the sum of their elements. For the quantity of\nmatter of bodies is and must be measured by those sensible properties\nof matter which undergo quantitative addition, subtraction and\ndivision, as the matter is added, subtracted, and divided. The quantity\nof matter cannot be known in any other way. But this mode of measuring\nthe quantity of matter, in order to be true at all, must be universally\ntrue. If it were only partially true--if some kinds of matter had\nweight and others had not--the limits of the mode of measuring matter\nby weight would be arbitrary: and therefore the whole procedure\nwould be arbitrary, and as a mode of obtaining philosophical truth,\naltogether futile. But we suppose truth respecting the composition of\nbodies to be attainable; therefore we must suppose the rule, which is\nthe necessary basis of such truth, to be itself true.\n\nSir W. Hamilton has replied to these arguments, but, as I conceive,\nwithout affecting the force of them. I will repeat here the answer\nwhich I have already given[306], and will reprint in the Appendix the\nMemoir by which his objections were occasioned.\n\nHe says, (1), that our reasoning assumes that we must necessarily have\nit in our power to ascertain the Quantity of Matter; whereas this may\nbe a problem out of the reach of human determination.\n\nTo this I reply, that my reasoning _does_ assume that there is a\nscience, or sciences, which make assertions concerning the Quantity\nof Matter: Mechanics and Chemistry are such sciences. My assertion\nis, that to make such sciences possible, Quantity of Matter must\nbe proportional to Weight. If my opponent deny that Mechanics and\nChemistry can exist as science, he may invalidate my proof; but not\notherwise.\n\n(2) He says that there are two conceivable ways of estimating the\nQuantity of Matter: by the Space occupied, and by the Weight or\nInertia; and that I assume the second measure gratuitously.\n\nTo which I reply, that the most elementary steps in Mechanics and\nin Chemistry contradict the notion that the Quantity of Matter is\nproportionate to the Space. They proceed necessarily on a distinction\nbetween Space and Matter:--between mere Extension and material\nSubstance.\n\n(3) He allows that we cannot make the Extension of a body the\nmeasure of the Quantity of Matter, because, he says, we do not\nknow if \"the compressing force\" is such as to produce \"the closest\ncompression.\" That is, he assumes a compressing force, assumes a\n\"closest compression,\" assumes a peculiar (and very improbable) atomic\nhypothesis; and all this, to supply a reason why we are not to believe\nthe first simple principle of Mechanics and Chemistry.\n\n(4) He speaks of \"a series of apparent fluids (as Light or its vehicle,\nthe Calorific, the Electro-galvanic, and Magnetic agents) which we can\nneither denude of their character of substance, nor clothe with the\nattribute of weight.\"\n\nTo which my reply is, that precisely because I cannot \"clothe\" these\nagents with the attribute of Weight, I _do_ \"denude them of the\ncharacter of Substance.\" They are not substances, but agencies. These\nImponderable Agents are not properly called \"Imponderable Fluids.\" This\nI conceive that I have proved; and the proof is not shaken by denying\nthe conclusion without showing any defect in the reasoning.\n\n(5) Finally, my critic speaks about \"a logical canon,\" and about \"a\ncriterion of truth, subjectively necessary and objectively certain;\"\nwhich matters I shall not waste the reader's time by discussing.\n\n\nFOOTNOTES:\n\n[Footnote 303: B. iv. c. i.]\n\n[Footnote 304: Reid's _Works_, Supplementary Dissertation D.]\n\n[Footnote 305: _Hist. Sc. Id._ b. iii.]\n\n[Footnote 306: _Hist. Sc. Id._ b. vi. c. iii.]\n\n\n\n\nCHAPTER XXVIII.\n\nINFLUENCE OF GERMAN SYSTEMS OF PHILOSOPHY IN BRITAIN.\n\n\nThe philosophy of Kant, as I have already said, involved a definite\ndoctrine on the subject of the Fundamental Antithesis, and a correction\nof some of the errors of Locke and his successors. It was not however\nat first favourably received among British philosophers, and those who\naccepted it were judged somewhat capriciously and captiously. I will\nsay a word on these points[307].\n\n1. (_Stewart_)--Dugald Stewart, in his _Dissertation on the Progress\nof the Moral Sciences_, repeatedly mentions Kant's speculations, and\nalways unfavourably. In Note I to Part I. of the Dissertation he says,\n\"In our own times, Kant and his followers seem to have thought that\nthey had thrown a strong light on the nature of _space_ and also of\n_time_, when they introduced the word _form_ (_form of the intellect_)\nas a common term applicable to both. Is not this to revert to the\nscholastic folly of verbal generalization?\" And in Part II. he gives a\nlong and laborious criticism of a portion of Kant's speculations; of\nwhich the spirit may be collected from his describing them as resulting\nin \"the metaphysical _conundrum_, that the human mind (considered as\na _noumenon_ and not as a _phenomenon_) neither exists in space nor\ntime.\" And after mentioning Meiners and Herder along with Kant, he\nadds, \"I am ashamed to say that in Great Britain the only one of these\nnames which has been much talked of is Kant.\" And again in Note EE, he\ntranslates some portion of the German philosopher, adding, that to the\nexpressions so employed he can attach no meaning.\n\nStewart, in his criticism of Kant's doctrines, remarks that, in\nasserting that the human mind possesses, in its own ideas, an element\nof necessary and universal truth, not derived from experience, Kant had\nbeen anticipated by Price, by Cudworth, and even by Plato; to whose\n_The\u00e6tetus_ both Price and Cudworth refer, as containing views similar\nto their own. And undoubtedly this doctrine of ideas, as indispensable\nsources of necessary truths, was promulgated and supported by weighty\narguments in the _The\u00e6tetus_; and has ever since been held by many\nphilosophers, in opposition to the contrary doctrine, also extensively\nheld, that all truth is derived from experience. But, in pointing out\nthis circumstance as diminishing the importance of Kant's speculations,\nStewart did not sufficiently consider that doctrines, fundamentally the\nsame, may discharge a very different office at different periods of\nthe history of philosophy. Plato's Dialogues did not destroy, nor even\ndiminish, the value of Cudworth's \"Immutable Morality.\" Notwithstanding\nCudworth's publications, Price's doctrines came out a little afterwards\nwith the air and with the effect of novelties. Cudworth's assertion of\nideas did not prevent the rise of Hume's skepticism; and it was Hume's\nskepticism which gave occasion to Kant's new assertion of necessary\nand universal truth, and to his examination into the grounds of the\npossibility and reality of such truth. To maintain such doctrine\n_after_ the appearance of intermediate speculations, and with reference\nto them, was very different from maintaining it before; and this is the\nmerit which Kant's admirers claim for him. Nor can it be denied that\nhis writings produced an immense effect upon the mode of treating such\nquestions in Germany; and have had, even in this country, an influence\nfar beyond what Mr. Stewart would have deemed their due.\n\n\n2. (_Mr. G. H. Lewes._)--But as injustice has thus been done to Kant by\nconfounding his case with that of his predecessors of like opinions,\nso on the other hand, injustice has also been done, both to him and\nthose who have followed him in the assertion of ideas, by confounding\n_their_ case with his. This injustice seems to me to be committed by a\nwriter on the History of Philosophy, who has given an account of the\nsuccessive schools of philosophy up to our own time;--has assigned\nto Kant an important and prominent place in the recent history of\nmetaphysics;--but has still maintained that Kant's philosophy, and\nindeed every philosophy, is and must be a failure. In order to prove\nthis thesis, the author naturally has to examine Kant's doctrines and\nthe reasons assigned for them, and to point out what he conceives to be\nthe fallacy of these arguments. This accordingly he professes to do;\nbut as soon as he has entered upon the argument, he substitutes, as\nhis opponent, for the philosopher of K\u00f6nigsberg, a writer of our own\ntime and country, who does not profess himself a Kantian, who has been\nrepeatedly accused, with whatever justice, of misrepresenting what he\nhas borrowed from Kant, and whose main views are, in the opinion of\nthe writer himself, very different from Kant's. Mr. Lewes[308], in the\nchapter entitled \"Examination of Kant's Fundamental Principles,\" after\na preliminary statement of the points he intends to consider, says \"Now\nto the question. As Kant confessedly was led to his own system by the\nspeculations of Hume,\" and so on; and forthwith he introduces the name\nof _Dr. Whewell_ as the writer whose views he has to criticize, without\nstating how he connects him with Kant, and goes on arguing against\n_him_ for a dozen pages to the end of the Chapter.\n\n3. It is true, however, that I had adopted some of Kant's views, or at\nleast some of his arguments. The chapters[309] on the Ideas of Space\nand Time in the _Philosophy of the Inductive Sciences_, were almost\nliteral translations of chapters in the _Kritik der Reinen Vernunft_.\nYet the author was charged by a reviewer at the time, with explaining\nthese doctrines \"in a manner incompatible with the clear views of\nEmanuel Kant.\" It appeared to be assumed by the English admirers of the\nKantian philosophy, that Kant's views were true and clear in Germany,\nbut became untenable when adopted in England.\n\n\n4. (_Mr. Mansel_)--But the most important of my critics on this\nground is Mr. Mansel, who has revived the censure of my speculations\nas not doing justice to the Kantian philosophy. \"It is much to be\nregretted,\" he says[310], \"that Dr. Whewell, who has made good use of\nKantian principles in many parts of his _Philosophy of the Inductive\nSciences_,\" has not more accurately observed Kant's distinction between\nthe necessary laws under which all men think, and the contingent\nlaws under which certain men think of certain things. And further on\nMr. Mansel, after giving great praise to the general spirit of the\n_Philosophy of the Inductive Sciences_, says, \"It is to be regretted\nthat the accuracy of his theory has been in so many instances vitiated\nby a stumble at the threshold of the Critical Philosophy.\" Mr. Mansel\nis, indeed, by much the most zealous English Kantian whose writings I\nhave seen;--among those, I mean, who have brought original powers of\nphilosophical thought to bear upon such subjects; and have not been, as\nsome have been, enslaved by an admiration of German systems, just as\nbigotted as the contempt of them which others feel. And as Mr. Mansel\nhas stated distinctly some of the points in which he conceives that I\nhave erred in deviating from the doctrines of Kant, I should wish to\nmake a few remarks on those points.\n\n5. Kant considers that Space and Time are conditions of perception,\nand hence sources of necessary and universal truth. Dr. Whewell agrees\nwith Kant in placing in the mind certain sources of necessary truth;\nhe calls these Fundamental Ideas, and reckons, besides Space and Time,\nothers, as Cause, Likeness, Substance, and several more. Mr. Mill,\nthe most recent and able expounder of the opposite doctrine, derives\nall truths from Observation, and denies that there is such a separate\nsource of truth as Ideas. Mr. Mansel does not agree either with Mr.\nMill or Dr. Whewell; he adheres to the original Kantian thesis, that\nSpace and Time are sources of necessary truths, but denies the office\nto the other Fundamental Ideas of Dr. Whewell. In reading what has\nbeen said by Mr. Mill, Mr. Mansel, and other critics, on the subject\nof what I have called _Fundamental Ideas_, I am led to perceive that\nI have expressed myself incautiously, with regard to the identity of\ncharacter between the first two of these Fundamental Ideas, namely,\nSpace and Time, and the others, as Force, Composition, and the like.\nAnd I am desirous of explaining, to those who take an interest in these\nspeculations, how far I claim for the other Fundamental Ideas the same\ncharacter and attributes as for Space and Time.\n\n6. The special and characteristic property of all the Fundamental Ideas\nis what I have already mentioned, that they are the mental sources of\nnecessary and universal scientific truths. I call them _Ideas_, as\nbeing something not derived from sensation, but governing sensation,\nand consequently giving form to our experience;--_Fundamental_, as\nbeing the foundation of knowledge, or at least of Science. And the way\nin which those Ideas become the foundations of Science is, that when\nthey are clearly and distinctly entertained in the mind, they give rise\nto inevitable convictions or intuitions, which may be expressed as\n_Axioms_; and these Axioms are the foundations of Sciences respective\nof each Idea. The Idea of Space, when clearly possessed, gives rise\nto geometrical Axioms, and is thus the foundation of the Science of\nGeometry. The Idea of Mechanical Force, (a modification of the Idea of\nCause,) when clearly developed in the mind, gives birth to Axioms which\nare the foundation of the Science of Mechanics. The Idea of Substance\ngives rise to the Axiom which is universally accepted,--that we cannot,\nby any process, (for instance, by chemical processes,) create or\ndestroy matter, but can only combine and separate elements;--and thus\ngives rise to the Science of Chemistry.\n\n\n7. Now it may be observed, that in giving this account of the\nfoundation of Science, I lay stress on the condition that the Ideas\nmust be _clearly and distinctly possessed_. The Idea of Space must be\nquite clear in the mind, or else the Axioms of Geometry will not be\nseen to be true: there will be no _intuition_ of their truth; and for\na mind in such a state, there can be no Science of Geometry. A man may\nhave a confused and perplexed, or a vacant and inert state of mind, in\nwhich it is not clearly apparent to him, that two straight lines cannot\ninclose a space. But this is not a frequent case. The Idea of Space is\nmuch more commonly clear in the minds of men than the other Ideas on\nwhich science depends, as Force, or Substance. It is much more common\nto find minds in which these latter Ideas are not so clear and distinct\nas to make the Axioms of Mechanics or of Chemistry self-evident.\nIndeed the examples of a state of mind in which the Ideas of Force\nor of Substance are so clear as to be made the basis of science, are\ncomparatively few. They are the examples of minds scientifically\ncultivated, at least to some extent. Hence, though the Axioms of\nMechanics or of Chemistry may be, in their own nature, as evident as\nthose of Geometry, they are not evident to so many persons, nor at so\nearly a period of intellectual or scientific culture. And this being\nthe case, it is not surprising that some persons should doubt whether\nthese Axioms are evident at all;--should think that it is an error to\nassert that there exist, in such sciences as Mechanics or Chemistry,\nFundamental Ideas, fit to be classed with Space, as being, like it, the\norigin of Axioms.\n\nIn speaking of all the Fundamental Ideas as being alike the source of\nAxioms when clearly possessed, without dwelling sufficiently upon the\namount of mental discipline which is requisite to give the mind this\nclear possession of most of them; and in not keeping before the reader\nthe different degrees of evidence which, in most minds, the Axioms\nof different sciences naturally have, I have, as I have said, given\noccasion to my readers to misunderstand me. I will point out one or two\npassages which show that this misunderstanding has occurred, and will\ntry to remove it.\n\n8. The character of axiomatic truths seen by intuition is, that\nthey are not only seen to be true, but to be necessary;--that the\ncontrary of them is not only false, but inconceivable. But this\ninconceivableness depends entirely upon the clearness of the Ideas\nwhich the axioms involve. So long as those Ideas are vague and\nindistinct, the contrary of an Axiom may be assented to, though it\ncannot be distinctly conceived. It may be assented to, not because it\nis possible, but because _we_ do not see clearly what _is_ possible. To\na person who is only beginning to think geometrically, there may appear\nnothing absurd in the assertion, that two straight lines may inclose\na space. And in the same manner, to a person who is only beginning\nto think of mechanical truths, it may not appear to be absurd, that\nin mechanical processes, Reaction should be greater or less than\nAction; and so, again, to a person who has not thought steadily\nabout Substance, it may not appear inconceivable, that by chemical\noperations, we should generate new matter, or destroy matter which\nalready exists.\n\nHere then we have a difficulty:--the test of Axioms is that the\ncontrary of them is inconceivable; and yet persons, till they have in\nsome measure studied the subject, do not see this inconceivableness.\nHence our Axioms must be evident only to a small number of thinkers;\nand seem not to deserve the name of self-evident or necessary truths.\n\nThis difficulty has been strongly urged by Mr. Mill, as supporting\nhis view, that all knowledge of truth is derived from experience. And\nin order that the opposite doctrine, which I have advocated, may not\nlabour under any disadvantages which really do not belong to it, I must\nexplain, that I do not by any means assert that those truths which\nI regard as necessary, are all equally evident to common thinkers,\nor evident to persons in all stages of intellectual development. I\nmay even say, that some of those truths which I regard as necessary,\nand the necessity of which I believe the human mind to be capable of\nseeing, by due preparation and thought, are still such, that this\namount of preparation and thought is rare and peculiar; and I will\nwillingly grant, that to attain to and preserve such a clearness and\nsubtlety of mind as this intuition requires, is a task of no ordinary\ndifficulty and labour.\n\n9. This doctrine,--that some truths may be seen by intuition, but yet\nthat the intuition of them may be a rare and difficult attainment,--I\nhave not, it would seem, conveyed with sufficient clearness to obviate\nmisapprehension. Mr. Mill has noticed a passage of my _Philosophy_\non this subject, which he has understood in a sense different from\nthat which I intended. Speaking of the two Principles of Chemical\nScience,--that combinations are definite in kind, and in quantity,--I\nhad tried to elevate myself to the point of view in which these\nPrinciples are seen, not only to be true, but to be necessary. I was\naware that even the profoundest chemists had not ventured to do this;\nyet it appeared to me that there were considerations which seemed to\nshow that any other rule would imply that the world was a world on\nwhich the human mind could not employ itself in scientific speculation\nat all. These considerations I ventured to put forwards, not as views\nwhich could at present be generally accepted, but as views to which\nchemical philosophy appeared to me to tend. Mr. Mill, not unnaturally,\nI must admit, supposed me to mean that the two Principles of Chemistry\njust stated, are self-evident, in the same way and in the same\ndegree as the Axioms of Geometry are so. I afterwards explained that\nwhat I meant to do was, to throw out an opinion, that _if_ we could\nconceive the composition of bodies _distinctly_, we might be able to\nsee that it is necessary that the modes of this composition should\nbe definite. This Mr. Mill does not object to[311]: but he calls it\na great attenuation of my former opinion; which he understood to be\nthat we, (that is, men in general,) already see, or may see, or ought\nto see, this necessity. Such a general apprehension of the necessity\nof definite chemical composition I certainly never reckoned upon;\nand even in my own mind, the thought of such a necessity was rather\nan anticipation of what the intuitions of philosophical chemists in\nanother generation would be, than an assertion of what they now are or\nought to be; much less did I expect that persons, neither chemists nor\nphilosophers, would already, or perhaps ever, see that a proposition,\nso recently discovered to be true, is not only true, but necessary.\n\n10. Of the bearing of this view on the question at issue between Mr.\nMill and me, I may hereafter speak; but I will now notice other persons\nwho have misunderstood me in the same way.\n\nAn able writer in the _Edinburgh Review_[312] has, in like manner,\nsaid, \"Dr. Whewell seems to us to have gone much too far in reducing\nto necessary truths what assuredly the generality of mankind will not\nfeel to be so.\" It is a fact which I do not at all contest, that the\n_generality of mankind_ will not feel the Axioms of Chemistry, or even\nof Mechanics, to be necessary truths. But I had said, not that the\ngenerality of mankind would feel this necessity, but (in a passage\njust before quoted by the Reviewer) that the mind under certain\ncircumstances _attains a point of view_ from which it can pronounce\nmechanical (and other) fundamental truths to be necessary in their\nnature, though disclosed to us by experience and observation.\n\nBoth the Edinburgh Reviewer and Mr. Mansel appear to hold a distinction\nbetween the fundamental truths of Geometry, and those of the other\nsubjects which I have classed with them. The latter says, that\nperhaps metaphysicians may hereafter establish the existence of other\nsubjective conditions of intuitions (or, as I should call them,\nFundamental Ideas,) besides Space and Time, but that in asserting\nsuch to exist in the science of Mechanics, I certainly go too far:\nand he gives as an instance my Essay,--\"Demonstration that all matter\nis heavy.\" I certainly did not expect that the Principles asserted\nin that Essay would be assented to as readily or as generally as the\nAxioms of Geometry; but I conceive that I have there proved that\nChemical Science, using the balance as one of its implements, cannot\nadmit \"imponderable bodies\" among its elements. This impossibility\nwill, I think, not only be found to exist in fact, but seen to exist\nnecessarily, by chemists, in proportion as they advance towards general\npropositions of Chemical Science in which the so-called \"imponderable\nfluids\" enter. But even if I be right in this opinion, to how few will\nthis necessity be made apparent, and how slowly will the intuition\nspread! I am as well aware as my critics, that the necessity will\nprobably never be apparent to ordinary thinkers.\n\n\n11. Though Mr. Mansel does not acknowledge any subjective conditions\nof intuition besides Space and Time, he does recognize other _kinds\nof necessity_, which I should equally refer to Fundamental Ideas;\nbecause they are, no less than Space and Time, the foundations of\nuniversal and necessary truths in science. Such are[313] the Principle\nof Substance;--All Qualities exist in some subject: and the Principle\nof Causality;-- Every Event has its Cause. To these Principles he\nascribes a \"metaphysical necessity,\" the nature and grounds of which\nhe analyses with great acuteness. But what I have to observe is, that\nwhatever _differences_ may be pointed out between the _grounds_ of\nthe necessity, in this case of _metaphysical_ necessity, and in that\nwhich Mr. Mansel calls _mathematical_ necessity which belongs to the\nConditions or Ideas of Space and of Time; still, it is not the less\ntrue that the Ideas of Substance and of Cause, _do_ afford a foundation\nfor necessary truths, and that on these truths are built Sciences. That\nevery Change must have a Cause, with the corresponding Axioms,--that\nthe Cause is known by the Effect, and Measured by it,--is the basis\nof the Science of Mechanics. That there is a Substance to which\nqualities belong, with the corresponding Axiom,--that we cannot create\nor destroy Substance, though we may alter Qualities by combining and\nseparating Substances,--is the basis of the Science of Chemistry. And\nthat this doctrine of the Indestructibility of Substance is a primary\naxiomatic truth, is certain; both because it has been universally taken\nfor granted by men seeking for general truths; and because it is not\nand cannot be proved by experience[314]. So that I have here, even\naccording to Mr. Mansel's own statement, other grounds besides Space\nand Time, for necessary truths in Science.\n\n12. Besides mathematical and metaphysical necessity, Mr. Mansel\nrecognizes also a _logical necessity_. I will not pretend to say\nthat this kind of necessity is exactly represented by any of those\nFundamental Ideas which are the basis of Science; but yet I think it\nwill be found that this logical necessity mainly operates through\nthe attribution of Names to things; and that a large portion of its\ncogency arises from these maxims,--that names must be so imposed that\nGeneral Propositions shall be possible,--and so that Reasoning shall be\npossible. Now these maxims are really the basis of Natural History,\nand are so stated in the _Philosophy of the Inductive Sciences_. The\nformer maxim is the principle of all Classification; and though we have\nno syllogisms in Natural History, the apparatus of _genus_, _species_,\n_differentia_, and the like, which was introduced in the analysis of\nsyllogistic reasoning, is really more constantly applied in Natural\nHistory than in any other science.\n\n13. Besides the different kinds of necessity which Mr. Mansel thus\nacknowledges, I do not see why he should not, on his own principles,\nrecognize others; as indeed he appears to me to do. He acknowledges,\nI think, the distinction of Primary and Secondary qualities; and\nthis must involve him in the doctrine that Secondary Qualities are\nnecessarily perceived by means of a _Medium_. Again: he would, I\nthink, acknowledge that in organized bodies, the parts exist for a\n_Purpose_; and Purpose is an Idea which cannot be inferred by reasoning\nfrom facts, without being possessed and applied as an Idea. So that\nthere would, I conceive, exist, in his philosophy, all the grounds of\nnecessary truth which I have termed Fundamental Ideas; only that he\nwould further subdivide, classify, and analyse, the kinds and grounds\nof this necessity.\n\nIn this he would do well; and some of his distinctions and analyses\nof this kind are, in my judgment, very instructive. But I do not see\nwhat objection there can be to my putting together all these kinds of\nnecessity, when my purpose requires it; and, inasmuch as they all are\nthe bases of Science, I may call them by a general name; for instance,\nGrounds of Scientific Necessity; and these are precisely what I mean by\n_Fundamental Ideas_.\n\nThat some steady thought, and even some progress in the construction\nof Science, is needed in order to see the necessity of the Axioms thus\nintroduced, is true, and is repeatedly asserted and illustrated in the\nHistory of the Sciences. The necessity of such Axioms is seen, but it\nis not seen at first. It becomes clearer and clearer to each person,\nand clear to one person after another, as the human mind dwells more\nand more steadily on the several subjects of speculation. _There are\nscientific truths which are seen by intuition, but this intuition\nis progressive._ This is the remark which I wish to make in answer\nto those of my critics who have objected that truths which I have\npropounded as Axioms, are not evident to all.\n\n\n14. That the Axioms of Science are not evident _to all_, is true\nenough, and too true. Take the Axiom of Substance:--that we may change\nthe condition of a substance in various ways, but cannot destroy it.\nThis has been assumed as evident by philosophers in all ages; but if\nwe ask an ordinary person whether a body can be destroyed by fire, or\ndiminished, will he unhesitatingly reply, that it cannot? It requires\nsome thought to say[315], as the philosopher said, that the weight of\nthe smoke is to be found by subtracting the weight of the ashes from\nthat of the fuel; nay, even when this is said, it appears, at first,\nrather an epigram than a scientific truth. Yet it is by thinking only,\nnot by an experiment, that, from a happy guess it becomes a scientific\ntruth. And the thought is the basis, not the result, of experimental\ntruths; for which reason I ascribe it to a Fundamental Idea. And so,\nsuch truths are the genuine growth of the human mind; not innate,\nas if they needed not to grow; still less, dead twigs plucked from\nexperience and stuck in from without; not universal, as if they grew\nup everywhere; but not the less, under favourable circumstances, the\ngenuine growth of the scientific intellect.\n\n15. Not only do I hold that the Axioms, on which the truths of science\nrest, grow from guesses into Axioms in various ways, and often\ngradually, and at different periods in different minds, and partially,\neven in the end; but I conceive that this may be shown by the history\nof science, as having really happened, with regard to all the most\nconspicuous of such principles. The scientific insight which enabled\ndiscoverers to achieve their exploits, implied that they were among\nthe first to acquire an intuitive conviction of the Axioms of their\nScience: the controversies which form so large a portion of the history\nof science, arise from the struggles between the clear-sighted and\nthe dimsighted, between those who were forwards and those who were\nbackwards in the progress of ideas; and these controversies have very\noften ended in diffusing generally a clearness of thought, on the\ncontroverted subject, which at first, the few only, or perhaps not\neven they, possessed. The History of Science consists of the History\nof Ideas, as well as of the History of Experience and Observation.\nThe latter portion of the subject formed the principal matter of my\n_History_ of the Inductive Sciences; the former occupied a large\nportion of the _Philosophy_ of the Inductive Sciences[316]; which, I\nmay perhaps be allowed to explain, is, for the most part, a Historical\nWork no less than the other; and was written in a great measure, at the\nsame time, and from the same survey of the works of scientific writers.\n\n16. I am aware that the explanation which I have given, may naturally\nprovoke the opponents of the doctrine of scientific necessity to\nrepeat their ordinary fundamental objections, in a form adapted to\nthe expressions which I have used. They may say, the fact that these\nso-called Axioms thus become evident only during the progress of\nexperience, proves that they are derived from experience: they may,\nin reply to our image, say, that truths are stuck into the mind by\nexperience, as seeds are stuck into the ground; and that to maintain\nthat they can grow under any other conditions, is to hold the\ndoctrine of spontaneous generation, which is equally untenable in the\nintellectual and in the physical world. I shall not however here resume\nthe general discussion; but shall only say briefly in reply, that\nAxioms,--for instance, this Axiom, that _material substances cannot be\ncreated or annihilated by any process which we can apply_,--though it\nbecomes evident in the progress of experience, cannot be derived from\nexperience; for it is a proposition which never has nor can be proved\nby experience; but which, nevertheless, has been always assumed by men,\nseeking for general truths, as necessarily true, and as controlling\nand correcting all possible experience. And with regard to the image\nof vegetable development, I may say, that as such development implies\nboth inherent forms in the living seed, and nutritive powers in earth\nand air; so the development of our scientific ideas implies both a\nformative power, and materials acted on; and that, though the analogy\nmust be very defective, we conceive that we best follow it by placing\nthe formative power in the living mind, and in the external world the\nmaterials acted on: while the doctrine that all truth is derived from\nexperience only, appears to reject altogether one of these elements, or\nto assert the two to be one.\n\n\nFOOTNOTES:\n\n[Footnote 307: The remarks contained in this chapter have for the most\npart been already printed and circulated in a _Letter to the Author of\nProlegomena Logica_, 1852.]\n\n[Footnote 308: _Biographical History of Philosophy_, 1846. In a more\nrecent edition the author of this work has modified his expressions,\nbut still employs himself in arguing against Dr. Whewell, in order to\noverthrow Kant. So far as his arguments affect my philosophy, they are,\nas I conceive, answered in the various expositions which I have given\nof that philosophy.]\n\n[Footnote 309: B. ii. The Philosophy of the Pure Sciences. Chap.\nii. Of the Idea of Space. Chap. iii. Of some peculiarities of the\nIdea of Space. Chap. vii. Of the Idea of Time. Chap. viii. Of some\npeculiarities of the Idea of Time.]\n\n[Footnote 310: _Prolegomena Logica_, by H. L. Mansel, M.A. 1851.]\n\n[Footnote 311: _Logic_, i. p. 273, 3rd edit.]\n\n[Footnote 312: No. 193, p. 29.]\n\n[Footnote 313: _Prol. Log._ p. 123.]\n\n[Footnote 314: See _Phil. Ind. Sc._ b. vi. c. iii.]\n\n[Footnote 315: Kant.]\n\n[Footnote 316: Republished as _The History of Scientific Ideas_.]\n\n\n\n\nCHAPTER XXIX.\n\nNECESSARY TRUTH IS PROGRESSIVE.\n\n\nOBJECTIONS CONSIDERED.\n\nThe doctrine that necessary truth is progressive is a doctrine very\nimportant in its bearing upon the nature of the human mind; and, as\nI conceive, in its theological bearing also. But it is a doctrine to\nwhich objections are likely to be made from various quarters, and I\nwill consider some of these objections.\n\n1. Necessary truths, it will be said, cannot increase in number. New\nones cannot be added to the old ones. For necessary truths are those of\nwhich the necessity is plain and evident to all mankind--to the common\nsense of man; such as the axioms of geometry. But that which is evident\nto all mankind must be evident from the first: that which is plain to\nthe common sense of man cannot require scientific discovery: that which\nis necessarily true cannot require accumulated proof.\n\nTo this I reply, that necessary truths require for their apprehension\na certain growth and development of the human mind. Though it is seen\nthat they are necessarily true, this is seen only by those who think\nsteadily and clearly, and to think steadily and clearly on any kind\nof subject, requires time and attention;--requires mental culture.\nThis may be seen even in the case of the axioms of geometry. These\naxioms are self-evident: but to _whom_ are they self-evident? Not to\nuncultured savages, or young children; or persons of loose vague habits\nof thought. To see the truth and necessity of geometrical axioms, we\nneed geometrical culture.\n\nTherefore that any axioms are not evident without patient thought and\ncontinued study of the subject, does not disprove their necessity.\nPrinciples may be axiomatic and necessary, although they require time,\nand the progress of thought and of knowledge, to bring them to light.\nAnd axioms may be thus gradually brought to light by the progress of\nknowledge.\n\nNor is it difficult to give examples of such axioms, other than\ngeometrical. There is an axiom which has obtained currency among\nthoughtful men from the time that man began to speculate about himself\nand the universe:--_E nihilo nil fit_: Nothing can be made of nothing.\nNo material substance can be produced or destroyed by natural causes,\nthough its form and consistence may be changed indefinitely. Is not\nthis an axiom? a necessary truth? Yet it is not evident to all men\nat first, and without mental culture. At first and before habits of\nsteady and consistent thought are formed, men think familiarly of the\ncreation and destruction of matter. Only when the mind has received\nsome philosophical culture does it see the truth and necessity of the\naxiom of substance, and _then_ it does see it.\n\nAnd the axioms on which the science of mechanics rests, that the cause\nis measured by the effects, that reaction is equal and opposite to\naction, and the like,--are not these evident to a mind cultivated by\nsteady thought on such subjects? and do they not require such culture\nof the mind in order to see them? Are they not obscure or uncertain\nto those who are not so cultured, that is to common thinkers: to the\ngeneral bulk of mankind? Thus then it requires the discipline of the\nscience of mechanics to enable the mind to see the axioms of that\nscience.\n\nAnd does not this go further, as science and the careful study of\nthe grounds of science go further? To a person well disciplined in\nmechanical reasoning it has become, not a conclusion, but a principle,\nthat in mechanical action what is gained in power is lost in time:\nor that in any change, the force gained is equal to the force lost,\nso that new force cannot be generated, any more than new matter, by\nnatural changes. Is this an axiom? a necessary fundamental truth? It\nappears so to at least one great thinker and discoverer now alive\namong us. If it do not appear so to us, or not in the same sense,\nmay not this be because we have not yet reached his point of view?\nMay not the conviction which is now his alone become hereafter the\nconviction of the philosophical world? And whatever the case may be\nin this instance, have there not been examples of this progress? Did\nnot Galileo and the disciples of Galileo reduce several mechanical\nprinciples to the character of necessary truths, after they had by\nexperiment and reasoning discovered them to be actually true? And\nhave we not in these cases so many proofs that necessary truth is\nprogressive, along with the progress of knowledge?\n\n2. But, it will be said, the necessary character claimed for such\ntruths is an illusion. The propositions so brought into view are really\nestablished by observation: by the study of external facts: and it is\nonly the effect of habit and familiarity which makes men of science,\nwhen they well know them to be true, think them to be necessarily true.\nThey are really the results of experience, as their history shows; and\ntherefore cannot be necessary and _\u00e0 priori_ truths.\n\nTo which I reply: Such principles as I have mentioned,--that material\nsubstance cannot be produced or destroyed--that the cause is measured\nby the effect--that reaction is equal and opposite to action: are not\nthe results of experience, nor can be. No experience can prove them;\nthey are necessarily assumed as the interpretation of experience.\nThey were not proved in the course of scientific investigations, but\nbrought to light as such investigations showed their necessity. They\nare not the results, but the conditions of experimental sciences.\nIf the Axiom of Substance were not true, and were not assumed, we\ncould not have such a science as Chemistry, that is, we could have\nno knowledge at all respecting the changes of form of substances.\nIf the Axioms of Mechanics were not true and were not assumed, we\ncould have no science of Mechanics, that is, no knowledge of the laws\nof force acting on matter. It is not any special _results_ of the\nscience in such cases; but the _existence_, the _possibility_, of\nany science, which establishes the necessity of these axioms. They\nare not the consequences of knowledge, acquired from without, but\nthe internal condition of our being able to know. And when we are to\n_know_ concerning any new subject contained in the universe, it is not\ninconceivable nor strange that there should be new conditions of our\nknowledge.\n\nIt is not inconceivable or strange, therefore, that as new sciences\nare formed, new axioms, the foundations of such sciences, should come\ninto view. As the light of clear and definite knowledge is kindled in\nsuccessive chambers of the universe, it may disclose, not only the\naspect of those new apartments, but also the form and structure of the\nlamp which man is thus allowed to carry from point to point, and to\ntransmit from hand to hand. And though the space illumined to man's\nvision may always be small in comparison with the immeasurable abyss of\ndarkness by which it is surrounded, and though the light may be dim and\nfeeble, as well as partial; this need not make us doubt that, so far as\nwe can by the aid of this lamp, we see truly: so far as we discern the\nnecessary laws of the universe, the laws are true, and their truth is\nrooted in that in which the being of the universe is rooted.\n\nAnd, to dwell for a moment longer on this image, we may also\nconceive that all that this lamp--the intellect of man cultivated by\nscience,--does, by the light which it gives, is this--that it dispels a\ndarkness which is dark for man alone, and discloses to him some things\nin some measure as all things lie in clear and perfect light before the\neye of God. To the Divine Mind all the laws of the universe are plain\nand clear in all their multiplicity, extent and depth. The human mind\nis capable of seeing some of these laws, though only a few; to some\nextent, though but a little way; to some depth, though never to the\nbottom. But the Human Mind, can, in the course of ages and generations,\nby the long exercise of thought, successfully employed in augmenting\nknowledge, improve its powers of vision; and may thus come to see more\nlaws than at first, to trace their extent more largely, to understand\nthem more thoroughly; and thus the inward intellectual light of man may\nbecome broader and broader from age to age, though ever narrow when\ncompared with completeness.\n\n3. Is it strange to any one that inward light, as well as outward\nknowledge, should thus increase in the course of man's earthly career?\nthat as knowledge extends, the foundations of knowledge should expand?\nthat as man goes on discovering new truths, he should also discover\nsomething concerning the conditions of truth? Is it wonderful that\nas science is progressive the philosophy of science also should be\nprogressive? that as we know more of everything else, we should also\ncome to know more of our powers of knowing?\n\nThis does not seem to have been supposed by philosophers in general;\nor rather, they have assumed that they could come to know more about\nthe powers of knowing by thinking about them, even without taking\ninto account the light thrown upon the nature of knowledge by the\nprogress of knowledge. From Plato downwards, through Aristotle,\nthrough the Schoolmen, to Descartes, to Locke, to Kant, Schelling and\nHegel, philosophers have been perpetually endeavouring to explore\nthe nature, the foundations, the consequences of our knowledge. But\nsince Plato, scarcely one of them has ever proceeded as if new light\nwere thrown upon knowledge by new knowledge. They have, many or all\nof them, attempted to establish fundamental truths, some of them new\nfundamental truths, about the human mind and the nature and conditions\nof its knowledge. These attempts show that they do not deny or doubt\nthat there may be such new fundamental truths. Such new fundamental\ntruths respecting the human mind and respecting knowledge must be, in\nmany cases at least, (as it will be seen that they _are_, on examining\nthe systems proposed by the philosophers just mentioned,) seen by\ntheir own light to be true. They are _new axioms_ in philosophy. These\nphilosophers therefore, or their disciples, cannot consistently blame\nus for holding the possibility of new axioms being introduced into\nphilosophy from age to age, as there arise philosophers more and more\nclear-sighted.\n\n4. But though _they_ have no ground for rejecting _our_ new axioms\nmerely because they are new, _we_ may have good ground for doubting\nthe value of _their_ new axioms, that is, of the foundations of their\nsystems; because they are new truths about knowledge gathered by\nmerely exploring the old fields of knowledge. We found our hopes of\nobtaining a larger view of the constitution of the human mind than the\nearly philosophers had, on this:--that we obtain our view by studying\nthe operation of the human mind _since their time_; its progress\nin acquiring a large stock of uncontested truths and in obtaining\na wide and real knowledge of the universe. Here are new materials\nwhich the ancients had not; and which may therefore justify the hope\nthat we may build our philosophy higher than the ancients did. But\nmodern philosophers who use only the same materials as the ancient\nphilosophers used, have not the same grounds for hope which we have. If\nthey borrow all their examples and illustrations of man's knowledge of\nthe universe, from the condition of the universe as existing in Space\nand Time, that is, from the geometrical condition of the universe, they\nmay fail to obtain the light which might be obtained if they considered\nthat the universe is also subject to conditions of _Substance_, of\n_Cause_ and _Effect_, of _Force_ and _Matter_: is filled with _Kinds_\nof things, in whose structure we assume _Design_ and _Ends_; and so on;\nand if they reflected that these conditions or _Ideas_ are not mere\nvague notions, but the bases of sciences which all thoughtful persons\nallow to be certain and real.\n\nIt is then, as I have said, from taking advantage of the progressive\ncharacter which physical science, in the history of man, has been\nfound to possess, that I hope to learn more of the nature and\nprospects of the human mind and soul, than those can learn who still\ntake their stand on the old limited ground of man's knowledge.\nThe knowledge of Geometry by the Greeks was the starting-point of\ntheir sound philosophy. It showed that something might be certainly\nknown, and it showed, in some degree, how it was known. It thus\nrefuted the skepticism which was destroying philosophy, and offered\nspecimens of solid truth for the philosopher to analyse. But the\nGreeks tried to go beyond geometry in their knowledge of the universe.\nThey tried to construct a science of Astronomy--of Harmonics--of\nOptics--of Mechanics. In the two former subjects, they succeeded to\na very considerable extent. The question then arose, What was the\nphilosophical import of these new sciences? What light did they throw\non the nature of the universe, on the nature of knowledge, on the\nnature of the human mind? These questions Plato attempted to answer. He\nsaid that the lesson of these new sciences is this:--that the universe\nis framed upon the _Divine Ideas_; that man can to a certain extent\nobtain sight of these Ideas; and that when he does this, he _knows_\nconcerning the universe. And again, he also put the matter otherwise:\nthere is an _Intelligible World_, of which the Visible and Sensible\nworld is only a dim image. _Science_ consists in understanding the\nIntelligible World, which man is to a certain extent able to do, by the\nnature of his understanding. This was Plato's philosophy, founded upon\nthe progress which human knowledge had made up to his time. Since his\ntime, knowledge, that is science, has made a large additional progress.\nWhat is the philosophical lesson to be derived from this progress,\nand from the new provinces thus added to human knowledge? This is a\nquestion which I have tried to answer. I am not aware that any one\nsince Plato has taken this line of speculation;--I mean, has tried\nto spell out the lesson of philosophy which is taught us, not by one\nspecimen, or a few only, of the knowledge respecting the universe which\nman has acquired; but by including in his survey all the provinces of\nhuman knowledge, and the whole history of each. At any rate, whatever\nany one else may have done in this way, it seems to me that new\ninferences remain to be drawn, of the nature of those which Plato drew:\nand those I here attempt to deduce and to illustrate.\n\n\n\n\nCHAPTER XXX.\n\nTHE THEOLOGICAL BEARING OF THE PHILOSOPHY OF DISCOVERY.\n\n\nThat necessary truth is progressive;--that science is the idealization\nof facts, and that this process goes on from age to age, and advances\nwith the advance of scientific discovery;--these are doctrines which\nI have endeavoured to establish and to elucidate. If these doctrines\nare true, they are so important that I may be excused should I return\nto them again and again, and trace their consequences in various\ndirections. Especially I would examine the bearing of these doctrines\nupon our religious philosophy. I have hitherto abstained in a great\nmeasure from discussing religious doctrines; but such a reserve carried\ntoo far must deprive our philosophy of all completeness. No philosophy\nof science can be complete which is not also a philosophy of the\nuniverse; and no philosophy of the universe can satisfy thoughtful\nmen, which does not include a reference to the power by which the\nuniverse came to be what it is. Supposing, then, such a reference to be\nadmitted, let us see what aspect our doctrines give to it.\n\n\n1. (_How can there be necessary truths concerning the actual\nuniverse?_)--In looking at the bearing of our doctrine on the\nphilosophy of the universe, we are met by a difficulty, which is\nindeed, only a former difficulty under a new aspect. When we are come\nto the conclusion that science consists of facts idealized, we are led\nto ask, How this can be? _How can_ facts be idealized? How can that\nwhich is a fact of external observation become a result of internal\nthought? How can that which was known _\u00e0 posteriori_ become known _\u00e0\npriori_? How can the world of things be identified with the world\nof thoughts? How can we discover a necessary connexion among mere\nphenomena?\n\nOr to put the matter otherwise: How is it that the deductions of the\nintellect are verified in the world of sense? How is it that the truths\nof science obtained _\u00e0 priori_ are exemplified in the general rules of\nfacts observed _\u00e0 posteriori_? How is it that facts, in science, always\ndo correspond to our ideas?\n\nI have propounded this paradox in various forms, because I wish it\nto be seen that it is, at first sight, a real, not merely a verbal\ncontradiction, or at least a difficulty. If we can discover the\nsolution of this difficulty in any one form, probably we can transpose\nthe answer so as to suit the other forms of the question.\n\n2. Suppose the case to be as I have stated it; that in some sciences at\nleast, laws which were at first facts of observation come to be seen as\nnecessary truths; and let us see to what this amounts in the several\nsciences.\n\nIt amounts to this: the truths of Geometry, such as we discern them by\nthe exercise of our own thoughts, are always verified in the world of\nobservation. The laws of space, derived from our Ideas, are universally\ntrue in the external world.\n\nIn the same way, as to number: the laws or truths respecting number,\nwhich are deduced from our Idea of Number, are universally true in the\nexternal world.\n\nIn the same way, as to the science which deals with matter and force:\nthe truths of which I have spoken as derived from Ideas:--that\naction is equal to reaction; and that causes are measured by their\neffects;--are universally verified in all the laws of phenomena of the\nexternal world, which are disclosed by the science of Mechanics.\n\nIn the same way with regard to the composition and resolution of bodies\ninto their elements; the truths derived from our Idea of Matter:--that\nno composition or resolution can increase or diminish the quantity\nof matter in the world, and that the properties of compounds are\ndetermined by their composition;--are truths derived from Ideas of\nquantity of matter, and of composition and resolution; but these truths\nare universally verified when we come to the facts of Chemistry.\n\nIn the same way it is a truth flowing from the Ideas of the Kinds of\nthings, (as the possible subject of general propositions expressed in\nlanguage,) that the kinds of things must be definite; and this law is\nverified whenever we express general propositions in general terms: for\ninstance, when we distinguish species in Mineralogy.\n\n3. This last example may appear to most readers doubtful. I have\npurposely pursued the enumeration till I came to a doubtful example,\nbecause it is, and I conceive always will be, impossible to extend this\ngeneral view to _all_ the Sciences. On the contrary, this doctrine\napplies at present to only a very few of the sciences, even in the eyes\nof those who hold the existence of ideal truths. The doctrine extends\nat present to a few only of the sciences, even if it extend to one\nor two besides those which have been mentioned--Geometry, Mechanics,\nChemistry, Mineralogy: and though it may hereafter appear that Ideal\nTruths are possible and attainable for a few other sciences, yet the\nlaws disclosed by sciences which cannot be reduced to ideal elements\nwill, I conceive, always very far outnumber those which can be so\nreduced. The great body of our scientific knowledge will always be\nknowledge obtained by mere observation, not knowledge obtained by the\nuse of theories alone.\n\n4. The survey of the history and philosophy of the Sciences which we\nhave attempted in previous works enables us to offer a sort of estimate\nof the relative portions of science which have and which have not\nthus been idealized. For the Aphorisms[317] which we have collected\nfrom that survey, contain Axioms which may be regarded as the Ideal\nportions of the various sciences; and the inspection of that series of\naphorisms will show us to how such a portion of science, anything of\nthis axiomatic or ideal character can he applied. These Axioms are the\nAxioms of Geometry (Aphorism XXVI); of Arithmetic (XXXVI); of Causation\n(XLVII); of a medium for the sensation of secondary qualities (LVIII),\nand their measure (LXIX); of Polarity (LXXII); of Chemical Affinity\n(LXXVI); of Substance (LXXVII); of Atoms (LXXIX).\n\nHave we any axioms in the sciences which succeed these in our survey,\nas Botany, Zoology, Biology, Pal\u00e6ontology?\n\nThere is the Axiom of Symmetry (LXXX); of Kind, (already in some\nmeasure spoken of, (LXXXIII)); of Final Cause (CV); of First Cause\n(CXVI).\n\n\n5. (_Small extent of necessary truth._)--It is easily seen how small\na portion of each of these latter sciences is included in these\naxioms: while, with regard to the sciences first mentioned, the Axioms\ninclude, in a manner, the whole of the science. The science is only\nthe consequence of the Axioms. The whole science of Mechanics is only\nthe development of the Axioms concerning action and reaction, and\nconcerning cause and its measures, which I have mentioned as a part of\nour Ideal knowledge.\n\nIn fact, beginning from Geometry and Arithmetic, and going through\nthe sciences of Mechanics, of Secondary Qualities, and of Chemistry,\nonwards to the sciences which deal with Organized Beings, we find that\nour ideal truths occupy a smaller and smaller share of the sciences\nin succession, and that the vast variety of facts and phenomena\nwhich nature offers to us, is less and less subject to any rules or\nprinciples which we can perceive to be necessary.\n\nBut still, that there are principles,--necessary principles, which\nprevail universally even in these higher parts of the natural\nsciences,--appears on a careful consideration of the axioms which I\nhave mentioned:--that in symmetrical natural bodies the similar parts\nare similarly affected;--that every event must have a cause;--that\nthere must be a First Cause, and the like.\n\n6. It being established, then, that in the progress of science,\nfacts are idealized--that _\u00e0 posteriori_ truths become _\u00e0 priori_\ntruths;--that the world of things is identified with the world of\nthoughts to a certain extent;--to an extent which grows larger as we\nsee into the world of things more clearly; the question recurs which I\nhave already asked: How can this be?\n\nHow can it be that the world without us is thus in some respects\nidentical with the world within us?--that is our question.\n\n\n7. (_How did things come to be as they are?_)--It would seem that we\nmay make a step in the solution of this question, if we can answer this\nother: How did the world without us and the world within us come to be\nwhat they are?\n\nTo this question, two very different answers are returned by those who\ndo and those who do not believe in a Supreme Mind or Intelligence, as\nthe cause and foundation of the world.\n\nThose who do not believe that the world has for its cause and\nfoundation a Supreme Intelligence, or who do not connect their\nphilosophy with this belief, would reply to our inquiry, that the\nreason why man's thoughts and ideas agree with the world is, that they\nare borrowed from the world; and that the persuasion that these Ideas\nand truths derived from them have any origin except the world without\nus, is an illusion.\n\nOn this view I shall not now dwell; for I wish to trace out the\nconsequences of the opposite view, that there exists a Supreme Mind,\nwhich is the cause and foundation of the universe. Those who hold this,\nand who also hold that the human mind can become possessed of necessary\ntruths, if they are asked how it is that these necessary truths are\nuniversally verified in the material world, will reply, that it is\nso because the Supreme Creative-Mind has made it so to be:--that the\ntruths which exist or can be generated in man's mind agree with the\nlaws of the universe, because He who has made and sustains man and the\nuniverse has caused them to agree:--that our Ideas correspond to the\nFacts of the world, and the Facts to our Ideas, because our Ideas are\ngiven us by the same power which made the world, and given so that\nthese can and must agree with the world so made.\n\n\n8. (_View of the Theist_).--This, in its general form, would be the\nanswer of the _theist_, (so we may call him who believes in a Supreme\nIntelligent Cause of the world and of man,) to the questions which we\nhave propounded--the perplexity or paradox which we have tried to bring\ninto view. But we must endeavour to trace this view--this answer--more\ninto detail.\n\nIf a Supreme Intelligence be the cause of the world and of the Laws\nwhich prevail among its phenomena, these Laws must exist as Acts of\nthat Intelligence--as Laws caused by the thoughts of the Supreme\nMind--as Ideas in the Mind of God. And then the question would be, How\nwe are to conceive these thoughts, these Ideas, to be at the same time\nDivine and human:--to be at the same time Ideas in the Divine Mind, and\nnecessary truths in the human mind; and this is the question which I\nwould now inquire into.\n\n\n9. (_Is this Platonism?_)--To the terms in which the inquiry is now\npropounded it may be objected that I am taking for granted the Platonic\ndoctrine, that the world is constituted according to the Ideas of the\nDivine Mind. It may be said that this doctrine is connected with gross\nextravagancies of speculation and fiction, and has long been obsolete\namong sound philosophers.\n\nTo which I reply, that if such doctrines have been pushed into\nextravagancies, with _them_ I have nothing to do, nor have I any\ndisposition or wish to revive them. But I do not conceive the doctrine,\nto the extent to which I have stated it, to be at all obsolete:--that\nthe Cause and Foundation of the Universe is a Divine Mind: and from\nthat doctrine it necessarily follows, that the laws of the Universe are\nin the Ideas of the Divine Mind.\n\nI would then, as I have said, examine the consequences of this\ndoctrine, in reference to the question of which I have spoken. And\nin order to do this, it may help us, if we consider separately the\nbearing of this doctrine upon separate portions of our knowledge of\nthe universe;--separately its bearing upon the laws which form the\nsubject-matter of different sciences:--if we take particular human\nIdeas, and consider what the Divine Ideas must be with regard to each\nof them.\n\n10. (_Idea of Space._)--Let us take, in the first place, the Idea\nof Space. Concerning this Idea we possess necessary truths; namely,\nthe Axioms of Geometry; and, as necessarily resulting from them, the\nwhole body of Geometry. And our former inquiry, as narrowed within the\nlimits of this Idea, will be, How is it that the truths of Geometry--_\u00e0\npriori_ truths--are universally verified in the observed phenomena of\nthe universe? And the theist's answer which we have given will now\nassume this form:--This is so because the Supreme Mind has constituted\nand constitutes the universe according to the Idea of Space. The\nuniverse conforms to the Idea of Space, and the Idea of Space exists\nin the human mind;--is necessarily evoked and awakened in the human\nmind existing in the universe. And since the Idea of Space, which is\na constituent of the universe, is also a constituent of the human\nmind, the consequences of this Idea in the universe and in the human\nmind necessarily coincide; that is, the _spacial_ Laws of the universe\nnecessarily coincide with the _spacial_ Science which man elaborates\nout of his mind.\n\n11. To this it may be objected, that we suppose the Idea of Space in\nthe Divine Mind (according to which Idea, among others, the universe is\nconstituted,) to be identical with the Idea of Space in the human mind;\nand this, it may be urged, is too limited and material a notion of the\nDivine Mind to be accepted by a reverent philosophy.\n\nI reply, that I suppose the Divine Idea of Space and the human Idea\nof Space to coincide, _only so far_ as the human Idea goes; and\nthat the Divine Idea may easily have so much more luminousness and\ncomprehensiveness as Divine Ideas may be supposed to have compared with\nhuman. Further, that this Idea of Space, the first of the Ideas on\nwhich human science is founded, is the most luminous and comprehensive\nof such Ideas; and there are innumerable other Ideas, the foundations\nof sciences more or less complete, which are extremely obscure and\nlimited in the human mind, but which must be conceived to be perfectly\nclear and unlimitedly comprehensive in the Divine Mind. And thus, the\ndistance between the human and the Divine Mind, even as to the views\nwhich constitute the most complete of the human sciences, is as great\nin our view as in any other.\n\n12. That the Idea of Space in the human mind, though sufficiently clear\nand comprehensive to be the source of necessary truths, is far too\nobscure and limited to be regarded as identical with the Divine Idea,\nwill be plain to us, if we call to mind the perplexities which the\nhuman mind falls into when it speculates concerning space infinite.\nAn Intelligence in which all these perplexities should vanish by the\nlight of the Idea itself, would be infinitely elevated in clearness and\ncomprehensiveness of intellectual vision above human intelligence, even\nthough its Idea of Space should coincide with the human Idea as far as\nthe human Idea goes.\n\nI do not shrink from saying, therefore, that the Idea of Space which\nis a constituent of the human mind existing in the universe is, as far\nas it goes, identical with the Idea of Space which is a constituent of\nthe universe. And this I give as the answer to the question, How it is\nthat the necessary truths of Geometry universally coincide with the\nrelations of the phenomena of the universe? And this doctrine, it is\nto be remembered, carries us to the further doctrine, that the Idea of\nSpace in the human mind is, so far as it goes, coincident with the Idea\nof Space in the Divine Mind.\n\n\n13. (_Idea of Time._)--What I have said of the Idea of Space, may\nbe repeated, for the most part, with regard to the Idea of Time;\nexcept that the Idea of Time, as such, does not give rise to a large\ncollection of necessary truths, such as the propositions of Geometry.\nSome philosophers regard Number as a modification or derivative of\nthe Idea of Time. If we accept this view, we have, in the Science of\nArithmetic, a body of necessary truths which flow from the Idea of\nTime. But this doctrine, whichever way held, does not bear much on\nthe question with which we are now concerned. That which we do hold\nis, that the Idea of Time in the human mind is, so far as it goes,\ncoincident with the Idea of Time in the Divine Mind: and that this\nis the reason why the events of the universe, as contemplated by us,\nconform to necessary laws of succession: while at the same time we must\nsuppose that all the perplexities in the Idea of Time which embarrass\nthe human mind--the perplexities, for instance, which arise from\ncontemplating a past and a future eternity, are, in the Divine Mind,\nextinguished in the Light of the Idea itself.\n\nSpace and Time have, and have generally been regarded as having,\npeculiar prerogatives in our speculations concerning the constitution\nof the universe. We see and perceive all things as subject to the laws\nof Space and Time; or rather (for the term _Law_ does not here satisfy\nus), as being and happening _in_ space and _in_ time: and probably most\npersons will have no repugnance to the doctrine that the Divine Mind,\nas well as the human, so regards them, and has so constituted them and\nus that they _must_ be so regarded. Space and Time are human Ideas\nwhich include all objects and events, and are the foundation of all\nhuman Science. And we can conceive that Space and Time are also Divine\nIdeas which the Divine Mind causes to include all objects and events,\nand makes to be the foundation of all existence. So far as these Ideas\ngo, our doctrine is not difficult or new.\n\n\n14. (_Ideas of Force and Matter._)--But what are we to say of the\nIdeas which come next in the survey of the sciences, Force and Matter?\nThese are human Ideas--the foundations of several sciences--of the\nmechanical sciences in particular. But are they the foundations of\nnecessary truths? Have we necessary truths respecting Force and Matter?\nWe have endeavoured to prove that we have:--that certain fundamental\npropositions in the Science of Mechanics, although, historically\nspeaking, they were discovered by observation and experience, are yet,\nphilosophically speaking, necessary propositions. And being such, the\nfacts of the universe must needs conform to these propositions; and\nthe reason why they do so, we hold, in this as in the former case,\nto be, that these Ideas, Force and Matter, are Ideas in the Divine\nMind:--Ideas according to which the universe is, by the Divine Cause,\nconstituted and established.\n\n15. That Force and Matter are Ideas existing in the Divine Mind, and\ncoincident with the Idea of Force and Matter in the human mind, as\nfar as these go, is a doctrine which is important in our view of the\nuniverse in relation to its Cause and Foundation.\n\nThese are very comprehensive and fundamental Ideas, and there are\ncertain universal relations among external things which rest upon these\nIdeas. The two, Force and Matter, are, in a certain way, the necessary\nantithesis and opposite condition each of the other. Force (that is\nMechanical Force, Pressure or Impulse) cannot act without matter to\nact upon. Matter (that is Body) cannot exist without Force by which\nit is kept in its place, by which its parts are held together, and by\nwhich it excludes every other body from the place which it occupies. We\ncannot conceive Force without Matter, or Matter without Force; the two\nare, as Action and Reaction, necessarily co-ordinate and coexistent.\nIn every part of the universe they must be so. In every part of the\nuniverse, if there be material objects, there must be Force; if there\nbe Force, there must be material objects.\n\nOur apprehension of this universal necessity arises from our having the\nIdeas of Force and Matter which are human Ideas. The actuality of this\nuniversal antithesis arises from the Ideas of Force and Matter being\nIdeas in the Divine Mind;--Ideas realized as a part of the fundamental\nconstitution of the universe.\n\nThat Force and Matter are thus among the Ideas in the Divine Mind,\nand that, with them, the Ideas of Force and Matter in the human mind,\nregarded in their most general form, agree so far as they go, is\nanother step in the doctrine which I am trying to unfold. That the\nIdeas of Force and Matter in the Divine Mind are such as to banish by\ntheir own light, innumerable contradictions and perplexities which\ndarken these Ideas in the human mind, is to be supposed: and thus the\nDivine Mind is infinitely luminous and comprehensive compared with the\nhuman mind.\n\n\n16. (_Creation of Matter._)--It may perhaps be urged, as an objection\nto this doctrine, that it asserts Matter to be a necessary constituent\nof the universe, and thus involves the assertion of the eternity of\nMatter. But in reality the doctrine asserts Matter to be eternal, only\nin the way in which time and space are eternal. Whether we hold that\nthere was a creation before which time and space did not exist,--with\nthe poet who says\n\n  Ere Time and Space _were_ Time and Space were _not_,--\n\nis not essential to our present inquiry. Certainly we cannot conceive\nsuch a state, and therefore cannot reason about it. We have no occasion\nhere to speak of Creation, nor have spoken of it. What I have said\nis, that Space and Time, Force and Matter are universal elements,\nprinciples, constituents, of the universe as it is--and necessary\nIdeas of the human mind existing in that universe. If there ever\nwas a Creation before which Matter did not exist, it was a Creation\nbefore which Force did not exist. And in the universe as it is, the\ntwo are necessarily co-existent in the human thought because they are\nco-existent in the Divine Thought which makes the world.\n\nWe apply then to Force and Matter the doctrine--the Platonic doctrine,\nif any one please so to call it,--that the world is constituted\naccording to the Ideas of the Divine Mind, and that the human mind\napprehends the inward and most fundamental relations of the universe by\nsharing in some measure of those same Ideas.\n\n\n17. (_Platonic Ideas._)--But do we go on with Plato to extend this\ndoctrine of Ideas to all the objects and all the aspects of objects\nwhich constitute the material universe? Do we say with Plato that there\nis not only an Idea of a Triangle by conformity to which a figure is a\ntriangle, but an Idea of Gold, by conformity to which a thing is gold,\nand Idea of a Table, by conformity to which a thing is a table?\n\nWe say none of these things. We say nothing which at all approaches to\nthem. We do not say that there is an Idea of a Triangle, the archetype\nof all triangles; we only say that man has an Idea of Space, which is\nan Idea of a fundamental reality; and that therefore from this Idea\nflow real and universal truths--about triangles and other figures.\nStill less do we say that we have an archetypal Idea of Gold, or of a\nMetal in general, or of any of the kinds of objects which exist in the\nworld. Here we part company with Plato altogether.\n\nBut have we any Ideas at all with regard to objects which we thus speak\nof as separable into Kinds? We can have knowledge,--even exact and\ngeneral knowledge, that is, science--with regard to such things--with\nregard to plants and metals--gold and iron. Do we possess in our minds,\nwith regard to those objects, any Ideas, any universal principles, such\nas we possess with regard to geometrical figures or mechanical actions?\nAnd if so, are those human Ideas verified in the universe, as the Ideas\nhitherto considered are? and do they thus afford us further examples\nof Ideas in the human mind which are also Ideas in the Divine Mind,\nmanifested in the constitution of the universe?\n\n\n18. (_Idea of Kinds._)--We answer _Yes_ to these questions, on this\nground:--the objects that exist in the world, plants and metals, gold\nand iron, for example, in order that they may be objects with regard\nto which we can have any knowledge, must be objects of distinct and\ndefinite thought. Plant must differ from metal, gold from iron, in\norder that we may know anything at all about any of these objects.\nThe differences by which such objects differ need not necessarily\nbe expressed by _definitions_, as the difference of a triangle and\na square are expressed; but there must manifestly _be_ fixed and\ndefinite differences, in order that we may have any knowledge about\nthem. These Kinds of things must be so far distinct and definite, as\nto be objects of distinct and definite thought. The _Kinds_ of natural\nobjects must differ, and we must think of things as of different Kinds,\nin order that we may know anything about natural objects. Living in a\nworld in which we exercise our Intellect upon the natural objects which\nsurround us, we must regard them as distinct from each other in Kind.\nWe must have an Idea of Kinds of natural objects.\n\n19. The Idea of a Kind involves this principle: That where the Kind\ndiffers the Properties may differ, but so far as the Kind is the same\nthe Properties contemplated in framing the notion of each Kind are the\nsame. Gold cannot have the distinctive properties of Iron without being\nIron.\n\nIn the case of human knowledge, each Kind is marked by a _word_--a\n_name_; and the doctrine that the notion of the Kind must be so applied\nthat this same Kind of object shall have the same properties, has\nbeen otherwise expressed by saying that Names must be so applied that\ngeneral propositions may be possible. We must so apply the name of Gold\nthat we may be able to say, gold has a specific gravity of a certain\namount and is ductile in a certain degree.\n\n20. But this condition of the names of Kinds,--that they must be\nsuch that general propositions about these Kinds of objects shall be\npossible;--is it a necessary result of the Idea of Kind? And if so, can\nthe Idea of Kind, thus implying the use of language, and a condition\ndepending on the use of language, be an Idea in the Divine as well as\nin the human mind? Can it be, in this respect, like the Ideas which we\nhave already considered, Space and Time, Force and Matter?\n\nWe cannot suppose that the Ideas which exist in the Divine Mind imply,\nin the Supreme Intelligence, the need of language, like human language.\nBut there is no incongruity in supposing that they imply that which\nwe take as the _condition_ of such language as we speak of, namely,\ndistinct thought. There is nothing incongruous in supposing that the\nSupreme Intelligence regards the objects which exist in the universe as\ndistinct in Kind: and that the Idea of Kind in the human mind agrees\nwith the Idea of Kind in the Divine Mind, as far as it goes. And as\nwe have seen, the Idea of Properties is correlative and coexistent\nwith the Idea of Kind, so that the one changing, the other changes\nalso. There is nothing incongruous in supposing that the Divine Mind\nmanifests in the universe of which it is the Cause and Foundation,\nthese two, its co-ordinate Ideas: and that the human mind sees that\nthese two Ideas are co-ordinate and coexistent, in virtue of its\nparticipating in these Ideas of the Divine Mind. The universe is full\nof things which man perceives do and must differ correspondingly in\nkind and in properties; and this is so, because the Ideas of various\nKinds and various Properties are part of the scheme of the universe in\nthe Divine Mind.\n\n21. That the Ideas of Kinds and Properties as coordinate and\ninterdependent, though common, to a certain extent, to the human and\nthe Divine Mind, are immeasurably more luminous, penetrating and\ncomprehensive in the Divine than in the human mind, is abundantly\nevident. In fact, though man assents to such axioms as these,--that\nthe Properties of Things depend upon their Kinds, and that the Kinds\nof Things are determined by their Properties,--yet the nature of\nconnexion of Kinds and Properties is a matter in which man's mind is\nall but wholly dark, and on which the Divine Mind must be perfectly\nclear. For in how few cases--if indeed in any one--can we know what\nis the essence of any Kind;--what is the real nature of the connexion\nbetween the character of the Kind and its Properties! Yet on this point\nwe must suppose that the Divine Intellect, which is the foundation of\nthe world, is perfectly clear. Every Kind of thing, every genus and\nspecies of object, appears to Him in its essential character, and its\nproperties follow as necessary consequences. He sees the essences of\nthings through all time and through all space; while we, slowly and\npainfully, by observation and experiment, which we cannot idealize or\ncan idealize only in the most fragmentary manner, make out a few of the\nproperties of each Kind of thing. Our Science here is but a drop in the\nocean of that truth, which is known to the Divine Mind but kept back\nfrom us; but still, that we can know and do know anything, arises from\nour taking hold of that principle, human as well as Divine, that there\nare differences of Kinds of things, and corresponding differences of\ntheir properties.\n\n\n22. (_Idea of Substance._)--I shall not attempt to enumerate all\nthe Ideas which, being thus a part of the foundation of Science in\nthe human mind and of Existence in the universe, are shown to be at\nthe same time Ideas in the Divine and in the human mind. But there\nis one other of which the necessary and universal application is so\nuncontested, that it may well serve further to exemplify our doctrine.\nIn all reasonings concerning the composition and resolution of the\nelements of bodies, it is assumed that the quantity of matter cannot be\nincreased or diminished by anything which we can do to them. We have an\nIdea of _Substance_, as something which may have its qualities altered\nby our operations upon it, but cannot have its quantity changed.\nAnd this Idea of Substance is universally verified in the facts of\nobservation and experiment. Indeed it cannot fail to be so; for it\nregulates and determines the way in which we interpret the facts of\nobservation and experiment. It authorized the philosopher who was asked\nthe weight of a column of smoke to reply, \"Subtract the weight of the\nashes from that of the fuel, and you have the weight of the smoke:\"\nfor in virtue of that idea we assume that, in combustion, or in any\nother operation, all the substance which is subjected to the operation\nmust exist in the result in some form or other. Now why may we\nreasonably make this assumption, and thus, as it were, prescribe laws\nto the universe? Our reply is, Because Substance is one of the Ideas\naccording to which the universe is constituted. The material things\nwhich make up the universe are substance according to this Idea. They\nare substance according to this Idea in the Divine Mind, and they are\nsubstance according to this Idea in the human mind, because the human\nmind has this Idea, to a certain extent, in common with the Divine\nMind. In this, as in the other cases, the Idea must be immeasurably\nmore clear and comprehensive in the Divine Mind than in the human.\nThe human Idea of substance is full of difficulty and perplexity: as\nfor instance; how a substance can assume successively a solid, fluid\nand airy form; how two substances can be combined so as entirely to\npenetrate one another and have new qualities: and the like. All these\nperplexities and difficulties we must suppose to vanish in the Divine\nIdea of Substance. But still there remains in the human, as in the\nDivine Idea, the source and root of the universal truth, that though\nsubstances may be combined or separated or changed in form in the\nprocesses of nature or of art, no portion of substance can come into\nbeing or cease to be.\n\n\n23. (_Idea of Final Cause._)--There is yet one other Idea which I shall\nmention, though it is one about which difficulties have been raised,\nsince the consideration of such difficulties may be instructive:\nthe Idea of a purpose, or as it is often termed, a _Final Cause_,\nin organized bodies. It has been held, and rightly[318], that the\nassumption of a Final Cause of each part of animals and plants is as\ninevitable as the assumption of an efficient cause of every event.\nThe maxim, that in organized bodies nothing is _in vain_, is as\nnecessarily true as the maxim that nothing happens _by chance_. I have\nelsewhere[319] shown fully that this Idea is not deduced from any\nspecial facts, but is assumed as a law governing all facts in organic\nnature, directing the researches and interpreting the observations\nof physiologists. I have also remarked that it is not at variance\nwith that other law, that plants and that animals are constructed\nupon general plans, of which plans, it may be, we do not see the\nnecessity, though we see how wide is their generality. This Idea of a\npurpose,--of a Final Cause,--then, thus supplied by our minds, is found\nto be applicable throughout the organic world. It is in virtue of this\nIdea that we conceive animals and plants as subject to _disease_; for\ndisease takes place when the parts do not fully answer their _purpose_;\nwhen they do not do what they _ought_ to do. How is it then that we\nthus find an Idea which is _supplied_ by our own minds, but which is\n_exemplified_ in every part of the organic world? Here perhaps the\nanswer will be readily allowed. It is because this Idea is an Idea of\nthe Divine Mind. There _is_ a Final Cause in the constitution of these\nparts of the universe, and therefore we can interpret them by means of\nthe Idea of Final Cause. We can _see_ a purpose, because there _is_\na purpose. Is it too presumptuous to suppose that we can thus enter\ninto the Ends and Purposes of the Divine Mind? We willingly grant and\ndeclare that it would be presumptuous to suppose that we can enter into\nthem to any but a very small degree. They doubtless go immeasurably\nbeyond our mode of understanding or conceiving them. But to a certain\nextent we _can_ go. We can go so far as to see that they _are_ Ends and\nPurposes. It is _not_ a vain presumption in us to suppose that we know\nthat the eye was made for seeing and the ear for hearing. In this the\nmost pious of men see nothing impious: the most cautious philosophers\nsee nothing rash. And that we can see thus far into the designs of\nthe Divine Mind, arises, we hold, from this:--that we have an Idea of\nDesign and of Purpose which, so far as it is merely _that_, is true;\nand so far, is Design and Purpose in the same sense in the one case and\nin the other.\n\nI am very far from having exhausted the list of Fundamental Ideas which\nthe human mind possesses and which have been made the foundations of\nSciences. Of all such Ideas, I might go on to remark, that they are of\nuniversal validity and application in the region of external Facts. In\nall the cases I might go on to inquire, How is it that man's Ideas,\ndeveloped in his internal world, are found to coincide universally\nwith the laws of the external world? By what necessity, on what ground\ndoes this happen? And in all cases I should have had to reply, that\nthis happens, and must happen, because these Ideas of the human mind\nare also Ideas of the Divine Mind according to which the universe is\nconstituted. Man has these thoughts, and sees them verified in the\nuniverse, because God had these thoughts and exemplifies them in the\nuniverse.\n\n\n24. (_Human immeasurably inferior to Divine_).--But of all these Ideas,\nI should also have to remark, that the way in which man possesses them\nis immeasurably obscure and limited in comparison with the way in\nwhich God must be supposed to possess them. These human Ideas, though\nclear and real as far as they go, in every case run into obscurity and\nperplexity, from which the Ideas of the Divine Mind must be supposed to\nbe free. In every case, man, by following the train of thought involved\nin each Idea, runs into confusion and seeming contradictions. It may\nbe that by thinking more and more, and by more and more studying the\nuniverse, he may remove some of this confusion and solve some of these\ncontradictions. But when he has done in this way all that he can, an\nimmeasurable region of confusion and contradiction will still remain;\nnor can he ever hope to advance very far, in dispelling the darkness\nwhich hangs over the greater part of the universe. His knowledge, his\nscience, his Ideas, extend only so far as he can keep his footing\nin the shallow waters which lie on the shore of the vast ocean of\nunfathomable truth.\n\n25. But further, we have not, even so, exhausted our estimate of the\nimmeasurable distance between the human mind and the Divine Mind:--very\nfar from it: we have only spoken of the smallest portion of the region\nof truth,--that about which we have Sciences and Scientific Ideas.\nIn that region alone do we claim for man the possession of Ideas the\nclearness of which has in it something divine. But how narrow is the\nprovince of Science compared with the whole domain of human thought! We\nmay enumerate the sciences of which we have been speaking, and which\ninvolve such Ideas as I have mentioned. How many are they? Geometry,\nArithmetic, Chemistry, Classification, Physiology. To these we might\nhave added a few others; as the sciences which deal with Light, Heat,\nPolarities; Geology and the other Pal\u00e6tiological Sciences; and there\nour enumeration at present must stop. For we can hardly as yet claim to\nhave Sciences, in the rigorous sense in which we use the term, about\nthe Vital Powers of man, his Mental Powers, his historical attributes,\nas Language, Society, Arts, Law, and the like. On these subjects few\nphilosophers will pretend to exhibit to us Ideas of universal validity,\nprevailing through all the range of observation. Yet all these things\nproceed according to Ideas in the Divine Mind by which the universe,\nand by which man, is constituted. In such provinces of knowledge,\nat least, we have no difficulty in seeing or allowing how blind man\nis with regard to their fundamental and constituent principles; how\nweak his reason; how limited his view. If on some of the plainest\nportions of possible knowledge, man have Ideas which may be regarded\nas coincident to a certain extent with those by which the universe is\nreally constituted; still on by far the largest portion of the things\nwhich most concern him, he has no knowledge but that which he derives\nfrom experience, and which he cannot put in so general a form as to\nhave any pretensions to rest it upon a foundation of connate Ideas.\n\n\n26. (_Science advances towards the Divine Ideas._)--But there is yet\none remark tending somewhat in the opposite direction, which I must\nmake, as a part of the view which I wish to present. Science, in the\nrigorous sense of the term, involves, we have said, Ideas which to a\ncertain extent agree with the Ideas of the Divine Mind. But science in\nthat sense is progressive; new sciences are formed and old sciences\nextended. Hence it follows that the Ideas which man has, and which\nagree with the Ideas of the Divine Mind, may receive additions to their\nnumber from time to time. This may seem a bold assertion; yet this is\nwhat, with due restriction, we conceive to be true. Such Ideas as we\nhave spoken of receive additions, in respect of their manifestation\nand development. The Ideas, the germ of them at least, were in the\nhuman mind before; but by the progress of scientific thought they are\nunfolded into clearness and distinctness. That this takes place with\nregard to scientific Ideas, the history of science abundantly shows.\nThe Ideas of Space and Time indeed, were clear and distinct from the\nfirst, and accordingly the Sciences of Geometry and Arithmetic have\nexisted from the earliest times of man's intellectual history. But the\nIdeas upon which the Science of Mechanics depends, having been obscure\nin the ancient world, are become clear in modern times. The Ideas of\nComposition and Resolution have only in recent centuries become so\nclear as to be the basis of a definite science. The Idea of Substance\nindeed was always assumed, though vaguely applied by the ancients; and\nthe Idea of a Design or End in vital structures is at least as old as\nSocrates. But the Idea of Polarities was never put forth in a distinct\nform till quite recently; and the Idea of Successive Causation, as\napplied in Geology and in the other Pal\u00e6tiological Sciences, was never\nscientifically applied till modern times: and without attempting to\nprove the point by enumeration, it will hardly be doubted that many\nScientific Ideas are clear and distinct among modern men of science\nwhich were not so in the ancient days.\n\nNow all such scientific Ideas are, as I have been urging, points on\nwhich the human mind is a reflex of the Divine Mind. And therefore in\nthe progress of science, we obtain, not indeed new points where the\nhuman mind reflects the Divine, but new points where this reflection is\nclear and luminous. We do not assert that the progress of science can\nbring _into existence_ new elements of truth in the human mind, but it\nmay bring them _into view_. It cannot add to the characters of Divine\norigin in the human mind, but it may add to or unfold the _proofs_ of\nsuch an origin. And this is what we conceive it does. And though we\ndo not conceive that the Ideas which science thus brings into view\nare the most important of man's thoughts in other respects, yet they\nmay, and we conceive do, supply a proof of the Divine nature of the\nhuman mind, which proof is of peculiar cogency. What other proofs may\nbe collected from other trains of human thought, we shall hereafter\nconsider.\n\n\n27. (_Recapitulation._)--This, then, is the argument to which we\nhave been led by the survey of the sciences in which we have been\nengaged:--That the human mind can and does put forth, out of its\nnatural stores, duly unfolded, certain Ideas as the bases of scientific\ntruths: These Ideas are universally and constantly verified in the\nuniverse: And the reason of this is, that they agree with the Ideas\nof the Divine Mind according to which the universe is constituted and\nsustained: The human mind has thus in it an element of resemblance to\nthe Divine Mind: To a certain extent it looks upon the universe as\nthe Divine Mind does; and therefore it is that it can see a portion\nof the truth: And not only can the human mind thus see a portion of\nthe truth, as the Divine Mind sees it: but this portion, though at\npresent immeasurably small, and certain to be always immeasurably small\ncompared with the whole extent of truth which with greater intellectual\npowers, he might discern, nevertheless may increase from age to age.\n\nThis is then, I conceive, one of the results of the progress of\nscientific discovery--the Theological Result of the Philosophy of\nDiscovery, as it may, I think, not unfitly be called:--That by every\nstep in such discovery by which external facts assume the aspect of\nnecessary consequences of our Ideas, we obtain a fresh proof of the\nDivine nature of the human mind: And though these steps, however far\nwe may go in this path, can carry us only a very little way in the\nknowledge of the universe, yet that such knowledge, so far as we do\nobtain it, is Divine in its kind, and shows that the human mind has\nsomething Divine in its nature.\n\nThe progress by which external facts assume the aspect of necessary\nconsequences of our Ideas, we have termed the idealization of facts;\nand in this sense we have said, that the progress of science consists\nin the Idealization of Facts. But there is another way in which the\noperation of man's mind may be considered--an opposite view of the\nidentification of Ideas with Facts; which we must consider, in order to\ncomplete our view of the bearing of the progress of human thought upon\nthe nature of man.\n\n\nFOOTNOTES:\n\n[Footnote 317: Given in the _Novum Organon Renovatum_.]\n\n[Footnote 318: _Nov. Org. Ren._ Aph. cv.]\n\n[Footnote 319: _Hist. Sc. Id._ b. ix. c. vi.]\n\n\n\n\nCHAPTER XXXI.\n\nMAN'S KNOWLEDGE OF GOD.\n\n\n1. Man's powers and means of knowledge are so limited and imperfect\nthat he can know _little_ concerning God. It is well that men in their\ntheological speculations should recollect that it is so, and should\npursue all such speculations in a modest and humble spirit.\n\nBut this humility and modesty defeat their own ends, when they lead us\nto think that we can know _nothing_ concerning God: for to be modest\nand humble in dealing with this subject, implies that we know _this_,\nat least, that God is a proper object of modest and humble thought.\n\n2. Some philosophers have been led, however, by an examination of man's\nfaculties and of the nature of being, to the conclusion that man can\nknow _nothing_ concerning God. But we may very reasonably doubt the\ntruth of this conclusion. We may ask, How can we _know_ that we _can_\nknow nothing? If we can know nothing, we cannot even know that.\n\nIt is much more reasonable to begin with things that we really do know,\nand to examine how far such knowledge can carry us, respecting God, as\nwell as anything else. This is the course which we have been following,\nand its results are very far from being trifling or unimportant.\n\nIn thus beginning from what we know, we start from two points, on each\nof which we have, we conceive, some real and sure knowledge:--namely,\nmathematical and physical knowledge of the universe without us; and a\nknowledge of our own moral and personal nature within us.\n\n\n3. (_From Nature we learn something of God._)--In pursuing the first\nline of thought, we are led to reason thus. The universe is governed\nby certain Ideas: for instance, everything which exists and happens in\nthe universe, exists and happens IN _Space_ and _Time_. Why is this?\nIt is, we conceive, because God has constituted and constitutes the\nuniverse so that it may be so; that is, because the Ideas of Space and\nof Time are Ideas according to which God has established and upholds\nthe universe.\n\nBut we may proceed further in this way, as we have already said.\nThe universe not only exists in space and time, but it has in it\nsubstances--material substances: or taking it collectively, Material\n_Substance_. Can we know anything concerning this substance? Yes:\nsomething we can know; for we know that material substance cannot be\nbrought into being or annihilated by any natural process. We have then\nan Idea of Substance which is a Law of the universe. How is this?--We\nreply, that it is because our Idea of Substance is an Idea on which God\nhas established and upholds the universe.\n\nCan we proceed further still? Can we discern any other Ideas according\nto which the universe is constituted? Yes: as we have already remarked,\nwe can discern several, though as we go on from one to another\nthey become gradually fainter in their light, less cogent in their\nnecessity. We can see that Force as well as Material Substance is\nan Idea on which the universe is constituted, and that _Force_ and\n_Matter_ are a necessary and universal antithesis: we can see that\nthe Things which occupy the universe must be of definite _Kinds_, in\norder that an intelligent mind may occupy itself about them, and thus\nthat the Idea of Kind is a constitutive Idea of the universe. We can\nsee that some kinds of things have life, and our Idea of Life is,\nthat every part of a living thing is a means to an End; and thus we\nrecognize _End_, or Final Cause, as an Idea which prevails throughout\nthe universe, and we recognize this Idea as an Idea according to which\nGod constitutes and upholds the universe.\n\nSince we know so much concerning the universe, and since every Law of\nthe universe which is a necessary form of thought about the universe\nmust exist in the _Divine_ Mind, in order that it may find a place in\n_our_ minds, how can we say that we can know nothing concerning the\nDivine Mind?\n\n\n4. (_Though but Little._)--But on the other hand, we easily see how\nlittle our knowledge is, compared with what we do not know. Even the\nparts of our knowledge which are the clearest are full of perplexities;\nand of the Laws of the universe, including living as well as lifeless\nthings, how small a portion do we know at all!\n\nEven the parts of our knowledge which are the clearest, I say, are\nfull of perplexities. Infinite Space and an infinite Past, an infinite\nFuture,--how helplessly our reason struggles with these aspects of\nour Ideas! And with regard to _Substance_, how did ingenerable and\nindestructible substance come into being? And with regard to _Matter_,\nhow can passive Matter be endued with living force? And with regard to\n_Kinds_, how immeasurably beyond our power of knowing are their numbers\nand their outward differences: still more their internal differences\nand central essence! And with regard to the _Design_ which we see in\nthe organs of living things, though we can confidently say we see it,\nhow obscurely is it shown, and how much is our view of it disturbed by\nother Laws and Analogies! And the Life of things, the end to which such\nDesign tends, how full of impenetrable mysteries is it! or rather how\nentirely a mass of mystery into which our powers of knowledge strive in\nvain to penetrate!\n\nThere is therefore no danger that by following this train of thought\nwe should elevate our view of man too high, or bring down God in our\nthoughts to the likeness of man. Even if we were to suppose the Idea\nof the Divine Mind to be of the same kind as the Ideas of the human\nmind, the very few Ideas of this kind, which man possesses, compared\nwith the whole range of the universe, and the scanty length to which\nhe can follow each, make his knowledge so small and imperfect, that\nhe has abundant reason to be modest and humble in his contemplations\nconcerning the Intelligence that knows all and constitutes all. He can,\nas I have already said, wade but a few steps into the margin of the\nboundless and unfathomable ocean of truth.\n\n5. But the Ideas of the Divine Mind must necessarily be different in\nkind, as well as in number and extent, from the Ideas of the human\nmind, on this very account, that they are complete and perfect. The\nMind which can conceive all the parts and laws of the universe in all\ntheir mutual bearings, fundamental reasons, and remote consequences,\nmust be different in kind, as well as in extent, from the mind which\ncan only trace a few of these parts, and see these laws in a few of\ntheir aspects, and cannot sound the whole depth of any of them. The\nDivine Mind differs from the human, in the way in which we must needs\nsuppose what is Divine to differ from what is human.\n\n6. It has sometimes been said that the Divine Mind differs from the\nhuman as the Infinite from the finite. And this has been given as a\nreason why we cannot know anything concerning God; for we cannot,\nit is said, know _anything_ concerning the Infinite. Our conception\nof the Infinite being merely negative, (the negation of a limit,)\nmakes all knowledge about it impossible. But this is not truly said.\nOur conception of the Infinite is _not_ merely negative. As I have\nelsewhere remarked, our conception of the Infinite is positive in this\nway:--that in order to form this conception, we begin to follow a given\nIdea in a given direction; and then, having thus begun, we suppose that\nthe progress of thought goes on in that direction without limit. To\narrive at our Idea of infinite space, for example, we must determine\nwhat kind of space we mean,--line, area or solid; and from what origin\nwe begin: and infinite space has different attributes as we take\ndifferent beginnings in this way.\n\nAnd so with regard to the kinds of infinity (for there are many) which\nbelong to the Divine Mind. _We_ have a few Ideas which represent the\nLaws of the universe:--as Space, Time, Substance, Force, Matter, Kind,\nEnd; of such Ideas the Divine Mind may have an infinite number. These\nIdeas in the human mind are limited in depth and clearness: in the\nDivine Mind they must be infinitely clearer than the clearest human\nIntuition; infinitely more profound than the profoundest human thought.\nAnd in this way, and, as we shall see, in other ways also, the Divine\nMind infinitely transcends the human mind when most fully instructed\nand unfolded.\n\nIn this way and in other ways also, I say. For we have hitherto spoken\nof the human mind only as contemplating the external world;--as\ndiscerning, to a certain small extent, the laws of the universe. We\nhave spoken of the world of things without: we must now speak of the\nworld within us;--of the world of our thoughts, our being, our moral\nand personal being.\n\n\n7. (_From ourselves we learn something concerning God._)--We must\nspeak of this: for this is, as I have said, another starting point and\nanother line in which we may proceed from what we know, and see how far\nour knowledge carries us, and how far it teaches us anything concerning\nGod.\n\nLooking at ourselves, we perceive that we have to act, as well as\nto contemplate: we are practical as well as speculative beings. And\ntracing the nature and conditions of our actions, in the depths of our\nthought we find that there is in the aspect of actions a supreme and\ninevitable distinction of right and wrong. We cannot help judging of\nour actions as right and wrong. We acknowledge that there must be such\na judgment appropriate to them. We have these Ideas of _right_ and\n_wrong_ as attributes of actions; and thus we are _moral_ beings.\n\n8. And again: the actions are _our_ actions. _We_ act in this way or\nthat. And _we_ are not mere _things_, which move and change as they\nare acted on, but which do not themselves act, as man acts. I am not a\nThing but a _Person_; and the men with whom I act, who act with me--act\nin various ways towards me, well or ill--are also persons. Man is a\npersonal being.\n\nThe Ideas of right and wrong--the _moral_ Ideas of man--are then a part\nof the scheme of the universe to which man belongs. Could they be this,\nif they were not also a part of the nature of that Divine Mind which\nconstitutes the universe?--It would seem not: the Moral Law of the\nuniverse must be a Law of the Divine Mind, in order that it may be a\nLaw felt and discerned by man.\n\n\n9. (_Objection answered._)--But, it may be objected, the Moral Law\nof the universe is a Law in a different sense from the Laws of the\nuniverse of which we spoke before--the mathematical and physical laws\nof the universe. Those were laws according to which things _are_, and\nevents _occur_: but Moral Laws are Laws according to which men _ought_\nto act, and according to which actions _ought_ to be. There is a\ndifference, so that we cannot reason from the human to the Divine Mind\nin the same manner in this case as in the other.\n\nTrue: we cannot reason _in the same manner_. But we can reason still\nmore confidently. For the Law directing what _ought to be_ is the\n_Supreme Law_, and the mind which constitutes the Supreme Law is the\n_Supreme Mind_, that is, the Divine Mind.\n\n10. That the Moral Law is not verified among men in fact, is not a\nground for doubting that it is a Law of the Divine Mind; but it is a\nground for inquiring what consequences the Divine Mind has annexed to\nthe violation of the Law; and in what manner the supremacy of the Law\nwill be established in the total course of the history of the universe,\nincluding, it may be, the history of other worlds than that in which we\nnow live.\n\nConsidering how dimly and imperfectly we see what consequences the\nDivine Governor has annexed to the violation of the Moral Law, He who\nsees all these consequences and has provided for the establishment of\nHis Law in the whole history of the human race, must be supposed to be\ninfinitely elevated above man in wisdom;--more even in virtue of this\naspect of His nature, than in virtue of that which is derived from the\ncontemplation of the universe.\n\n11. Man is a person; and his personality is his _highest_ attribute,\nor at least, that which makes all his highest attributes possible.\nAnd the highest attribute which belongs to the finite minds which\nexist in the universe must exist also in the Infinite Mind which\nconstitutes the universe as it is. The Divine Mind must reside in a\n_Divine Person_. And as man, by his personality, acts in obedience to\nor in transgression of a moral law, so God, by His Personality, acts in\nestablishing the Law and in securing its supremacy in the whole history\nof the world.\n\n\n12. (_Creation._)--Acknowledging a Divine Mind which is the foundation\nand support of the world as it is, constituting and upholding its laws,\nit may be asked, Does this view point to a beginning of the world?\nWas there a time when the Divine Mind called into being the world,\nbefore non-existent? Was there a Creation of the world?\n\nI do not think that an answer to this question, given either way,\naffects the argument which I have been urging. The Laws of the\nUniverse discoverable by the human mind, are the Laws of the Divine\nMind, whether or not there was a time when these Laws first came into\noperation, or first produced the world which we see. The argument\nrespecting the nature of the Divine Mind is the same, whether or not we\nsuppose a Creation.\n\nBut, in point of fact, every part of our knowledge of the Universe does\nseem to point to a beginning. Every part of the world has been, so far\nas we can see, formed by natural causes out of something different\nfrom what it now is. The Earth, with its lands and seas, teeming with\ninnumerable forms of living things, has been produced from an earth\nformed of other lands and seas, occupied with quite different forms of\nlife: and if we go far enough back, from an earth in which there was\nno life. The stars which we call _fixed_ move and change; the nebul\u00e6\nin their shape show that they too are moving and changing. The Earth\nwas, some at least hold, produced by the condensation of a nebula.\nThe history of man, as well as of others of its inhabitants, points\nto a beginning. Languages, Arts, Governments, Histories, all seem to\nhave begun from a starting-point, however remote. Indeed not only a\nbeginning, but a beginning at no remote period, appears to be indicated\nby most of the sciences which carry us backwards in the world's history.\n\nBut we must allow, on the other hand, that though all such lines of\nresearch point _towards_ a beginning, none of them can be followed _up\nto_ a beginning. All the lines converge, but all melt away before they\nreach the point of convergence. As I have elsewhere said[320], in no\nscience has man been able to arrive at a beginning which is homogeneous\nwith the known course of events, though we can often go very far\nback, and limit the hypotheses respecting the origin. We have, in the\nimpossibility of thus coming to any conclusion by natural reason on the\nsubject of creation, another evidence of the infinitely limited nature\nof the human mind, when compared with the Creative or Constitutive\nDivine Mind.\n\n\n13. (_End of the World._)--But if our natural reason, aided by all\nthat science can teach, can tell us nothing respecting the origin\nand beginning of this world, still less can reason tell us anything\nwith regard to the _End_ of this world. On this subject, the natural\nsciences are even more barren of instruction than on the subject of\nCreation. Yet we may say that as the Constitution of the Universe, and\nits conformity to a Collection of eternal and immutable Ideas as its\nelements, are not inconsistent with the supposition of a Beginning of\nthe present course of the world, so neither are they inconsistent with\nthe supposition of an End. Indeed it would not be at all impossible\nthat physical inquiries should present the prospect of an End, even\nmore clearly than they afford the retrospect of a Beginning. If, for\ninstance, it should be found that the planets move in a resisting\nmedium which constantly retards their velocity, and must finally\nmake them fall in upon the central sun, there would be an end of the\nearth as to its present state. We cannot therefore, on the grounds of\nScience, deny either a Beginning or an End of the present world.\n\n\n14. But here another order of considerations comes into play, namely,\nthose derived from moral and theological views of the world. On these\nwe must, in conclusion, say a few words.\n\nIt is very plain that these considerations may lead us to believe in\na view of the Beginning, Middle, and End of the history of the world,\nvery different from anything which the mere physical and natural\nsciences can disclose to us. And these expressions to which I have\nbeen led, the _Beginning_, the _Middle_, and the _End_ of the world's\nhistory according to theological views, are full of suggestions of the\nhighest interest. But the interest which belongs to these suggestions\nis of a solemn and peculiar kind; and the considerations to which\nsuch suggestions point are better, I think, kept apart from such\nspeculations as those with which I have been concerned in the present\nvolume.\n\n\nFOOTNOTES:\n\n[Footnote 320: _Hist. Ind. Sc._ b. xviii. c. vi. sect. 5]\n\n\n\n\nCHAPTER XXXII.\n\nANALOGIES OF PHYSICAL AND RELIGIOUS PHILOSOPHY.\n\n\n1. Any assertion of analogy between physical and religious philosophy\nwill very properly be looked upon with great jealousy as likely to\nbe forced and delusive; and it is only in its most general aspects\nthat a sound philosophy on the two subjects can offer any points of\nresemblance. But in some of its general conditions the discovery of\ntruth in the one field of knowledge and in the other may offer certain\nanalogies, as well as differences, which it may be instructive to\nnotice; and to some such aspects of our philosophy I shall venture to\nrefer.\n\nFor the physical sciences--the sciences of observation and\nspeculation--the progress of our exact and scientific knowledge, as\nI have repeatedly said, consists in reducing the objects and events\nof the universe to a conformity with Ideas which we have in our own\nminds:--the Ideas, for instance, of Space, Force, Substance, and the\nlike. In this sense, the intellectual progress of men consists in the\nIdealization of Facts.\n\n2. In moral subjects, on the other hand, where man has not merely to\nobserve and speculate, but also to act;--where he does not passively\nleave the facts and events of the world such as they are, but tries\nactively to alter them and to improve the existing state of things,\nhis progress consists in doing this. He makes a moral advance when he\nsucceeds in doing what he thus attempts:--when he really improves the\nstate of things with which he has to do by removing evil and producing\ngood:--when he makes the state of things, namely, the relations between\nhim and other persons, his acts and their acts, conform more and\nmore to Ideas which he has in his own mind:--namely, to the Ideas of\nJustice, Benevolence, and the like. His moral progress thus consists in\nthe realization of Ideas.\n\nAnd thus we are led to the Aphorism, as we may call it, that _Man's\nIntellectual Progress consists in the Idealization of Facts, and his\nMoral Progress consists in the Realization of Ideas_.\n\n\n3. But further, though that progress of science which consists in\nthe idealization of facts may be carried through several stages, and\nindeed, in the history of science, has been carried through many\nstages, yet it is, and always must be, a progress exceedingly imperfect\nand incomplete, when compared with the completeness to which its nature\npoints. Only a few sciences have made much progress; none are complete;\nmost have advanced only a step or two. In none have we reduced all the\nFacts to Ideas. In all or almost all the unreduced Facts are far more\nnumerous and extensive than those which have been reduced. The general\nmass of the facts of the universe are mere facts, unsubdued to the rule\nof science. The Facts are not Idealized. The intellectual progress\nis miserably scanty and imperfect, and would be so, even if it were\ncarried much further than it is carried. How can we hope that it will\never approach to completeness?\n\n4. And in like manner, the _moral_ progress of man is still more\nmiserably scanty and incomplete. In how small a degree has he in this\nsense realized his Ideas! In how small a degree has he carried into\nreal effect, and embodied in the relations of society, in his own acts\nand in those of others with whom he is concerned, the Ideas of Justice\nand Benevolence and the like! How far from a complete realization of\nsuch moral Ideas are the acts of the best men, and the relations of\nthe best forms of society! How far from perfection in these respects\nis man! and how certain it is that he will always be very far from\nperfection! Far below even such perfection as he can conceive, he will\nalways be in his acts and feelings. The moral progress of man, of each\nman, and of each society, is, as I have said, miserably scanty and\nincomplete; and when regarded as the realization of his moral Ideas,\nits scantiness and incompleteness become still more manifest than\nbefore.\n\nHence we are led to another Aphorism:--_that man's progress in the\nrealization of Moral Ideas, and his progress in the Scientific\nidealization of Facts, are, and always will be, exceedingly scanty and\nincomplete_.\n\n\n5. But there is another aspect of Ideas, both physical and moral,\nin which this scantiness and incompleteness vanish. In the Divine\nMind, all the physical Ideas are entertained with complete fulness\nand luminousness; and it is because they are so entertained in the\nDivine Mind, and it is because the universe is constituted and framed\nupon them, that we find them verified in every part of the universe,\nwhenever we make our observation of facts and deduce their laws.\n\nIn like manner the Moral Ideas exist in the Divine Mind in complete\nfulness and luminousness; and we are naturally led to believe and\nexpect that they must be exemplified in the moral universe, as\ncompletely and universally as the physical laws are exemplified in the\nphysical universe. Is this so? or under what conditions can we conceive\nthis to be?\n\n6. In answering this question, we must consider how far the moral,\nstill more even than the physical Ideas of the Divine Mind, are\nelevated above our human Ideas; but yet not so far as to have no\nresemblance to our corresponding human Ideas; for if this were so, we\ncould not reason about them at all.\n\nIn speaking of man's moral Ideas, Benevolence, Justice, and the like,\nwe speak of them as belonging to man's _Soul_, rather than to his\n_Mind_, which we have commonly spoken of as the seat of his physical\nIdeas. A distinction is thus often made between the intellectual and\nthe moral faculties of man; but on this distinction we here lay no\nstress. We may speak of man's _Mind_ and _Soul_, meaning that part of\nhis being in which are all his Ideas, intellectual and moral.\n\nAnd now let us consider the question which has just been asked:--how we\ncan conceive the Divine Benevolence and Justice to be completely and\nuniversally realized in the moral world, as the Ideas of Space, Time,\n&c. are in the physical world?\n\n\n7. Our Ideas of Benevolence, Justice, and of other Virtues, may be\nelevated above their original narrowness, and purified from their\noriginal coarseness, by moral culture; as our Ideas of Force and\nMatter, of Substance and Elements, and the like, may be made clear\nand convincing by philosophical and scientific culture. This appears,\nin some degree, in the history of moral terms, as the progress of\nclearness and efficacy in the Idea of the material sciences appears in\nthe history of the terms belonging to such sciences. Thus among the\nRomans, while they confined their kindly affections within their own\nclass, a stranger was universally an enemy; _peregrinus_ was synonymous\nwith _hostis_. But at a later period, they regarded all _men_ as having\na claim on their kindness; and he who felt and acted on this claim was\ncalled _humane_. This meaning of the word _humanity_ shows the progress\n(in their Ideas at least) of the virtue which the word _humanity_\ndesignates.\n\n8. And as man can thus rise to a point of view where he sees that man\nis to be loved as man, so the humane and loving man inevitably assumes\nthat God loves all men; and thus assumes that there is, or may be, a\nlove of man in man's heart, which represents and resembles in kind,\nhowever remote in degree, the love of God to man.\n\nBut as in man's love of man there are very widely different stages,\nrising from the narrow love of a savage to his family or his tribe,\nto the widest and warmest feelings of the most enlightened and loving\nuniversal philanthropist;--so must we suppose that there are stages\nimmeasurably wider by which God's love of man is more comprehensive and\nmore tender than any love of man for man. The religious philosopher\nwill fully assent to the expressions of this conviction delivered by\npious men in all ages. \"The eternal God is thy refuge, and beneath\nthee are the everlasting arms.\" \"When my father and my mother forsake\nme the Lord taketh me up,\" is the expression of Divine Love, consistent\nwith philosophy as well as with revelation. But as the Divine Love is\nmore comprehensive and enduring than any human love, so is it in an\nimmeasurably greater degree, more enlightened. It is not a love that\nseeks merely the pleasure and gratification of its object; _that_\neven an enlightened human love does not do. It seeks the good of its\nobjects; and such a good as is the greatest good, to an Intelligence\nwhich can embrace all cases, causes, and contingencies. To our limited\nunderstanding, evil seems often to be inflicted, and the good of a\npart seems inconsistent with the good of another part. Our attempts to\nconceive a Supreme and complete Good provided for all the creatures\nwhich exist in the universe, baffle and perplex us, even more than our\nattempts to conceive infinite space, infinite time, and an infinite\nchain of causation. But as the most careful attention which we can\ngive to the Ideas of Space, Time, and Causation convinces us that\nthese Ideas are perfectly clear and complete in the Divine Mind, and\nthat _our_ perplexity and confusion on these subjects arise only from\nthe vast distance between the Divine Mind and our human mind, so is\nit reasonable to suppose the same to be the source of the confusion\nwhich we experience when we attempt to determine what most conduces to\nthe good of our fellow-creatures; and when, urged by love to them, we\nendeavour to promote this good. We can do little of what Infinite Love\nwould do, yet are we not thereby dispensed from seeking in some degree\nto imitate the working of Divine Love. We can see but little of what\nInfinite Intelligence sees, and this should be one source of confidence\nand comfort, when we stumble upon perplexities produced by the seeming\nmixture of good and evil in the world.\n\n9. But when we ask the questions which have already been stated:\nWhether this Infinite Divine Love is realized in the world, and if\nso, How: I conceive that we are irresistibly impelled to reply to the\nformer question, that it is: and we then turn to the latter. We are\nled to assume that there is in God an Infinite Love of man, a creature\nin a certain degree of a Divine nature. We must, as a consequence of\nthis, assume that the Love of God to man, necessarily is, in the end,\nand on the whole, completely and fully realized in the history of the\nworld. But what is the complete history of the world! Is it that which\nconsists in the lives of men such as we see them between their birth\nand their death? If the minds or souls of men are alive after the death\nof the body, that future life, as well as this present life, belongs to\nthe history of the world;--to that providential history, of which the\ntotality, as we have said, must be governed by Infinite Divine Love.\nAnd in addition to all other reasons for believing that the minds and\nsouls of men do thus survive their present life, is this:--that we thus\ncan conceive, what otherwise it is difficult or impossible to conceive,\nthe operation of Infinite Love in the whole of the history of mankind.\nIf there be a Future State in which men's souls are still under the\nauthority and direction of the Divine Governor of the world, all that\nis here wanting to complete the scheme of a perfect government of\nIntelligent Love may thus be applied: all seeming and partial evil may\nbe absorbed and extinguished in an ultimate and universal good.\n\n\n10. The Idea of Justice as belonging to God suggests to us some of the\nsame kind of reflexions as those which we have made respecting the\nDivine Love. We believe God to be just: otherwise, as has been said,\nHe would not be God. And as we thus, from the nature of our minds and\nsouls, believe God to be just, we must, in this belief, understand\nJustice according to the Idea which we have of Justice; that is, in\nsome measure, according to the Idea of Justice, as exemplified in\nhuman actions and feelings. It would be absurd to combine the two\npropositions, that we necessarily believe that God is just, and that by\n_just_, we mean something entirely different from the common meaning of\nthe word.\n\nBut though the Divine Idea of Justice must necessarily, in some\nmeasure, coincide with our Idea of Justice, we must believe in this,\nas in other cases, that the Divine Idea is immeasurably more profound,\ncomprehensive, and clear, than the human Idea. Even the human Idea of\nJustice is susceptible of many and large progressive steps, in the way\nof clearness, consistency, and comprehensiveness. In the moral history\nof man this Idea advances from the hard rigour of inflexible written\nLaw to the equitable estimation of the real circumstances of each case;\nit advances also from the narrow Law of a single community to a larger\nLaw, which includes and solves the conflicts of all such Laws. Further,\nthe administration of human Law is always imperfect, often erroneous,\nin consequence of man's imperfect knowledge of the facts of each case,\nand still more, from his ignorance of the designs and feelings of the\nactors. If the Judge could see into the heart of the person accused,\nand could himself rise higher and higher in judicial wisdom, he might\nexemplify the Idea of Justice in a far higher degree than has ever yet\nbeen done.\n\n11. But all such advance in the improvement of human Justice must\nstill be supposed to stop immeasurably short of the Divine Justice,\nwhich must include a perfect knowledge of all men's actions, and all\nmen's hearts and thoughts; and a universal application of the wisest\nand most comprehensive Laws. And the difference of the Divine and of\nthe human Idea of Justice may, like the differences of other Divine\nand human Ideas, include the solution of all the perplexities in which\nwe find ourselves involved when we would trace the Idea to all its\nconsequences. The Divine Idea is immeasurably elevated above the human\nIdea; in the Divine Idea all inconsistency, defect, and incompleteness\nvanish, and Justice includes in its administration every man, without\nany admixture of injustice. This is what we must conceive of the Divine\nadministration, since God is perfectly just.\n\n12. But here, as before, we have another conclusion suggested to us. We\nare, by the considerations just now spoken of, led to believe that, in\nthe Divine administration of the world is an administration of perfect\nJustice;--that is, such is the Divine Administration in the end and on\nthe whole, taking into account the whole of the providential history of\nthe world. But the course of the world, taking into account only what\nhappens to man in this present life, is not, we may venture to say, a\ncomplete and entire administration of justice. It often happens that\ninjustice is successful and triumphant, even in the end, so far as the\nend is seen here. It happens that wrong is done, and is not remedied\nor punished. It happens that blameless and virtuous men are subjected\nto pain, grief, violence, and oppression, and are not protected,\nextricated, or avenged. In the affairs of this world, the prevalence of\ninjustice and wrong-doing is so apparent, as to be a common subject of\ncomplaint: and though the complaint may be exaggerated, and though a\ncalm and comprehensive view may often discern compensating and remedial\ninfluences which are not visible at first sight, still we cannot regard\nthe lot of happiness or misery which falls to each man in this world\nand this life as apportioned according to a scheme of perfect and\nuniversal justice, such as in our thoughts we cannot but require the\nDivine administration to be.\n\n13. Here then we are again led to the same conviction by regarding the\nDivine administration of the world as the realization of the Divine\nJustice, to which we were before led by regarding it as the realization\nof the Divine Love. Since the Idea is not fully or completely realized\nin man's life in this present world, this present world cannot be the\nwhole of the Divine Administration. To complete the realization of the\nIdea of Justice, as an element of the Divine Administration, there\nmust be a life of man after his life in this present world. If man's\nmind and soul, the part of him which is susceptible of happiness and\nmisery, survive this present life, and be still subject to the Divine\nAdministration, the Idea of Divine Justice may still be completely\nrealized, notwithstanding all that here looks like injustice or\ndefective justice; and it belongs to the Idea of Justice to remedy\nand compensate, not to prevent wrong. And thus by this supposition\nof a Future State of man's existence, we are enabled to conceive\nthat, in the whole of the Divine Government of the universe, all\nseeming injustice and wrong may be finally corrected and rectified,\nin an ultimate and universal establishment of a reign of perfect\nRighteousness.\n\n\n14. Admitting the view thus presented, we may again discern a\nremarkable analogy between what we have called our _physical_ Ideas\n(those of Space, Time, Cause, Substance, and the like), and our _moral_\nIdeas, (those of Benevolence, Justice, &c.). In both classes we must\nsuppose that our human Ideas represent, though very incompletely and at\nan immeasurable distance, the Divine Ideas. Even our physical Ideas,\nwhen pursued to their consequences, are involved in a perplexity\nand confusion from which the Divine Ideas are free. Our Ideas of\nBenevolence and Justice are still more full of imperfections and\ninconsistency, when we would frame them into a complete scheme, and\nyet from such imperfections and inconsistency we must suppose that\nthe Divine Benevolence and Justice are exempt. Our physical Ideas we\nfind in every case exactly exemplified and realized in the universe,\nand we account for this by considering that they are the Divine Ideas,\non which the universe is constituted. Our moral Ideas, the Ideas of\nBenevolence and Justice in particular, must also be realized in the\nuniverse, as a scheme of Divine Government. But they are not realized\nin the world as constituted of man living this present life. The Divine\nScheme of the world, therefore, extends beyond this present life of\nman. If we could include in our survey the future life as well as the\npresent life of man, and the future course of the Divine Government, we\nshould have a scheme of the Moral Government of the universe, in which\nthe Ideas of Perfect Benevolence and Perfect Justice are as completely\nand universally exemplified and realized, as the Ideas of Space, Time,\nCause, Substance, and the like, are in the physical universe.\n\n\n15. There is one other remark bearing upon this analogy, which seems\nto deserve our attention. As I have said in the last chapter, the\nscheme of the world, as governed by our physical Ideas, seems to point\nto a Beginning of the world, or at least of the present course of the\nworld: and if we suppose a Beginning, our thoughts naturally turn to\nan End. But if our physical Ideas point to a Beginning and suggest an\nEnd, do our Ideas of Divine Benevolence and Justice in any way lend\nthemselves to this suggestion?--Perhaps we might venture to say that in\nsome degree they do, even to the eye of a mere philosophical reason.\nPerhaps our reason alone might suggest that there is a progression in\nthe human race, in various moral attributes--in art, in civilization,\nand even in humanity and in justice, which implies a beginning. And\nthat at any rate there is nothing inconsistent with our Idea of the\nDivine Government in the supposition that the history of this world has\na Beginning, a Middle and an End.\n\n16. If therefore there should be conveyed to us by some channel\nespecially appropriated to the communication and development of moral\nand religious Ideas, the knowledge that the world, as a scheme of\nDivine Government, has _a Beginning_, _a Middle_, and _an End_, of\na Kind, or at least, invested with circumstances quite different\nfrom any which our physical Ideas can disclose to us, there would\nbe, in such a belief, nothing at all inconsistent with the analogies\nwhich our philosophy--the philosophy of our Ideas illustrated by the\nwhole progress of science--has impressed upon us. On the grounds of\nthis philosophy, we need find no difficulty in believing that as the\nvisible universe exhibits the operation of the Divine Ideas of Space,\nTime, Cause, Substance, and the like, and discloses to us traces of\na Beginning of the present mode of operation, so the moral universe\nexhibits to us the operation of the Divine Benevolence and Justice; and\nthat these Divine attributes wrought in a special and peculiar manner\nin the Beginning; interposed in a peculiar and special manner in the\nMiddle; and will again act in a peculiar and special manner in the End\nof the world. And thus the conditions of the physical universe, and the\nGovernment of the Moral world, are both, though in different ways, a\npart of the work which God is carrying on from the Beginning of things\nto the End--_opus quod Deus operator a principio usque ad finem_.\n\n\n17. We are led by such analogies as I have been adducing to believe\nthat the whole course of events in which the minds and souls of men\nsurvive the present life, and are hereafter subjected to the Divine\ngovernment in such a way as to complete all that is here deficient in\nthe world's history, is a scheme of perfect Benevolence and Justice.\nNow, can we discern in man's mind or soul itself any indication of a\ndestiny like this? Are there in us any powers and faculties which seem\nas if they were destined to immortality? If there be, we have in such\nfaculties a strong confirmation of that belief in the future life of\nman which has already been suggested to us as necessary to render the\nDivine government conceivable.\n\n\n18. According to our philosophy there are powers and faculties which\ndo thus seem fitted to endure, and not fitted to terminate and be\nextinguished. The Ideas which we have in our minds--the physical\nIdeas, as we have called them, according to which the universe is\nconstituted,--agree, as far as they go, with the Ideas of the Divine\nMind, seen in the constitution of the universe. But these Divine\nIdeas are eternal and imperishable: we therefore naturally conclude\nthat the human mind which includes such elements, is also eternal and\nimperishable. Since the mind can take hold of eternal truths, it must\nbe itself eternal. Since it is, to a certain extent, the image of God\nin its faculties, it cannot ever cease to be the image of God. When it\nhas arrived at a stage in which it sees several aspects of the universe\nin the same form in which they present themselves to the Divine Mind,\nwe cannot suppose that the Author of the human mind will allow it and\nall its intellectual light to be extinguished.\n\n19. And our conviction that this extinction of the human mind cannot\ntake place becomes stronger still, when we consider that the mind,\nhowever imperfect and scanty its discernment of truth may be, is\nstill capable of a vast, and even of an unlimited progress in the\npursuit and apprehension of truth. The mind is capable of accepting\nand appropriating, through the action of its own Ideas, every step in\nscience which has ever been made--every step which shall hereafter\nbe made. Can we suppose that this vast and boundless capacity exists\nfor a few years only, is unfolded only into a few of its simplest\nconsequences, and is then consigned to annihilation? Can we suppose\nthat the wonderful powers which carry man on, generation by generation,\nfrom the contemplation of one great and striking truth to another, are\nburied with each generation? May we not rather suppose that that mind,\nwhich is capable of indefinite progression, is allowed to exist in an\ninfinite duration, during which such progression may take place?\n\n20. I propose this argument as a ground of hope and satisfactory\nreflexion to those who love to dwell on the natural arguments for the\nImmortality of the Soul. I do not attempt to follow it into detail.\nI know too well how little such a cause can gain by obstinate and\ncomplicated argumentation, to attempt to urge the argument in that\nmanner: and probably different persons, among those who accept the\nargument as valid, would give different answers to many questions of\ndetail, which naturally arise out of the acceptance of this argument.\nI will not here attempt to solve, or even to propound these questions.\nMy main purpose in offering these views and this argument at all, is\nto give some satisfaction to those who would think it a sad and blank\nresult of this long survey of the nature and progress of science in\nwhich we have been so long engaged (through this series of works), that\nit should in no way lead to a recognition of the Author of that world\nabout which our Science is, and to the high and consolatory hopes which\nlift man beyond this world. No survey of the universe can be at all\nsatisfactory to thoughtful men, which has not a theological bearing;\nnor can any view of man's powers and means of knowing be congenial to\nsuch men, which does not recognize an infinite destination for the mind\nwhich has an infinite capacity; an eternal being of the Faculty which\ncan take a steady hold of eternal being.\n\n\n21. And as we may derive such a conviction from our physical Ideas, so\ntoo may we no less from our moral Ideas. Our minds apprehend Space and\nTime and Force and the like, as Ideas which are not dependent on the\nbody; and hence we believe that our minds shall not perish with our\nbodies. And in the same manner our souls conceive pure Benevolence and\nperfect Justice, which go beyond the conditions of this mortal life;\nand hence we believe that our souls have to do with a life beyond this\nmortal life.\n\nIt is more difficult to speak of man's indefinite moral progression\neven than of his indefinite intellectual progression. Yet in every\npath of moral speculation we have such a progression suggested to us.\nWe may begin, for instance, with the ordinary feelings and affections\nof our daily nature:--Love, Hate, Scorn. But when we would elevate the\nSoul in our imagination, we ascend above these ordinary affections, and\ntake the repulsive and hostile ones as fitted only to balance their own\ninfluences. And thus the poet, speaking of a morally poetical nature,\ndescribes it:\n\n  The Poet in a golden clime was born,\n    With golden stars above.\n  He felt the hate _of_ hate, the scorn _of_ scorn,\n    The love _of_ love.\n\nBut the loftier moralist can rise higher than this, and can, and will,\nreject altogether Hate and Scorn from his view of man's better nature.\nHis description would rather be--\n\n  The good man in a loving clime was born,\n    With loving stars above.\n  He felt sorrow for hate, pity for scorn,\n    And love of love.\n\nHe would, in his conception of such a character, ascribe to it all\nthe virtues which result from the control and extinction of these\nrepulsive and hostile affections:--the virtues of magnanimity,\nforgivingness, unselfishness, self-devotion, tenderness, sweetness. And\nthese we can conceive in a higher and higher degree, in proportion as\nour own hearts become tender, forgiving, pure and unselfish. And though\nin every human stage of such a moral proficiency, we must suppose\nthat there is still some struggle with the remaining vestiges of our\nunkind, unjust, angry and selfish affections, we can see no limit to\nthe extent to which this struggle may be successful; no limit to the\ndegree in which these traces of the evil of our nature may be worn\nout by an enduring practice and habit of our better nature. And when\nwe contemplate a human character which has, through a long course of\nyears, and through many trials and conflicts, made a large progress in\nthis career of melioration, and is still capable, if time be given,\nof further progress towards moral perfection, is it not reasonable to\nsuppose that He who formed man capable of such progress, and who, as we\nmust needs believe, looks with approval on such progress where made,\nwill not allow the progress to stop when it has gone on to the end of\nman's short earthly life? Is it not rather reasonable to suppose that\nthe pure and elevated and all-embracing affection, extinguishing all\nvices and including all virtues, to which the good man thus tends,\nshall continue to prevail in him as a permanent and ever-during\ncondition, in a life after this?\n\nBut can man raise himself to such a stage of moral progress, by his own\nefforts? Such a progress is an approximation towards the perfection of\nmoral Ideas, and therefore an approximation towards the image of God,\nin whom that perfection resides: is it not then reasonable to suppose\nthat man needs a Divine Influence to enable him to reach this kind of\nmoral completeness? And is it not also reasonable to suppose that,\nas he needs such aid, in order that the Idea of his moral progress\nmay be realized, so he will receive such aid from the Divine Power\nwhich realizes the Idea of Divine Love in the world; and to do so,\nmust realize it in those human souls which are most fitted for such a\npurpose?\n\nBut these questions remind me how difficult, and indeed, how impossible\nit is to follow such trains of reflexion by the light of philosophy\nalone. To answer such questions, we need, not Religious Philosophy\nonly, but Religion: and as I do not here venture beyond the domain of\nphilosophy, I must, however abruptly, conclude.\n\n\nTHE END.\n\n\n\n\nAPPENDIX.\n\n\nAPPENDIX A.\n\nOF THE PLATONIC THEORY OF IDEAS.\n\n(_Cam. Phil. Soc._ Nov. 10, 1856.)\n\n\nThough Plato has, in recent times, had many readers and admirers\namong our English scholars, there has been an air of unreality and\ninconsistency about the commendation which most of these professed\nadherents have given to his doctrines. This appears to be no captious\ncriticism, for instance, when those who speak of him as immeasurably\nsuperior in argument to his opponents, do not venture to produce\nhis arguments in a definite form as able to bear the tug of modern\ncontroversy;--when they use his own Greek phrases as essential to the\nexposition of his doctrines, and speak as if these phrases could not be\nadequately rendered in English;--and when they assent to those among\nthe systems of philosophy of modern times which are the most clearly\nopposed to the system of Plato. It seems not unreasonable to require,\non the contrary, that if Plato is to supply a philosophy for us, it\nmust be a philosophy which can be expressed in our own language;--that\nhis system, if we hold it to be well founded, shall compel us to deny\nthe opposite systems, modern as well as ancient;--and that, so far as\nwe hold Plato's doctrines to be satisfactorily established, we should\nbe able to produce the arguments for them, and to refute the arguments\nagainst them. These seem reasonable requirements of the adherents of\n_any_ philosophy, and therefore, of Plato's.\n\nI regard it as a fortunate circumstance, that we have recently had\npresented to us an exposition of Plato's philosophy which does conform\nto those reasonable conditions; and we may discuss this exposition with\nthe less reserve, since its accomplished author, though belonging to\nthis generation, is no longer alive. I refer to the _Lectures_ on the\nHistory of Ancient Philosophy, by the late Professor Butler of Dublin.\nIn these Lectures, we find an account of the Platonic Philosophy which\nshows that the writer had considered it as, what it is, an attempt\nto solve large problems, which in all ages force themselves upon the\nnotice of thoughtful men. In Lectures VIII. and X., of the Second\nSeries, especially, we have a statement of the Platonic Theory of\nIdeas, which may be made a convenient starting point for such remarks\nas I wish at present to make. I will transcribe this account; omitting,\nas I do so, the expressions which Professor Butler uses, in order to\npresent the theory, not as a dogmatical assertion, but as a view, at\nleast not extravagant. For this purpose, he says, of the successive\nportions of the theory, that one is \"not too absurd to be maintained;\"\nthat another is \"not very extravagant either;\" that a third is \"surely\nallowable;\" that a fourth presents \"no incredible account\" of the\nsubject; that a fifth is \"no preposterous notion in substance, and no\nunwarrantable form of phrase.\" Divested of these modest formul\u00e6, his\naccount is as follows: [Vol. II. p. 117.]\n\n\"Man's soul is made to contain not merely a consistent scheme of its\nown notions, but a direct apprehension of _real and eternal laws beyond\nit_. These real and eternal laws are things _intelligible_, and not\nthings sensible.\n\n\"These laws impressed upon creation by its Creator, and apprehended\nby man, are something distinct equally from the Creator and from man,\nand the whole mass of them may fairly be termed the World of Things\nIntelligible.\n\n\"Further, there are qualities in the supreme and ultimate Cause of all,\nwhich are manifested in His creation, and not merely manifested, but,\nin a manner--after being brought out of his super-essential nature into\nthe stage of being [which is] below him, but next to him--are then by\nthe causative act of creation deposited in things, differencing them\none from the other, so that the things partake of them (\u03bc\u03b5\u03c4\u03ad\u03c7\u03bf\u03c5\u03c3\u03b9),\ncommunicate with them (\u03ba\u03bf\u03b9\u03bd\u03c9\u03bd\u03bf\u1fe6\u03c3\u03b9).\n\n\"The intelligence of man, excited to reflection by the impressions\nof these objects thus (though themselves transitory) participant of\na divine quality, may rise to higher conceptions of the perfections\nthus faintly exhibited; and inasmuch as these perfections are\nunquestionably _real_ existences, and _known_ to be such in the very\nact of contemplation,--this may be regarded as a direct intellectual\napperception of them,--a Union of the Reason with the Ideas in that\nsphere of being which is common to both.\n\n\"Finally, the Reason, in proportion as it learns to contemplate the\nPerfect and Eternal, _desires_ the enjoyment of such contemplations in\na more consummate degree, and cannot be fully satisfied, except in the\nactual fruition of the Perfect itself.\n\n\"These suppositions, taken together, constitute the Theory of Ideas.\"\n\nIn remarking upon the theory thus presented, I shall abstain from any\ndiscussion of the theological part of it, as a subject which would\nprobably be considered as unsuited to the meetings of this Society,\neven in its most purely philosophical form. But I conceive that it will\nnot be inconvenient, if it be not wearisome, to discuss the Theory of\nIdeas as an attempt to explain the existence of real knowledge; which\nProf. Butler very rightly considers as the necessary aim of this and\ncognate systems of philosophy[321].\n\nI conceive, then, that one of the primary objects of Plato's Theory\nof Ideas is, to explain the existence of real knowledge, that is, of\ndemonstrated knowledge, such as the propositions of geometry offer\nto us. In this view, the Theory of Ideas is one attempt to solve a\nproblem, much discussed in our times, What is the ground of geometrical\ntruth? I do not mean that this is the whole object of the Theory, or\nthe highest of its claims. As I have said, I omit its theological\nbearings; and I am aware that there are passages in the Platonic\nDialogues, in which the Ideas which enter into the apprehension and\ndemonstration of geometrical truths are spoken of as subordinate to\nIdeas which have a theological aspect. But I have no doubt that one\nof the main motives to the construction of the Theory of Ideas was,\nthe desire of solving the Problem, \"How is it possible that man should\napprehend necessary and eternal truths?\" That the truths are necessary,\nmakes them eternal, for they do not depend on time; and that they are\neternal, gives them at once a theological bearing.\n\nThat Plato, in attempting to explain the nature and possibility of\nreal knowledge, had in his mind geometrical truths, as examples of\nsuch knowledge is, I think, evident from the general purport of his\ndiscourses on such subjects. The advance of Greek geometry into a\nconspicuous position, at the time when the Heraclitean sect were\nproving that nothing could be proved and nothing could be known,\nnaturally suggested mathematical truth as the refutation of the\nskepticism of mere sensation. On the one side it was said, we can\nknow nothing except by our sensations; and that which we observe with\nour senses is constantly changing; or at any rate, may change at any\nmoment. On the other hand it was said, we _do_ know geometrical truths,\nand as truly as we know them, that they cannot change. Plato was quite\nalive to the lesson, and to the importance of this kind of truths.\nIn the _Meno_ and in the _Ph\u00e6do_ he refers to them, as illustrating\nthe nature of the human mind: in the _Republic_ and the _Tim\u00e6us_ he\nagain speaks of truths which far transcend anything which the senses\ncan teach, or even adequately exemplify. The senses, he argues in the\n_The\u00e6tetus_, cannot give us the knowledge which we have; the source\nof it must therefore be in the mind itself; in the _Ideas_ which\nit possesses. The impressions of sense are constantly varying, and\nincapable of giving any certainty: but the Ideas on which real truth\ndepends are constant and invariable, and the certainty which arises\nfrom these is firm and indestructible. Ideas are the permanent, perfect\nobjects, with which the mind deals when it contemplates necessary and\neternal truths. They belong to a region superior to the material world,\nthe world of sense. They are the objects which make up the furniture of\nthe Intelligible World; with which the Reason deals, as the Senses deal\neach with its appropriate Sensation.\n\nBut, it will naturally be asked, what is the Relation of Ideas to the\nObjects of Sense? Some connexion, or relation, it is plain, there\nmust be. The objects of sense can suggest, and can illustrate real\ntruths. Though these truths of geometry cannot be proved, cannot even\nbe exactly exemplified, by drawing diagrams, yet diagrams are of use\nin helping ordinary minds to see the proof; and to all minds, may\nrepresent and illustrate it. And though our conclusions with regard to\nobjects of sense may be insecure and imperfect, they have some show of\ntruth, and therefore some resemblance to truth. What does this arise\nfrom? How is it explained, if there is no truth except concerning Ideas?\n\nTo this the Platonist replied, that the phenomena which present\nthemselves to the senses partake, in a certain manner, of Ideas, and\nthus include so much of the nature of Ideas, that they include also\nan element of Truth. The geometrical diagram of Triangles and Squares\nwhich is drawn in the sand of the floor of the Gymnasium, partakes of\nthe nature of the true Ideal Triangles and Squares, so that it presents\nan imitation and suggestion of the truths which are true of them. The\nreal triangles and squares are in the mind: they are, as we have said,\nobjects, not in the Visible, but in the Intelligible World. But the\nVisible Triangles and Squares make us call to mind the Intelligible;\nand thus the objects of sense suggest, and, in a way, exemplify the\neternal truths.\n\nThis I conceive to be the simplest and directest ground of two primary\nparts of the Theory of Ideas;--The Eternal Ideas constituting an\nIntelligible World; and the Participation in these Ideas ascribed to\nthe objects of the world of sense. And it is plain that so far, the\nTheory meets what, I conceive, was its primary purpose; it answers the\nquestions, How can we have certain knowledge, though we cannot get it\nfrom Sense? and, How can we have knowledge, at least apparent, though\nimperfect, about the world of sense?\n\nBut is this the ground on which Plato himself rests the truth of his\nTheory of Ideas? As I have said, I have no doubt that these were the\nquestions which suggested the Theory; and it is perpetually applied\nin such a manner as to show that it was held by Plato in this sense.\nBut his applications of the Theory refer very often to another part\nof it;--to the Ideas, not of Triangles and Squares, of space and its\naffections; but to the Ideas of Relations--as the Relations of Like and\nUnlike, Greater and Less; or to things quite different from the things\nof which geometry treats, for instance, to Tables and Chairs, and other\nmatters, with regard to which no demonstration is possible, and no\ngeneral truth (still less necessary an eternal truth) capable of being\nasserted.\n\nI conceive that the Theory of Ideas, thus asserted and thus supported,\nstands upon very much weaker ground than it does, when it is\nasserted concerning the objects of thought about which necessary and\ndemonstrable truths are attainable. And in order to devise arguments\nagainst _this_ part of the Theory, and to trace the contradictions to\nwhich it leads, we have no occasion to task our own ingenuity. We find\nit done to our hands, not only in Aristotle, the open opponent of the\nTheory of Ideas, but in works which stand among the Platonic Dialogues\nthemselves. And I wish especially to point out some of the arguments\nagainst the Ideal Theory, which are given in one of the most noted of\nthe Platonic Dialogues, the _Parmenides_.\n\nThe _Parmenides_ contains a narrative of a Dialogue held between\nParmenides and Zeno, the Eleatic Philosophers, on the one side, and\nSocrates, along with several other persons, on the other. It may be\nregarded as divided into two main portions; the first, in which the\nTheory of Ideas is attacked by Parmenides, and defended by Socrates;\nthe second, in which Parmenides discusses, at length, the Eleatic\ndoctrine that _All things are One_. It is the former part, the\ndiscussion of the Theory of Ideas, to which I especially wish to direct\nattention at present: and in the first place, to that extension of\nthe Theory of Ideas, to things of which no general truth is possible;\nsuch as I have mentioned, tables and chairs. Plato often speaks of\na Table, by way of example, as a thing of which there must be an\nIdea, not taken from any special Table or assemblage of Tables; but\nan Ideal Table, such that all Tables are Tables by participating in\nthe nature of this Idea. Now the question is, whether there is any\nforce, or indeed any sense, in this assumption; and this question is\ndiscussed in the _Parmenides_. Socrates is there represented as very\nconfident in the existence of Ideas of the highest and largest kind,\nthe Just, the Fair, the Good, and the like. Parmenides asks him how\nfar he follows his theory. Is there, he asks, an Idea of Man, which is\ndistinct from us men? an Idea of Fire? of Water? \"In truth,\" replies\nSocrates, \"I have often hesitated, Parmenides, about these, whether\nwe are to allow such Ideas.\" When Plato had proceeded to teach that\nthere is an Idea of a Table, of course he could not reject such Ideas\nas Man, and Fire, and Water. Parmenides, proceeding in the same line,\npushes him further still. \"Do you doubt,\" says he, \"whether there\nare Ideas of things apparently worthless and vile? Is there an Idea\nof a Hair? of Mud? of Filth?\" Socrates has not the courage to accept\nsuch an extension of the theory. He says, \"By no means. These are not\nIdeas. These are nothing more than just what we see them. I have often\nbeen perplexed what to think on this subject. But after standing to\nthis a while, I have fled the thought, for fear of falling into an\nunfathomable abyss of absurdities.\" On this, Parmenides rebukes him for\nhis want of consistency. \"Ah Socrates,\" he says, \"you are yet young;\nand philosophy has not yet taken possession of you as I think she will\none day do--when you will have learned to find nothing despicable in\nany of these things. But now your youth inclines you to regard the\nopinions of men.\" It is indeed plain, that if we are to assume an Idea\nof a Chair or a Table, we can find no boundary line which will exclude\nIdeas of everything for which we have a name, however worthless or\noffensive. And this is an argument against the assumption of _such_\nIdeas, which will convince most persons of the groundlessness of the\nassumption:--the more so, as _for_ the assumption of such Ideas, it\ndoes not appear that Plato offers any argument whatever; nor does\nthis assumption solve any problem, or remove any difficulty[322].\nParmenides, then, had reason to say that consistency required Socrates,\nif he assumed any such Ideas, to assume all. And I conceive his reply\nto be to this effect; and to be thus a _reductio ad absurdum_ of the\nTheory of Ideas in this sense. According to the opinions of those\nwho see in the _Parmenides_ an exposition of Platonic doctrines, I\nbelieve that Parmenides is conceived in this passage, to suggest to\nSocrates what is necessary for the completion of the Theory of Ideas.\nBut upon either supposition, I wish especially to draw the attention\nof my readers to the position of superiority in the Dialogue in which\nParmenides is here placed with regard to Socrates.\n\nParmenides then proceeds to propound to Socrates difficulties with\nregard to the Ideal Theory, in another of its aspects;--namely, when it\nassumes Ideas of Relations of things; and here also, I wish especially\nto have it considered how far the answers of Socrates to these\nobjections are really satisfactory and conclusive.\n\n\"Tell me,\" says he (\u00a7 10, Bekker), \"You conceive that there are certain\nIdeas, and that things partaking of these Ideas, are called by the\ncorresponding names;--an Idea of _Likeness_, things partaking of\nwhich are called _Like_;--of _Greatness_, whence they are _Great_: of\n_Beauty_, whence they are _Beautiful_?\" Socrates assents, naturally:\nthis being the simple and universal statement of the Theory, in this\ncase. But then comes one of the real difficulties of the Theory. Since\nthe special things participate of the General Idea, has each got\nthe whole of the Idea, which is, of course, One; or has each a part\nof the Idea? \"For,\" says Parmenides, \"can there be any other way of\nparticipation than these two?\" Socrates replies by a similitude: \"The\nIdea, though One, may be wholly in each object, as the Day, one and the\nsame, is wholly in each place.\" The physical illustration, Parmenides\ndamages by making it more physical still. \"You are ingenious,\nSocrates,\" he says, (\u00a7 11) \"in making the same thing be in many places\nat the same time. If you had a number of persons wrapped up in a sail\nor web, would you say that each of them had the whole of it? Is not the\ncase similar?\" Socrates cannot deny that it is. \"But in this case, each\nperson has only a part of the whole; and thus your Ideas are partible.\"\nTo this, Socrates is represented as assenting in the briefest possible\nphrase; and thus, here again, as I conceive, Parmenides retains his\nsuperiority over Socrates in the Dialogue.\n\nThere are many other arguments urged against the Ideal Theory by\nParmenides. The next is a consequence of this partibility of Ideas,\nthus supposed to be proved, and is ingenious enough. It is this:\n\n\"If the Idea of Greatness be distributed among things that are Great,\nso that each has a part of it, each separate thing will be Great in\nvirtue of a part of Greatness which is less than Greatness itself. Is\nnot this absurd?\" Socrates submissively allows that it is.\n\nAnd the same argument is applied in the case of the Idea of Equality.\n\n\"If each of several things have a part of the Idea of Equality, it\nwill be Equal to something, in virtue of something which is less than\nEquality.\"\n\nAnd in the same way with regard to the Idea of Smallness.\n\n\"If each thing be small by having a part of the Idea of Smallness,\nSmallness itself will be greater than the small thing, since that is a\npart of itself.\"\n\nThese ingenious results of the partibility of Ideas remind us of the\ningenuity shown in the Greek geometry, especially the Fifth Book of\nEuclid. They are represented as not resisted by Socrates (\u00a7 12): \"In\nwhat way, Socrates, can things participate in Ideas, if they cannot\ndo so either integrally or partibly?\" \"By my troth,\" says Socrates,\n\"it does not seem easy to tell.\" Parmenides, who completely takes the\nconduct of the Dialogue, then turns to another part of the subject and\npropounds other arguments. \"What do you say to this?\" he asks.\n\n\"There is an Ideal Greatness, and there are many things, separate from\nit, and Great by virtue of it. But now if you look at Greatness and the\nGreat things together, since they are all Great, they must be Great in\nvirtue of some higher Idea of Greatness which includes both. And thus\nyou have a Second Idea of Greatness; and in like manner you will have a\nthird, and so on indefinitely.\"\n\nThis also, as an argument against the separate existence of Ideas,\nSocrates is represented as unable to answer. He replies interrogatively:\n\n\"Why, Parmenides, is not each of these Ideas a Thought, which, by its\nnature, cannot exist in anything except in the Mind? In that case your\nconsequences would not follow.\"\n\nThis is an answer which changes the course of the reasoning: but still,\nnot much to the advantage of the Ideal Theory. Parmenides is still\nready with very perplexing arguments. (\u00a7 13.)\n\n\"The Ideas, then,\" he says, \"are Thoughts. They must be Thoughts of\nsomething. They are Thoughts of something, then, which exists in all\nthe special things; some one thing which the Thought perceives in all\nthe special things; and this one Thought thus involved in all, is the\n_Idea_. But then, if the special things, as you say, participate in the\nIdea, they participate in the Thought; and thus, all objects are made\nup of Thoughts, and all things think; or else, there are thoughts in\nthings which do not think.\"\n\nThis argument drives Socrates from the position that Ideas are\nThoughts, and he moves to another, that they are Paradigms, Exemplars\nof the qualities of things, to which the things themselves are like,\nand their being thus like, is their participating in the Idea. But here\ntoo, he has no better success. Parmenides argues thus:\n\n\"If the Object be like the Idea, the Idea must be like the Object.\nAnd since the Object and the Idea are like, they must, according to\nyour doctrine, participate in the Idea of Likeness. And thus you have\none Idea participating in another Idea, and so on in infinitum.\"\nSocrates is obliged to allow that this demolishes the notion of objects\npartaking in their Ideas by likeness: and that he must seek some other\nway. \"You see then, O Socrates,\" says Parmenides, \"what difficulties\nfollow, if any one asserts the independent existence of Ideas!\"\nSocrates allows that this is true. \"And yet,\" says Parmenides, \"you\ndo not half perceive the difficulties which follow from this doctrine\nof Ideas.\" Socrates expresses a wish to know to what Parmenides\nrefers; and the aged sage replies by explaining that if Ideas exist\nindependently of us, we can never know anything about them: and that\neven the Gods could not know anything about man. This argument, though\nsomewhat obscure, is evidently stated with perfect earnestness, and\nSocrates is represented as giving his assent to it. \"And yet,\" says\nParmenides (end of \u00a7 18), \"if any one gives up entirely the doctrine of\nIdeas, how is any reasoning possible?\"\n\nAll the way through this discussion, Parmenides appears as vastly\nsuperior to Socrates; as seeing completely the tendency of every line\nof reasoning, while Socrates is driven blindly from one position to\nanother; and as kindly and graciously advising a young man respecting\nthe proper aims of his philosophical career; as well as clearly\npointing out the consequences of his assumptions. Nothing can be\nmore complete than the higher position assigned to Parmenides in the\nDialogue.\n\nThis has not been overlooked by the Editors and Commentators of Plato.\nTo take for example one of the latest; in Steinhart's Introduction to\nHieronymus M\u00fcller's translation of _Parmenides_ (Leipzig, 1852), p.\n261, he says: \"It strikes us, at first, as strange, that Plato here\nseems to come forward as the assailant of his own doctrine of Ideas.\nFor the difficulties which he makes Parmenides propound against that\ndoctrine are by no means sophistical or superficial, but substantial\nand to the point. Moreover there is among all these objections, which\nare partly derived from the Megarics, scarce one which does not appear\nagain in the penetrating and comprehensive argumentations of Aristotle\nagainst the Platonic Doctrine of Ideas.\"\n\nOf course, both this writer and other commentators on Plato offer\nsomething as a solution of this difficulty. But though these\nexplanations are subtle and ingenious, they appear to leave no\nsatisfactory or permanent impression on the mind. I must avow that, to\nme, they appear insufficient and empty; and I cannot help believing\nthat the solution is of a more simple and direct kind. It may seem bold\nto maintain an opinion different from that of so many eminent scholars;\nbut I think that the solution which I offer, will derive confirmation\nfrom a consideration of the whole Dialogue; and therefore I shall\nventure to propound it in a distinct and positive form. It is this:\n\nI conceive that the _Parmenides_ is not a Platonic Dialogue at all;\nbut Antiplatonic, or more properly, _Eleatic_: written, not by Plato,\nin order to explain and prove his Theory of Ideas, but by some one,\nprobably an admirer of Parmenides and Zeno, in order to show how strong\nwere his master's arguments against the Platonists and how weak their\nobjections to the Eleatic doctrine.\n\nI conceive that this view throws an especial light on every part of the\nDialogue, as a brief survey of it will show. Parmenides and Zeno come\nto Athens to the Panathenaic festival: Parmenides already an old man,\nwith a silver head, dignified and benevolent in his appearance, looking\nfive and sixty years old: Zeno about forty, tall and handsome. They are\nthe guests of Pythodorus, outside the Wall, in the Ceramicus; and there\nthey are visited by Socrates then young, and others who wish to hear\nthe written discourses of Zeno. These discourses are explanations of\nthe philosophy of Parmenides, which he had delivered in verse.\n\nSocrates is represented as showing, from the first, a disposition to\ncriticize Zeno's dissertation very closely; and without any prelude or\npreparation, he applies the Doctrine of Ideas to refute the Eleatic\nDoctrine that All Things are One. (\u00a7 3.) When he had heard to the\nend, he begged to have the first Proposition of the First Book read\nagain. And then, \"How is it, O Zeno, that you say, That if the Things\nwhich exist are Many, and not One, they must be at the same time like\nand unlike? Is this your argument? Or do I misunderstand you?\" \"No,\"\nsays Zeno, \"you understand quite rightly.\" Socrates then turns to\nParmenides, and says, somewhat rudely, as it seems, \"Zeno is a great\nfriend of yours, Parmenides: he shows his friendship not only in\nother ways, but also in what he writes. For he says the same things\nwhich you say, though he pretends that he does not. You say, in your\npoems, that All Things are One, and give striking proofs: he says that\nexistences are not many, and he gives many and good proofs. You seem\nto soar above us, but you do not really differ.\" Zeno takes this sally\ngood-humouredly, and tells him that he pursues the scent with the\nkeenness of a Laconian hound. \"But,\" says he (\u00a7 6), \"there really is\nless of ostentation in my writing than you think. My Essay was merely\nwritten as a defence of Parmenides long ago, when I was young; and is\nnot a piece of display composed now that I am older. And it was stolen\nfrom me by some one; so that I had no choice about publishing it.\"\n\nHere we have, as I conceive, Socrates already represented as placed\nin a disadvantageous position, by his abruptness, rude allusions, and\nreadiness to put bad interpretations on what is done. For this, Zeno's\ngentle pleasantry is a rebuke. Socrates, however, forthwith rushes into\nthe argument; arguing, as I have said, for his own Theory.\n\n\"Tell me,\" he says, \"do you not think there is an Idea of Likeness, and\nan Idea of Unlikeness? And that everything partakes of these Ideas? The\nthings which partake of Unlikeness are unlike. If all things partake of\nboth Ideas, they are both like and unlike; and where is the wonder? (\u00a7\n7.) If you could show that Likeness itself was Unlikeness, it would be\na prodigy; but if things which partake of these opposites, have both\nthe opposite qualities, it appears to me, Zeno, to involve no absurdity.\n\n\"So if Oneness itself were to be shown to be Maniness\" (I hope I may\nuse this word, rather than _multiplicity_) \"I should be surprised; but\nif any one say that _I_ am at the same time one and many, where is the\nwonder? For I partake of maniness: my right side is different from my\nleft side, my upper from my under parts. But I also partake of Oneness,\nfor I am here One of us seven. So that both are true. And so if any one\nsay that stocks and stones, and the like, are both one and many,--not\nsaying that Oneness is Maniness, nor Maniness Oneness, he says nothing\nwonderful: he says what all will allow. (\u00a7 8.) If then, as I said\nbefore, any one should take separately the Ideas or Essence of Things,\nas Likeness and Unlikeness, Maniness and Oneness, Rest and Motion, and\nthe like, and then should show that these can mix and separate again,\nI should be wonderfully surprised, O Zeno: for I reckon that I have\ntolerably well made myself master of these subjects[323]. I should\nbe much more surprised if any one could show me this contradiction\ninvolved in the Ideas themselves; in the object of the Reason, as well\nas in Visible objects.\"\n\nIt may be remarked that Socrates delivers all this argumentation with\nthe repetitions which it involves, and the vehemence of its manner,\nwithout waiting for a reply to any of his interrogations; instead\nof making every step the result of a concession of his opponent, as\nis the case in the Dialogues where he is represented as triumphant.\nEvery reader of Plato will recollect also that in those Dialogues,\nthe triumph of temper on the part of Socrates is represented as\nstill more remarkable than the triumph of argument. No vehemence or\nrudeness on the part of his adversaries prevents his calmly following\nhis reasoning; and he parries coarseness by compliment. Now in this\nDialogue, it is remarkable that this kind of triumph is given to the\nadversaries of Socrates. \"When Socrates had thus delivered himself,\"\nsays Pythodorus, the narrator of the conversation, \"we thought that\nParmenides and Zeno would both be angry. But it was not so. They\nbestowed entire attention upon him, and often looked at each other,\nand smiled, as in admiration of Socrates. And when he had ended,\nParmenides said: 'O Socrates, what an admirable person you are, for the\nearnestness with which you reason! Tell me then, Do you then believe\nthe doctrine to which you have been referring;--that there are certain\nIdeas, existing independent of Things; and that there are, separate\nfrom the Ideas, Things which partake of them? And do you think that\nthere is an Idea of Likeness besides the likeness which we have; and a\nOneness and a Maniness, and the like? And an Idea of the Right, and the\nGood, and the Fair, and of other such qualities?'\" Socrates says that\nhe does hold this; Parmenides then asks him, how far he carries this\ndoctrine of Ideas, and propounds to him the difficulties which I have\nalready stated; and when Socrates is unable to answer him, lets him off\nin the kind but patronizing way which I have already described.\n\nTo me, comparing this with the intellectual and moral attitude of\nSocrates in the most dramatic of the other Platonic Dialogues, it is\ninconceivable, that this representation of Socrates should be Plato's.\nIt is just what Zeno would have written, if he had wished to bestow\nupon his master Parmenides the calm dignity and irresistible argument\nwhich Plato assigns to Socrates. And this character is kept up to the\nend of the Dialogue. When Socrates (\u00a7 19) has acknowledged that he is\nat loss which way to turn for his philosophy, Parmenides undertakes,\nthough with kind words, to explain to him by what fundamental error in\nthe course of his speculative habits he has been misled. He says; \"You\ntry to make a complete Theory of Ideas, before you have gone through\na proper intellectual discipline. The impulse which urges you to such\nspeculations is admirable--is divine. But you must exercise yourself in\nreasoning which many think trifling, while you are yet young; if you\ndo not, the truth will elude your grasp.\" Socrates asks submissively\nwhat is the course of such discipline: Parmenides replies, \"The course\npointed out by Zeno, as you have heard.\" And then, gives him some\ninstructions in what manner he is to test any proposed Theory. Socrates\nis frightened at the laboriousness and obscurity of the process. He\nsays, \"You tell me, Parmenides, of an overwhelming course of study; and\nI do not well comprehend it. Give me an example of such an examination\nof a Theory.\" \"It is too great a labour,\" says he, \"for one so old\nas I am.\" \"Well then, you, Zeno,\" says Socrates, \"will you not give\nus such an example?\" Zeno answers, smiling, that they had better get\nit from Parmenides himself; and joins in the petition of Socrates to\nhim, that he will instruct them. All the company unite in the request.\nParmenides compares himself to an aged racehorse, brought to the course\nafter long disuse, and trembling at the risk; but finally consents.\nAnd as an example of a Theory to be examined, takes his own Doctrine,\nthat All Things are One, carrying on the Dialogue thenceforth, not\nwith Socrates, but with Aristoteles (not the Stagirite, but afterwards\none of the Thirty), whom he chooses as a younger and more manageable\nrespondent.\n\nThe discussion of this Doctrine is of a very subtle kind, and it would\nbe difficult to make it intelligible to a modern reader. Nor is it\nnecessary for my purpose to attempt to do so. It is plain that the\ndiscussion is intended seriously, as an example of true philosophy; and\neach step of the process is represented as irresistible. The Respondent\nhas nothing to say but _Yes_; or _No_; _How so_? _Certainly_; _It does\nappear_; _It does not appear_. The discussion is carried to a much\ngreater length than all the rest of the Dialogue; and the result of\nthe reasoning is summed up by Parmenides thus: \"If One exist, it is\nNothing. Whether One exist or do not exist, both It and Other Things\nboth with regard to Themselves and to Each other, All and Everyway are\nand are not, appear and appear not.\" And this also is fully assented\nto; and so the Dialogue ends.\n\nI shall not pretend to explain the Doctrines there examined that One\nexists, or One does not exist, nor to trace their consequences. But\nthese were Formul\u00e6, as familiar in the Eleatic school, as Ideas in the\nPlatonic; and were undoubtedly regarded by the Megaric contemporaries\nof Plato as quite worthy of being discussed, after the Theory of Ideas\nhad been overthrown. This, accordingly, appears to be the purport of\nthe Dialogue; and it is pursued, as we see, without any bitterness\ntoward Socrates or his disciples; but with a persuasion that they were\npoor philosophers, conceited talkers, and weak disputants.\n\nThe external circumstances of the Dialogue tend, I conceive, to confirm\nthis opinion, that it is not Plato's. The Dialogue begins, as the\n_Republic_ begins, with the mention of a Cephalus, and two brothers,\nGlaucon and Adimantus. But this Cephalus is not the old man of the\nPir\u00e6us, of whom we have so charming a picture in the opening of the\n_Republic_. He is from Clazomen\u00e6, and tells us that his fellow-citizens\nare great lovers of philosophy; a trait of their character which does\nnot appear elsewhere. Even the brothers Glaucon and Adimantus are not\nthe two brothers of Plato who conduct the Dialogue in the later books\nof the _Republic_: so at least Ast argues, who holds the genuineness of\nthe Dialogue. This Glaucon and Adimantus are most wantonly introduced;\nfor the sole office they have, is to say that they have a half-brother\nAntiphon, by a second marriage of their mother. No such half-brother of\nPlato, and no such marriage of his mother, are noticed in other remains\nof antiquity. Antiphon is represented as having been the friend of\nPythodorus, who was the host of Parmenides and Zeno, as we have seen.\nAnd Antiphon, having often heard from Pythodorus the account of the\nconversation of his guests with Socrates, retained it in his memory, or\nin his tablets, so as to be able to give the full report of it which we\nhave in the Dialogue _Parmenides_[324]. To me, all this looks like a\nclumsy imitation of the Introductions to the Platonic Dialogues.\n\nI say nothing of the chronological difficulties which arise\nfrom bringing Parmenides and Socrates together, though they are\nconsiderable; for they have been explained more or less satisfactorily;\nand certainly in the _The\u00e6tetus_, Socrates is represented as saying\nthat he when very young had seen Parmenides who was very old[325].\nAthen\u00e6us, however[326], reckons this among Plato's fictions.\nSchleiermacher gives up the identification and relation of the persons\nmentioned in the Introduction as an unmanageable story.\n\nI may add that I believe Cicero, who refers to so many of Plato's\nDialogues, nowhere refers to the _Parmenides_. Athen\u00e6us does refer to\nit; and in doing so blames Plato for his coarse imputations on Zeno\nand Parmenides. According to our view, these are hostile attempts to\nascribe rudeness to Socrates or to Plato. Stallbaum acknowledges that\nAristotle nowhere refers to this Dialogue.\n\nFOOTNOTES:\n\n[Footnote 321: P. 116. \"No amount of human knowledge can be adequate\nwhich does not solve the phenomena of these absolute certainties.\"]\n\n[Footnote 322: Prof. Butler, Lect. ix. Second Series, p. 136, appears\nto think that Plato had sufficient grounds (of a theological kind) for\nthe assumption of such Ideas; but I see no trace of them.]\n\n[Footnote 323: I am aware that this translation is different from the\ncommon translation. It appears to me to be consistent with the habit\nof the Greek language. It slightly leans in favour of my view; but I\ndo not conceive that the argument would be perceptibly weaker, if the\ncommon interpretation were adopted.]\n\n[Footnote 324: In the _First Alcibiades_, Pythodorus is mentioned as\nhaving paid 100 min\u00e6 to Zeno for his instructions (119 A).]\n\n[Footnote 325: P. 183 e.]\n\n[Footnote 326: _Deip._ xi. c. 15, p. 105.]\n\n\nAPPENDIX B.\n\nON PLATO'S SURVEY OF THE SCIENCES.\n\n(_Cam. Phil. Soc._ APRIL 23, 1855.)\n\n\nA survey by Plato of the state of the Sciences, as existing in his\ntime, may be regarded as hardly less interesting than Francis Bacon's\nReview of the condition of the Sciences of _his_ time, contained in the\n_Advancement of Learning_. Such a survey we have, in the seventh book\nof Plato's _Republic_; and it will be instructive to examine what the\nSciences then were, and what Plato aspired to have them become; aiding\nourselves by the light afforded by the subsequent history of Science.\n\nIn the first place, it is interesting to note, in the two writers,\nPlato and Bacon, the same deep conviction that the large and profound\nphilosophy which they recommended, had not, in their judgment, been\npursued in an adequate and worthy manner, by those who had pursued it\nat all. The reader of Bacon will recollect the passage in the _Novum\nOrganon_ (Lib. I. Aphorism 80) where he speaks with indignation of\nthe way in which philosophy had been degraded and perverted, by being\napplied as a mere instrument of utility or of early education: \"So that\nthe great mother of the Sciences is thrust down with indignity to the\noffices of a handmaid;--is made to minister to the labours of medicine\nor mathematics; or again, to give the first preparatory tinge to the\nimmature minds of youth[327].\"\n\nIn the like spirit, Plato says (_Rep._ VI. \u00a7 11, Bekker's ed.):\n\n\"Observe how boldly and fearlessly I set about my explanation of my\nassertion that philosophers ought to rule the world. For I begin by\nsaying, that the State must begin to treat the study of philosophy in a\nway opposite to that now practised. Now, those who meddle at all with\nthis study are put upon it when they are children, between the lessons\nwhich they receive in the farm-yard and in the shop[328]; and as soon\nas they have been introduced to the hardest part of the subject, are\ntaken off from it, even those who get the most of philosophy. By the\nhardest part, I mean, the discussion of principles--Dialectic[329].\nAnd in their succeeding years, if they are willing to listen to a\nfew lectures of those who make philosophy their business, they think\nthey have done great things, as if it were something foreign to the\nbusiness of life. And as they advance towards old age, with a very\nfew exceptions, philosophy in them is extinguished: extinguished far\nmore completely than the Heraclitean sun, for theirs is not lighted\nup again, as that is every morning:\" alluding to the opinion which\nwas propounded, by way of carrying the doctrine of the _unfixity_ of\nsensible objects to an extreme; that the Sun is extinguished every\nnight and lighted again in the morning. In opposition to this practice,\nPlato holds that philosophy should be the especial employment of men's\nminds when their bodily strength fails.\n\nWhat Plato means by _Dialectic_, which he, in the next Book, calls the\nhighest part of philosophy, and which is, I think, what he here means\nby the hardest part of philosophy, I may hereafter consider: but at\npresent I wish to pass in review the Sciences which he speaks of, as\nleading the way to that highest study. These Sciences are Arithmetic,\nPlane Geometry, Solid Geometry, Astronomy and Harmonics.\n\nThe view in which Plato here regards the Sciences is, as the\ninstruments of that culture of the philosophical spirit which is\nto make the philosopher the fit and natural ruler of the perfect\nState--the Platonic Polity. It is held that to answer this purpose, the\nmind must be instructed in something more stable than the knowledge\nsupplied by the senses;--a knowledge of objects which are constantly\nchanging, and which therefore can be no real permanent Knowledge, but\nonly Opinion. The real and permanent Knowledge which we thus require is\nto be found in certain sciences, which deal with _truths necessary and\nuniversal_, as we should now describe them: and which therefore are,\nin Plato's language, a knowledge of that which really _is_[330].\n\nThis is the object of the Sciences of which Plato speaks. And hence,\nwhen he introduces Arithmetic, as the first of the Sciences which are\nto be employed in this mental discipline, he adds (VII. \u00a7 8) that\nit must be not mere common Arithmetic, but a science which leads to\nspeculative truths[331], seen by Intuition[332]; not an Arithmetic\nwhich is studied for the sake of buying and selling, as among tradesmen\nand shopkeepers, but for the sake of pure and real Science[333].\n\nI shall not dwell upon the details with which he illustrates this view,\nbut proceed to the other Sciences which he mentions.\n\nGeometry is then spoken of, as obviously the next Science in order;\nand it is asserted that it really does answer the required condition\nof drawing the mind from visible, mutable phenomena to a permanent\nreality. Geometers indeed speak of their visible diagrams, as if their\nproblems were certain practical processes; to erect a perpendicular; to\nconstruct a square: and the like. But this language, though necessary,\nis really absurd. The figures are mere aids to their reasonings.\nTheir knowledge is really a knowledge not of visible objects, but of\npermanent realities: and thus, Geometry is one of the helps by which\nthe mind may be drawn to Truth; by which the philosophical spirit may\nbe formed, which looks upwards instead of downwards.\n\nAstronomy is suggested as the Science next in order, but Socrates, the\nleader of the dialogue, remarks that there is an intermediate Science\nfirst to be considered. Geometry treats of plane figures; Astronomy\ntreats of solids in motion, that is, of spheres in motion; for the\nastronomy of Plato's time was mainly the doctrine of the sphere. But\nbefore treating of solids in motion, we must have a science which\ntreats of solids simply. After taking space of two dimensions, we must\ntake space of three dimensions, length, breadth and depth, as in cubes\nand the like[334]. But such a Science, it is remarked, has not yet\nbeen discovered. Plato \"notes as deficient\" this branch of knowledge;\nto use the expression employed by Bacon on the like occasions in his\nReview. Plato goes on to say, that the cultivators of such a science\nhave not received due encouragement; and that though scorned and\nstarved by the public, and not recommended by any obvious utility, it\nhas still made great progress, in virtue of its own attractiveness.\n\nIn fact, researches in Solid Geometry had been pursued with great zeal\nby Plato and his friends, and with remarkable success. The five Regular\nSolids, the Tetrahedron or Pyramid, Cube, Octahedron, Dodecahedron\nand Icosahedron, had been discovered; and the curious theorem, that\nof Regular Solids there can be just so many, these and no others,\nwas known. The doctrine of these Solids was already applied in a\nway, fanciful and arbitrary, no doubt, but ingenious and lively, to\nthe theory of the Universe. In the _Tim\u00e6us_, the elements have these\nforms assigned to them respectively. Earth has the Cube: Fire has the\nPyramid: Water has the Octahedron: Air has the Icosahedron: and the\nDodecahedron is the plan of the Universe itself. This application of\nthe doctrine of the Regular Solids shows that the knowledge of those\nfigures was already established; and that Plato had a right to speak\nof Solid Geometry as a real and interesting Science. And that this\nsubject was so recondite and profound,--that these five Regular Solids\nhad so little application in the geometry which has a bearing on man's\nordinary thoughts and actions,--made it all the more natural for Plato\nto suppose that these solids had a bearing on the constitution of the\nUniverse; and we shall find that such a belief in later times found a\nready acceptance in the minds of mathematicians who followed in the\nPlatonic line of speculation.\n\nPlato next proceeds to consider Astronomy; and here we have an amusing\ntouch of philosophical drama. Glaucon, the hearer and pupil in the\nDialogue, is desirous of showing that he has profited by what his\ninstructor had said about the real uses of Science. He says Astronomy\nis a very good branch of education. It is such a very useful science\nfor seamen and husbandmen and the like. Socrates says, with a smile,\nas we may suppose: \"You are very amusing with your zeal for utility.\nI suppose you are afraid of being condemned by the good people of\nAthens for diffusing Useless Knowledge.\" A little afterwards Glaucon\ntries to do better, but still with no great success. He says, \"You\nblamed me for praising Astronomy awkwardly: but now I will follow your\nlead. Astronomy is one of the sciences which you require, because it\nmakes men's minds look upwards, and study things above. Any one can\nsee that.\" \"Well,\" says Socrates, \"perhaps any one can see it except\nme--I cannot see it.\" Glaucon is surprised, but Socrates goes on: \"Your\nnotice of 'the study of things above' is certainly a very magnificent\none. You seem to think that if a man bends his head back and looks at\nthe ceiling he 'looks upwards' with his mind as well as his eyes. You\nmay be right and I may be wrong: but I have no notion of any science\nwhich makes the _mind_ look upwards, except a science which is about\nthe permanent and the invisible. It makes no difference, as to that\nmatter, whether a man gapes and looks up or shuts his mouth and looks\ndown. If a man merely look up and stare at sensible objects, his mind\ndoes not look upwards, even if he were to pursue his studies swimming\non his back in the sea.\"\n\nThe Astronomy, then, which merely looks at phenomena does not satisfy\nPlato. He wants something more. What is it? as Glaucon very naturally\nasks.\n\nPlato then describes Astronomy as a real science (\u00a7 11). \"The\nvariegated adornments which appear in the sky, the visible luminaries,\nwe must judge to be the most beautiful and the most perfect things of\ntheir kind: but since they are mere visible figures, we must suppose\nthem to be far inferior to the true objects; namely, those spheres\nwhich, with their real proportions of quickness and slowness, their\nreal number, their real figures, revolve and carry luminaries in their\nrevolutions. These objects are to be apprehended by reason and mental\nconception, not by vision.\" And he then goes on to say that the varied\nfigures which the skies present to the eye are to be used as _diagrams_\nto assist the study of that higher truth; just as if any one were to\nstudy geometry by means of beautiful diagrams constructed by D\u00e6dalus or\nany other consummate artist.\n\nHere then, Plato points to a kind of astronomical science which goes\nbeyond the mere arrangement of phenomena: an astronomy which, it\nwould seem, did not exist at the time when he wrote. It is natural\nto inquire, whether we can determine more precisely what kind of\nastronomical science he meant, and whether such science has been\nbrought into existence since his time.\n\nHe gives us some further features of the philosophical astronomy which\nhe requires. \"As you do not expect to find in the most exquisite\ngeometrical diagrams the true evidence of quantities being equal, or\ndouble, or in any other relation: so the true astronomer will not think\nthat the proportion of the day to the month, or the month to the year,\nand the like, are real and immutable things. He will seek a deeper\ntruth than these. We must treat Astronomy, like Geometry, as a series\nof problems suggested by visible things. We must apply the intelligent\nportion of our mind to the subject.\"\n\nHere we really come in view of a class of problems which astronomical\nspeculators at certain periods have proposed to themselves. What is the\nreal ground of the proportion of the day to the month, and of the month\nto the year, I do not know that any writer of great name has tried to\ndetermine: but to ask the reason of these proportions, namely, that of\nthe revolution of the earth on its axis, of the moon in its orbit, and\nof the earth in its orbit, are questions just of the same kind as to\nask the reason of the proportion of the revolutions of the planets in\ntheir orbits, and of the proportion of the orbits themselves. Now who\nhas attempted to assign such reasons?\n\nOf course we shall answer, Kepler: not so much in the Laws of the\nPlanetary motions which bear his name, as in the Law which at an\nearlier period he thought he had discovered, determining the proportion\nof the distances of the several Planets from the Sun. And, curiously\nenough, this solution of a problem which we may conceive Plato to have\nhad in his mind, Kepler gave by means of the Five Regular Solids which\nPlato had brought into notice, and had employed in his theory of the\nUniverse given in the _Tim\u00e6us_.\n\nKepler's speculations on the subject just mentioned were given to the\nworld in the _Mysterium Cosmographicum_ published in 1596. In his\nPreface, he says \"In the beginning of the year 1595 I brooded with\nthe whole energy of my mind on the subject of the Copernican system.\nThere were three things in particular of which I pertinaciously sought\nthe causes; why they are not other than they are: the number, the\nsize, and the motion of the orbits.\" We see how strongly he had his\nmind impressed with the same thought which Plato had so confidently\nuttered: that there must be some reason for those proportions in the\nscheme of the Universe which appear casual and vague. He was confident\nat this period that he had solved two of the three questions which\nhaunted him;--that he could account for the number and the size of the\nplanetary orbits. His account was given in this way.--\"The orbit of\nthe Earth is a circle; round the sphere to which this circle belongs\ndescribe a dodecahedron; the sphere including this will give the orbit\nof Mars. Round Mars inscribe a tetrahedron; the circle including this\nwill be the orbit of Jupiter. Describe a cube round Jupiter's orbit;\nthe circle including this will be the orbit of Saturn. Now inscribe in\nthe Earth's orbit an icosahedron: the circle inscribed in it will be\nthe orbit of Venus. Inscribe an octahedron in the orbit of Venus; the\ncircle inscribed in it will be Mercury's orbit. This is the reason of\nthe number of the planets;\" and also of the magnitudes of their orbits.\n\nThese proportions were only approximations; and the Rule thus asserted\nhas been shown to be unfounded, by the discovery of new Planets. This\nLaw of Kepler has been repudiated by succeeding Astronomers. So far,\nthen, the Astronomy which Plato requires as a part of true philosophy\nhas not been brought into being. But are we thence to conclude\nthat the demand for such a kind of Astronomy was a mere Platonic\nimagination?--was a mistake which more recent and sounder views have\ncorrected? We can hardly venture to say that. For the questions which\nKepler thus asked, and which he answered by the assertion of this\nerroneous Law, are questions of exactly the same kind as those which\nhe asked and answered by means of the true Laws which still fasten his\nname upon one of the epochs of astronomical history. If he was wrong\nin assigning reasons for the number and size of the planetary orbits,\nhe was right in assigning a reason for the proportion of the motions.\nThis he did in the _Harmonice Mundi_, published in 1619: where he\nestablished that the squares of the periodic times of the different\nPlanets are as the cubes of their mean distances from the central Sun.\nOf this discovery he speaks with a natural exultation, which succeeding\nastronomers have thought well founded. He says: \"What I prophesied\ntwo and twenty years ago as soon as I had discovered the five solids\namong the heavenly bodies; what I firmly believed before I had seen\nthe _Harmonics_ of Ptolemy; what I promised my friends in the title of\nthis book (_On the perfect Harmony of the celestial motions_), which\nI named before I was sure of my discovery; what sixteen years ago I\nregarded as a thing to be sought; that for which I joined Tycho Brahe,\nfor which I settled in Prague, for which I devoted the best part of my\nlife to astronomical contemplations; at length I have brought to light,\nand have recognized its truth beyond my most sanguine expectations.\"\n(_Harm. Mundi_, Lib. V.)\n\nThus the Platonic notion, of an Astronomy which deals with doctrines\nof a more exact and determinate kind than the obvious relations of\nph\u00e6nomena, may be found to tend either to error or to truth. Such\naspirations point equally to the five regular solids which Kepler\nimagined as determining the planetary orbits, and to the Laws of\nKepler in which Newton detected the effect of universal gravitation.\nThe realities which Plato looked for, as something incomparably more\nreal than the visible luminaries, are found, when we find geometrical\nfigures, epicycles and eccentrics, laws of motion and laws of force,\nwhich explain the appearances. His Realities are Theories which account\nfor the Phenomena, Ideas which connect the Facts.\n\nBut, is Plato right in holding that such Realities as these are _more\nreal_ than the Phenomena, and constitute an Astronomy of a higher kind\nthan that of mere Appearances? To this we shall, of course, reply\nthat Theories and Facts have each their reality, but that these are\nrealities of different kinds. Kepler's Laws are as real as day and\nnight; the force of gravity tending to the Sun is as real as the Sun;\nbut not more so. True Theories and Facts are equally real, for true\nTheories _are_ Facts, and Facts are familiar Theories. Astronomy is, as\nPlato says, a series of Problems suggested by visible Things; and the\nThoughts in our own minds which bring the solutions of these Problems,\nhave a reality in the Things which suggest them.\n\nBut if we try, as Plato does, to separate and oppose to each other the\nAstronomy of Appearances and the Astronomy of Theories, we attempt that\nwhich is impossible. There are no Phenomena which do not exhibit some\nLaw; no Law can be conceived without Phenomena. The heavens offer a\nseries of Problems; but however many of these Problems we solve, there\nremain still innumerable of them unsolved; and these unsolved Problems\nhave solutions, and are not different in kind from those of which the\nextant solution is most complete.\n\nNor can we justly distinguish, with Plato, Astronomy into transient\nappearances and permanent truths. The theories of Astronomy are\npermanent, and are manifested in a series of changes: but the change is\nperpetual just _because_ the theory is permanent. The perpetual change\n_is_ the permanent theory. The perpetual changes in the positions\nand movements of the planets, for instance, manifest the permanent\nmachinery: the machinery of cycles and epicycles, as Plato would\nhave said, and as Copernicus would have agreed; while Kepler, with a\nprofound admiration for both, would have asserted that the motions\nmight be represented by ellipses, more exactly, if not more truly. The\ncycles and epicycles, or the ellipses, are as real as space and time,\n_in_ which the motions take place. But we cannot justly say that space\nand time and motion are more real than the bodies which move in space\nand time, or than the appearances which these bodies present.\n\nThus Plato, with his tendency to exalt Ideas above Facts,--to find a\nReality which is more real than Phenomena,--to take hold of a permanent\nTruth which is more true than truths of observation,--attempts what\nis impossible. He tries to separate the poles of the Fundamental\nAntithesis, which, however antithetical, are inseparable.\n\nAt the same time, we must recollect that this tendency to find a\nReality which is something beyond appearance, a permanence which is\ninvolved in the changes, is the genuine spring of scientific discovery.\nSuch a tendency has been the cause of all the astronomical science\nwhich we possess. It appeared in Plato himself, in Hipparchus, in\nPtolemy, in Copernicus, and most eminently in Kepler; and in him\nperhaps in a manner more accordant with Plato's aspirations when he\nfound the five Regular Solids in the Universe, than when he found there\nthe Conic Sections which determine the form of the planetary orbits.\nThe pursuit of this tendency has been the source of the mighty and\nsuccessful labours of succeeding astronomers: and the anticipations of\nPlato on this head were more true than he himself could have conceived.\n\nWhen the above view of the nature of true astronomy has been proposed,\nGlaucon says:\n\n\"That would be a task much more laborious than the astronomy now\ncultivated.\" Socrates replies: \"I believe so: and such tasks must be\nundertaken, if our researches are to be good for anything.\"\n\nAfter Astronomy, there comes under review another Science, which is\ntreated in the same manner. It is presented as one of the Sciences\nwhich deal with real abstract truth; and which are therefore suited to\nthat development of the philosophic insight into the highest truth,\nwhich is here Plato's main object. This Science is _Harmonics_, the\ndoctrine of the mathematical relations of musical sounds. Perhaps\nit may be more difficult to explain to a general audience, Plato's\nviews on this than on the previous subjects: for though Harmonics is\nstill acknowledged as a Science including the mathematical truths to\nwhich Plato here refers, these truths are less generally known than\nthose of geometry or astronomy. Pythagoras is reported to have been\nthe discoverer of the cardinal proposition in this Mathematics of\nMusic:--namely, that the musical notes which the ear recognizes as\nhaving that definite and harmonious relation which we call an _octave_,\na _fifth_, a _fourth_, a _third_, have also, in some way or other, the\nnumerical relation of 2 to 1, 3 to 2, 4 to 3, 5 to 4. I say \"some way\nor other,\" because the statements of ancient writers on this subject\nare physically inexact, but are right in the essential point, that\nthose simple numerical ratios are characteristic of the most marked\nharmonic relations. The numerical ratios really represent the rate of\nvibration of the air when those harmonics are produced. This perhaps\nPlato did not know: but he knew or assumed that those numerical ratios\nwere cardinal truths in harmony: and he conceived that the exactness\nof the ratios rested on grounds deeper and more intellectual than any\ntestimony which the ear could give. This is the main point in his mode\nof applying the subject, which will be best understood by translating\n(with some abridgement) what he says. Socrates proceeds:\n\n(\u00a7 11 near the end.) \"Motion appears in many aspects. It would take a\nvery wise man to enumerate them all: but there are two obvious kinds.\nOne which appears in astronomy, (the revolutions of the heavenly\nbodies,) and another which is the echo of that[335]. As the eyes are\nmade for Astronomy, so are the ears made for the motion which produces\nHarmony[336]: and thus we have two sister sciences, as the Pythagoreans\nteach, and we assent.\n\n(\u00a7 12.) \"To avoid unnecessary labour, let us first learn what _they_\ncan tell us, and see whether anything is to be added to it; retaining\nour own view on such subjects: namely this:--that those whose education\nwe are to superintend--real philosophers--are never to learn any\nimperfect truths:--anything which does not tend to that point (exact\nand permanent truth) to which all our knowledge ought to tend, as we\nsaid concerning astronomy. Now those who cultivate music take a very\ndifferent course from this. You may see them taking immense pains in\nmeasuring musical notes and intervals by the ear, as the astronomers\nmeasure the heavenly motions by the eye.\n\n\"Yes, says Glaucon, they apply their ears close to the instrument, as\nif they could catch the note by getting near to it, and talk of some\nkind of recurrences[337]. Some say they can distinguish an interval,\nand that this is the smallest possible interval, by which others are to\nbe measured; while others say that the two notes are identical: both\nparties alike judging by the ear, not by the intellect.\n\n\"You mean, says Socrates, those fine musicians who torture their\nnotes, and screw their pegs, and pinch their strings, and speak of the\nresulting sounds in grand terms of art. We will leave them, and address\nour inquiries to our other teachers, the Pythagoreans.\"\n\nThe expressions about the small interval in Glaucon's speech appear to\nme to refer to a curious question, which we know was discussed among\nthe Greek mathematicians. If we take a keyed instrument, and ascend\nfrom a key note by two _octaves_ and a _third_, (say from _A__{1} to\n_C__{3}) we arrive at the _same nominal note_, as if we ascend four\ntimes by a _fifth_ (_A__{1} to _E__{1}, _E__{1} to _B__{2}, _B__{2}\nto _F__{2}, _F__{2} to _C__{3}). Hence one party might call this the\n_same_ note. But if the Octaves, Fifths, and Third be perfectly true\nintervals, the notes arrived at in the two ways will not be really\nthe same. (In the one case, the note is \u00bd \u00d7 \u00bd \u00d7 \u2158; in the other\n\u2154 \u00d7 \u2154 \u00d7 \u2154 \u00d7 \u2154; which are \u2155 and 16/81, or in the ratio of\n81 to 80). This small interval by which the two notes really differ,\nthe Greeks called a _Comma_, and it was the smallest musical interval\nwhich they recognized. Plato disdains to see anything important in this\ncontroversy; though the controversy itself is really a curious proof\nof his doctrine, that there is a mathematical truth in Harmony, higher\nthan instrumental exactness can reach. He goes on to say:\n\n \"The musical teachers are defective in the same way as the\n astronomical. They do indeed seek numbers in the harmonic notes, which\n the ear perceives: but they do not ascend from them to the Problem,\n What are harmonic numbers and what are not, and what is the reason of\n each[338]?\" \"That\", says Glaucon, \"would be a sublime inquiry.\"\n\nHave we in Harmonics, as in Astronomy, anything in the succeeding\nHistory of the Science which illustrates the tendency of Plato's\nthoughts, and the value of such a tendency?\n\nIt is plain that the tendency was of the same nature as that which\ninduced Kepler to call his work on Astronomy _Harmonice Mundi_; and\nwhich led to many of the speculations of that work, in which harmonical\nare mixed with geometrical doctrines. And if we are disposed to judge\nseverely of such speculations, as too fanciful for sound philosophy, we\nmay recollect that Newton himself seems to have been willing to find an\nanalogy between harmonic numbers and the different coloured spaces in\nthe spectrum.\n\nBut I will say frankly, that I do not believe there really exists any\nharmonical relation in either of these cases. Nor can the problem\nproposed by Plato be considered as having been solved since his\ntime, any further than the recurrence of vibrations, when their\nratios are so simple, may be easily conceived as affecting the ear\nin a peculiar manner. The imperfection of musical scales, which the\n_comma_ indicates, has not been removed; but we may say that, in the\ncase of this problem, as in the other ultimate Platonic problems,\nthe duplication of the cube and the quadrature of the circle, the\nimpossibility of a solution has been already established. The problem\nof a perfect musical scale is impossible, because no power of 2 can\nbe equal to a power of 3; and if we further take the multiplier 5, of\ncourse it also cannot bring about an exact equality. This impossibility\nof a perfect scale being recognized, the practical problem is what is\nthe system of _temperament_ which will make the scale best suited for\nmusical purposes; and this problem has been very fully discussed by\nmodern writers.\n\n\nFOOTNOTES:\n\n[Footnote 327: Accedit et illud quod naturalis philosophia in iis ipsis\nviris, qui ei incubuerunt, vacantem et integrum hominem, pr\u00e6sertim\nhis recentioribus temporibus, vix nacta sit; nisi forte quis monachi\nalicujus in cellula, aut nobilis in villula lucubrantis, exemplum\nadduxerit; sed facta est demum naturalis philosophia instar transitus\ncujusdam et pontisternii ad alia. Atque magna ista scientiarum mater\nad officia ancill\u00e6 detrusa est; qu\u00e6 medicin\u00e6 aut mathematicis operibus\nministrat, et rursus qu\u00e6 adolescentium immatura ingenia lavat et imbuat\nvelut tinctura quadam prima, ut aliam postea felicius et commodius\nexcipiant.]\n\n[Footnote 328: \u03bc\u03b5\u03c4\u03b1\u03be\u1f7a \u03bf\u1f30\u03ba\u03bf\u03bd\u03bf\u03bc\u03af\u03b1\u03c2 \u03ba\u03b1\u1f76 \u03c7\u03c1\u03b5\u03bc\u03b1\u03c4\u03b9\u03c3\u03bc\u03bf\u1fe6, between house-keeping\nand money-getting.]\n\n[Footnote 329: \u03c4\u1f78  \u03c0\u03b5\u03c1\u1f76 \u03c4\u03bf\u1f7a\u03c2 \u03bb\u03cc\u03b3\u03bf\u03c5\u03c2.]\n\n[Footnote 330: The Sciences are to draw the mind from that which grows\nand perishes to that which really is: \u03bc\u03ac\u03b8\u03b7\u03bc\u03b1 \u03c8\u03c5\u03c7\u1fc6\u03c2 \u1f41\u03bb\u03ba\u1f78\u03bd \u1f00\u03c0\u1f78 \u03c4\u03bf\u1fe6\n\u03b3\u03b9\u03b3\u03bd\u03bf\u03bc\u03ad\u03bd\u03bf\u03c5 \u1f10\u03c0\u03b9 \u03c4\u1f78 \u1f45\u03bd.]\n\n[Footnote 331: \u1f10\u03c0\u1f76 \u03b8\u03ad\u03b1\u03bd \u03c4\u1fc6\u03c2 \u03c4\u1ff6\u03bd \u1f00\u03c1\u03b9\u03b8\u03bc\u1ff6\u03bd \u03c6\u03cd\u03c3\u03b5\u03c9\u03c2.]\n\n[Footnote 332: \u03c4\u1fc7 \u03bd\u03bf\u03b7\u03ae\u03c3\u03b5\u03b9 \u03b1\u1f50\u03c4\u1fc7.]\n\n[Footnote 333: He adds \"and for the sake of war;\" this point I have\npassed by. Plato does not really ascribe much weight to this use of\nScience, as we see in what he says of Geometry and Astronomy.]\n\n[Footnote 334: \u1f00\u03c1\u03b8\u1ff6\u03c2 \u1f15\u03c7\u03b5\u03b9 \u1f11\u03be\u1fc6\u03c2 \u03bc\u03b5\u03c4\u1f70 \u03b4\u03b5\u03c5\u03c4\u03ad\u03c1\u03b1\u03bd \u03b1\u1f55\u03be\u03b7\u03bd \u03c4\u03c1\u03af\u03c4\u03b7\u03bd \u03bb\u03b1\u03bc\u03b2\u03ac\u03bd\u03b5\u03b9\u03bd,\n\u1f15\u03c3\u03c4\u03b9 \u03b4\u03ad  \u03c0\u03bf\u03c5 \u03c4\u03bf\u1fe6\u03c4\u03bf \u03c0\u03b5\u03c1\u1f76 \u03c4\u1f74\u03bd \u03c4\u1ff6\u03bd \u03ba\u03cd\u03b2\u03c9\u03bd \u03b1\u03cd\u03be\u03b7\u03bd \u03ba\u03b1\u1f76 \u03c4\u1f78 \u03b2\u03ac\u03b8\u03bf\u03c5\u03c2 \u03bc\u03ad\u03c4\u03b5\u03c7\u03bf\u03bd.]\n\n[Footnote 335: \u1f00\u03bd\u03c4\u03af\u03c3\u03c4\u03c1\u03bf\u03c6\u03bf\u03bd \u03b1\u1f50\u03c4\u03bf\u1fe6.]\n\n[Footnote 336: \u03c0\u03c1\u1f78\u03c2 \u1f10\u03bd\u03b1\u03c1\u03bc\u03cc\u03bd\u03b9\u03bf\u03bd \u03c6\u03bf\u03c1\u1f70\u03bd \u1f66\u03c4\u03b1 \u03c0\u03b1\u03b3\u1fc6\u03bd\u03b1\u03b9.]\n\n[Footnote 337: \u03c0\u03c5\u03ba\u03bd\u03ce\u03bc\u03b1\u03c4\u03b1 \u1f04 \u03c4\u03c4\u03b1.]\n\n[Footnote 338: \u03c4\u03af\u03bd\u03b5\u03c2 \u03be\u03cd\u03bc\u03c6\u03c9\u03bd\u03bf\u03b9 \u1f00\u03c1\u03b9\u03b8\u03bc\u03bf\u1f76, &c.]\n\n\nAPPENDIX BB.\n\nON PLATO'S NOTION OF DIALECTIC.\n\n(_Cam. Phil. Soc._ MAY 7, 1855.)\n\n\nThe survey of the sciences, arithmetic, plane geometry, solid geometry,\nastronomy and harmonics--which is contained in the seventh Book of\nthe Republic (\u00a7 6-12), and which has been discussed in the preceding\npaper, represents them as instruments in an education, of which the\nend is something much higher--as steps in a progression which is to go\nfurther. \"Do you not know,\" says Socrates (\u00a7 12), \"that all this is\nmerely a prelude to the strain which we have to learn?\" And what that\nstrain is, he forthwith proceeds to indicate. \"That these sciences\ndo not suffice, you must be aware: for--those who are masters of\nsuch sciences--do they seem to you to be good in dialectic? \u03b4\u03b5\u03b9\u03bd\u03bf\u1f76\n\u03b4\u03b9\u03b1\u03bb\u03b5\u03ba\u03c4\u03b9\u03ba\u03bf\u1f76 \u03b5\u1f37\u03bd\u03b1\u03b9;\"\n\n\"In truth, says Glaucon, they are not, with very few exceptions, so far\nas I have fallen in with them.\"\n\n\"And yet, said I, if persons cannot give and receive a reason, they\ncannot attain that knowledge which, as we have said, men ought to have.\"\n\nHere it is evident that \"to give and to receive a reason,\" is a\nphrase employed as coinciding, in a general way at least, with being\n\"good in dialectic;\" and accordingly, this is soon after asserted in\nanother form, the verb being now used instead of the adjective. \"It is\ndialectic discussion \u03c4\u1f78 \u03b4\u03b9\u03b1\u03bb\u03ad\u03b3\u03b5\u03c3\u03b8\u03b1\u03b9, which executes the strain which we\nhave been preparing.\" It is further said that it is a progress to clear\nintellectual light, which corresponds to the progress of bodily vision\nin proceeding from the darkened cave described in the beginning of the\nBook to the light of day. This progress, it is added, of course you\ncall _Dialectic_ \u03b4\u03b9\u03b1\u03bb\u03b5\u03ba\u03c4\u03b9\u03ba\u03ae\u03bd.\n\nPlato further says, that other sciences cannot properly be called\nsciences. They begin from certain assumptions, and give us only the\nconsequences which follow from reasoning on such assumptions. But these\nassumptions they cannot prove. To do so is not in the province of\neach science. It belongs to a higher science: to the science of Real\nExistences. You call the man Dialectical, who requires a reason of the\nessence of each thing[339].\n\nAnd as Dialectic gives an account of other real existences, so does\nit of that most important reality, the true guide of Life and of\nPhilosophy, the Real Good. He who cannot follow this through all the\nwindings of the battle of Life, knows nothing to any purpose. And\nthus Dialectic is the pinnacle, the top stone of the edifice of the\nsciences[340].\n\nDialectic is here defined or described by Plato according to the\n_subject_ with which it treats, and the _object_ with which it is to\nbe pursued: but in other parts of the Platonic Dialogues, Dialectic\nappears rather to imply a certain _method_ of investigation;--to\ndescribe the _form_ rather than the _matter_ of discussion; and it will\nperhaps be worth while to compare these different accounts of Dialectic.\n\n(_Ph\u00e6drus._) One of the cardinal passages on this Point is in the\nPh\u00e6drus, and may be briefly quoted. Ph\u00e6drus, in the Dialogue which\nbears his name, appears at first as an admirer of Lysias, a celebrated\nwriter of orations, the contemporary of Plato. In order to expose this\nwriter's style of composition as frigid and shallow, a specimen of it\nis given, and Socrates not only criticises this, but delivers, as rival\ncompositions, two discourses on the same subject. Of these discourses,\ngiven as the inspiration of the moment, the first is animated and\nvigorous; the second goes still further, and clothes its meaning in a\ngorgeous dress of poetical and mythical images. Ph\u00e6drus acknowledges\nthat his favourite is outshone; and Socrates then proceeds to point\nout that the real superiority of his own discourse consists in its\nhaving a dialectical structure, beneath its outward aspect of imagery\nand enthusiasm. He says: (\u00a7 109, Bekker. It is to be remembered that\nthe subject of all the discourses was _Love_, under certain supposed\nconditions.)\n\n\"The rest of the performance may be taken as play: but there were, in\nwhat was thus thrown out by a random impulse, two features, of which,\nif any one could reduce the effect to an art, it would be a very\nagreeable and useful task.\n\n\"What are they? Ph\u00e6drus asks.\n\n\"In the first place, Socrates replies, the taking a connected view of\nthe scattered elements of a subject, so as to bring them into one\nIdea; and thus to give a definition of the subject, so as to make it\nclear what we are speaking of; as was then done in regard to _Love_.\nA definition was given of it, what it is: whether the definition was\ngood or bad, at any rate there was a definition. And hence, in what\nfollowed, we were able to say what was clear and consistent with itself.\n\n\"And what, Ph\u00e6drus asks, was the other feature?\n\n\"The dividing the subject into kinds or elements, according to the\nnature of the thing itself:--not breaking its natural members, like a\nbad carver who cannot hit the joint. So the two discourses which we\nhave delivered, took the irrational part of the mind, as their common\nsubject; and as the body has two different sides, the right and the\nleft, with the same names for its parts; so the two discourses took\nthe irrational portion of man; and the one took the left-hand portion,\nand divided this again, and again subdivided it, till, among the\nsubdivisions, it found a left-handed kind of Love, of which nothing\nbut ill was to be said. While the discourse that followed out the\nright-hand side of phrenzy, (the irrational portion of man's nature,)\nwas led to something which bore the name of _Love_ like the other,\nbut which is divine, and was praised as the source of the greatest\nblessing.\"\n\n\"Now I,\" Socrates goes on to say, \"am a great admirer of these\nprocesses of division and comprehension, by which I endeavour to speak\nand to think correctly. And if I can find any one who is able to see\nclearly what is by nature reducible to one and manifested in many\nelements, I follow his footsteps as a divine guide. Those who can do\nthis, I call--whether rightly or not, God knows--but I have hitherto\nbeen in the habit of calling them _dialectical_ men.\"\n\nIt is of no consequence to our present purpose whether either of the\ndiscourses of Socrates in the Ph\u00e6drus, or the two together, as is here\nassumed, do contain a just division and subdivision of that part of the\nhuman soul which is distinguishable from Reason, and do thus exhibit,\nin its true relations, the affection of Love. It is evident that\ndivision and subdivision of this kind is here presented as, in Plato's\nopinion, a most valuable method; and those who could successfully\npractise this method are those whom he admires as dialectical men. This\nis here his _Dialectic_.\n\n(_Sophistes._) We are naturally led to ask whether this method of\ndividing a subject as the best way of examining it, be in any other\npart of the Platonic Dialogues more fully explained than it is in the\nPh\u00e6drus; or whether any rules are given for this kind of Dialectic.\n\nTo this we may reply, that in the Dialogue entitled _The Sophist_, a\nmethod of dividing a subject, in order to examine it, is explained\nand exemplified with extraordinary copiousness and ingenuity. The\nobject proposed in that Dialogue is, to define what a Sophist is;\nand with that view, the principal speaker, (who is represented as an\nEleatic stranger,) begins by first exemplifying what is his method of\nframing a definition, and by applying it to define an _Angler_. The\ncourse followed, though it now reads like a burlesque of philosophical\nmethods, appears to have been at that time a _bona fide_ attempt to be\nphilosophical and methodical. It proceeds thus:\n\n\"We have to inquire concerning _Angling_. Is it an Art? It is. Now\nwhat kind of art? All art is an art of making or an art of getting:\n(_Poietic_ or _Ktetic_.) It is Ktetic. Now the art of getting, is\nthe art of getting by exchange or by capture: (_Metabletic_ or\n_Chirotic_.) Getting by capture is by contest or by chase: (_Agonistic_\nor _Thereutic_.) Getting by chase is a chase of lifeless or of living\nthings: (the first has no name, the second is _Zootheric_.) The chase\nof living things is the chase of land animals or of water animals:\n(_Pezotheric_ or _Enygrotheric_.) Chase of water animals is of birds\nor of fish: (_Ornithothereutic_ and _Halieutic_.) Chase of fish is by\ninclosing or by striking them: (_Hercotheric_ or _Plectic_.) We strike\nthem by day with pointed instruments, or by night, using torches:\n(hence the division _Ankistreutic_ and _Pyreutic_.) Of Ankistreutic,\none kind consists in spearing the fish downwards from above, the other\nin twitching them upwards from below: (these two arts are _Triodontic_\nand _Aspalieutic_.) And thus we have, what we sought, the notion and\nthe description of angling: namely that it is a Ktetic, Chirotic,\nThereutic, Zootheric, Enygrotheric, Halieutic, Plectic, Ankistreutic,\nAspalieutic Art.\"\n\nSeveral other examples are given of this ingenious mode of definition,\nbut they are all introduced with reference to the definition of the\nSophist. And it will further illustrate this method to show how,\naccording to it, the Sophist is related to the Angler.\n\nThe Sophistical Art is an art of getting, by capture, living things,\nnamely men. It is thus a Ktetic, Chirotic, Thereutic art, and so far\nagrees with that of the Angler. But here the two arts diverge, since\nthat of the Sophist is Pezotheric, that of the Angler Enygrotheric.\nTo determine the Sophist still more exactly, observe that the chase\nof land animals is either of tame animals (including man) or of\nwild animals: (_Hemerotheric_ and _Agriotheric_.) The chase of tame\nanimals is either by violence, (as kidnapping, tyranny, and war in\ngeneral,) or by persuasion, (as by the arts of speech;) that is, it\nis _Biaiotheric_ or _Pithanurgic_. The art of persuasion is a private\nor a public proceeding: (_Idiothereutic_ or _Demosiothereutic_.)\nThe art of private persuasion is accompanied with the giving of\npresents, (as lovers do,) or with the receiving of pay: (thus it is\n_Dorophoric_ or _Mistharneutic_.) To receive pay as the result of\npersuasion, is the course, either of those who merely earn their bread\nby supplying pleasure, namely flatterers, whose art is _Hedyntic_;\nor of those who profess for pay to teach virtue. And who are they?\nPlainly the Sophists. And thus _Sophistic_ is that kind of Ktetic,\nChirotic, Thereutic, Zootheric, Pezotheric, Hemerotheric, Pithanurgic,\nIdiothereutic, Mistharneutic art, which professes to teach virtue, and\ntakes money on that account.\n\nThe same process is pursued along several other lines of inquiry: and\nat the end of each of them the Sophist is detected, involved in a\nnumber of somewhat obnoxious characteristics. This process of division\nit will be observed, is at every step bifurcate, or as it is called,\n_dichotomous_. Applied as it is in these examples, it is rather the\nvehicle of satire than of philosophy. Yet, I have no doubt that this\nbifurcate method was admired by some of the philosophers of Plato's\ntime, as a clever and effective philosophical invention. We may the\nmore readily believe this, inasmuch as one of the most acute persons\nof our own time, who has come nearer than any other to the ancient\nheads of sects in the submission with which his followers have accepted\nhis doctrines, has taken up this Dichotomous Method, and praised it\nas the only philosophical mode of dividing a subject. I refer to Mr.\nJeremy Bentham's _Chrestomathia_ (published originally in 1816), in\nwhich this exhaustive bifurcate method, as he calls it, was applied\nto classify sciences and arts, with a view to a scheme of education.\nHow exactly the method, as recommended by him, agrees with the method\nillustrated in the _Sophist_, an examination of any of his examples\nwill show. Thus to take Mineralogy as an example: according to Bentham,\nOntology is C\u0153noscopic or Idioscopic: the Idioscopic is Somatoscopic\nor Pneumatoscopic; the Somatoscopic is Pososcopic or Poioscopic:\nPoioscopic is Physiurgoscopic or Anthropurgoscopic: Physiurgoscopic is\nUranoscopic or Epigeoscopic: Epigeoscopic is Abioscopic or Embioscopic.\nAnd thus Mineralogy is the Science Idioscopic, Somatoscopic,\nPoioscopic, Physiurgoscopic, Epigeoscopic, Abioscopic: inasmuch as\nit is the science which regards bodies, with reference to their\nqualities,--bodies, namely, the works of nature, terrestrial, lifeless.\n\nI conceive that this bifurcate method is not really philosophical or\nvaluable: but that is not our business here. What we have to consider\nis whether this is what Plato meant by the term _Dialectic_.\n\nThe general description of Dialectic in the _Sophistes_ agrees very\nclosely with that quoted from the _Ph\u00e6drus_, that it is the separation\nof a subject according to its natural divisions.\n\nThus, see in the Sophist the passage \u00a7 83: \"To divide a subject\naccording to the kinds of things, so as neither to make the same\nkind different nor different kinds identical, is the office of the\nDialectical Science.\" And this is illustrated by observing that it is\nthe office of the science of Grammar to determine what letters may be\ncombined and what may not; it is the office of the science of Music to\ndetermine what sounds differing as acute and grave, may be combined,\nand what may not: and in like manner it is the office of the science of\nDialectic to determine what _kinds_ may be combined in one subject and\nwhat may not. And the proof is still further explained.\n\nIn many of the Platonic Dialogues, the Dialectic which Socrates is thus\nrepresented as approving, appears to include the form of Dialogue,\nas well as the subdivision of the subject into its various branches.\nSocrates is presented as attaching so much importance to this form,\nthat in the Protagoras (\u00a7 65) he rises to depart, because his opponent\nwill not conform to this practice. And generally in Plato, Dialectic is\nopposed to Rhetoric, as a string of short questions and answers to a\ncontinuous dissertation.\n\nXenophon also seems to imply (_Mem._ IV. 5, 11) that Socrates included\nin his notion of Dialectic the form of Dialogue as well as the division\nof the subject.\n\nBut that the method of close Dialogue was not called _Dialectic_ by\nthe author of the _Sophist_, we have good evidence in the work itself.\nAmong other notions which are analysed by the bifurcate division here\nexhibited, is that of getting by contest (_Agonistic_, previously given\nas a division of _Ktetic_). Now getting by contest may be by peaceful\ntrial of superiority, or by fight: (_Hamilletic_ or _Machelic_). The\nfight may be of body against body, or of words against words: these\nmay be called _Biastic_ and _Amphisbetic_. The fight of words about\nright and wrong, may be by long discourses opposed to each other, as\nin judicial cases; or by short questions and answers: the former may\nbe called _Dicanic_, the latter _Antilogic_. Of these colloquies,\nabout right and wrong, some are natural and spontaneous, others\nartificial and studied: the former need no special name; the latter are\ncommonly called _Eristic_. Of Eristic colloquies, some are a source\nof expense to those who hold them, some of gain: that is, they are\n_Chrematophthoric_ or _Chrematistic_: the former, the occupation of\nthose who talk for pleasure's and for company's sake, is _Adoleschic_,\nwasteful garrulity; the latter, that of those who talk for the sake\nof gain, is _Sophistic_. And thus Sophistic is an art Eristic, which\nis part of Antilogic, which is part of Amphisbetic, which is part of\nAgonistic, which is part of Chirotic, which is a part of Ktetic. (\u00a7 23.)\n\nWe may notice here an indication that satire rather than exact reason\ndirects these analyses; in that Sophistic, which was before a part of\nthe _thereutic_ branch of _chirotic_ and _ktetic_, is here a part of\nthe other branch, _agonistic_.\n\nBut the remark which I especially wish to make here is, that the art of\ndiscussing points of right and wrong by short questions and answers,\nbeing here brought into view, is not called _Dialectic_, which we\nmight have expected; but _Antilogic_. It would seem therefore that the\nAuthor of the Sophist did not understand by _Dialectic_ such a process\nas Socrates describes in Xenophon; (_Mem._ IV. 5, 11, 12;) where he\nsays it was called _Dialectic_, because it was followed by persons\n_dividing things into their kinds in conversation_: (\u03ba\u03bf\u03b9\u03bd\u1fc7 \u03b2\u03bf\u03c5\u03bb\u03b5\u03cd\u03b5\u03c3\u03b8\u03b1\u03b9\n\u03b4\u03b9\u03b1\u03bb\u03ad\u03b3\u03bf\u03bd\u03c4\u03b1\u03c2:)or such as the Socrates of Plato insisted upon in the\nProtagoras and the Gorgias. Of the two elements which the Dialectical\nProcess of Socrates implied, Division of the subject and Dialogue, the\nauthor of the _Sophistes_ does not claim the name of _Dialectic_ for\neither, and seems to reject it for the second.\n\nBut without insisting upon the name, are we to suppose that the\nDichotomous Method of the _Sophistes_ Dialogue, (I may add of the\n_Politicus_, for the method is the same in this Dialogue also,) is the\nmethod of division of a subject according to its natural members, of\nwhich Plato speaks in the _Ph\u00e6drus_?\n\nIf the _Sophistes_ be the work of Plato, the answer is difficult either\nway. If this method be Plato's _Dialectic_, how came he to omit to say\nso there? how came he even to seem to deny it? But on the other hand,\nif this dichotomous division be a different process from the division\ncalled _Dialectic_ in the Ph\u00e6drus, had Plato two methods of division of\na subject? and yet has he never spoken of them as two, or marked their\ndistinction?\n\nThis difficulty would be removed if we were to adopt the opinion, to\nwhich others, on other grounds, have been led, that the Sophistes,\nthough of Plato's time, is not Plato's work. The grounds of this\nopinion are,--that the doctrines of the Sophistes are not Platonic:\n(the doctrine of Ideas is strongly impugned and weakly defended:)\nSocrates is not the principal speaker, but an Eleatic stranger: and\nthere is, in the Dialogue, none of the dramatic character which we\ngenerally have in Plato. The Dialogue seems to be the work of some\nEleatic opponent of Plato, rather than his.\n\n(_Rep._ B. VII.) But we can have no doubt that the _Ph\u00e6drus_ contains\nPlato's real view of the nature of Dialectic, as to its form; let us\nsee how this agrees with the view of Dialectic, as to its matter and\nobject, given in the seventh Book of the _Republic_.\n\nAccording to Plato, Real Existences are the objects of the exact\nsciences (as number and figure, of Arithmetic and Geometry). The things\nwhich are the objects of sense transitory phenomena, which have no\nreality, because no permanence. Dialectic deals with Realities in a\nmore general manner. This doctrine is everywhere inculcated by Plato,\nand particularly in this part of the _Republic_. He does not tell us\nhow we are to obtain a view of the higher realities, which are the\nobjects of Dialectic: only he here assumes that it will result from\nthe education which he enjoins. He says (\u00a7 13) that the Dialectic\nProcess (\u1f21 \u03b4\u03b9\u03b1\u03bb\u03b5\u03ba\u03c4\u03b9\u03ba\u1f74 \u03bc\u03ad\u03b8\u03bf\u03b4\u03bf\u03c2) alone leads to true science: it makes\nno assumptions, but goes to First Principles, that its doctrines may\nbe firmly grounded: and thus it purges the eye of the soul, which was\nimmersed in barbaric mud, and turns it upward; using for this purpose\nthe aid of the sciences which have been mentioned. But when Glaucon\ninquires about the details of this Dialectic, Socrates says he will not\nthen answer the inquiry. We may venture to say, that it does not appear\nthat he had any answer ready.\n\nLet us consider for a moment what is said about a philosophy rendering\na reason for the First Principles of each Science, which the Science\nitself cannot do. That there is room for such a branch of philosophy\nin some sciences, we easily see. Geometry, for instance, proceeds\nfrom Axioms, Definitions and Postulates; but by the very nature of\nthese terms, does not prove these First Principles. These--the Axioms,\nDefinitions and Postulates,--are, I conceive, what Plato here calls the\n_Hypotheses_ upon which Geometry proceeds, and for which it is not the\nbusiness of Geometry to render a reason. According to him, it is the\nbusiness of \"Dialectic\" to give a just account of these \"Hypotheses.\"\nWhat then is _Dialectic?_\n\n(_Aristotle._) It is, I think, well worthy of remark, that Aristotle,\ngiving an account in many respects different from that of Plato, of\nthe nature of Dialectic, is still led in the same manner to consider\nDialectic as the branch of philosophy which renders a reason for First\nPrinciples. In the _Topics_, we have a distinction drawn between\nreasoning demonstrative, and reasoning dialectical: and the distinction\nis this:--(_Top_. I. 1) that demonstration is by syllogisms from true\nfirst principles, or from true deductions from such principles; and\nthat the Dialectical Syllogism is that which syllogizes from probable\npropositions (\u1f20\u03be \u1f20\u03bd\u03b4\u03cc\u03be\u03c9\u03bd). And he adds that probable propositions are\nthose which are accepted by all, or by the greatest part, or by the\nwise. In the next chapter, he speaks of the uses of Dialectic, which,\nhe says, are three, mental discipline, debates, and philosophical\nscience. And he adds (_Top_. I. 2, 6) that it is also useful with\nreference to the First Principles in each Science: for from the\nappropriate Principles of each science we cannot deduce anything\nconcerning First Principles, since these principles are the beginning\nof reasoning. But from the probable principles in each province of\nscience we must reason concerning First Principles: and this is either\nthe peculiar office of Dialectic, or the office most appropriate to it;\nfor it is a process of investigation, and must lead to the Principles\nof all methods.\n\nThat a demonstrative science, as such, does not explain the origin\nof its own First Principles, is undoubtedly true. Geometry does not\nundertake to give a reason for the Axioms, Definitions, and Postulates.\nThis has been attempted, both in ancient and in modern times, by the\nMetaphysicians. But the Metaphysics employed on such subjects has not\ncommonly been called Dialectic. The term has certainly been usually\nemployed rather as describing a Method, than as determining the subject\nof investigation. Of the Faculty which apprehends First Principles,\nboth according to Plato and to Aristotle, I will hereafter say a few\nwords.\n\nThe object of the dichotomous process pursued in the Sophistes, and\nits result in each case, is a Definition. Definition also was one of\nthe main features of the inquiries pursued by Socrates, Induction\nbeing the other; and indeed in many cases Induction was a series of\nsteps which ended in Definition. And Aristotle also taught a peculiar\nmethod, the object and result of which was the construction of\nDefinitions:--namely his _Categories_. This method is one of division,\nbut very different from the divisions of the Sophistes. His method\nbegins by dividing the whole subject of possible inquiry into ten heads\nor _Categories_--Substance, Quantity, Quality, Relation, Place, Time,\nPosition, Habit, Action, Passion. These again are subdivided: thus\nQuality is Habit or Disposition, Power, Affection, Form. And we have\nan example of the application of this method to the construction of a\nDefinition in the Ethics; where he determines Virtue to be a Habit with\ncertain additional limitations.\n\nThus the Induction of Socrates, the Dichotomy of the Eleatics, the\nCategories of Aristotle, may all be considered as methods by which we\nproceed to the construction of Definitions. If, by any method, Plato\ncould proceed to the construction of a Definition, or rather of an\nIdea, of the Absolute Realities on which First Principles depend,\nsuch a method would correspond with the notion of Dialectic in the\n_Republic_. And if it was a method of division like the Eleatic or\nAristotelic, it would correspond with the notion of Dialectic in the\n_Ph\u00e6drus_.\n\nThat Plato's notion, however, cannot have been exactly either of these\nis, I think, plain. The colloquial method of stimulating and testing\nthe progress of the student in Dialectic is implied, in the sequel\nof this discussion of the effect of scientific study. And the method\nof Dialogue, as the instrument of instruction, being thus supposed,\nthe continuation of the account in the _Republic_, implies that Plato\nexpected persons to be made dialectical by the study of the exact\nsciences in a comprehensive spirit. After insisting on Geometry and\nother sciences, he says (_Rep._ VII. \u00a7 16): \"The synoptical man is\ndialectical; and he who is not the one, is not the other.\"\n\nBut, we may ask, does a knowledge of sciences lead naturally to a\nknowledge of Ideas, as absolute realities from which First Principles\nflow? And supposing this to be true, as the Platonic Philosophy\nsupposes, is the Idea of the Good, as the source of moral truths, to\nbe thus attained to? That it is, is the teaching of Plato, here and\nelsewhere; but have the speculations of subsequent philosophers in the\nsame direction given any confirmation of this lofty assumption?\n\nIn reply to this inquiry, I should venture to say, that this assumption\nappears to be a remnant of the Socratic doctrine from which Plato\nbegan his speculations, that Virtue is a kind of knowledge; and that\nall attempts to verify the assumption have failed. What Plato added to\nthe Socratic notion was, that the inquiry after The Good, the Supreme\nGood, was to be aided by the analogy or suggestions of those sciences\nwhich deal with necessary and eternal truths; the supreme good being\nof the nature of those necessary and eternal truths. This notion is a\nstriking one, as a suggestion, but it has always failed, I think, in\nthe attempts to work it out. Those who in modern times, as Cudworth\nand Samuel Clarke, have supposed an analogy between the necessary\ntruths of Geometry and the truths of Morality, though they have used\nthe like expressions concerning the one and the other class of truths,\nhave failed to convey clear doctrines and steady convictions to their\nreaders; and have now, I believe, few or no followers.\n\nThe result of our investigation appears to be, that though Plato added\nmuch to the matter by means of which the mind was to be improved and\ndisciplined in its research after Principles and Definitions, he did\nnot establish any form of Method according to which the inquiry\nmust be conducted, and by which it might be aided. The most definite\nnotion of Dialectic still remained the same with the original informal\nview which Socrates had taken of it, as Xenophon tells us, (_Mem._\nIV. 5, 11) when he says: \"He said that Dialectic (\u03c4\u1f78 \u03b4\u03b9\u03b1\u03bb\u03ad\u03b3\u03b5\u03c3\u03b8\u03b1\u03b9)\nwas so called because it is an inquiry pursued by persons who take\ncounsel together, separating the subjects considered according to\ntheir kinds (\u03b4\u03b9\u03b1\u03bb\u03ad\u03b3\u03bf\u03bd\u03c4\u03b1\u03c2). He held accordingly that men should try\nto be well prepared for such a process, and should pursue it with\ndiligence: by this means, he thought, they would become good men,\nfitted for responsible offices of command, and truly dialectical\"\n(\u03b4\u03b9\u03b1\u03bb\u03ad\u03ba\u03c4\u03b9\u03ba\u03c9\u03c4\u03ac\u03c4\u03bf\u03c5\u03c2). And this is, I conceive, the answer to Mr. Grote's\ninterrogatory exclamation (Vol. VIII. p. 577): \"Surely the Etymology\nhere given by Xenophon or Socrates of the word (\u03b4\u03b9\u03b1\u03bb\u03ad\u03b3\u03b5\u03c3\u03b8\u03b1\u03b9) cannot\nbe considered as satisfactory.\" The two notions, of investigatory\nDialogue, and Distribution of notions according to their kinds, which\nare thus asserted to be connected in etymology, were, among the\nfollowers of Socrates, connected in fact; the dialectic dialogue was\nsupposed to involve of course the dialectic division of the subject.\n\n\nFOOTNOTES:\n\n[Footnote 339: \u0397 \u03ba\u03b1\u1f76 \u03b4\u03b9\u03b1\u03bb\u03b5\u03ba\u03c4\u03b9\u03ba\u1f78\u03bd \u03ba\u03b1\u03bb\u03b5\u1fd6\u03c2 \u03c4\u1f78\u03bd \u03bb\u03cc\u03b3\u03bf\u03bd \u1f10\u03ba\u03ac\u03c3\u03c4\u03bf\u03c5 \u03bb\u03b1\u03bc\u03b2\u03ac\u03bd\u03bf\u03bd\u03c4\u03b1\n\u03c4\u1fc6\u03c2 \u03bf\u1f50\u03c3\u03af\u03b1\u03c2; (\u00a7 14).]\n\n[Footnote 340: \u1f65\u03c3\u03c0\u03b5\u03c1 \u03b8\u03c1\u03b9\u03b3\u03b3\u1f78\u03c2 \u03c4\u03bf\u1fd6\u03c2 \u03bc\u03b1\u03b8\u03ae\u03bc\u03b1\u03c3\u03b9\u03bd \u1f21 \u03b4\u03b9\u03b1\u03bb\u03b5\u03ba\u03c4\u03b9\u03ba\u1f74 \u1f26\u03bc\u03b9\u03bd \u1f10\u03c0\u03ac\u03bd\u03c9\n\u03ba\u03b5\u1fd6\u03c3\u03b8\u03b1\u03b9. (\u00a7 14).]\n\n\nAPPENDIX C.\n\nOF THE INTELLECTUAL POWERS ACCORDING TO PLATO.\n\n(_Cam. Phil. Soc._ NOV. 10, 1856.)\n\n\nIn the Seventh Book of Plato's _Republic_, we have certain sciences\ndescribed as the instruments of a philosophical and intellectual\neducation; and we have a certain other intellectual employment spoken\nof, namely, Dialectic, as the means of carrying the mind beyond these\nsciences, and of enabling it to see the sources of those truths which\nthe sciences assume as their first principles. These points have been\ndiscussed in the two preceding papers. But this scheme of the highest\nkind of philosophical education proceeds upon a certain view of the\nnature and degrees of knowledge, and of the powers by which we know;\nwhich view had been presented in a great measure in the Sixth Book;\nthis view I shall now attempt to illustrate.\n\nTo analyse the knowing powers of man is a task so difficult, that we\nneed not be surprised if there is much obscurity in this portion of\nPlato's writings. But as a reason for examining what he has said, we\nmust recollect that if there be in it anything on this subject which\nwas true then, it is true still; and also, that if we know any truth on\nthat subject now, we shall find something corresponding to that truth\nin the best speculations of sagacious ancient writers, like Plato.\nIt may therefore be worth while to discuss the Platonic doctrines on\nthis matter, and to inquire how they are to be expressed in modern\nphraseology.\n\nPlato's doctrine will perhaps be most clearly understood, if we begin\nby considering the _diagram_ by which he illustrates the different\ndegrees of knowledge[341]. He sets out from the distinction of\n_visible_ and _intelligible_ things. There are visible objects,\nsquares and triangles, for instance; but these are not the squares\nand triangles about which the Geometer reasons. The exactness of\nhis reasoning does not depend on the exactness of his diagrams. He\nreasons from certain mental squares and triangles, as he conceives and\nunderstands them. \"Thus there are visible and there are intelligible\nthings. There is a visible and an intelligible world[342]: and there\nare two different regions about which our knowledge is concerned.\nNow take a line divided into two unequal segments to represent these\ntwo regions: and again, divide each segment in the same ratio. The\nparts of each segment are to represent differences of clearness and\ndistinctness, and in the visible world these parts are _things_ and\n_images_. By _images_ I mean shadows, and reflections in water, and in\npolished bodies; and by _things_, I mean that of which these images\nare the resemblances; as animals, plants, things made by man. This\ndifference corresponds to the difference of _Knowledge_ and mere\n_Opinion_; and the _Opinable_ is to the _Knowable_ as the Image to the\nReality.\"\n\nThis analogy is assented to by Glaucon; and thus there is assumed a\nground for a further construction of the diagram.\n\n\"Now,\" he says, \"we have to divide the segment which represents\nIntelligible Things in the same way in which we have divided that which\nrepresents Visible Things. The one part must represent the knowledge\nwhich the mind gets by dealing as it were with images, and by reasoning\ndownwards _from_ Principles; the other that which it has by dealing\nwith the Ideas themselves, and going _to_ First Principles.\n\n\"The one part depends upon assumptions or hypotheses[343], the other is\nunhypothetical or absolute truth.\n\n\"One kind of Intelligible Things, then, is Conceptions; for instance,\ngeometrical conceptions of figures, by means of which we reason\ndownwards, assuming certain First Principles.\n\n\"Now the other kind of Intelligible Things is this:--that which the\nReason includes in virtue of its power of reasoning, when it regards\nthe assumptions of the Sciences as, what they are, assumptions only;\nand uses them as occasions and starting points, that from these it may\nascend to the _absolute_, (\u1f00\u03bd\u03c5\u03c0\u03cc\u03b8\u03b5\u03c4\u03bf\u03bd, unhypothetical,) which does\nnot depend upon assumption, but is the origin of scientific truth.\nThe Reason takes hold of this first principle of truth; and availing\nitself of all the connections and relations of this principle, it\nproceeds to the conclusion; using no sensible image in doing this, but\ncontemplating the Ideas alone; and with these Ideas the process begins,\ngoes on, and terminates.\"\n\nThis account of the matter will probably seem to require at least\nfurther explanation; and that accordingly is acknowledged in the\nDialogue itself. Glaucon says:\n\n\"I apprehend your meaning in a certain degree, but not very clearly,\nfor the matter is somewhat abstruse. You wish to prove that the\nknowledge which, by the Reason, we acquire, of Real Existence and\nIntelligible Things, is of a higher degree of certainty than the\nknowledge which belongs to what are commonly called Sciences. Such\nsciences, you say, have certain assumptions for their bases; and these\nassumptions are, by the students of such sciences, apprehended, not\nby Sense (that is, the Bodily Senses), but by a Mental Operation,--by\nConception. But inasmuch as such students ascend no higher than the\nassumptions, and do not go to the First Principles of Truth, they do\nnot seem to you to have true knowledge--intuitive insight--_Nous_--on\nthe subject of their reasonings, though the subjects are intelligible,\nalong with their principle. And you call this habit and practice of the\nGeometers and others by the name _Conception_, not _Intuition_[344];\ntaking Conception to be something between Opinion on the one side, and\nIntuitive Insight on the other.\"\n\n\"You have explained it well, said I. And now consider the four sections\n(of the line) of which we have spoken, as corresponding to four\naffections in the mind. Intuition, the highest; Conception, the next;\nthe third, Belief; and the fourth, Conjecture (from likenesses); and\narrange them in order, so that they may have more or less of certainty,\nas their objects have more or less of truth[345].\n\n\"I understand, said he. I agree to what you say, and I arrange them as\nyou direct.\"\n\nAnd so the Sixth Book ends: and the Seventh Book opens with the\ncelebrated image of the Cave, in which men are confined, and see all\nexternal objects only by the shadows which they cast on the walls of\ntheir prison. And this imperfect knowledge of things is to the true\nvision of them, which is attained by those who ascend to the light of\nday, as the ordinary knowledge of men is to the knowledge attainable by\nthose whose minds are purged and illuminated by a true philosophy.\n\nConfining ourselves at present to the part of Plato's speculations\nwhich we have mentioned, namely, the degrees of knowledge, and the\ndivision of our knowing faculties, we may understand, and may in a\ngreat degree accept, Plato's scheme. We have already (in the preceding\npapers) seen that, by the knowledge of real things, he means, in the\nfirst place, the knowledge of universal and necessary truths, such\nas Geometry and the other exact sciences deal with. These _we_ call\nsciences of Demonstration; and we are in the habit of contrasting the\nknowledge which constitutes such sciences with the knowledge obtained\nby the Senses, by Experience or mere Observation. This distinction of\nDemonstrative and Empirical knowledge is a cardinal point in Plato's\nscheme also; the former alone being allowed to deserve the name of\n_Knowledge_, and the latter being only _Opinion_. The Objects with\nwhich Demonstration deals may be termed _Conceptions_, and the objects\nwith which Observation or Sense has to do, however much speculation may\nreduce them to mere Sensations, are commonly described as _Things_. Of\nthese Things, there may be Shadows or Images, as Plato says; and as we\nmay obtain a certain kind of knowledge, namely Opinion or Belief, by\nseeing the Things themselves, we may obtain an inferior kind of Opinion\nor Belief by seeing their Images, which kind of opinion we may for the\nmoment call _Conjecture_. Whether then we regard the distinctions of\nknowledge itself or of the objects of it, we have three terms before us.\n\n  If we consider the kinds of knowledge, they are\n  Demonstration: Belief: Conjecture.\n  If the objects of this knowledge, they are\n  Conceptions: Things: Images.\n\nBut in each of these Series, the first term is evidently wanting: for\nDemonstration supposes Principles to reason from. Conceptions suppose\nsome basis in the mind which gives them their evidence. What then is\nthe first term in each of these two Series?\n\nThe Principles of Demonstration must be seen by _Intuition_.\n\nConceptions derive their properties from certain powers or attributes\nof the mind which we may term _Ideas_.\n\nTherefore the two series are\n\n  Intuition: Demonstration: Belief: Conjecture.\n  Ideas: Conceptions: Things: Images.\n\nPlato further teaches that the two former terms in each Series belong\nto the Intelligible, the two latter to the Visible World: and he\nsupposes that the ratio of these two primary segments of the line is\nthe same as the ratio in which each segment is divided[346].\n\nIn using the term _Ideas_ to describe the mental sources from which\nConceptions derive their validity in demonstration, I am employing a\nphraseology which I have already introduced in the _Philosophy of the\nInductive Sciences_. But independently altogether of this, I do not\nsee what other term could be employed to denote the mental objects,\nattributes, or powers, whatever they be, from which Conceptions derive\ntheir evidence, as Demonstrative Truths derive their evidence from\nIntuitive Truths.\n\nThat the Scheme just presented is Plato's doctrine on this subject,\nI do not conceive there can be any doubt. There is a little want of\nprecision in his phraseology, arising from his mixing together the two\nseries. In fact, his final series\n\n  _No\u00ebsis_: _Dianoia_: _Pistis_: _Eikasia_;\n\nis made by putting in the second place, instead of _Demonstration_,\nwhich is the _process_ pursued, or _Science_, which is the _knowledge_\nobtained, _Conception_, which is the _object_ with which the mind\ndeals. Such deviations from exact symmetry and correlation in speaking\nof the faculties of the mind, are almost unavoidable in every language.\nAnd there is yet another source of such inaccuracies of language; for\nwe have to speak, not only of the process of acquiring knowledge, and\nof the objects with which the mind deals, but of the Faculties of the\nmind which are thus employed. Thus _Intuition_ is the Process; _Ideas_\nare the Object, in the first term of our series. The Faculty also we\nmay call _Intuition_; but the Greek offers a distinction. _No\u00ebsis_ is\nthe _Process_ of Intuition; but the _Faculty_ is _Nous_. If we wish to\npreserve this distinction in English, what must we call the Faculty?\nI conceive we must call it _the Intuitive Reason_, a term well known\nto our older philosophical writers[347]. Again: taking the second\nterm of the series, _Demonstration_ is the process, _Science_, the\nresult; and _Conceptions_ are the objects with which the mind deals.\nBut what is the _Faculty_ thus employed? What is the Faculty employed\nin Demonstration? The same philosophical writers of whom I spoke would\nhave answered at once, _the Discursive Reason_; and I do not know\nthat, even now, we can suggest any better term. The Faculty employed\nin acquiring the two lower kinds of knowledge, the Faculty which deals\nwith Things and their Images is, of course, _Sense_, or _Sensation_.\n\nThe assertion of a Faculty of the mind by which it apprehends Truth,\nwhich Faculty is higher than the Discursive Reason, as the Truth\napprehended by it is higher than mere Demonstrative Truth, agrees (as\nit will at once occur to several of my readers) with the doctrine\ntaught and insisted upon by the late Samuel Taylor Coleridge. And so\nfar as he was the means of inculcating this doctrine, which, as we\nsee, is the doctrine of Plato, and I might add, of Aristotle, and of\nmany other philosophers, let him have due honour. But in his desire\nto impress the doctrine upon men's minds, he combined it with several\nother tenets, which will not bear examination. He held that the two\nFaculties by which these two kinds of truth are apprehended, and which,\nas I have said, our philosophical writers call _the Intuitive Reason_\nand _the Discursive Reason_, may be called, and ought to be called,\nrespectively, _The Reason_ and _The Understanding_; and that the second\nof these is of the nature of the _Instinct_ of animals, so as to be\nsomething intermediate between Reason and Instinct. These opinions,\nI may venture to say, are altogether erroneous. The Intuitive Reason\nand the Discursive Reason are not, by any English writers, called the\nReason and the Understanding; and accordingly, Coleridge has had to\nalter all the passages, namely, those taken from Leighton, Harrington,\nand Bacon, from which his exposition proceeds. The Understanding is so\nfar from being especially the Discursive or Reasoning Faculty, that\nit is, in universal usage, and by our best writers, _opposed_ to the\nDiscursive or Reasoning Faculty. Thus this is expressly declared by Sir\nJohn Davis in his poem _On the Immortality of the Soul_. He says, of\nthe soul,\n\n    When she _rates_ things, and moves from ground to ground,\n        The name of _Reason_ (_Ratio_) she acquires from this:\n    But when by reason she truth hath found,\n        And standeth fixt, she _Understanding_ is.\n\nInstead of the Reason being fixed, and the Understanding discursive,\nas Mr. Coleridge says, the Reason is distinctively discursive; that\nis, it obtains conclusions by running from one point to another. This\nis what is meant by _Discursus_; or, taking the full term, _Discursus\nRationis_, _Discourse of Reason_. Understanding is fixed, that is, it\ndwells upon one view of a subject, and not upon the steps by which that\nview is obtained. The verb _to reason_, implies the substantive, _the\nReason_, though it is not coextensive with it: for as I have said,\nthere is the Intuitive Reason as well as the Discursive Reason. But it\nis by the Faculty of Reason that we are capable of reasoning; though\nundoubtedly the practice or the pretence of reasoning may be carried so\nfar as to seem at variance with reason in the more familiar sense of\nthe term; as is the case also in French. Moliere's Crisale says (in the\n_Femmes Savantes_),\n\n  Raisonner est l'emploi de toute ma maison,\n  Et le raisonnement en bannit la Raison.\n\nIf Mr. Coleridge's assertion were true, that the Understanding is the\ndiscursive and the Reason the fixed faculty, we should be justified in\nsaying that _The Understanding is the faculty by which we reason, and\nthe Reason is the faculty by which we understand_. But this is not so.\n\nNor is the Understanding of the nature of Instinct, nor does it\napproach nearer than the Reason to the nature of Instinct, but the\ncontrary. The Instincts of animals bear a very obscure resemblance\nto any of man's speculative Faculties; but so far as there is any\nsuch resemblance, Instinct is an obscure image of Reason, not of\nUnderstanding. Animals are said to act as if they reasoned, rather than\nas if they understood. The verb _understand_ is especially applied to\nman as distinguished from animals. Mr. Coleridge tells a tale from\nHuber, of certain bees which, to prevent a piece of honey from falling,\nbalanced it by their weight, while they built a pillar to support it.\nThey did this by Instinct, not _understanding_ what they did; men,\ndoing the same, would have _understood_ what they were doing. Our\nTranslation of the Scriptures, in making it the special distinction of\nman and animals, that _he has Understanding_ and they have not, speaks\nquite consistently with good philosophy and good English.\n\nMr. Coleridge's object in his speculations is nearly the same as\nPlato's; namely, to declare that there is a truth of a higher kind than\ncan be obtained by mere reasoning; and also to claim, as portions of\nthis higher truth, certain fundamental doctrines of Morality. Among\nthese, Mr. Coleridge places the Authority of Conscience, and Plato, the\nSupreme Good. Mr. Coleridge also holds, as Plato held, that the Reason\nof man, in its highest and most comprehensive form, is a portion of a\nSupreme and Universal Reason; and leads to Truth, not in virtue of its\nspecial attributes in each person, but by its own nature.\n\nMany of the opinions which are combined with these doctrines, both\nin Plato and in Coleridge, are such as we should, I think, find it\nimpossible to accept, upon a careful philosophical examination of them;\nbut on these I shall not here dwell.\n\nI will only further observe, that if any one were to doubt whether the\nterm \u039d\u03bf\u1fe6\u03c2 is rightly rendered _Intuitive Reason_, we may find proof\nof the propriety of such a rendering in the remarkable discussion\nconcerning the Intellectual Virtues, which we have in the Sixth Book\nof the Nicomachean Ethics. It can hardly be questioned that Aristotle\nhad in his mind, in writing that passage, the doctrines of Plato, as\nexpounded in the passage just examined, and similar passages. Aristotle\nthere says that there are five Intellectual Virtues, or Faculties\nby which the Mind aims at Truth in asserting or denying:--namely,\n_Art_, _Science_, _Prudence_, _Wisdom_, _Nous_. In this enumeration,\npassing over Art, Prudence, and Wisdom, as virtues which are mainly\nconcerned from practical life, we have, in the region of speculative\nTruth, a distinction propounded between _Science_ and _Nous_: and this\ndistinction is further explained (c. 6) by the remarks that Science\nreasons with Principles; and that these Principles cannot be given\n_by_ Science, because Science reasons _from_ them; nor by Art, nor\nPrudence, for these are conversant with matters contingent, not with\nmatters demonstrable; nor can the First Principles of the Reasonings\nof Science be given by Wisdom, for Wisdom herself has often to reason\nfrom Principles. Therefore the First Principles of Demonstrative\nReasoning must be given by a peculiar Faculty, _Nous_. As we have\nsaid, _Intuitive Reason_ is the most appropriate English term for this\nFaculty.\n\nThe view thus given of that higher kind of Knowledge which Plato and\nAristotle place above ordinary Science, as being the Knowledge of and\nFaculty of learning First Principles, will enable us to explain some\nexpressions which might otherwise be misunderstood. Socrates, in the\nconcluding part of this Sixth Book of the _Republic_, says, that this\nkind of knowledge is \"that of which the Reason (\u03bb\u03cc\u03b3\u03bf\u03c2) takes hold,\n_in virtue of its power of reasoning_[348].\" Here we are plainly not\nto understand that we arrive at First Principles _by reasoning_: for\nthe very opposite is true, and is here taught;--namely, that First\nPrinciples are not what we reason _to_, but what we reason _from_.\nThe meaning of this passage plainly is, that First Principles are\nthose of which the Reason takes hold _in virtue of its power of\nreasoning_;--they are the conditions which must exist in order to make\nany reasoning possible:--they are the propositions which the Reason\nmust involve implicitly, in order that we may reason explicitly;--they\nare the intuitive roots of the dialectical power.\n\nIn accordance with the views now explained, Plato's Diagram may be\nthus further expanded. The term \u03b9\u03b4\u03ad\u03b1 is not used in this part of the\n_Republic_; but, as is well known, occurs in its peculiar Platonic\nsense in the Tenth Book.\n\n +---------+------------------------------------+-----------------------+\n |         |    Intelligible World. \u03bd\u03bf\u03ae\u03c4\u03bf\u03bd.     | Visible World. \u1f41\u03c1\u03b1\u03c4\u03bf\u03bd.|\n +---------+-----------------+------------------+-----------------------+\n |_Object_ |     Ideas       |    Conceptions   |  Things   |   Images  |\n |         |     \u1f30\u03b4\u03ad\u03b1\u03b9       |      \u03b4\u03b9\u03ac\u03bd\u03bf\u03b9\u03b1     | \u03b6\u1ff6\u03b1 \u03ba.\u03c4.\u03bb.|   \u03b5\u1f30\u03ba\u1f30\u03bd\u03b5\u03c2 |\n +---------+-----------------+------------------+-----------------------+\n |_Process_|   Intuition     |   Demonstration  |  Belief   | Conjecture|\n |         |    \u03bd\u1f30\u03b7\u03c3\u03b9\u03c2       |     \u1f10\u03c0\u03b9\u03c3\u03c4\u03ae\u03bc\u03b7     |  \u03c0\u03af\u03c3\u03c4\u03b9\u03c2   |  \u03b5\u03af\u03ba\u03b1\u03c3\u03af\u03b1  |\n +---------+-----------------+------------------+-----------------------+\n |_Faculty_|Intuitive Reason | Discursive Reason|        Sensation      |\n |         |      \u03bd\u03bf\u1fe6\u03c2       |       \u03bb\u03cc\u03b3\u03bf\u03c2      |        \u03b1\u1f34\u03c3\u03b8\u03b7\u03c3\u03b9\u03c2       |\n +---------+-----------------+------------------+-----------------------+\n\n\nFOOTNOTES:\n\n[Footnote 341: _Pol_. vi. \u00a7 19.]\n\n[Footnote 342: He adds, \"This _oraton_, this visible world, I will not\nsay has any connexion with _ouranon_, heaven, that I may not be accused\nof playing upon words.\"]\n\n[Footnote 343: It is plain that Plato, by _Hypotheses_, in this place,\nmeans the usual foundations of Arithmetic and Geometry; namely,\nDefinitions and Postulates. He says that \"the arithmeticians and\ngeometers take as hypotheses (h\u03c5\u03c0\u03bf\u03b8\u03b5\u03bc\u03b5\u03bd\u03bf\u03b9) odd and even, and the\nthree kinds of angles (right, acute, and obtuse); and figures, (as\na triangle, a square,) and the like.\" I say his \"hypotheses\" are\nthe Definitions and Postulates, not the Axioms: for the Axioms of\nArithmetic and Geometry belong to the Higher Faculty, which ascends\nto First Principles. But this Faculty operates rather in using these\naxioms than in enunciating them. It knows them implicitly rather than\nexpresses them explicitly.]\n\n[Footnote 344: \u03b4\u03b9\u03ac\u03bd\u03bf\u03b9\u03b1\u03bd \u03ac\u03bb\u03bb' \u03bf\u1f50 \u03bd\u03bf\u1fe6\u03bd.]\n\n[Footnote 345: The Diagram, as here described, would be this:\n\n  +---------------------------+---------------------------+\n  |   _Intelligible World._   |      _Visible World._     |\n  |-------------+-------------+-------------+-------------+\n  | Intuition.  | Conception. |   Things.   |   Images.   |\n  +-------------+-------------+-------------+-------------+\n\nPlato supposes the whole, and each of the two parts, to be divided in\nthe same ratio, in order that the _analogy_ of the division in each\ncase may be represented.]\n\n[Footnote 346: The four segments might be as 4: 2: 2: 1; or as 9: 6: 6:\n4; or generally, as _a_: _ar_: _ar_: _ar_^2.]\n\n[Footnote 347:\n\n           Hence the mind Reason receives\n  Intuitive or Discursive.\n\n  MILTON.]\n\n[Footnote 348: \u03c4\u1fc7 \u03c4\u03bf\u1fe6 \u03b4\u03b9\u03b1\u03bb\u03ad\u03b3\u03b5\u03c3\u03b8\u03b1\u03b9 \u03b4\u03c5\u03bd\u03cc\u03bc\u03b5\u03b9.]\n\n\nAPPENDIX D.\n\nCRITICISM OF ARISTOTLE'S ACCOUNT OF INDUCTION.\n\n(_Cam. Phil. Soc._ FEB. 11, 1850.)\n\n\nThe Cambridge Philosophical Society has willingly admitted among\nits proceedings not only contributions to science, but also to the\nphilosophy of science; and it is to be presumed that this willingness\nwill not be less if the speculations concerning the philosophy of\nscience which are offered to the Society involve a reference to ancient\nauthors. Induction, the process by which general truths are collected\nfrom particular examples, is one main point in such philosophy: and the\ncomparison of the views of Induction entertained by ancient and modern\nwriters has already attracted much notice. I do not intend now to go\ninto this subject at any length; but there is a cardinal passage on the\nsubject in Aristotle's _Analytics_, (_Analyt. Prior._ II. 25) which I\nwish to explain and discuss. I will first translate it, making such\nemendations as are requisite to render it intelligible and consistent,\nof which I shall afterwards give an account.\n\nI will number the sentences of this chapter of Aristotle in order that\nI may afterwards be able to refer to them readily.\n\n\u00a7 1. \"We must now proceed to observe that we have to examine not only\nsyllogisms according to the aforesaid _figures_,--syllogisms logical\nand demonstrative,--but also rhetorical syllogisms,--and, speaking\ngenerally, any kind of proof by which belief is influenced, following\nany method.\n\n\u00a7 2. \"All belief arises either from Syllogism or from Induction: [we\nmust now therefore treat of Induction.]\n\n\u00a7 3. \"Induction, and the Inductive Syllogism, is when by means of one\nextreme term we infer the other extreme term to be true of the middle\nterm.\n\n\u00a7 4. \"Thus if _A_, _C_, be the extremes, and _B_ the mean, we have to\nshow, by means of _C_, that _A_ is true of _B_.\n\n\u00a7 5. \"Thus let _A_ be _long-lived_; _B_, _that which has no\ngall-bladder;_ and _C_, particular long-lived animals, as _elephant_,\n_horse_, _mule_.\n\n\u00a7 6. \"Then every _C_ is _A_, for all the animals above named are\nlong-lived.\n\n\u00a7 7. \"Also every _C_ is _B_, for all those animals are destitute of\ngall-bladder.\n\n\u00a7 8. \"If then _B_ and _C_ are convertible, and the mean (_B_) does not\nextend further than extreme (_C_), it necessarily follows that every\n_B_ is _A_.\n\n\u00a7 9. \"For it was shown before, that, if any two things be true of the\nsame, and if either of them be convertible with the extreme, the other\nof the things predicated is true of the convertible (extreme).\n\n\u00a7 10. \"But we must conceive that _C_ consists of a collection of all\nthe particular cases; for Induction is applied to all the cases.\n\n\u00a7 11. \"But such a syllogism is an inference of a first truth and\nimmediate proposition.\n\n\u00a7 12. \"For when there is a mean term, there is a demonstrative\nsyllogism through the mean; but when there is not a mean, there is\nproof by Induction.\n\n\u00a7 13. \"And in a certain way, Induction is contrary to Syllogism; for\nSyllogism proves, by the middle term, that the extreme is true of the\nthird thing: but Induction proves, by means of the third thing, that\nthe extreme is true of the mean.\n\n\u00a7 14. \"And Syllogism concluding by means of a middle term is prior\nby nature and more usual to us; but the proof by Induction, is more\nluminous.\"\n\nI think that the chapter, thus interpreted, is quite coherent and\nintelligible; although at first there seems to be some confusion, from\nthe author sometimes saying that Induction is a kind of Syllogism, and\nat other times that it is not. The amount of the doctrine is this.\n\nWhen we collect a general proposition by Induction from particular\ncases, as for instance, that all animals destitute of gall-bladder\n(_acholous_), are long-lived, (if this proposition were true, of which\nhereafter,) we may express the process in the form of a Syllogism, if\nwe will agree to make a collection of particular cases our middle term,\nand assume that the proposition in which the second extreme term occurs\nis convertible. Thus the known propositions are\n\n  Elephant, horse, mule, &c., are long-lived.\n  Elephant, horse, mule, &c., are _acholous_.\n\nBut if we suppose that the latter proposition is convertible, we shall\nhave these propositions:\n\n  Elephant, horse, mule, &c., are long-lived.\n  All acholous animals are elephant, horse, mule, &c.,\n\nfrom whence we infer, quite rigorously as to _form_,\n\n  All acholous animals are long-lived.\n\nThis mode of putting the Inductive inference shows both the strong and\nthe weak point of the illustration of Induction by means of Syllogism.\nThe strong point is this, that we make the inference perfect as to\nform, by including an indefinite collection of particular cases,\nelephant, horse, mule, &c., in a single term, _C_. The Syllogism then is\n\n  All _C_ are long-lived.\n  All acholous animals are _C_.\n  Therefore all acholous animals are long-lived.\n\nThe weak point of this illustration is, that, at least in some\ninstances, when the number of actual cases is necessarily indefinite,\nthe representation of them as a single thing involves an unauthorized\nstep. In order to give the reasoning which really passes in the mind,\nwe must say\n\n  Elephant, horse, &c., are long-lived.\n  All acholous animals are _as_ elephant, horse, &c.,\n  Therefore all acholous animals are long-lived.\n\nThis \"_as_\" must be introduced in order that the \"all _C_\" of the first\nproposition may be justified by the \"_C_\" of the second.\n\nThis step is, I say, necessarily unauthorized, where the number of\nparticular cases is indefinite; as in the instance before us, the\nspecies of acholous animals. We do not know how many such species\nthere are, yet we wish to be able to assert that _all_ acholous\nanimals are long-lived. In the proof of such a proposition, put in a\nsyllogistic form, there must necessarily be a logical defect; and the\nabove discussion shows that this defect is the substitution of the\nproposition, \"All acholous animals are _as_ elephant, &c.,\" for the\nconverse of the experimentally proved proposition, \"elephant, &c., are\nacholous.\"\n\nIn instances in which the number of particular cases is limited, the\nnecessary existence of a logical flaw in the syllogistic translation\nof the process is not so evident. But in truth, such a flaw exists in\nall cases of Induction _proper_: (for Induction by _mere enumeration_\ncan hardly be called _Induction_). I will, however, consider for a\nmoment the instance of a celebrated proposition which has often been\ntaken as an example of Induction, and in which the number of particular\ncases is, or at least is at present supposed to be, limited. Kepler's\nlaws, for instance the law that the planets describe ellipses, may\nbe regarded as examples of Induction. The law was inferred, we will\nsuppose, from an examination of the orbits of Mars, Earth, Venus. And\nthe syllogistic illustration which Aristotle gives, will, with the\nnecessary addition to it, stand thus,\n\n  Mars, Earth, Venus describe ellipses.\n  Mars, Earth, Venus are planets.\n\nAssuming the convertibility of this last proposition, _and its\nuniversality_, (which is the necessary addition in order to make\nAristotle's syllogism valid) we say\n\n  All the planets are as Mars, Earth, Venus.\n\nWhence it follows that all the planets describe ellipses.\n\nIf, instead of this assumed universality, the astronomer had made a\nreal enumeration, and had established the fact of each particular, he\nwould be able to say\n\n Saturn, Jupiter, Mars, Earth, Venus, Mercury, describe ellipses.\n\n Saturn, Jupiter, Mars, Earth, Venus, Mercury are all the planets.\n\nAnd he would obviously be entitled to convert the second proposition,\nand then to conclude that\n\n  All the planets describe ellipses.\n\nBut then, if this were given as an illustration of Induction by means\nof syllogism, we should have to remark, in the first place, that the\nconclusion that \"all the planets describe ellipses,\" adds nothing to\nthe major proposition, that \"S., J., M., E., V., m., do so.\" It is\nmerely the same proposition expressed in other words, so long as S.,\nJ., M., E., V., m., are supposed to be all the planets. And in the\nnext place we have to make a remark which is more important; that the\nminor, in such an example, must generally be either a very precarious\ntruth, or, as appears in this case, a transitory error. For that the\nplanets known at any time are _all_ the planets, must always be a\ndoubtful assertion, liable to be overthrown to-night by an astronomical\nobservation. And the assertion, as received in Kepler's time, has been\noverthrown. For Saturn, Jupiter, Mars, Earth, Venus, Mercury, are\nnot all the planets. Not only have several new ones been discovered\nat intervals, as Uranus, Ceres, Juno, Pallas, Vesta, but we have new\nones discovered every day; and any conclusion depending upon this\npremiss that _A_, _B_, _C_, _D_, _E_, _F_, _G_, _H_, to _Z_ are all the\nplanets, is likely to be falsified in a few years by the discovery of\n_A\u00b4_, _B\u00b4_, _C\u00b4_, &c. If, therefore, this were the syllogistic analysis\nof Induction, Kepler's discovery rested upon a false proposition;\nand even if the analysis were now made conformable to our present\nknowledge, that induction, analysed as above, would still involve a\nproposition which to-morrow may show to be false. But yet no one, I\nsuppose, doubts that Kepler's discovery was really a discovery--the\nestablishment of a scientific truth on solid grounds; or, that it is\na scientific truth for us, notwithstanding that we are constantly\ndiscovering new planets. Therefore the syllogistic analysis of it now\ndiscussed (namely, that which introduces simple enumeration as a step)\nis not the right analysis, and does not represent the grounds of the\nInductive Truth, that all the planets describe ellipses.\n\nIt may be said that all the planets discovered since Kepler's time\nconform to his law, and thus confirm his discovery. This we grant:\nbut they only _confirm_ the discovery, they do not make it; they are\nnot its groundwork. It was a discovery before these new cases were\nknown; it was an inductive truth without them. Still, an objector might\nurge, if any one of these new planets had contradicted the law, it\nwould have overturned the discovery. But this is too boldly said. A\ndiscovery which is so precise, so complex (in the phenomena which it\nexplains), so supported by innumerable observations extending through\nspace and time, is not so easily overturned. If we find that Uranus,\nor that Encke's comet, deviates from Kepler's and Newton's laws, we\ndo not infer that these laws must be false; we say that there must\nbe some disturbing cause in these cases. We seek, and we find these\ndisturbing causes: in the case of Uranus, a new planet; in the case\nof Encke's comet, a resisting medium. Even in this case therefore,\nthough the number of particulars is limited, the Induction was not\nmade by a simple enumeration of all the particulars. It was made from\na few cases, and when the law was discerned to be true in these, it\nwas extended to all; the conversion and assumed universality of the\nproposition that \"these are planets,\" giving us the proposition which\nwe need for the syllogistic exhibition of Induction, \"all the planets\nare as these.\"\n\nI venture to say further, that it is plain, that Aristotle did not\nregard Induction as the result of simple enumeration. This is plain,\nin the first place, from his example. Any proposition with regard to\na special class of animals, cannot be proved by simple enumeration:\nfor the number of particular cases, that is, of animal species in\nthe class, is indefinite at any period of zoological discovery, and\nmust be regarded as infinite. In the next place, Aristotle says (\u00a7\n10 of the above extract), \"We must conceive that _C_ consists of a\ncollection of all the particular cases; for induction is applied to\nall the cases.\" We must _conceive_ (\u03bd\u03bf\u03b5\u1fd6\u03bd) that _C_ in the major,\nconsists of all the cases, in order that the conclusion may be true\nof all the cases; but we cannot _observe_ all the cases. But the\nevident proof that Aristotle does not contemplate in this chapter an\nInduction by simple enumeration, is the contrast in which he places\nInduction and Syllogism. For Induction by simple enumeration stands\nin no contrast to Syllogism. The Syllogism of such Induction is quite\nlogical and conclusive. But Induction from a comparatively small\nnumber of particular cases to a general law, does stand in opposition\nto Syllogism. It gives us a truth,--a truth which, as Aristotle\nsays (\u00a7 14), is more luminous than a truth proved syllogistically,\nthough Syllogism may be _more natural and usual_. It gives us (\u00a7 11)\nimmediate propositions, obtained directly from observation, and not\nby a chain of reasoning: \"first truths,\" the principles from which\nsyllogistic reasonings may be deduced. The Syllogism proves by means of\na middle term (\u00a7 13) that the extreme is true of a third thing: thus,\n(_acholous_ being the middle term):\n\n  Acholous animals are long-lived:\n  All elephants are acholous animals:\n  Therefore all elephants are long-lived.\n\nBut Induction proves by means of a third thing (namely, particular\ncases) that the extreme is true of the mean; thus (_acholous_, still\nbeing the middle term)\n\n  Elephants are long-lived:\n  Elephants are acholous animals:\n  Therefore acholous animals are long-lived.\n\nIt may be objected, such reasoning as this is quite inconclusive:\nand the answer is, that this is precisely what we, and as I believe,\nAristotle, are here pointing out. Induction _is_ inconclusive _as\nreasoning_. It is not reasoning: it is another way of getting at\ntruth. As we have seen, no reasoning can prove such an inductive\ntruth as this, that all planets describe ellipses. It is _known_ from\nobservation, but it is not _demonstrated_. Nevertheless, no one doubts\nits universal truth, (except, as aforesaid, when disturbing causes\nintervene). And thence, Induction is, as Aristotle says, opposed to\nsyllogistic reasoning, and yet is a means of discovering truth: not\nonly so, but a means of discovering primary truths, immediately derived\nfrom observation.\n\nI have elsewhere taught that all Induction involves a _Conception_ of\nthe mind applied to facts. It may be asked whether this applies in\nsuch a case as that given by Aristotle. And I reply, that Aristotle's\ninstance is a very instructive example of what I mean. The Conception\nwhich is applied to the facts in order to make the induction possible\nis the want of the gall-bladder;--and Aristotle supplies us with a\nspecial term for this conception; _acholous_[349]. But, it may be\nsaid, that the animals observed, the elephant, horse, mule, &c., are\nacholous, is a mere fact of observation, not a Conception. I reply\nthat it is a _Selected_ Fact, a fact selected and compared in several\ncases, which is what we mean by a _Conception_. That there is needed\nfor such selection and comparison a certain activity of the mind, is\nevident; but this also may become more clear by dwelling a little\nfurther on the subject. Suppose that Aristotle, having a desire to know\nwhat class of animals are long-lived, had dissected for that purpose\nmany animals; elephants, horses, cows, sheep, goats, deer and the like.\nHow many resemblances, how many differences, must he have observed\nin their anatomy! He was very likely long in fixing upon any one\nresemblance which was common to all the long-lived. Probably he tried\nseveral other characters, before he tried the presence and absence\nof the gall-bladder:--perhaps, trying such characters, he found them\nsucceed for a few cases, and then fail in others, so that he had to\nreject them as useless for his purpose. All the while, the absence of\nthe gall-bladder in the long-lived animals was a fact: but it was of\nno use to him, because he had not selected it and drawn it forth from\nthe mass of other facts. He was looking for a mean term to connect his\nfirst extreme, _long-lived_, with his second, the special cases. He\nsought this middle term in the entrails of the many animals which he\nused as extremes: it _was_ there, but he could not find it. The fact\nexisted, but it was of no use for the purpose of Induction, because\nit did not become a special Conception in his mind. He considered the\nanimals in various points of view, it may be, as ruminant, as horned,\nas hoofed, and the contrary; but not as _acholous_ and the contrary.\nWhen he looked at animals in that point of view,--when he took up that\ncharacter as the ground of distinction, he forthwith imagined that he\nfound a separation of long-lived and short-lived animals. When that\nFact became a Conception, he obtained an inductive truth, or, at any\nrate, an inductive proposition.\n\nHe obtained an inductive proposition by applying the Conception\n_acholous_ to his observation of animals. This Conception divided\nthem into two classes; and these classes were, he fancied, long-lived\nand short-lived respectively. That it was the Conception, and not\nthe Fact which enabled him to obtain his inductive proposition, is\nfurther plain from this, that the supposed Fact is not a fact. Acholous\nanimals are not longer-lived than others. The presence or absence of\nthe gall-bladder is no character of longevity. It is true, that in one\nfamiliar class of animals, the herbivorous kind, there is a sort of\nfirst seeming of the truth of Aristotle's asserted rule: for the horse\nand mule which have not the gall-bladder are longer-lived than the\ncow, sheep, and goat, which have it. But if we pursue the investigation\nfurther, the rule soon fails. The deer-tribe that want the gall-bladder\nare not longer-lived than the other ruminating animals which have it.\nAnd as a conspicuous evidence of the falsity of the rule, man and the\nelephant are perhaps, for their size, the longest-lived animals, and\nof these, man has, and the elephant has not, the organ in question.\nThe inductive proposition, then, is false; but what we have mainly\nto consider is, where the fallacy enters, according to Aristotle's\nanalysis of Induction into Syllogism. For the two premisses are still\ntrue; that elephants, &c., are long-lived; and that elephants, &c.,\nare acholous. And it is plain that the fallacy comes in with that\nconversion and generalization of the latter proposition, which we have\nnoted as necessary to Aristotle's illustration of Induction. When we\nsay \"All acholous animals are as elephants, &c.,\" that is, as those\nin their biological conditions, we say what is not true. Aristotle's\ncondition (\u00a7 8) is not complied with, that the middle term shall not\nextend beyond the extreme. For the character _acholous_ does extend\nbeyond the elephant and the animals biologically resembling it; it\nextends to deer, &c., which are not like elephants and horses, in the\npoint in question. And thus, we see that the assumed conversion and\ngeneralization of the minor proposition, is the seat of the fallacy of\nfalse Inductions, as it is the seat of the peculiar logical character\nof true Inductions.\n\nAs true Inductive Propositions cannot be logically demonstrated by\nsyllogistic rules, so they cannot be discovered by any rule. There\nis no formula for the discovery of inductive truth. It is caught by\na peculiar sagacity, or power of divination, for which no precepts\ncan be given. But from what has been said, we see that this sagacity\nshows itself in the discovery of propositions which are both _true_,\nand _convertible_ in the sense above explained. Both these steps may\nbe difficult. The former is often very laborious: and when the labour\nhas been expended, and a true proposition obtained, it may turn out\nuseless, because the proposition is not convertible. It was a matter\nof great labour to Kepler to prove (from calculation of observations)\nthat Mars moves elliptically. Before he proved this, he had tried\nto prove many similar propositions:--that Mars moved according to\nthe \"bisection of the eccentricity,\"--according to the \"vicarious\nhypothesis,\"--according to the \"physical hypothesis,\"--and the like;\nbut none of these was found to be exactly true. The proposition that\nMars moves elliptically was proved to be true. But still, there was\nthe question, Is it convertible? Do all the planets move as Mars\nmoves? This was proved, (suppose,) to be true, for the Earth and\nVenus. But still the question remains, Do all the planets move as\nMars, Earth, Venus, do? The inductive generalizing impulse boldly\nanswers, Yes, to this question; though the rules of Syllogism do not\nauthorize the answer, and though there remain untried cases. The\ninductive Philosopher tries the cases as fast as they occur, in order\nto confirm his previous conviction; but if he had to wait for belief\nand conviction till he had tried every case, he never could have belief\nor conviction of such a proposition at all. He is prepared to modify or\nadd to his inductive truth according as new cases and new observations\ninstruct him; but he does not fear that new cases or new observations\nwill overturn an inductive proposition established by exact comparison\nof many complex and various phenomena.\n\nAristotle's example offers somewhat similar reflections. He had to\nestablish a proposition concerning long-lived animals, which should\nbe true, and should be susceptible of generalized conversion. To\nprove that the elephant, horse and mule are destitute of gall-bladder\nrequired, at least, the labour of anatomizing those animals in the\nseat of that organ. But this labour was not enough; for he would find\nthose animals to agree in many other things besides in being acholous.\nHe must have selected that character somewhat at a venture. And the\nguess was wrong, as a little more labour would have shown him; if\nfor instance he had dissected deer: for they are acholous, and yet\nshort-lived. A trial of this kind would have shown him that the extreme\nterm, _acholous_, did extend beyond the mean, namely, animals such\nas elephant, horse, mule; and therefore, that the conversion was not\nallowable, and that the Induction was untenable. In truth, there is no\nrelation between bile and longevity[350], and this example given by\nAristotle of generalization from induction is an unfortunate one.\n\n       *       *       *       *       *\n\nIn discussing this passage of Aristotle, I have made two alterations in\nthe text, one of which is necessary on account of the fact; the other\non account of the sense. In the received text, the particular examples\nof long-lived animals given are _man_, horse, and mule (\u1f10\u03c6' \u1fa7 \u03b4\u1f72 \u0393, \u03c4\u1f78\n\u03ba\u03b1\u03b8\u03ad\u03ba\u03b1\u03c3\u03c4\u03bf\u03bd \u03bc\u03b1\u03ba\u03c1\u03cc\u03b2\u03b9\u03bf\u03bd, \u03bf\u1f37\u03bf\u03bd \u1f04\u03bd\u03b8\u03c1\u03c9\u03c0\u03bf\u03c2, \u03ba\u03b1\u1f76 \u1f35\u03c0\u03c0\u03bf\u03c2, \u03ba\u03b1\u1f76 \u1f21\u03bc\u03af\u03bf\u03bd\u03bf\u03c2). And it is\nafterwards said that all these are _acholous_: (\u1f00\u03bb\u03bb\u1f70 \u03ba\u03b1\u1f76 \u03c4\u1f78 \u0392, \u03c4\u1f78 \u03bc\u1f74\n\u1f14\u03c7\u03bf\u03bd \u03c7\u03bf\u03bb\u1f74\u03bd, \u03c0\u03b1\u03bd\u03c4\u1f76 \u1f51\u03c0\u03ac\u03c1\u03c7\u03b5\u03b9 \u03c4\u1ff7 \u0393). But man _has_ a gall-bladder: and the\nfact was well known in Aristotle's time, for instance, to Hippocrates;\nso that it is not likely that Aristotle would have made the mistake\nwhich the text contains. But at any rate, it is a mistake; if not of\nthe transcriber, of Aristotle; and it is impossible to reason about the\npassage, without correcting the mistake. The substitution of \u1f14\u03bb\u03b5\u03c6\u03b1\u03c2\nfor \u1f04\u03bd\u03b8\u03c1\u03c9\u03c0\u03bf\u03c2 makes the reasoning coherent; but of course, any other\nacholous long-lived animal would do so equally well.\n\nThe other emendation which I have made is in \u00a7 6. In the received text\n\u00a7 6 and 7 stand thus:\n\n 6. Then every _C_ is _A_, for _every acholous animal is long-lived_\n\n (\u03c4\u1ff7 \u03b4\u1f74 \u0393 \u1f45\u03bb\u03c9 \u1f51\u03c0\u03ac\u03c1\u03c7\u03b5\u03b9 \u03c4\u1f78 \u0391, \u03c0\u1fb6\u03bd \u03b3\u1f70\u03c1 \u03c4\u1f78 \u1f04\u03c7\u03bf\u03bb\u03bf\u03bd \u03bc\u03b1\u03ba\u03c1\u03cc\u03b2\u03b9\u03bf\u03bd).\n\n 7. Also every _C_ is _B_, for all _C_ is destitute of bile.\n\nWhence it may be inferred, says Aristotle, under certain conditions,\nthat every _B_ is _A_ (\u03c4\u1f78 \u0391 \u03c4\u1ff7 \u0392 \u1f51\u03c0\u03ac\u03c1\u03c7\u03b5\u03b9\u03bd) that is, that _every\nacholous animal is long-lived_. But this conclusion is, according\nto the common reading, identical with the major premiss; so that\nthe passage is manifestly corrupt. I correct it by substituting for\n\u1f04\u03c7\u03bf\u03bb\u03bf\u03bd, \u0393; and thus reading \u03c0\u1fb6\u03bd \u03b3\u1f70\u03c1 \u03c4\u1f78 \u0393 \u03bc\u03b1\u03ba\u03c1\u03cc\u03b2\u03b9\u03bf\u03bd \"for every _C_ is\nlong-lived:\" just as in the parallel sentence, 7, we have \u1f00\u03bb\u03bb\u1f70 \u03ba\u03b1\u1f76 \u03c4\u1f78\n\u0392, \u03c4\u1f78 \u03bc\u1f74 \u1f14\u03c7\u03bf\u03bd \u03c7\u03bf\u03bb\u03b7\u03bd, \u03c0\u03b1\u03bd\u03c4\u1f76 \u1f51\u03c0\u03ac\u03c1\u03c7\u03b5\u03b9 \u03c4\u1ff7 \u0393. In this way the reasoning\nbecomes quite clear. The corrupt substitution of \u1f04\u03c7\u03bf\u03bb\u03bf\u03bd for \u0393 may have\nbeen made in various ways; which I need not suggest. As my business is\nwith the sense of the passage, and as it makes no sense without the\nchange, and very good sense with it, I cannot hesitate to make the\nemendation. And these emendations being made, Aristotle's view of the\nnature and force of Induction becomes, I think, perfectly clear and\nvery instructive.\n\n       *       *       *       *       *\n\nADDITIONAL NOTE.\n\nI take the liberty of adding to this Memoir the following remarks, for\nwhich I am indebted to Mr. Edleston, Fellow of Trinity College.\n\nSeveral of the earlier editions of Aristotle have \u03b3 instead of \u1f04\u03c7\u03bf\u03bb\u03bf\u03bd\nin the passage referred to in the above paper: ex. gr.\n\n(1) The edition printed at Basle, 1539 (after Erasmus): \"\u03c4\u1f78 \u03b3.\"\n\n(2) Basil (Erasmus) 1550. \"\u03c4\u1f78 \u03b3.\"\n\n(3) Burana's Latin version, Venet. 1552, has \"omne enim _C_ long\u00e6vum.\"\n\n(4) Sylburg, Francf. 1587 \"\u03c4\u1f78 \u03b3\" is printed in brackets thus: \"[\u03c4\u1f78 \u03b3]\n\u03c4\u1f78 \u1f04\u03c7\u03bf\u03bb\u03bf\u03bd.\"\n\n(5) So also in Casaubon's edition, 1590.\n\n(6) Casaub. 1605 \"\u03c4\u1f78 \u03b3,\" (though the Latin version has \"vacans bile;\")\nnot \"[\u03c4\u1f78 \u03b3] \u03c4\u1f78 \u1f04\u03c7\u03bf\u03bb\u03bf\u03bd,\" as the edition of 1590.\n\n(7) In the edition printed Aurel. Allobr. 1607, \"[\u03c4\u1f78 \u03b3] \u03c4\u1f78 \u1f04\u03c7\u03bf\u03bb\u03bf\u03bd,\" as\nin (4) and (5).\n\n(8) Du Val's editions, Paris, 1619, 1629, 1654 \"\u03c4\u1f78 \u03b3,\" though in\nPacius's translation in the adjacent column we find \"vacans bile.\"\n\n(9) In the critical notes to Waitz's edition of the _Organon_ (Lips.\n1844) it is stated that \"post \u1f04\u03c7\u03bf\u03bb\u03bf\u03bd del. \u03b3. _n_,\" implying apparently,\nthat in the MS. marked _n_, the letter \u03b3, which had been originally\nwritten after \u1f04\u03c7\u03bf\u03bb\u03bf\u03bd, had been erased.\n\n       *       *       *       *       *\n\nThe following passages throw light upon the question whether \u1f04\u03bd\u03b8\u03c1\u03c9\u03c0\u03bf\u03c2\nought or ought not to be retained in the passage discussed in the\nMemoir.\n\n(A) Aristot. _De Animalibus Histor._ II. 15, 9 (Bekk.), \u03c4\u1ff6\u03bd \u03bc\u1f72\u03bd\n\u03b6\u03c9\u03bf\u03c4\u03cc\u03ba\u03c9\u03bd \u03ba\u03b1\u1f76 \u03c4\u03b5\u03c4\u03c1\u03b1\u03c0\u03cc\u03b4\u03c9\u03bd \u1f14\u03bb\u03b1\u03c6\u03bf\u03c2 \u03bf\u1f50\u03ba \u1f14\u03c7\u03b5\u03b9 [\u03c7\u03bf\u03bb\u03ae\u03bd] \u03bf\u1f50\u03b4\u1f72 \u03c0\u03c1\u03cc\u03be, \u1f15\u03c4\u03b9 \u03b4\u1f72\n\u1f35\u03c0\u03c0\u03bf\u03c2, \u1f40\u03c1\u03b5\u03cd\u03c2, \u1f44\u03bd\u03bf\u03c2, \u03c6\u03ce\u03ba\u03b7 \u03ba\u03b1\u1f76 \u03c4\u1ff6\u03bd \u1f51\u1ff6\u03bd \u1f14\u03bd\u03b9\u03bf\u03b9.... \u1f1c\u03c7\u03b5\u03b9 \u03b4\u1f72 \u03ba\u03b1\u1f76 \u1f41 \u1f10\u03bb\u03ad\u03c6\u03b1\u03c2 \u03c4\u1f78\n\u1fc6\u03c0\u03b1\u03c1 \u1f04\u03c7\u03bf\u03bb\u03bf\u03bd \u03bc\u03ad\u03bd, \u03ba.\u03c4.\u03bb.\n\n(B) Conf. Ib. I. 17, 10, 11. (In the beginning of Chap. 16, he says\nthat the external \u03bc\u03bf\u03c1\u03b9\u03b1 of man are \u03b3\u03bd\u03ce\u03c1\u03b9\u03bc\u03b1, \"\u03c4\u1f70 \u03b4' \u1f10\u03bd\u03c4\u1f78\u03c2 \u03c4\u03bf\u1f50\u03bd\u03b1\u03bd\u03c4\u03af\u03bf\u03bd.\n\u1f0c\u03b3\u03bd\u03c9\u03c3\u03c4\u03b1 \u03b3\u03ac\u03c1 \u1f10\u03c3\u03c4\u03b9 \u03bc\u03ac\u03bb\u03b9\u03c3\u03c4\u03b1 \u03c4\u1f70 \u03c4\u1ff6\u03bd \u1f00\u03bd\u03b8\u03c1\u03ce\u03c0\u03c9\u03bd, \u1f61\u03c3\u03c4\u03b5 \u03b4\u03b5\u1fd6 \u03c0\u03c1\u1f78\u03c2 \u03c4\u1f70 \u03c4\u1ff6\u03bd \u1f04\u03bb\u03bb\u03c9\u03bd \u03bc\u03cc\u03c1\u03b9\u03b1\n\u03b6\u03ce\u03c9\u03bd \u1f00\u03bd\u03ac\u03b3\u03bf\u03bd\u03c4\u03b1\u03c2 \u03c3\u03ba\u03bf\u03c0\u03b5\u1fd6\u03bd,\" ...)\n\n(C) Id _De Part. Animal._ IV. 2, 2. \u03c4\u1f70 \u03bc\u1f72\u03bd \u03b3\u1f70\u03c1 \u1f45\u03bb\u03c9\u03c2 \u03bf\u1f50\u03ba \u1f15\u03c7\u03b5\u03b9 \u03c7\u03bf\u03bb\u03ae\u03bd,\n\u03bf\u1f37\u03bf\u03bd \u1f31\u03c0\u03c0\u03bf\u03c2 \u03ba\u03b1\u03b9 \u1f40\u03c1\u03b5\u03cd\u03c2 \u03ba\u03b1\u1f76 \u03bf\u03bd\u03bf\u03c2 \u03ba\u03b1\u1f76 \u1f14\u03bb\u03b1\u03c6\u03bf\u03c2 \u03ba\u03b1\u1f76 \u03c0\u03c1\u03cc\u03be..... \u1f18\u03bd \u03b4\u1f72 \u03c4\u03bf\u1fd6\u03c2\n\u03b3\u03ad\u03bd\u03b5\u03c3\u03b9 \u03c4\u03bf\u1fd6\u03c2 \u03b1\u1f50\u03c4\u03bf\u1fd6\u03c2 \u03c4\u1f70 \u03bc\u1f72\u03bd \u1f14\u03c7\u03b5\u03b9\u03bd \u03c6\u03b1\u03af\u03bd\u03b5\u03c4\u03b1\u03b9, \u03c4\u1f70 \u03b4' \u03bf\u1f50\u03ba \u1f14\u03c7\u03b5\u03b9\u03bd, \u03bf\u1f37\u03bf\u03bd \u1f10\u03bd\n\u03c4\u1ff7 \u03c4\u1ff6\u03bd \u03bc\u03c5\u1ff6\u03bd. \u03a4\u03bf\u03cd\u03c4\u03c9\u03bd \u03b4' \u1f10\u03c3\u03c4\u1f76 \u03ba\u03b1\u1f76 \u1f41 \u1f04\u03bd\u03b8\u03c1\u03c9\u03c0\u03bf\u03c2\u00b7 \u1f14\u03bd\u03b9\u03bf\u03b9 \u03bc\u1f72\u03bd \u03b3\u1f70\u03c1 \u03c6\u03b1\u03af\u03bd\u03bf\u03bd\u03c4\u03b1\u03b9\n\u1f14\u03c7\u03bf\u03bd\u03c4\u03b5\u03c2 \u03c7\u03bf\u03bb\u1f74\u03bd \u1f10\u03c0\u1f76 \u03c4\u03bf\u03c5 \u1f25\u03c0\u03b1\u03c4\u03bf\u03c2, \u1f14\u03bd\u03b9\u03bf\u03b9 \u03b4' \u03bf\u1f50\u03ba \u1f14\u03c7\u03bf\u03bd\u03c4\u03b5\u03c2. \u0394\u03b9\u03bf \u03ba\u03b1\u1f76 \u03b3\u03af\u03bd\u03b5\u03c4\u03b1\u03b9\n\u1f00\u03bc\u03c6\u03b9\u03c3\u03b2\u03ae\u03c4\u03b7\u03c3\u03b9\u03c2 \u03c0\u03b5\u03c1\u1f76 \u1f41\u03bb\u03bf\u03c5 \u03c4\u03bf\u1fe6 \u03b3\u03ad\u03bd\u03bf\u03c5\u03c2\u00b7 \u03bf\u1f31 \u03b3\u1f70\u03c1 \u1f10\u03bd\u03c4\u03c5\u03c7\u03cc\u03bd\u03c4\u03b5\u03c2 \u1f41\u03c0\u03bf\u03c4\u03b5\u03c1\u03c9\u03c3\u03bf\u1fe6\u03bd \u1f14\u03c7\u03bf\u03c5\u03c3\u03b9\n\u03c0\u03b5\u03c1\u1f76 \u03c0\u03ac\u03bd\u03c4\u03c9\u03bd \u1f51\u03c0\u03bf\u03bb\u03b1\u03bc\u03b2\u03ac\u03bd\u03bf\u03c5\u03c3\u03b9\u03bd \u1f61\u03c2 \u1f01\u03c0\u03ac\u03bd\u03c4\u03c9\u03bd \u1f10\u03c7\u03cc\u03bd\u03c4\u03c9\u03bd.....\n\n(D) Ib. \u00a7 11. \u0394\u03b9\u1f78 \u03ba\u03b1\u1f76 \u03c7\u03b1\u03c1\u03b9\u03ad\u03c3\u03c4\u03b1\u03c4\u03b1 \u03bb\u03ad\u03b3\u03bf\u03c5\u03c3\u03b9 \u03c4\u1ff6\u03bd \u1ff6\u03c1\u03c7\u03b1\u03af\u03c9\u03bd \u1f41\u03b9 \u03c6\u03ac\u03c3\u03ba\u03bf\u03bd\u03c4\u03b5\u03c2\n\u03b1\u1f34\u03c4\u03b9\u03bf\u03bd \u03b5\u1fd6\u03bd\u03b1\u03b9 \u03c4\u03bf\u1fe6 \u03c0\u03bb\u03b5\u03af\u03c9 \u03b6\u1fc6\u03bd \u03c7\u03c1\u03cc\u03bd\u03bf\u03bd \u03c4\u03bf \u03bc\u1f74 \u1f14\u03c7\u03b5\u03b9\u03bd \u03c7\u03bf\u03bb\u03ae\u03bd, \u03b2\u03bb\u03ad\u03c8\u03b1\u03bd\u03c4\u03b5\u03c2 \u1f10\u03c0\u1f76 \u03c4\u1f70\n\u03bc\u03c9\u03bd\u03c5\u03c7\u03b1 \u03ba\u03b1\u03b9 \u03c4\u1f70\u03c2 \u03b5\u03bb\u03b1\u03c6\u03bf\u03c5\u03c2\u00b7 \u03c4\u03b1\u1fe6\u03c4\u03b1 \u03b3\u1f70\u03c1 \u1f04\u03c7\u03bf\u03bb\u03ac \u03c4\u03b5 \u03ba\u03b1\u1f76 \u03b6\u1fc7 \u03c0\u03bf\u03bb\u1f7a\u03bd \u03c7\u03c1\u03cc\u03bd\u03bf\u03bd. \u1f1c\u03c4\u03b9\n\u03b4\u1f72 \u03ba\u03b1\u1f76 \u03c4\u1f70 \u03bc\u1f74 \u1f11\u03c9\u03c1\u03b1\u03bc\u03ad\u03bd\u03b1 \u1f51\u03c0' \u1f10\u03ba\u03b5\u03af\u03bd\u03c9\u03bd \u1f41\u03c4\u03b9 \u03bf\u1f50\u03ba \u1f14\u03c7\u03b5\u03b9 \u03c7\u03bf\u03bb\u03ae\u03bd, \u03bf\u1f37\u03bf\u03bd \u03b4\u03b5\u03bb\u03c6\u03b9\u03c2 \u03ba\u03b1\u1f76\n\u03ba\u03ac\u03bc\u03b7\u03bb\u03bf\u03c2, \u03ba\u03b1\u1f76 \u03c4\u03b1\u1fe6\u03c4\u03b1 \u03c4\u03c5\u03b3\u03c7\u03ac\u03bd\u03b5\u03b9 \u03bc\u03b1\u03ba\u03c1\u03cc\u03b2\u03b9\u03b1 \u1f44\u03bd\u03c4\u03b1. \u0395\u1f54\u03bb\u03bf\u03b3\u03bf\u03bd \u03b3\u03ac\u03c1, \u03ba.\u03c4.\u03bb.\n\n(E) The elephant and man are mentioned together as long-lived animals\n(_De Long. et Brev. Vit\u00e6_, IV. 2, and _De Generat. Animal._ IV. 10, 2.)\n\n       *       *       *       *       *\n\nThe following is the import of these passages:\n\n(_A_) \"Of viviparous quadrupeds, the deer, roe, horse, mule, ass, seal,\nand some of the swine have not the gall-bladder....\n\nThe elephant also has the liver without gall-bladder, &c.\"\n\n(_B_) \"The external parts of man are well known: the internal parts are\nfar from being so. The parts of man are in a great measure unknown; so\nthat we must judge concerning them by reference to the analogy of other\nanimals....\"\n\n(_C_) \"Some animals are altogether destitute of gall-bladder, as the\nhorse, the mule, the ass, the deer, the roe.... But in some kinds it\nappears that some have it, and some have it not, as the mice kind. And\namong these is man; for some men appear to have a gall-bladder on the\nliver, and some not to have one. And thus there is a doubt as to the\nspecies in general; for those who have happened to examine examples of\neither kind, hold that all the cases are of that kind.\"\n\n(_D_) Those of the ancients speak most plausibly, who say that the\nabsence of the gall-bladder is the cause of long life; looking at\nanimals with uncloven hoof, and deer: for these are destitute of\ngall-bladder, and live a long time. And further, those animals in which\nthe ancients had not the opportunity of ascertaining that they have not\nthe gall-bladder, as the dolphin, and the camel, are also long-lived\nanimals.\"\n\nIt appears, from these passages, that Aristotle was aware that some\npersons had asserted man to have a gall-bladder, but that he also\nconceived this not to be universally true. He may have inclined to\nthe opinion, that the opposite case was the more usual, and may have\nwritten \u1f04\u03bd\u03b8\u03c1\u03c9\u03c0\u03bf\u03c2 in the passage which I have been discussing. Another\nmistake of his is the reckoning deer among long-lived animals.\n\nIt appears probable, from the context of the passages (_C_) and (_D_),\nthat the conjecture of a connexion between absence of the gall-bladder\nand length of life was suggested by some such notion as this:--that\nthe gall, from its bitterness, is the cause of irritation, mental and\nbodily, and that irritation is adverse to longevity. The opinion is\nascribed to \"the ancients,\" not claimed by Aristotle as his own.\n\n\nFOOTNOTES:\n\n[Footnote 350: Mr. Owen, to whom I am indebted for the physiological\npart of this criticism, tells me, \"All mammalia have bile, the\ncarnivora in greater proportion than the herbivora: the gall-bladder\nis a comparatively unimportant accessory to the biliary apparatus;\nadjusting it to certain modifications of stomach and intestine: there\nis no relation between natural longevity and bile. Neither has the\npresence or absence of the gall-bladder any connexion with age. Man and\nthe elephant are perhaps for their size the longest lived animals, and\nthe latest at coming to maturity: one has the gall-bladder, and the\nother not.\"]\n\n\nAPPENDIX E.\n\nON THE FUNDAMENTAL ANTITHESIS OF PHILOSOPHY.\n\n(_Cam. Phil. Soc._ FEB. 5, 1844.)\n\n\n1. All persons who have attended in any degree to the views generally\ncurrent of the nature of reasoning are familiar with the distinction\nof _necessary_ truths and _truths of experience_; and few such\npersons, or at least few students of mathematics, require to have this\ndistinction explained or enforced. All geometricians are satisfied that\nthe geometrical truths with which they are conversant are necessarily\ntrue: they not only are true, but they must be true. The meaning of the\nterms being understood, and the proof being gone through, the truth\nof the proposition must be assented to. That parallelograms upon the\nsame base and between the same parallels are equal;--that angles in the\nsame segment are equal;--these are propositions which we learn to be\ntrue by demonstrations deduced from definitions and axioms; and which,\nwhen we have thus learnt them, we see could not be otherwise. On the\nother hand, there are other truths which we learn from experience;\nas for instance, that the stars revolve round the pole in one day;\nand that the moon goes through her phases from full to full again in\nthirty days. These truths we see to be true; but we know them only\nby experience. Men never could have discovered them without looking\nat the stars and the moon; and having so learnt them, still no one\nwill pretend to say that they are necessarily true. For aught we can\nsee, things might have been otherwise; and if we had been placed in\nanother part of the solar system, then, according to the opinions of\nastronomers, experience would have presented them otherwise.\n\n2. I take the astronomical truths of experience to contrast with the\ngeometrical necessary truths, as being both of a familiar definite\nsort; we may easily find other examples of both kinds of truth. The\ntruths which regard numbers are necessary truths. It is a necessary\ntruth, that 27 and 38 are equal to 65; that half the sum of two\nnumbers added to half their difference is equal to the greater\nnumber. On the other hand, that sugar will dissolve in water; that\nplants cannot live without light; and in short, the whole body of our\nknowledge in chemistry, physiology, and the other inductive sciences,\nconsists of truths of experience. If there be any science which offer\nto us truths of an ambiguous kind, with regard to which we may for a\nmoment doubt whether they are necessary or experiential, we will defer\nthe consideration of them till we have marked the distinction of the\ntwo kinds more clearly.\n\n3. One mode in which we may express the difference of necessary truths\nand truths of experience, is, that necessary truths are those _of\nwhich we cannot distinctly conceive the contrary_. We can very readily\nconceive the contrary of experiential truths. We can conceive the stars\nmoving about the pole or across the sky in any kind of curves with any\nvelocities; we can conceive the moon always appearing during the whole\nmonth as a luminous disk, as she might do if her light were inherent\nand not borrowed. But we cannot conceive one of the parallelograms on\nthe same base and between the same parallels larger than the other;\nfor we find that, if we attempt to do this, when we separate the\nparallelograms into parts, we have to conceive one triangle larger\nthan another, both having all their parts equal; which we cannot\nconceive at all, if we conceive the triangles distinctly. We make this\nimpossibility more clear by conceiving the triangles to be placed so\nthat two sides of the one coincide with two sides of the other; and it\nis then seen, that in order to conceive the triangles unequal, we must\nconceive the two bases which have the same extremities both ways, to\nbe different lines, though both straight lines. This it is impossible\nto conceive: we assent to the impossibility as an axiom, when it is\nexpressed by saying, that two straight lines cannot inclose a space;\nand thus we cannot distinctly conceive the contrary of the proposition\njust mentioned respecting parallelograms.\n\n4. But it is necessary, in applying this distinction, to bear in mind\nthe terms of it;--that we cannot _distinctly_ conceive the contrary\nof a necessary truth. For in a certain loose, indistinct way, persons\nconceive the contrary of necessary geometrical truths, when they\nerroneously conceive false propositions to be true. Thus, Hobbes\nerroneously held that he had discovered a means of geometrically\ndoubling the cube, as it is called, that is, finding two mean\nproportionals between two given lines; a problem which cannot be solved\nby plane geometry. Hobbes not only proposed a construction for this\npurpose, but obstinately maintained that it was right, when it had\nbeen proved to be wrong. But then, the discussion showed how indistinct\nthe geometrical conceptions of Hobbes were; for when his critics had\nproved that one of the lines in his diagram would not meet the other\nin the point which his reasoning supposed, but in another point near\nto it; he maintained, in reply, that one of these points was large\nenough to include the other, so that they might be considered as the\nsame point. Such a mode of conceiving the opposite of a geometrical\ntruth, forms no exception to the assertion, that this opposite cannot\nbe distinctly conceived.\n\n5. In like manner, the indistinct conceptions of children and of rude\nsavages do not invalidate the distinction of necessary and experiential\ntruths. Children and savages make mistakes even with regard to numbers;\nand might easily happen to assert that 27 and 38 are equal to 63 or\n64. But such mistakes cannot make such arithmetical truths cease to be\nnecessary truths. When any person conceives these numbers and their\naddition distinctly, by resolving them into parts, or in any other way,\nhe sees that their sum is necessarily 65. If, on the ground of the\npossibility of children and savages conceiving something different, it\nbe held that this is not a necessary truth, it must be held on the same\nground, that it is not a necessary truth that 7 and 4 are equal to 11;\nfor children and savages might be found so unfamiliar with numbers as\nnot to reject the assertion that 7 and 4 are 10, or even that 4 and 3\nare 6, or 8. But I suppose that no persons would on such grounds hold\nthat these arithmetical truths are truths known only by experience.\n\n6. Necessary truths are established, as has already been said, by\ndemonstration, proceeding from definitions and axioms, according to\nexact and rigorous inferences of reason. Truths of experience are\ncollected from what we see, also according to inferences of reason,\nbut proceeding in a less exact and rigorous mode of proof. The former\ndepend upon the relations of the ideas which we have in our minds:\nthe latter depend upon the appearances or phenomena, which present\nthemselves to our senses. Necessary truths are formed from our\nthoughts, the elements of the world within us; experiential truths are\ncollected from things, the elements of the world without us. The truths\nof experience, as they appear to us in the external world, we call\nFacts; and when we are able to find among our ideas a train which will\nconform themselves to the apparent facts, we call this a Theory.\n\n7. This distinction and opposition, thus expressed in various forms;\nas Necessary and Experiential Truth, Ideas and Senses, Thoughts and\nThings, Theory and Fact, may be termed the _Fundamental Antithesis\nof Philosophy_; for almost all the discussions of philosophers have\nbeen employed in asserting or denying, explaining or obscuring this\nantithesis. It may be expressed in many other ways; but is not\ndifficult, under all these different forms, to recognize the same\nopposition: and the same remarks apply to it under its various forms,\nwith corresponding modifications. Thus, as we have already seen, the\nantithesis agrees with that of Reasoning and Observation: again, it\nis identical with the opposition of Reflection and Sensation: again,\nsensation deals with Objects; facts involve Objects, and generally all\nthings without us are Objects:--Objects of sensation, of observation.\nOn the other hand, we ourselves who thus observe objects, and in whom\nsensation is, may be called the Subjects of sensation and observation.\nAnd this distinction of Subject and Object is one of the most general\nways of expressing the fundamental antithesis, although not yet perhaps\nquite familiar in English. I shall not scruple however to speak of\nthe Subjective and Objective element of this antithesis, where the\nexpressions are convenient.\n\n8. All these forms of antithesis, and the familiar references to them\nwhich men make in all discussions, show the fundamental and necessary\ncharacter of the antithesis. We can have no knowledge without the\nunion, no philosophy without the separation, of the two elements. We\ncan have no knowledge, except we have both impressions on our senses\nfrom the world without, and thoughts from our minds within:--except we\nattend to things, and to our ideas;--except we are passive to receive\nimpressions, and active to compare, combine, and mould them. But on\nthe other hand, philosophy seeks to distinguish the impressions of our\nsenses from the thoughts of our minds;--to point out the difference of\nideas and things;--to separate the active from the passive faculties\nof our being. The two elements, sensations and ideas, are both\nrequisite to the existence of our knowledge, as both matter and form\nare requisite to the existence of a body. But philosophy considers the\nmatter and the form separately. The properties of the form are the\nsubject of geometry, the properties of the matter are the subject of\nchemistry or mechanics.\n\n9. But though philosophy considers these elements of knowledge\nseparately, they cannot really be separated, any more than can matter\nand form. \"We cannot exhibit matter without form, or form without\nmatter; and just as little can we exhibit sensations without ideas, or\nideas without sensations;--the passive or the active faculties of the\nmind detached from each other.\n\nIn every act of my knowledge, there must be concerned the things\nwhereof I know, and thoughts of me who know: I must both passively\nreceive or have received impressions, and I must actively combine\nthem and reason on them. No apprehension of things is purely ideal:\nno experience of external things is purely sensational. If they\nbe conceived as _things_, the mind must have been awakened to the\nconviction of things by sensation: if they be _conceived_ as things,\nthe expressions of the senses must have been bound together by\nconceptions. If we _think_ of any _thing_, we must recognize the\nexistence both of thoughts and of things. _The fundamental antithesis\nof philosophy is an antithesis of inseparable elements._\n\n10. Not only cannot these elements be separately exhibited, but they\ncannot be separately conceived and described. The description of them\nmust always imply their relation; and the names by which they are\ndenoted will consequently always bear a relative significance. And thus\n_the terms which denote the fundamental antithesis of philosophy cannot\nbe applied absolutely and exclusively in any case_. We may illustrate\nthis by a consideration of some of the common modes of expressing the\nantithesis of which we speak. The terms Theory and Fact are often\nemphatically used as opposed to each other: and they are rightly so\nused. But yet it is impossible to say absolutely in any case, This is\na Fact and not a Theory; this is a Theory and not a Fact, meaning by\nTheory, true Theory. Is it a fact or a theory that the stars appear\nto revolve round the pole? Is it a fact or a theory that the earth is\na globe revolving round its axis? Is it a fact or a theory that the\nearth revolves round the sun? Is it a fact or a theory that the sun\nattracts the earth? Is it a fact or a theory that a loadstone attracts\na needle? In all these cases, some persons would answer one way and\nsome persons another. A person who has never watched the stars, and has\nonly seen them from time to time, considers their circular motion round\nthe pole as a theory, just as he considers the motion of the sun in the\necliptic as a theory, or the apparent motion of the inferior planets\nround the sun in the zodiac. A person who has compared the measures of\ndifferent parts of the earth, and who knows that these measures cannot\nbe conceived distinctly without supposing the earth a globe, considers\nits globular form a fact, just as much as the square form of his\nchamber. A person to whom the grounds of believing the earth to revolve\nround its axis and round the sun, are as familiar as the grounds for\nbelieving the movements of the mail-coaches in this country, conceives\nthe former events to be facts, just as steadily as the latter. And a\nperson who, believing the fact of the earth's annual motion, refers it\ndistinctly to its mechanical course, conceives the sun's attraction as\na fact, just as he conceives as a fact the action of the wind which\nturns the sails of a mill. We see then, that in these cases we cannot\napply absolutely and exclusively either of the terms, Fact or Theory.\nTheory and Fact are the elements which correspond to our Ideas and our\nSenses. The Facts are facts so far as the Ideas have been combined with\nthe sensations and absorbed in them: the Theories are Theories so far\nas the Ideas are kept distinct from the sensations, and so far as it is\nconsidered as still a question whether they can be made to agree with\nthem. A true Theory is a fact, a Fact is a familiar theory.\n\nIn like manner, if we take the terms Reasoning and Observation; at\nfirst sight they appear to be very distinct. Our observation of the\nworld without us, our reasonings in our own minds, appear to be clearly\nseparated and opposed. But yet we shall find that we cannot apply\nthese terms absolutely and exclusively. I see a book lying a few feet\nfrom me: is this a matter of observation? At first, perhaps, we might\nbe inclined to say that it clearly is so. But yet, all of us, who\nhave paid any attention to the process of vision, and to the mode in\nwhich we are enabled to judge of the distance of objects, and to judge\nthem to be distant objects at all, know that this judgment involves\ninferences drawn from various sensations;--from the impressions on\nour two eyes;--from our muscular sensations; and the like. These\ninferences are of the nature of reasoning, as much as when we judge of\nthe distance of an object on the other side of a river by looking at\nit from different points, and stepping the distance between them. Or\nagain: we observe the setting sun illuminate a gilded weathercock; but\nthis is as much a matter of reasoning as when we observe the phases of\nthe moon, and infer that she is illuminated by the sun. All observation\ninvolves inferences, and inference is reasoning.\n\n11. Even the simplest terms by which the antithesis is expressed cannot\nbe applied: ideas and sensations, thoughts and things, subject and\nobject, cannot in any case be applied absolutely and exclusively. Our\nsensations require ideas to bind them together, namely, ideas of space,\ntime, number, and the like. If not so bound together, sensations do not\ngive us any apprehension of things or objects. All things, all objects,\nmust exist in space and in time--must be one or many. Now space, time,\nnumber, are not sensations or things. They are something different\nfrom, and opposed to sensations and things. We have termed them ideas.\nIt may be said they are _relations_ of things, or of sensations. But\ngranting this form of expression, still a _relation_ is not a thing\nor a sensation; and therefore we must still have another and opposite\nelement, along with our sensations. And yet, though we have thus these\ntwo elements in every act of perception, we cannot designate any\nportion of the act as absolutely and exclusively belonging to one of\nthe elements. Perception involves sensation, along with ideas of time,\nspace, and the like; or, if any one prefers the expression, involves\nsensations along with the apprehension of relations. Perception is\nsensation, along with such ideas as make sensation into an apprehension\nof things or objects.\n\n12. And as perception of objects implies ideas, as observation implies\nreasoning; so, on the other hand, ideas cannot exist where sensation\nhas not been: reasoning cannot go on when there has not been previous\nobservation. This is evident from the necessary order of development\nof the human faculties. Sensation necessarily exists from the first\nmoments of our existence, and is constantly at work. Observation\nbegins before we can suppose the existence of any reasoning which is\nnot involved in observation. Hence, at whatever period we consider\nour ideas, we must consider them as having been already engaged in\nconnecting our sensations, and as modified by this employment. By being\nso employed, our ideas are unfolded and defined, and such development\nand definition cannot be separated from the ideas themselves. We\ncannot conceive space without boundaries or forms; now forms involve\nsensations. We cannot conceive time without events which mark the\ncourse of time; but events involve sensations. We cannot conceive\nnumber without conceiving things which are numbered; and things imply\nsensations. And the forms, things, events, which are thus implied in\nour ideas, having been the objects of sensation constantly in every\npart of our life, have modified, unfolded and fixed our ideas, to\nan extent which we cannot estimate, but which we must suppose to be\nessential to the processes which at present go on in our minds. We\ncannot say that objects create ideas; for to perceive objects we must\nalready have ideas. But we may say, that objects and the constant\nperception of objects have so far modified our ideas, that we cannot,\neven in thought, separate our ideas from the perception of objects.\n\nWe cannot say of any ideas, as of the idea of space, or time, or\nnumber, that they are absolutely and exclusively ideas. We cannot\nconceive what space, or time, or number would be in our minds, if we\nhad never perceived any thing or things in space or time. We cannot\nconceive ourselves in such a condition as never to have perceived any\nthing or things in space or time. But, on the other hand, just as\nlittle can we conceive ourselves becoming acquainted with space and\ntime or numbers as objects of sensation. We cannot reason without\nhaving the operations of our minds affected by previous sensations; but\nwe cannot conceive reasoning to be merely a series of sensations. In\norder to be used in reasoning, sensation must become observation; and,\nas we have seen, observation already involves reasoning. In order to\nbe connected by our ideas, sensations must be things or objects, and\nthings or objects already include ideas. And thus, as we have said,\nnone of the terms by which the fundamental antithesis is expressed can\nbe absolutely and exclusively applied.\n\n13. I now proceed to make one or two remarks suggested by the views\nwhich have thus been presented. And first I remark, that since, as\nwe have just seen, none of the terms which express the fundamental\nantithesis can be applied absolutely and exclusively, the absolute\napplication of the antithesis in any particular case can never be a\nconclusive or immoveable principle. This remark is the more necessary\nto be borne in mind, as the terms of this antithesis are often used\nin a vehement and peremptory manner. Thus we are often told that such\na thing is a _Fact_ and not a Theory, with all the emphasis which, in\nspeaking or writing, tone or italics or capitals can give. \"We see from\nwhat has been said, that when this is urged, before we can estimate the\ntruth, or the value of the assertion, we must ask to whom is it a fact?\nwhat habits of thought, what previous information, what ideas does\nit imply, to conceive the fact as a fact? Does not the apprehension\nof the fact imply assumptions which may with equal justice be called\ntheory, and which are perhaps false theory? in which case, the fact is\nno fact. Did not the ancients assert it as a fact, that the earth stood\nstill, and the stars moved? and can any fact have stronger apparent\nevidence to justify persons in asserting it emphatically than this\nhad? These remarks are by no means urged in order to show that no fact\ncan be certainly known to be true; but only to show that no fact can\nbe certainly shown to be a fact merely by calling it a fact, however\nemphatically. There is by no means any ground of general skepticism\nwith regard to truth involved in the doctrine of the necessary\ncombination of two elements in all our knowledge. On the contrary,\nideas are requisite to the essence, and things to the reality of our\nknowledge in every case. The proportions of geometry and arithmetic are\nexamples of knowledge respecting our ideas of space and number, with\nregard to which there is no room for doubt. The doctrines of astronomy\nare examples of truths not less certain respecting the external world.\n\n14. I remark further, that since in every act of knowledge, observation\nor perception, both the elements of the fundamental antithesis are\ninvolved, and involved in a manner inseparable even in our conceptions,\nit must always be possible to derive one of these elements from the\nother, if we are satisfied to accept, as proof of such derivation,\nthat one always co-exists with and implies the other. Thus an\nopponent may say, that our ideas of space, time, and number, are\nderived from our sensations or perceptions, because we never were\nin a condition in which we had the ideas of space and time, and had\nnot sensations or perceptions. But then, we may reply to this, that\nwe no sooner perceive objects than we perceive them as existing in\nspace and time, and therefore the ideas of space and time are not\nderived from the perceptions. In the same manner, an opponent may\nsay, that all knowledge which is involved in our reasonings is the\nresult of experience; for instance, our knowledge of geometry. For\nevery geometrical principle is presented to us by experience as true;\nbeginning with the simplest, from which all others are derived by\nprocesses of exact reasoning. But to this we reply, that experience\ncannot be the origin of such knowledge; for though experience shows\nthat such principles are true, it cannot show that they _must be_ true,\nwhich we also know. We never have seen, as a matter of observation,\ntwo straight lines inclosing a space; but we venture to say further,\nwithout the smallest hesitation, that we never shall see it; and if any\none were to tell us that, according to his experience, such a form was\noften seen, we should only suppose that he did not know what he was\ntalking of. No number of acts of experience can add to the certainty\nof our knowledge in this respect; which shows that our knowledge is\nnot made up of acts of experience. We cannot test such knowledge by\nexperience; for if we were to try to do so, we must first know that the\nlines with which we make the trial _are_ straight; and we have no test\nof straightness better than this, that two such lines cannot inclose a\nspace. Since then, experience can neither destroy, add to, nor test our\naxiomatic knowledge, such knowledge cannot be derived from experience.\nSince no one act of experience can affect our knowledge, no numbers of\nacts of experience can make it.\n\n15. To this a reply has been offered, that it is a characteristic\nproperty of geometric forms that the ideas of them exactly resemble the\nsensations; so that these ideas are as fit subjects of experimentation\nas the realities themselves; and that by such experimentation we learn\nthe truth of the axioms of geometry. I might very reasonably ask those\nwho use this language to explain how a particular class of ideas can\nbe said to resemble sensations; how, if they do, we can know it to be\nso; how we can prove this resemblance to belong to geometrical ideas\nand sensations; and how it comes to be an especial characteristic of\nthose. But I will put the argument in another way. Experiment can only\nshow what is, not what must be. If experimentation on ideas shows what\nmust be, it is different from what is commonly called experience.\n\nI may add, that not only the mere use of our senses cannot show that\nthe axioms of geometry _must be_ true, but that, without the light\nof our ideas, it cannot even show that they _are_ true. If we had a\nsegment of a circle a mile long and an inch wide, we should have two\nlines inclosing a space; but we could not, by seeing or touching any\npart of either of them, discover that it was a bent line.\n\n16. That mathematical truths are not derived from experience is perhaps\nstill more evident, if greater evidence be possible, in the case of\nnumbers. We assert that 7 and 8 are 15. We find it so, if we try with\ncounters, or in any other way. But we do not, on that account, say that\nthe knowledge is derived from experience. We refer to our conceptions\nof seven, of eight, and of addition, and as soon as we possess these\nconceptions distinctly, we see that the sum must be fifteen. We cannot\nbe said to make a trial, for we should not believe the apparent result\nof the trial if it were different. If any one were to say that the\nmultiplication table is a table of the results of experience, we should\nknow that he could not be able to go along with us in our researches\ninto the foundations of human knowledge; nor, indeed, to pursue with\nsuccess any speculations on the subject.\n\n17. Attempts have also been made to explain the origin of axiomatic\ntruths by referring them to the association of ideas. But this is\none of the cases in which the word _association_ has been applied so\nwidely and loosely, that no sense can be attached to it. Those who\nhave written with any degree of distinctness on the subject, have\ntruly taught, that the habitual association of the ideas leads us to\nbelieve a connexion of the things: but they have never told us that\nthis association gave us the power of forming the ideas. Association\nmay determine belief, but it cannot determine the possibility of our\nconceptions. The African king did not believe that water could become\nsolid, because he had never seen it in that state. But that accident\ndid not make it impossible to conceive it so, any more than it is\nimpossible for us to conceive frozen quicksilver, or melted diamond,\nor liquefied air; which we may never have seen, but have no difficulty\nin conceiving. If there were a tropical philosopher really incapable\nof conceiving water solidified, he must have been brought into that\nmental condition by abstruse speculations on the necessary relations of\nsolidity and fluidity, not by the association of ideas.\n\n18. To return to the results of the nature of the Fundamental\nAntithesis. As by assuming universal and indissoluble connexion of\nideas with perceptions, of knowledge with experience, as an evidence\nof derivation, we may assert the former to be derived from the latter,\nso might we, on the same ground, assert the latter to be derived from\nthe former. We see all forms in space; and we might hence assert all\nforms to be mere modifications of our idea of space. We see all events\nhappen in time; and we might hence assert all events to be merely\nlimitations and boundary-marks of our idea of time. We conceive all\ncollections of things as two or three, or some other number: it might\nhence be asserted that we have an original idea of number, which is\nreflected in external things. In this case, as in the other, we are met\nat once by the impossibility of this being a complete account of our\nknowledge. Our ideas of space, of time, of number, however distinctly\nreflected to us with limitations and modifications, must be reflected,\nlimited and modified by something different from themselves. We must\nhave visible or tangible forms to limit space, perceived events to mark\ntime, distinguishable objects to exemplify number. But still, in forms,\nand events, and objects, we have a knowledge which they themselves\ncannot give us. For we know, without attending to them, that whatever\nthey are, they will conform and must conform to the truths of geometry\nand arithmetic. There is an ideal portion in all our knowledge of the\nexternal world; and if we were resolved to reduce all our knowledge\nto one of its two antithetical elements, we might say that all our\nknowledge consists in the relation of our ideas. Wherever there is\nnecessary truth, there must be something more than sensation can\nsupply: and the necessary truths of geometry and arithmetic show us\nthat our knowledge of objects in space and time depends upon necessary\nrelations of ideas, whatever other element it may involve.\n\n19. This remark may be carried much further than the domain of geometry\nand arithmetic. Our knowledge of matter may at first sight appear\nto be altogether derived from the senses. Yet we cannot derive from\nthe senses our knowledge of a truth which we accept as universally\ncertain;--namely, that we cannot by any process add to or diminish\nthe quantity of matter in the world. This truth neither is nor can be\nderived from experience; for the experiments which we make to verify\nit pre-suppose its truth. When the philosopher was asked what was\nthe weight of smoke, he bade the inquirer subtract the weight of\nthe ashes from the weight of the fuel. Every one who thinks clearly\nof the changes which take place in matter, assents to the justice of\nthis reply: and this, not because any one had found by trial that such\nwas the weight of the smoke produced in combustion, but because the\nweight lost was assumed to have gone into some other form of matter,\nnot to have been destroyed. When men began to use the balance in\nchemical analysis, they did not prove by trial, but took for granted,\nas self-evident, that the weight of the whole must be found in the\naggregate weight of the elements. Thus it is involved in the idea of\nmatter that its amount continues unchanged in all changes which take\nplace in its consistence. This is a necessary truth: and thus our\nknowledge of matter, as collected from chemical experiments, is also\na modification of our idea of matter as the material of the world\nincapable of addition or diminution.\n\n20. A similar remark may be made with regard to the mechanical\nproperties of matter. Our knowledge of these is reduced, in our\nreasonings, to principles which we call the laws of motion. These laws\nof motion, as I have endeavoured to show[351], depend upon the idea\nof Cause, and involve necessary truths, which are necessarily implied\nin the idea of cause;--namely, that every change of motion must have\na cause--that the effect is measured by the cause;--that reaction\nis equal and opposite to action. These principles are not derived\nfrom experience. No one, I suppose, would derive from experience the\nprinciple, that every event must have a cause. Every attempt to see\nthe traces of cause in the world assumes this principle. I do not say\nthat these principles are anterior to experience; for I have already,\nI hope, shown, that neither of the two elements of our knowledge is,\nor can be, anterior to the other. But the two elements are co-ordinate\nin the development of the human mind; and the ideal element may be\nsaid to be the origin of our knowledge with the more propriety of the\ntwo, inasmuch as our knowledge is the relation of ideas. The other\nelement of knowledge, in which sensation is concerned, and which\nembodies, limits, and defines the necessary truths which express the\nrelations of our ideas, may be properly termed experience; and I have,\nin the discussion just quoted, endeavoured to show how the principles\nconcerning mechanical causation, which I have just stated, are, by\nobservation and experiment, limited and defined, so that they become\nthe laws of motion. And thus we see that such knowledge is derived\nfrom ideas, in a sense quite as general and rigorous, to say the least,\nas that in which it is derived from experience.\n\n21. I will take another example of this; although it is one less\nfamiliar, and the consideration of it perhaps a little more difficult\nand obscure. The objects which we find in the world, for instance,\nminerals and plants, are of different kinds; and according to their\nkinds, they are called by various names, by means of which we know\nwhat we mean when we speak of them. The discrimination of these kinds\nof objects, according to their different forms and other properties,\nis the business of chemistry and botany. And this business of\ndiscrimination, and of consequent classification, has been carried on\nfrom the first periods of the development of the human mind, by an\nindustrious and comprehensive series of observations and experiments;\nthe only way in which any portion of the task could have been effected.\nBut as the foundation of all this labour, and as a necessary assumption\nduring every part of its progress, there has been in men's minds\nthe principle, that objects are so distinguishable by resemblances\nand differences, that they may be named, and known by their names.\nThis principle is involved in the idea of a Name; and without it no\nprogress could have been made. The principle may be briefly stated\nthus:--Intelligible Names of kinds are possible. If we suppose this\nnot to be so, language can no longer exist, nor could the business\nof human life go on. If instead of having certain definite kinds of\nminerals, gold, iron, copper and the like, of which the external forms\nand characters are constantly connected with the same properties and\nqualities, there were no connexion between the appearance and the\nproperties of the object;--if what seemed externally iron might turn\nout to resemble lead in its hardness; and what seemed to be gold during\nmany trials, might at the next trial be found to be like copper; not\nonly all the uses of these minerals would fail, but they would not be\ndistinguishable kinds of things, and the names would be unmeaning. And\nif this entire uncertainty as to kind and properties prevailed for all\nobjects, the world would no longer be a world to which language was\napplicable. To man, thus unable to distinguish objects into kinds, and\ncall them by names, all knowledge would be impossible, and all definite\napprehension of external objects would fade away into an inconceivable\nconfusion. In the very apprehension of objects as intelligibly sorted,\nthere is involved a principle which springs within us, contemporaneous,\nin its efficacy, with our first intelligent perception of the kinds\nof things of which the world consists. We assume, as a necessary\nbasis of our knowledge, that things are of definite kinds; and the aim\nof chemistry, botany, and other sciences is to find marks of these\nkinds; and along with these, to learn their definitely-distinguished\nproperties. Even here, therefore, where so large a portion of our\nknowledge comes from experience and observation, we cannot proceed\nwithout a necessary truth derived from our ideas, as our fundamental\nprinciple of knowledge.\n\n22. What the marks are, which distinguish the constant differences of\nkinds of things (definite marks, selected from among many unessential\nappearances), and what their definite properties are, when they\nare so distinguished, are parts of our knowledge to be learnt from\nobservation, by various processes; for instance, among others, by\nchemical analysis. We find the differences of bodies, as shown by such\nanalysis, to be of this nature:--that there are various elementary\nbodies, which, combining in different definite proportions, form kinds\nof bodies definitely different. But, in arriving at this conclusion,\nwe introduce a new idea, that of Elementary Composition, which is not\nextracted from the phenomena, but supplied by the mind, and introduced\nin order to make the phenomena intelligible. That this notion of\nelementary composition is not supplied by the chemical phenomena of\ncombustion, mixture, &c. as merely an observed fact, we see from this;\nthat men had in ancient times performed many experiments in which\nelementary composition was concerned, and had not seen the fact. It\nnever was truly seen till modern times; and when seen, it gave a new\naspect to the whole body of known facts. This idea of elementary\ncomposition, then, is supplied by the mind, in order to make the\nfacts of chemical analysis and synthesis intelligible _as_ analysis\nand synthesis. And this idea being so supplied, there enters into our\nknowledge along with it a corresponding necessary principle;--That the\nelementary composition of a body determines its kind and properties.\nThis is, I say, a principle assumed, as a consequence of the idea of\ncomposition, not a result of experience; for when bodies have been\ndivided into their kinds, we take for granted that the analysis of a\nsingle specimen may serve to determine the analysis of all bodies of\nthe same kind: and without this assumption, chemical knowledge with\nregard to the kinds of bodies would not be possible. It has been said\nthat we take only one experiment to determine the composition of any\nparticular kind of body, because we have a thousand experiments to\ndetermine that bodies of the same kind have the same composition. But\nthis is not so. Our belief in the principle that bodies of the same\nkind have the same composition is not established by experiments,\nbut is assumed as a necessary consequence of the ideas of Kind and of\nComposition. If, in our experiments, we found that bodies supposed\nto be of the same kind had not the same composition, we should not\nat all doubt of the principle just stated, but conclude at once that\nthe bodies were _not_ of the same kind;--that the marks by which the\nkinds are distinguished had been wrongly stated. This is what has very\nfrequently happened in the course of the investigations of chemists and\nmineralogists. And thus we have it, not as an experiential fact, but\nas a necessary principle of chemical philosophy, that the Elementary\nComposition of a body determines its Kind and Properties.\n\n23. How bodies differ in their elementary composition, experiment must\nteach us, as we have already said, that experiment has taught us. But\nas we have also said, whatever be the nature of this difference, kinds\nmust be definite, in order that language may be possible: and hence,\nwhatever be the terms in which we are taught by experiment to express\nthe elementary composition of bodies, the result must be conformable\nto this principle, That the differences of elementary composition\nare definite. The law to which we are led by experiment is, that the\nelements of bodies continue in definite proportions according to\nweight. Experiments add other laws; as for instance, that of multiple\nproportions in different kinds of bodies composed of the same elements;\nbut of these we do not here speak.\n\n24. We are thus led to see that in our knowledge of mechanics,\nchemistry, and the like, there are involved certain necessary\nprinciples, derived from our ideas, and not from experience. But to\nthis it may be objected, that the parts of our knowledge in which these\nprinciples are involved has, in historical fact, all been acquired by\nexperience. The laws of motion, the doctrine of definite proportions,\nand the like, have all become known by experiment and observation; and\nso far from being seen as necessary truths, have been discovered by\nlong-continued labours and trials, and through innumerable vicissitudes\nof confusion, error, and imperfect truth. This is perfectly true: but\ndoes not at all disprove what has been said. Perception of external\nobjects and experience, experiment and observation are needed,\nnot only, as we have said, to supply the objective element of all\nknowledge--to embody, limit, define, and modify our ideas; but this\nintercourse with objects is also requisite to unfold and fix our ideas\nthemselves. As we have already said, ideas and facts can never be\nseparated. Our ideas cannot be exercised and developed in any other\nform than in their combination with facts, and therefore the trials,\ncorrections, controversies, by which the matter of our knowledge is\ncollected, is also the only way in which the form of it can be rightly\nfashioned. Experience is requisite to the clearness and distinctness of\nour ideas, not because they are derived from experience, but because\nthey can only be exercised upon experience. And this consideration\nsufficiently explains how it is that experiment and observation have\nbeen the means, and the only means, by which men have been led to a\nknowledge of the laws of nature. In reality, however, the necessary\nprinciples which flow from our ideas, and which are the basis of such\nknowledge, have not only been inevitably assumed in the course of such\ninvestigations, but have been often expressly promulgated in words\nby clear-minded philosophers, long before their true interpretation\nwas assigned by experiment. This has happened with regard to such\nprinciples as those above mentioned; That every event must have a\ncause; That reaction is equal and opposite to action; That the quantity\nof matter in the world cannot be increased or diminished: and there\nwould be no difficulty in finding similar enunciations of the other\nprinciples above mentioned;--That the kinds of things have definite\ndifferences, and that these differences depend upon their elementary\ncomposition. In general, however, it may be allowed, that the necessary\nprinciples which are involved in those laws of nature of which we have\na knowledge become then only clearly known, when the laws of nature are\ndiscovered which thus involve the necessary ideal element.\n\n25. But since this is allowed, it may be further asked, how we are to\ndistinguish between the necessary principle which is derived from our\nideas, and the law of nature which is learnt by experience. And to this\nwe reply, that the necessary principle may be known by the condition\nwhich we have already mentioned as belonging to such principles: ...\nthat it is impossible distinctly to conceive the contrary. We cannot\nconceive an event without a cause, except we abandon all distinct idea\nof cause; we cannot distinctly conceive two straight lines inclosing\nspace; and if we seem to conceive this, it is only because we conceive\nindistinctly. We cannot conceive 5 and 3 making 7 or 9; if a person\nwere to say that he could conceive this, we should know that he was a\nperson of immature or rude or bewildered ideas, whose conceptions had\nno distinctness. And thus we may take it as the mark of a necessary\ntruth, that we cannot conceive the contrary distinctly.\n\n26. If it be asked what is the test of distinct conception (since it\nis upon the distinctness of conception that the matter depends), we\nmay consider what answer we should give to this question if it were\nasked with regard to the truths of geometry. If we doubted whether\nanyone had these distinct conceptions which enable him to see the\nnecessary nature of geometrical truth, we should inquire if he could\nunderstand the axioms as axioms, and could follow, as demonstrative,\nthe reasonings which are founded upon them. If this were so, we should\nbe ready to pronounce that he had distinct ideas of space, in the sense\nnow supposed. And the same answer may be given in any other case. That\nreasoner has distinct conceptions of mechanical causes who can see\nthe axioms of mechanics as axioms, and can follow the demonstrations\nderived from them as demonstrations. If it be said that the science,\nas presented to him, may be erroneously constructed; that the axioms\nmay not be axioms, and therefore the demonstrations may be futile, we\nstill reply, that the same might be said with regard to geometry: and\nyet that the possibility of this does not lead us to doubt either of\nthe truth or of the necessary nature of the propositions contained\nin Euclid's Elements. We may add further, that although, no doubt,\nthe authors of elementary books maybe persons of confused minds, who\npresent as axioms what are not axiomatic truths; yet that in general,\nwhat is presented as an axiom by a thoughtful man, though it may\ninclude some false interpretation or application of our ideas, will\nalso generally include some principle which really is necessarily true,\nand which would still be involved in the axiom, if it were corrected\nso as to be true instead of false. And thus we still say, that if in\nany department of science a man can conceive distinctly at all, there\nare principles the contrary of which he cannot distinctly conceive, and\nwhich are therefore necessary truths.\n\n27. But on this it may be asked, whether truth can thus depend upon\nthe particular state of mind of the person who contemplates it; and\nwhether that can be a necessary truth which is not so to all men. And\nto this we again reply, by referring to geometry and arithmetic. It\nis plain that truths may be necessary truths which are not so to all\nmen, when we include men of confused and perplexed intellects; for to\nsuch men it is not a necessary truth that two straight lines cannot\ninclose a space, or that 14 and 17 are 31. It need not be wondered\nat, therefore, if to such men it does not appear a necessary truth\nthat reaction is equal and opposite to action, or that the quantity of\nmatter in the world cannot be increased or diminished. And this view of\nknowledge and truth does not make it depend upon the state of mind of\nthe student, any more than geometrical knowledge and geometrical truth,\nby the confession of all, depend upon that state. We know that a man\ncannot have any knowledge of geometry without so much of attention to\nthe matter of the science, and so much of care in the management of\nhis own thoughts, as is requisite to keep his ideas distinct and clear.\nBut we do not, on that account, think of maintaining that geometrical\ntruth depends merely upon the state of the student's mind. We conceive\nthat he knows it because it is true, not that it is true because he\nknows it. We are not surprised that attention and care and repeated\nthought should be requisite to the clear apprehension of truth. For\nsuch care and such repetition are requisite to the distinctness and\nclearness of our ideas: and yet the relations of these ideas, and\ntheir consequences, are not produced by the efforts of attention or\nrepetition which we exert. They are in themselves something which\nwe may discover, but cannot make or change. The idea of space, for\ninstance, which is the basis of geometry, cannot give rise to any\ndoubtful propositions. What is inconsistent with the idea of space\ncannot be truly obtained from our ideas by any efforts of thought or\ncuriosity; if we blunder into any conclusion inconsistent with the idea\nof space, our knowledge, so far as this goes, is no knowledge: any more\nthan our observation of the external world would be knowledge, if, from\nhaste or inattention, or imperfection of sense, we were to mistake the\nobject which we see before us.\n\n28. But further: not only has truth this reality, which makes it\nindependent of our mistakes, that it must be what is really consistent\nwith our ideas; but also, a further reality, to which the term\nis more obviously applicable, arising from the principle already\nexplained, that ideas and perceptions are inseparable. For since,\nwhen we contemplate our ideas, they have been frequently embodied and\nexemplified in objects, and thus have been fixed and modified; and\nsince this compound aspect is that under which we constantly have\nthem before us, and free from which they cannot be exhibited; our\nattempts to make our ideas clear and distinct will constantly lead us\nto contemplate them as they are manifested in those external forms\nin which they are involved. Thus in studying geometrical truth, we\nshall be led to contemplate it as exhibited in visible and tangible\nfigures;--not as if these could be sources of truth, but as enabling\nus more readily to compare the aspects which our ideas, applied to the\nworld of objects, may assume. And thus we have an additional indication\nof the reality of geometrical truth, in the necessary possibility of\nits being capable of being exhibited in a visible or tangible form. And\nyet even this test by no means supersedes the necessity of distinct\nideas, in order to a knowledge of geometrical truth. For in the case\nof the duplication of the cube by Hobbes, mentioned above, the diagram\nwhich he drew made two points appear to coincide, which did not\nreally, and by the nature of our idea of space, coincide; and thus\nconfirmed him in his error.\n\n_Thus the inseparable nature of the Fundamental Antithesis of Ideas and\nThings gives reality to our knowledge, and makes objective reality a\ncorrective of our subjective imperfections in the pursuit of knowledge.\nBut this objective exhibition of knowledge can by no means supersede a\ncomplete development of the subjective condition, namely, distinctness\nof ideas. And that there is a subjective condition, by no means makes\nknowledge altogether subjective, and thus deprives it of reality;\nbecause, as we have said, the subjective and the objective elements are\ninseparably bound together in the fundamental antithesis._\n\n29. It would be easy to apply these remarks to other cases, for\ninstance, to the case of the principle we have just mentioned, that\nthe differences of elementary composition of different kinds of bodies\nmust be definite. We have stated that this principle is necessarily\ntrue;--that the contrary proposition cannot be distinctly conceived.\nBut by whom? Evidently, according to the preceding reasoning, by a\nperson who distinctly conceives Kinds, as marked by intelligible\nnames, and Composition, as determining the kinds of bodies. Persons\nnew to chemical and classificatory science may not possess these ideas\ndistinctly; or rather, cannot possess them distinctly; and therefore\ncannot apprehend the impossibility of conceiving the opposite of\nthe above principle; just as the schoolboy cannot apprehend the\nimpossibility of the numbers in his multiplication table being other\nthan they are. But this inaptitude to conceive, in either case, does\nnot alter the necessary character of the truth: although, in one case,\nthe truth is obvious to all except schoolboys and the like, and the\nother is probably not clear to any except those who have attentively\nstudied the philosophy of elementary compositions. At the same time,\nthis difference of apprehension of the truth in different persons does\nnot make the truth doubtful or dependent upon personal qualifications;\nfor in proportion as persons attain to distinct ideas, they will see\nthe truth; and cannot, with such ideas, see anything as truth which\nis not truth. When the relations of elements in a compound become as\nfamiliar to a person as the relations of factors in a multiplication\ntable, he will then see what are the necessary axioms of chemistry, as\nhe now sees the necessary axioms of arithmetic.\n\n30. There is also one other remark which I will here make. In the\nprogress of science, both the elements of our knowledge are constantly\nexpanded and augmented. By the exercise of observation and experiment,\nwe have a perpetual accumulation of facts, the materials of knowledge,\nthe objective element. By thought and discussion, we have a perpetual\ndevelopment of man's ideas going on: theories are framed, the materials\nof knowledge are shaped into form; the subjective element is evolved;\nand by the necessary coincidence of the objective and subjective\nelements, the matter and the form, the theory and the facts, each of\nthese processes furthers and corrects the other: each element moulds\nand unfolds the other. Now it follows, from this constant development\nof the ideal portion of our knowledge, that we shall constantly be\nbrought in view of new Necessary Principles, the expression of the\nconditions belonging to the Ideas which enter into our expanding\nknowledge. These principles, at first dimly seen and hesitatingly\nasserted, at last become clearly and plainly self-evident. Such is the\ncase with the principles which are the basis of the laws of motion.\nSuch may soon be the case with the principles which are the basis\nof the philosophy of chemistry. Such may hereafter be the case with\nthe principles which are to be the basis of the philosophy of the\nconnected and related polarities of chemistry, electricity, galvanism,\nmagnetism. That knowledge is possible in these cases, we know; that\nour knowledge may be reduced to principles, gradually more simple,\nwe also know; that we have reached the last stage of simplicity of\nour principles, few cultivators of the subject will be disposed to\nmaintain; and that the additional steps which lead towards very simple\nand general principles will also lead to principles which recommend\nthemselves by a kind of axiomatic character, those who judge from the\nanalogy of the past history of science will hardly doubt. That the\nprinciples thus axiomatic in their form, do also express some relation\nof our ideas, of which experiment and observation have given a true\nand real interpretation, is the doctrine which I have here attempted\nto establish and illustrate in the most clear and undoubted of the\nexisting sciences; and the evidence of this doctrine in those cases\nseems to be unexceptionable, and to leave no room to doubt that such is\nthe universal type of the progress of science. Such a doctrine, as we\nhave now seen, is closely connected with the views here presented of\nthe nature of the Fundamental Antithesis of Philosophy, which I have\nendeavoured to illustrate.\n\n\nFOOTNOTES:\n\n[Footnote 351: _Hist. Sc. Ind._ b. iii.]\n\n\nAPPENDIX F.\n\nREMARKS ON A REVIEW OF THE PHILOSOPHY OF THE INDUCTIVE SCIENCES.\n\n\n  _Trinity Lodge, April 11th, 1844._\n\n  MY DEAR HERSCHEL,\n\nBeing about to send you a copy of a paper on a philosophical question\njust printed in the Transactions of our Cambridge Society, I am tempted\nto add, as a private communication, a few Remarks on another aspect of\nthe same question. These Remarks I think I may properly address to you.\nThey will refer to an Article in the _Quarterly Review_ for June, 1841,\nrespecting my _History_ and _Philosophy_ of the Inductive Sciences; and\nwithout assigning any other reason, I may say that the interest I know\nyou to take in speculations on such subjects makes me confident that\nyou will give a reasonable attention to what I may have to say on the\nsubject of that Article. With the Reviewal itself, I am so far from\nhaving any quarrel, that when it appeared I received it as affording\nall that I hoped from Public Criticism. The degree and the kind of\nadmiration bestowed upon my works by a writer so familiar with science,\nso comprehensive in his views, and so equitable in his decisions, as\nthe Reviewer manifestly was, I accepted as giving my work a stamp of\nacknowledged value which few other hands could have bestowed.\n\nYou may perhaps recollect, however, that the Reviewer dissented\naltogether from some of the general views which I had maintained,\nand especially from a general view which is also, in the main, that\npresented in the accompanying Memoir, namely, that, besides Facts,\nIdeas are an indispensable source of our knowledge; that Ideas are\nthe ground of necessary truth; that the Idea of Space, in particular,\nis the ground of the necessary truths of geometry. This question,\nand especially as limited to the last form, will be the subject of\nmy Remarks in the first place; and I wish to consider the Reviewer's\nobjections with the respect which their subtlety and depth of thought\nwell deserve.\n\nThe Reviewer makes objections to the account which I have given of\nthe source whence geometrical truth derives its characters of being\nnecessary and universal; but he is not one of those metaphysicians\nwho deny those characters to the truths of geometry. He allows in the\nmost ample manner that the truths of geometry _are_ necessary. The\nquestion between us therefore is from what this character is derived.\nThe Reviewer prefers, indeed, to have it considered that the question\nis not concerning the necessity, but, as he says, the universality of\nthese truths; or rather, the nature and grounds of our conviction of\ntheir universality. He might have said, with equal justice, the nature\nand grounds of our conviction of their necessity. For his objection to\nthe term _necessity_ in this case--\"that all the propositions about\nrealities are necessarily true, since every reality must be consistent\nwith itself,\" (p. 206)--does not apply to our conviction of necessity,\nsince we may not be able to see what are the properties of real things;\nand therefore may have no conviction of their necessity. It may be a\nnecessary property of salt to be soluble, but we see no such necessity;\nand therefore the assertion of such a property is not one of the\nnecessary truths with which we are here concerned. But to turn back to\nthe necessary or universal truths of geometry, and the ground of those\nattributes: The main difference between the Author and the Reviewer is\nbrought into view, when the Reviewer discusses the general argument\nwhich I had used, in order to show that truths which we see to be\nnecessary and universal cannot be derived from experience. The argument\nis this,--\n\n\"Experience must always consist of a limited number of observations;\nand however numerous these may be, they can show nothing with regard\nto the infinite number of cases in which the experiment has not been\nmade.... Truths can only be known to be general, not universal, if\nthey depend upon experience alone. Experience cannot bestow that\nuniversality which she herself cannot have; nor that necessity of which\nshe has no comprehension.\" (_Phil._ _i._ pp. 60, 61.)\n\nHere is that which must be considered as the cardinal argument on this\nsubject. It is therefore important to attend to the answer which the\nReviewer makes to it. He says,--\n\n\"We conceive that a full answer to this argument is afforded by the\nnature of the inductive propensity,--by the irresistible impulse of\nthe mind to generalize _ad infinitum_, when nothing in the nature of\nlimitation or opposition offers itself to the imagination; and by our\ninvoluntary application of the law of continuity to fill up, by the\nsame ideal substance of truth, every interval which uncontradicted\nexperience may have left blank in our inductive conclusion.\" (p. 207.)\n\nNow here we have two rival explanations of the same thing,--the\nconviction of the universality of geometrical truths. The one\nexplanation is, that this universality is imposed upon such truths by\ntheir involving a certain element, derived from the universal mode of\nactivity of the mind when apprehending such truths, which element I\nhave termed an Idea. The other explanation is, that this universality\narises from the _inductive propensity_--from the _irresistible impulse\nto generalize ad infinitum_--from the _involuntary application of the\nlaw of continuity_--from the _filling up all intervals with the same\nideal substance of truth_.\n\nWith regard to these two explanations, I may observe, that so far as\nthey are thus stated they do not necessarily differ. They both agree\nin expressing this; that the ground of the universality of geometrical\ntruths is a certain law of the mind's activity, which determines its\nprocedure when it is concerned in apprehending the external world.\nOne explanation says, that we impress upon the external world the\nrelations of our ideas, and thus believe more than we see,--the\nother says, that we have an irresistible impulse to introduce into\nour conviction a relation between what we do observe and what we do\nnot, namely, to generalize _ad infinitum_ from what we do see. One\nexplanation says, that we perceive all external objects as included\nin absolute ideal space,--the other, that we fill up the intervals of\nthe objects which we perceive with the same ideal substance of truth.\nBoth sets of expressions may perhaps be admissible; and if admitted,\nmay be understood as expressing the same opinions, or opinions which\nhave much in common. The Author's expressions have the advantage, which\nought to belong to them, as the expressions employed in a systematic\nwork, of being fixed expressions, technical phrases, intentionally\nselected, uniformly and steadily employed whenever the occasion recurs.\nThe Reviewer's expressions are more lively and figurative, and such\nas well become an occasional composition; but hardly such as could\nbe systematically applied to the subject in a regular treatise. We\ncould not, as a standard and technical phrase, talk of filling up\nthe intervals of observation with the same ideal substance of truth;\nand the inevitable impulse to generalize would hardly sufficiently\nexpress that we generalize according to a certain idea, namely, the\nidea of space. Perhaps that which is suggested to us as the common\nimport of the two sets of expressions may be conveyed by some other\nphrase, in a manner free from the objections which lie against both the\nAuthor's and the Critic's terms. Perhaps the mental idea governing\nour experience, and the irresistible impulse to generalize our\nobservation, may both be superseded by our speaking of a law of the\nmind's _activity_, which is really implied in both. There operates, in\nobserving the external world, a law of the mind's activity, by which it\nconnects its observations; and this law of the mind's activity may be\nspoken of either as the idea of space, or as the irresistible impulse\nto generalize the relations of space which it observes. And this\nexpression--_the laws of the mind's activity_--thus opposed to that\nmerely passive function by which the mind receives the impressions of\nsense, may be applied to other ideas as well as to the idea of space,\nand to the impulse to generalize in other truths as well as those of\ngeometry.\n\nSo far, it would seem, that the Author and the Critic may be brought\ninto much nearer agreement than at first seemed likely, with regard\nto the grounds of the necessity and universality in our knowledge.\nBut even if we adopt this conciliatory suggestion, and speak of the\nnecessity and universality of certain truths as arising from the laws\nof the mind's activity, we cannot, without producing great confusion,\nallow ourselves to say, as the Critic says, that these truths are thus\nderived from _experience_, or from _observation_. It will, I say, be\nfound fatal to all philosophical precision of thought and language,\nto say that the fundamental truths of geometry, the axioms, with the\nconviction of their necessary truth, are derived from experience. Let\nus take any axiomatic truth of geometry, and ask ourselves if this is\nnot so.\n\nIt is, for example, an axiom in geometry that if a straight line cut\none of two parallel straight lines, it must cut the other also. Is this\ntruth derived or derivable from observation of actual parallel lines,\nand a line cutting them, exhibited to our senses? Let those who say\nthat we do acquire this truth by observation, imagine to themselves\nthe mode in which the observation must be made. We have before us two\nparallel straight lines, and we see that a straight line which cuts\nthe one cuts the other also. We see this again in another case, it\nmay be the angles and the distances being different, and in a third,\nand in a fourth; and so on; and generalizing, we are irresistibly\nled to believe the assertion to be universally true. But can any one\nreally imagine this to be the mode in which we arrive at this truth?\n\"We see,\" says this explanation, \"two parallel straight lines, cut by\na third.\" But how do we know that the observed lines are parallel?\nIf we apply any test of parallelism, we must assume some property of\nparallels, and thus involve some axiom on the subject, which we have no\nmore right to assume than the one now under consideration. We should\nthus destroy our explanation as an account of the mode of arriving\nat independent geometrical axioms. But probably those who would give\nsuch an explanation would not do this. They would not suppose that in\nobserving this property of parallels we try by measurement whether the\nlines are parallel. They would say, I conceive, that we suppose lines\nto be parallel, and that then we see that the straight line which cuts\nthe one must cut the other. That when we make this supposition, we are\npersuaded of the truth of the conclusion, is certain. But what I have\nto remark is, that this being so, the conclusion is the result, not of\nobservation, but of the hypothesis. The geometrical truth here spoken\nof, after this admission, no longer flows from experience, but from\nsupposition. It is not that we _ascertain_ the lines to be parallel,\nand then _find_ that they have this property: but we _suppose_ the\nlines to be parallel, and _therefore_ they have this property. This is\nnot a truth of experience.\n\nThis, it may be said, is so evident that it cannot have been overlooked\nby a very acute reasoner, such as you describe your Critic to be.\nWhat, it may be asked, is the answer which he gives to so palpable an\nobjection as this? How does he understand his assertion that we learn\nthe truth of geometrical axioms from experience (p. 208), so as to make\nit tenable on his own principles? What account does he give of the\norigin of such axioms which makes them in any sense to be derived from\nexperience?\n\nIn justice to the Reviewer's fairness (which is unimpeachable\nthroughout his argumentation) it must be stated that he does give an\naccount in which he professes to show how this is done. And the main\nstep of his explanation consists in introducing the conception of\n_direction_, and _unity of direction_. He says (p. 208), \"The _unity of\ndirection_, or that we cannot march from a given point by more than one\npath _direct to the same object_, is a matter of practical experience,\nlong before it can by possibility become matter of abstract thought.\"\nWe might ask here, as in the former case, how this can be a matter of\nexperience, except we have some independent test of directness? and we\nmight demand to know what this test is. Or do we not rather, here as\nin the other case, _suppose_ the directness of the path; and is not\nthe singleness of the direct path a consequence, not of its observed\nform, but of its hypothetical directness; and thus by no means a\nresult of experience? But we may put our remark upon this deduction\nof the geometrical axiom in another form. We generalize, it is said,\nthe observations which we have made ever since we were born. But this\nterm \"generalize\" is far too vague to pass for an explanation, without\nbeing itself explained. We are impelled to believe that to be true in\ngeneral which we see to be true in particular. But how do we see any\ntruth? How do we pick out any proposition with respect to a diagram\nwhich we see before us? We see in particular, and state in general,\nsome truth respecting straight lines, or parallel lines, or concerning\ndirection. But where do we find the conception of straightness, or\nparallelism, or direction? These conceptions are not upon the surface\nof things. The child does not, from his birth, see straightness\nand parallelism so as to know that he sees them. How then does his\nexperience bear upon a proposition in which these conceptions are\ninvolved? It is said that it is a matter of experience long before it\nis a matter of abstract thought. But how can there be any experience\nby which we learn these properties of a straight line, till our\nthoughts are at least so abstract as to conceive what straightness is?\nIf it be said that this conception grows with our experience, and is\ngradually unfolded with our unfolding materials of knowledge, so as\nto give import and significance to them: I need make no objection to\nsuch a statement, except this--that this power of unfolding out of the\nmind conceptions which give meaning to our experience, is something\nin addition to the mere employment of our senses upon the external\nworld. It is what I have called the ideal part of our knowledge. It\nimplies, not only an impulse to generalize from experience, but also\nan impulse to form conceptions by which generalization is possible. It\nrequires, not only that nothing should oppose the tendency, but that\nthe direction in which the tendency is to operate should be determined\nby the laws of the mind's activity; by an internal, not by an external\nagency.\n\nOne main ground on which the Reviewer is disposed to quarrel with and\nreject several of the expressions used in the _Philosophy_;--such as\nthat space is an idea, a form of our perception, and the like,--is\nthis; that such expressions appear to deprive the external world of its\nreality; to make it, or at least most of its properties, a creation of\nthe observing mind. He quotes the following argument which is urged in\nthe _Philosophy_, in order to prove that space is not a notion obtained\nfrom experience: \"Experience gives us information concerning things\nwithout us, but our apprehending them as without us takes for granted\ntheir existence in space. Experience acquaints us with the form,\nposition, magnitude, &c. of particular objects, but that they _have_\nform, position, magnitude, pre-supposes that they are in space.\" From\nthis statement he altogether dissents. No, says he, \"the reason why we\napprehend things as without us is that they _are_ without us. We take\nfor granted that they exist in space, because they _do_ so exist, and\nbecause such their existence is a matter of direct perception, which\ncan neither be explained in words nor contravened in imagination:\nbecause, in short, space is a _reality_, and not a mere matter of\nconvention or imagination.\"\n\nNow, if by calling space an idea, we suggest any doubt of its reality\nand of the reality of the external world, we certainly run the risk\nof misleading our readers; for the external world is real if anything\nbe real: the bodies which exist in space are things, if things are\nanywhere to be found. That bodies do exist in space, and that _that_ is\nthe reason why we apprehend them as existing in space, I readily grant.\nBut I conceive that the term Idea ought not to suggest any such doubt\nof the reality of the knowledge in which it is involved. Ideas are\nalways, in our knowledge, conjoined with facts. Our real knowledge is\nknowledge, because it involves ideas, real, because it involves facts.\nWe apprehend things as existing in space because they do so exist: and\nour idea of space enables us so to observe them, and so to conceive\nthem.\n\nBut we want, further, a reason why, apprehending them as they are, we\nalso apprehend, that in certain relations they could not be otherwise\n(that two straight linear objects could not inclose a space, for\ninstance). This circumstance is no way accounted for by saying that we\napprehend them as they are; and is, I presume to say, inexplicable,\nexcept by supposing that it arises from some property of the observing\nmind:--an Idea, as I have termed it,--an irresistible Impulse to\ngeneralize, as the Reviewer expresses it. Or, as I have suggested, we\nmay adopt a third phrase, a Law of the mind's activity: and in order\nthat no question may remain, whether we ascribe reality to the objects\nand relations which we observe, we may describe it as \"a Law of the\nmind's activity in apprehending what is.\" And thus the real existence\nof the object, and the ideal element which our apprehension of it\nintroduces, would both be clearly asserted.\n\nI am ready to use expressions which recognize the reality of space\nand other external things more emphatically than those expressions\nwhich I have employed in the _Philosophy_, if expressions can be\nfound which, while they do this, enable us to explain the possibility\nof knowledge, and to analyze the structure of truth. It is, indeed,\nextremely difficult to find, in speaking of this subject, expressions\nwhich are satisfactory. The reality of the objects which we perceive\nis a profound, apparently an insoluble problem[352]. We cannot but\nsuppose that existence is something different from our knowledge of\nexistence:--that which exists, does not exist merely in our knowing\nthat it does:--truth is truth whether we know it or not. Yet how can we\nconceive truth, otherwise than as something known? How can we conceive\nthings as existing, without conceiving them as objects of perception?\nIdeas and Things are constantly opposed, yet necessarily co-existent.\nHow they are thus opposite and yet identical, is the ultimate problem\nof all philosophy. The successive phases of philosophy have consisted\nin separating and again uniting these two opposite elements; in\ndwelling sometimes upon the one and sometimes upon the other, as the\nprincipal or original or only element; and then in discovering that\nsuch an account of the state of the case was insufficient. Knowledge\nrequires ideas. Reality requires things. Ideas and things co-exist.\nTruth _is_, and is known. But the complete explanation of these points\nappears to be beyond our reach. At least it is not necessary for the\npurposes of our philosophy. The separation of ideas and sensations\nin order to discover the conditions of knowledge is our main task.\nHow ideas and sensations are united so as to form things, does not so\nimmediately concern us.\n\nI have stated that we may, without giving up any material portion\nof the Philosophy of Science to which I have been led, express the\nconclusions in other phraseology; and that instead of saying that all\nour knowledge involves certain Fundamental Ideas, the sources from\nwhich all universal truth is derived, we may say that there are certain\nLaws of Mental Activity according to which alone all the real relations\nof things are apprehended. If this alteration in the phraseology will\nmake the doctrines more generally intelligible or acceptable, there is\nno reason why it should not be adopted. But I may remark, that a main\npurpose of the _Philosophy_ was not merely to prove that there _are_\nsuch Fundamental Ideas or Laws of mental activity, but to enumerate\nthose of them which are involved in the existing sciences; and to state\nthe fundamental truths to which the fundamental ideas lead. This was\nthe task which was attempted; and if this have been executed with any\ntolerable success, it may perhaps be received as a contribution to the\nphilosophy of science, of which the value is not small, in whatever\nterms it be expressed. And this enumeration of fundamental ideas, and\nof truths derived from them, must have something to correspond to it,\nin any other mode of expressing that view of the nature of knowledge\nwhich we are led to adopt. If instead of _Fundamental Ideas_, we speak\nof Impulses of generalization, or of _Laws of mental activity_, we\nmust still distinguish such Impulses, or such Laws, according to the\ndistinctions of ideas to which the survey of science led us. We shall\nthus have a series of groups of Laws, or of classes of generalizing\nImpulses, corresponding to the series of Fundamental Ideas already\ngiven. If we employ the language of the Reviewer, we shall have one\ngeneralizing Impulse which suggests relations of Space; another which\ndirects us to properties of Numbers; another which deals with Time;\nanother with Cause: another which groups objects according to Likeness;\nanother which suggests a purpose as a necessary relation among\nthem; to which may be added, even while we confine ourselves to the\nphysical sciences, several others, as may be seen in the _Philosophy_.\nNow when the fundamental conditions and elements of truth are thus\narranged into groups, it is not a matter of so much consequence to\ndecide whether each group shall be said to be bound together by an\nidea or by an impulse of generalization; as it is to see that, if\nthis happen in virtue of ideas, here are so many distinct ideas which\nenter into the structure of science, and give universality to its\nmatter; and again, if this happen in virtue of an irresistible impulse\nof generalization in each case, we have so many different kinds of\nimpulses of generalization. The main purpose in the _Philosophy_ was to\nanalyze scientific truth into its conditions and elements; and I did\nnot content myself with saying that those elements are Sensations and\nIdeas; the Ideas being that element which makes universal knowledge\nconceivable and possible. I went further: I enumerated the Ideas\nwhich thus enter into science. I showed that in the sciences which\nI passed in review, the most acute and profound inquirers had taken\nfor granted that certain truths in each science are of universal and\nnecessary validity, and I endeavoured to select the idea in which this\nuniversality and necessity resided, and to separate it from all other\nideas involved in other sciences. If therefore it be thought better\nto say that those principles in each science upon which, as upon the\naxioms in geometry, the universality and necessity of scientific truth\ndepends, are arrived at, not by ideas, but by an irresistible impulse\nof generalization, those who employ such phraseology, if they make a\nclassification of such impulses corresponding to my classification of\nideas, will still adopt the greater part of my philosophy, altering\nonly the phraseology. Or if, as I suggested, instead of \"Fundamental\nIdeas,\" we use the phrase \"Laws of Mental Activity,\" then our primary\nintellectual Code--the Constitution of our minds, as it may be\ntermed--will consist of a Body of Laws of which the Titles correspond\nwith the Fundamental Ideas of the _Philosophy_.\n\nMy object was, from the writings of the most sagacious and profound\nphilosophers who have laboured on each science, to extract such a\ncode, such a constitution. If I have in any degree succeeded in this,\nthe result must have a reality and a value independently of all forms\nof expression. Still I do not think that any language can ever serve\nfor such legislation, in which the two elements of truth are not\ndistinguished. Even if we adopt the phraseology which I have just\nemployed, we shall have to recollect that Law and Fact must be kept\ndistinct, and that the Constitution has its Principles as well as its\nHistory.\n\nBut I will not longer detain you by seeking other modes of expressing\nthe Fundamental Antithesis to which the accompanying Memoir refers.\nThe Remarks which I here send you were written three years ago, on the\nappearance of the Review which I have quoted. If I succeed in obtaining\nfor them a few minutes' attention from you and a few other friends, I\nshall be glad that they have been preserved.\n\n  I am, my dear Herschel,\n  always truly yours,\n  W. WHEWELL.\n\nP.S. I have abstained from sending you a large portion of my Remarks\nas originally written. I had gone on to show that, in my _Philosophy_,\nI had not only enumerated and analyzed a great number of different\nFundamental Ideas which belong to the different existing sciences,\nbut that I had also shown in what manner these ideas enter into their\nrespective sciences; namely, by the statement or use of Axioms, which\ninvolve the ideas, and which form the basis of each science when\nsystematically exhibited. A number of these Axioms belonging to most\nof the physical sciences, are stated in the _Philosophy_. I might have\nadded also that I have attempted to classify the historical steps\nby which such Axioms are brought into view and applied. But it is\nnot necessary to dwell upon these points, in order to illustrate the\ndifference and the agreement between the Reviewer and me.\n\n  _Sir John F. W. Herschel, Bart. &c._\n\n\nAPPENDIX G.\n\nON THE TRANSFORMATION OF HYPOTHESES IN THE HISTORY OF SCIENCE.\n\n(_Cam. Phil. Soc._ MAY 19, 1851.)\n\n\n1. The history of science suggests the reflection that it is very\ndifficult for the same person at the same time to do justice to two\nconflicting theories. Take for example the Cartesian hypothesis of\nvortices and the Newtonian doctrine of universal gravitation. The\nadherents of the earlier opinion resisted the evidence of the Newtonian\ntheory with a degree of obstinacy and captiousness which now appears\nto us quite marvellous: while on the other hand, since the complete\ntriumph of the Newtonians, _they_ have been unwilling to allow any\nmerit at all to the doctrine of vortices. It cannot but seem strange,\nto a calm observer of such changes, that in a matter which depends\nupon mathematical proofs, the whole body of the mathematical world\nshould pass over, as in this and similar cases they seem to have done,\nfrom an opinion confidently held, to its opposite. No doubt this must\nbe, in part, ascribed to the lasting effects of education and early\nprejudice. The old opinion passes away with the old generation: the new\ntheory grows to its full vigour when its congenital disciples grow to\nbe masters. John Bernoulli continues a Cartesian to the last; Daniel,\nhis son, is a Newtonian from the first. Newton's doctrines are adopted\nat once in England, for they are the solution of a problem at which his\ncontemporaries have been labouring for years. They find no adherents\nin France, where Descartes is supposed to have already explained\nthe constitution of the world; and Fontenelle, the secretary of the\nAcademy of Sciences at Paris, dies a Cartesian seventy years after\nthe publication of Newton's _Principia_. This is, no doubt, a part\nof the explanation of the pertinacity with which opinions are held,\nboth before and after a scientific revolution: but this is not the\nwhole, nor perhaps the most instructive aspect of the subject. There\nis another feature in the change, which explains, in some degree, how\nit is possible that, in subjects, mainly at least mathematical, and\ntherefore claiming demonstrative evidence, mathematicians should hold\ndifferent and even opposite opinions. And the object of the present\npaper is to point out this feature in the successions of theories, and\nto illustrate it by some prominent examples drawn from the history of\nscience.\n\n2. The feature to which I refer is this; that when a prevalent\ntheory is found to be untenable, and consequently, is succeeded by a\ndifferent, or even by an opposite one, the change is not made suddenly,\nor completed at once, at least in the minds of the most tenacious\nadherents of the earlier doctrine; but is effected by a transformation,\nor series of transformations, of the earlier hypothesis, by means of\nwhich it is gradually brought nearer and nearer to the second; and\nthus, the defenders of the ancient doctrine are able to go on as if\nstill asserting their first opinions, and to continue to press their\npoints of advantage, if they have any, against the new theory. They\nborrow, or imitate, and in some way accommodate to their original\nhypothesis, the new explanations which the new theory gives, of the\nobserved facts; and thus they maintain a sort of verbal consistency;\ntill the original hypothesis becomes inextricably confused, or breaks\ndown under the weight of the auxiliary hypotheses thus fastened upon\nit, in order to make it consistent with the facts.\n\nThis often-occurring course of events might be illustrated from the\nhistory of the astronomical theory of epicycles and eccentrics, as\nis well known. But my present purpose is to give one or two brief\nillustrations of a somewhat similar tendency from other parts of\nscientific history; and in the first place, from that part which has\nalready been referred to, the battle of the Cartesian and Newtonian\nsystems.\n\n3. The part of the Cartesian system of vortices which is most\nfamiliarly known to general readers is the explanation of the motions\nof the planets by supposing them carried round the sun by a kind\nof whirlpool of fluid matter in which they are immersed: and the\nexplanation of the motions of the satellites round their primaries by\nsimilar subordinate whirlpools, turning round the primary, and carried,\nalong with it, by the primary vortex. But it should be borne in mind\nthat a part of the Cartesian hypothesis which was considered quite as\nimportant as the cosmical explanation, was the explanation which it\nwas held to afford of terrestrial gravity. Terrestrial gravity was\nasserted to arise from the motion of the vortex of subtle matter which\nrevolved round the earth's axis and filled the surrounding space. It\nwas maintained that by the rotation of such a vortex, the particles\nof the subtle matter would exert a centrifugal force, and by virtue of\nthat force, tend to recede from the center: and it was held that all\nbodies which were near the earth, and therefore immersed in the vortex,\nwould be pressed towards the center by the effort of the subtle matter\nto recede from the center[353].\n\nThese two assumed effects of the Cartesian vortices--to carry bodies\nin their stream, as straws are carried round by a whirlpool, and to\npress bodies to the center by the centrifugal effort of the whirling\nmatter--must be considered separately, because they were modified\nseparately, as the progress of discussion drove the Cartesians from\npoint to point. The former effect indeed, the _dragging_ force\nof the vortex, as we may call it, would not bear working out on\nmechanical principles at all; for as soon as the law of motion was\nacknowledged (which Descartes himself was one of the loudest in\nproclaiming), that a body in motion keeps all the motion which it has,\nand receives in addition all that is impressed upon it; as soon, in\nshort, as philosophers rejected the notion of an inertness in matter\nwhich constantly retards its movements,--it was plain that a planet\nperpetually dragged onwards in its orbit by a fluid moving quicker than\nitself, must be perpetually accelerated; and therefore could not follow\nthose constantly-recurring cycles of quicker and slower motion which\nthe planets exhibit to us.\n\nThe Cartesian mathematicians, then, left untouched the calculation of\nthe progressive motion of the planets; and, clinging to the assumption\nthat a vortex would produce a tendency of bodies to the center, made\nvarious successive efforts to construct their vortices in such a manner\nthat the centripetal forces produced by them should coincide with those\nwhich the phenomena required, and therefore of course, in the end, with\nthose which the Newtonian theory asserted.\n\nIn truth, the Cartesian vortex was a bad piece of machinery for\nproducing a central force: from the first, objections were made to the\nsufficiency of its mechanism, and most of these objections were very\nunsatisfactorily answered, even granting the additional machinery which\nits defenders demanded. One formidable objection was soon started,\nand continued to the last to be the torment of the Cartesians. If\nterrestrial gravity, it was urged, arise from the centrifugal force of\na vortex which revolves about the earth's axis, terrestrial gravity\nought to act in planes perpendicular to the earth's axis, instead\nof tending to the earth's center. This objection was taken by James\nBernoulli[354], and by Huyghens[355] not long after the publication of\nDescartes's _Principia_. Huyghens (who adopted the theory of vortices\nwith modifications of his own) supposes that there are particles of the\nfluid matter which move about the earth in every possible direction,\nwithin the spherical space which includes terrestrial objects; and\nthat the greater part of these motions being in spherical surfaces\nconcentric with the earth, produces a tendency towards the earth's\ncenter.\n\nThis was a procedure tolerably arbitrary, but it was the best which\ncould be done. Saurin, a little later[356], gave nearly the same\nsolution of this difficulty. The solution, identifying a vortex of some\nkind with a central force, made the hypothesis of vortices applicable\nwherever central forces existed; but then, in return, it deprived the\nimage of a vortex of all that clearness and simplicity which had been\nits first great recommendation.\n\nBut still there remained difficulties not less formidable. According\nto this explanation of gravity, since the tendency of bodies to the\nearth's center arose from the superior centrifugal force of the\nwhirling matter which pushed them inward as water pushes a light body\nupward, bodies ought to tend more strongly to the center in proportion\nas they are less dense. The rarest bodies should be the heaviest;\ncontrary to what we find.\n\nDescartes's original solution of this difficulty has a certain degree\nof ingenuity. According to him (_Princip._ IV. 23) a terrestrial body\nconsists of particles of the _third element_, and the more it has\nof such particles, the more it excludes the parts of the _celestial\nmatter_, from the revolution of which matter gravity arises; and\ntherefore the denser is the terrestrial body, and the heavier it will\nbe.\n\nBut though this might satisfy him, it could not satisfy the\nmathematicians who followed him, and tried to reduce his system to\ncalculation on mechanical principles. For how could they do this,\nif the celestial matter, by the operation of which the phenomena\nof force and motion were produced, was so entirely different from\nordinary matter, which alone had supplied men with experimental\nillustrations of mechanical principles? In order that the celestial\nmatter, by its whirling, might produce the gravity of heavy bodies,\nit was mechanically necessary that it must be very dense; and _dense_\nin the ordinary sense of the term; for it was by regarding density in\nthe ordinary sense of the term that the mechanical necessity had been\nestablished.\n\nThe Cartesians tried to escape this result (Huyghens, _Pesanteur_, p.\n161, and John Bernoulli, _Nouvelles Pens\u00e9es_, Art. 31) by saying that\nthere were two meanings of _density_ and _rarity_; that some fluids\nmight be rare by having their particles far asunder, others, by having\ntheir particles very small though in contact. But it is difficult to\nthink that they could, as persons well acquainted with mechanical\nprinciples, satisfy themselves with this distinction; for they could\nhardly fail to see that the mechanical effect of any portion of fluid\ndepends upon the total mass moved, not on the size of its particles.\n\nAttempts made to exemplify the vortices experimentally only showed more\nclearly the force of this difficulty. Huyghens had found that certain\nbodies immersed in a whirling fluid tended to the center of the vortex.\nBut when Saulmon[357] a little later made similar experiments, he had\nthe mortification of finding that the heaviest bodies had the greatest\ntendency to recede from the axis of the vortex. \"The result is,\" as\nthe Secretary of the Academy (Fontenelle) says, \"exactly the opposite\nof what we could have wished, for the [Cartesian] system of gravity:\nbut we are not to despair; sometimes in such researches disappointment\nleads to ultimate success.\"\n\nBut, passing by this difficulty, and assuming that in some way or\nother a centripetal force arises from the centrifugal force of the\nvortex, the Cartesian mathematicians were naturally led to calculate\nthe circumstances of the vortex on mechanical principles; especially\nHuyghens, who had successfully studied the subject of centrifugal\nforce. Accordingly, in his little treatise on the _Cause of\nGravitation_ (p. 143), he calculates the velocity of the fluid matter\nof the vortex, and finds that, at a point in the equator, it is 17\ntimes the velocity of the earth's rotation.\n\nIt may naturally be asked, how it comes to pass that a stream of fluid,\ndense enough to produce the gravity of bodies by its centrifugal force,\nmoving with a velocity 17 times that of the earth (and therefore\nmoving round the earth in 85 minutes), does not sweep all terrestrial\nobjects before it. But to this Huyghens had already replied (p. 137),\nthat there are particles of the fluid moving _in all directions_, and\ntherefore that they neutralize each other's action, so far as lateral\nmotion is concerned.\n\nAnd thus, as early as this treatise of Huyghens, that is, in three\nyears from the publication of Newton's _Principia_, a vortex is made\nto mean nothing more than some machinery or other for producing a\ncentral force. And this is so much the case, that Huyghens commends\n(p. 165), as confirming his own calculation of the velocity of his\nvortex, Newton's proof that at the Moon's orbit the centripetal force\nis equal to the centrifugal; and that thus, this force is less than the\ncentripetal force at the earth's surface in the inverse proportion of\nthe squares of the distances.\n\nJohn Bernoulli, in the same manner, but with far less clearness\nand less candour, has treated the hypothesis of vortices as being\nprincipally a hypothetical cause of central force. He had repeated\noccasions given him of propounding his inventions for propping up the\nCartesian doctrine, by the subjects proposed for prizes by the Paris\nAcademy of Sciences; in which competition Cartesian speculations were\nfavourably received. Thus the subject of the Prize Essays for 1730\nwas, the explanation of the Elliptical Form of the planetary orbits\nand of the Motion of their Aphelia, and the prize was assigned to\nJohn Bernoulli, who gave the explanation on Cartesian principles. He\nexplains the elliptical figure, not as Descartes himself had done,\nby supposing the vortex which carries the planet round the sun to be\nitself squeezed into an elliptical form by the pressure of contiguous\nvortices; but he supposes the planet, while it is carried round by the\nvortex, to have a limited oscillatory motion to and from the center,\nproduced by its being originally, not at the distance at which it would\nfloat in equilibrium in the vortex, but above or below that point. On\nthis supposition, the planet would oscillate to and from the center,\nBernoulli says, like the mercury when deranged in a barometer: and\nit is evident that such an oscillation, combined with a motion round\nthe center, might produce an oval curve, either with a fixed or with\na moveable aphelion. All this however merely amounts to a possibility\nthat the oval _may_ be an ellipse, not to a proof that it will be so;\nnor does Bernoulli advance further.\n\nIt was necessary that the vortices should be adjusted in such a manner\nas to account for Kepler's laws; and this was to be done by making\nthe velocity of each stratum of the vortex depend in a suitable\nmanner on its radius. The Abb\u00e9 de Moli\u00e8res attempted this on the\nsupposition of elliptical vortices, but could not reconcile Kepler's\nfirst two laws, of equal elliptical areas in equal times, with his\nthird law, that the squares of the periodic times are as the cubes\nof the mean distances[358]. Bernoulli, with his circular vortices,\ncould accommodate the velocities at different distances so that they\nshould explain Kepler's laws. He pretended to prove that Newton's\ninvestigations respecting vortices (in the ninth Section of the Second\nBook of the _Principia_) were mechanically erroneous; and in truth,\nit must be allowed that, besides several arbitrary assumptions, there\nare some errors of reasoning in them. But for the most part, the more\nenlightened Cartesians were content to accept Newton's account of the\nmotions and forces of the solar system as part of their scheme; and to\nsay only that the hypothesis of vortices explained the origin of the\nNewtonian forces; and that thus theirs was a philosophy of a higher\nkind. Thus it is asserted (_M\u00e9m. Acad._ 1734), that M. de Moli\u00e8res\nretains the beautiful theory of Newton entire, only he renders it\nin a sort less Newtonian, by disentangling it from attraction, and\ntransferring it from a vacuum into a plenum. This plenum, though\nnot its native region, frees it from the need of attraction, which\nis all the better for it. These points were the main charms of the\nCartesian doctrine in the eyes of its followers;--the getting rid of\nattractions, which were represented as a revival of the Aristotelian\n\"occult qualities,\" \"substantial forms,\" or whatever else was the\nmost disparaging way of describing the bad philosophy of the dark\nages[359];--and the providing some material intermedium, by means of\nwhich a body may affect another at a distance; and thus avoid the\nreproach urged against the Newtonians, that they made a body act where\nit was not. And we are the less called upon to deny that this last\nfeature in the Newtonian theory was a difficulty, inasmuch as Newton\nhimself was never unwilling to allow that gravity might be merely an\neffect produced by some ulterior cause.\n\nWith such admissions on the two sides, it is plain that the Newtonian\nand Cartesian systems would coincide, if the hypothesis of vortices\ncould be modified in such a way as to produce the force of gravitation.\nAll attempts to do this, however, failed: and even John Bernoulli,\nthe most obstinate of the mathematical champions of the vortices,\nwas obliged to give them up. In his Prize Essay for 1734, (on the\nInclinations of the Planetary Orbits[360],) he says (Art. VIII.), \"The\ngravitation of the Planets towards the center of the Sun and the weight\nof bodies towards the center of the earth has not, for its cause,\neither the attraction of M. Newton, or the centrifugal force of the\nmatter of the vortex according to M. Descartes;\" and he then goes on to\nassert that these forces are produced by a perpetual torrent of matter\ntending to the center on all sides, and carrying all bodies with it.\nSuch a hypothesis is very difficult to refute. It has been taken up in\nmore modern times by Le Sage[361], with some modifications; and may be\nmade to account for the principal facts of the universal gravitation\nof matter. The great difficulty in the way of such a hypothesis is,\nthe overwhelming thought of the whole universe filled with torrents\nof an invisible but material and tangible substance, rushing in every\ndirection in infinitely prolonged straight lines and with immense\nvelocity. Whence can such matter come, and whither can it go? Where\ncan be its perpetual and infinitely distant fountain, and where the\nocean into which it pours itself when its infinite course is ended?\nA revolving whirlpool is easily conceived and easily supplied; but\nthe central torrent of Bernoulli, the infinite streams of particles\nof Le Sage, are an explanation far more inconceivable than the thing\nexplained.\n\nBut however the hypothesis of vortices, or some hypothesis substituted\nfor it, was adjusted to explain the facts of attraction to a\ncenter, this was really nearly all that was meant by a vortex or a\n\"tourbillon,\" when the system was applied. Thus in the case of the last\nact of homage to the Cartesian theory which the French Academy rendered\nin the distribution of its prizes, the designation of a Cartesian\nEssay in 1741 (along with three Newtonian ones) as worthy of a prize\nfor an explanation of the Tides; the difference of high and low water\nwas not explained, as Descartes has explained it, by the pressure, on\nthe ocean, of the terrestrial vortex, forced into a strait where it\npasses under the Moon; but the waters were supposed to rise towards the\nMoon, the terrestrial vortex being disturbed and broken by the Moon,\nand therefore less effective in forcing them down. And in giving an\naccount of a Tourmaline from Ceylon (Acad. Sc. 1717), when it has been\nascertained that it attracts and repels substances, the writer adds, as\na matter of course, \"It would seem that it has a vortex.\" As another\nexample, the elasticity of a body was ascribed to vortices between its\nparticles: and in general, as I have said, a vortex implied what we now\nimply by speaking of a central force.\n\n4. In the same manner vortices were ascribed to the Magnet, in order\nto account for its attractions and repulsions. But we may note a\ncircumstance which gave a special turn to the hypothesis of vortices as\napplied to this subject, and which may serve as a further illustration\nof the manner in which a transition may be made from one to the other\nof two rival hypotheses.\n\nIf iron filings be brought near a magnet, in such a manner as to be\nat liberty to assume the position which its polar action assigns to\nthem; (for instance, by strewing them upon a sheet of paper while\nthe two poles of the magnet are close below the paper;) they will\narrange themselves in certain curves, each proceeding from the N. to\nthe S. pole of the magnet, like the meridians in a map of the globe.\nIt is easily shown, on the supposition of magnetic attraction and\nrepulsion, that these _magnetic curves_, as they are termed, are each\na curve whose tangent at every point is the direction of a small line\nor particle, as determined by the attraction and repulsion of the two\npoles. But if we suppose a _magnetic vortex_ constantly to flow out\nof one pole and into the other, in streams which follow such curves,\nit is evident that such a vortex, being supposed to exercise material\npressure and impulse, would arrange the iron filings in corresponding\nstreams, and would thus produce the phenomenon which I have described.\nAnd the hypothesis of _central torrents_ of Bernoulli or Le Sage which\nI have referred to, would, in its application to magnets, really become\nthis hypothesis of a magnetic vortex, if we further suppose that the\nmatter of the torrents which proceed to one pole and from the other,\nmingles its streams, so as at each point to produce a stream in the\nresulting direction. Of course we shall have to suppose two sets of\nmagnetic torrents;--a boreal torrent, proceeding to the north pole,\nand from the south pole of a magnet; and an austral torrent proceeding\nto the south and from the north pole:--and with these suppositions,\nwe make a transition from the hypothesis of attraction and repulsion,\nto the Cartesian hypothesis of vortices, or at least, torrents, which\ndetermine bodies to their magnetic positions by impulse.\n\nOf course it is to be expected that, in this as in the other case,\nwhen we follow the hypothesis of impulse into detail, it will need to\nbe loaded with so many subsidiary hypotheses, in order to accommodate\nit to the phenomena, that it will no longer seem tenable. But the\nplausibility of the hypothesis in its first application cannot be\ndenied:--for, it may be observed, the two _opposite_ streams would\ncounteract each other so as to produce no local _motion_, only\n_direction_. And this case may put us on our guard against other\nsuggestions of forces acting in curve lines, which may at first sight\nappear to be discerned in magnetic and electric phenomena. Probably\nsuch curve lines will all be found to be only resulting lines, arising\nfrom the direct action and combination of elementary attraction and\nrepulsion.\n\n5. There is another case in which it would not be difficult to devise\na mode of transition from one to the other of two rival theories;\nnamely, in the case of the emission theory and the undulation theory\nof Light. Indeed several steps of such a transition have already\nappeared in the history of optical speculation; and the conclusive\nobjection to the emission theory of light, as to the Cartesian theory\nof vortices, is, that no amount of additional hypotheses will reconcile\nit to the phenomena. Its defenders had to go on adding one piece of\nmachinery after another, as new classes of facts came into view, till\nit became more complex and unmechanical than the theory of epicycles\nand eccentrics at its worst period. Otherwise, as I have said, there\nwas nothing to prevent the emission theory from migrating into the\nundulatory theory, and as the theory of vortices did into the theory\nof attraction. For the emissionists allow that rays may _interfere_;\nand that these interferences may be modified by alternate _fits_ in the\nrays; now these fits are already a kind of _undulation_. Then again the\nphenomena of polarized light show that the fits or undulations must\nhave a _transverse_ character: and there is no reason why emitted rays\nshould not be subject to _fits_ of _transverse_ modification as well\nas to any other fits. In short, we may add to the emitted rays of the\none theory, all the properties which belong to the undulations of the\nother, and thus account for all the phenomena on the emission theory;\nwith this limitation only, that the emission will have no share in the\nexplanation, and the undulations will have the whole. If, instead of\nconceiving the universe full of a _stationary_ ether, we suppose it\nto be full of etherial particles moving in every direction; and if we\nsuppose, in the one case and in the other, this ether to be susceptible\nof undulations proceeding from every luminous point; the results of the\ntwo hypotheses will be the same; and all we shall have to say is, that\nthe supposition of the emissive motion of the particles is superfluous\nand useless.\n\n6. This view of the manner in which rival theories pass into one\nanother appears to be so unfamiliar to those who have only slightly\nattended to the history of science, that I have thought it might be\nworth while to illustrate it by a few examples.\n\nIt might be said, for instance, by such persons[362], \"Either the\nplanets are not moved by vortices, or they do not move by the law by\nwhich heavy bodies fall. It is impossible that both opinions can be\ntrue.\" But it appears, by what has been said above, that the Cartesians\ndid hold both opinions to be true; and one with just as much reason as\nthe other, on their assumptions. It might be said in the same manner,\n\"Either it is false that the planets are made to describe their orbits\nby the above quasi-Cartesian theory of Bernoulli, or it is false that\nthey obey the Newtonian theory of gravitation.\" But this would be\nsaid quite erroneously; for if the hypothesis of Bernoulli be true,\nit is so because it agrees in its result with the theory of Newton.\nIt is not only possible that both opinions may be true, but it is\ncertain that if the first be so, the second is. It might be said again,\n\"Either the planets describe their orbits by an inherent virtue, or\naccording to the Newton theory.\" But this again would be erroneous,\nfor the Newtonian doctrine decided nothing as to whether the force of\ngravitation was inherent or not. Cotes held that it was, though Newton\nstrongly protested against being supposed to hold such an opinion.\nThe word _inherent_ is no part of the physical theory, and will be\nasserted or denied according to our metaphysical views of the essential\nattributes of matter and force.\n\nOf course, the possibility of two rival hypotheses being true, one\nof which takes the explanation a step higher than the other, is\nnot affected by the impossibility of two contradictory assertions\nof the _same order_ of generality being both true. If there be a\nnew-discovered comet, and if one astronomer asserts that it will return\nonce in _every_ twenty years, and another, that it will return once in\nevery thirty years, both cannot be right. But if an astronomer says\nthat though its interval was in the last instance 30 years, it will\nonly be 20 years to the next return, in consequence of perturbation and\nresistance, he may be perfectly right.\n\nAnd thus, when different and rival explanations of the same phenomena\nare held, till one of them, though long defended by ingenious men, is\nat last driven out of the field by the pressure of facts, the defeated\nhypothesis is transformed before it is extinguished. Before it has\ndisappeared, it has been modified so as to have all palpable falsities\nsqueezed out of it, and subsidiary provisions added, in order to\nreconcile it with the phenomena. It has, in short, been penetrated,\ninfiltrated, and metamorphosed by the surrounding medium of truth,\nbefore the merely arbitrary and erroneous residuum has been finally\nejected out of the body of permanent and certain knowledge.\n\n\nFOOTNOTES:\n\n[Footnote 352: These remarks were written in 1841. The accompanying\nMemoir contains a further discussion of this problem.]\n\n\nAPPENDIX H.\n\nON HEGEL'S CRITICISM OF NEWTON'S PRINCIPIA.\n\n(_Cam. Phil. Soc._ MAY 21, 1849.)\n\n\nThe Newtonian doctrine of universal gravitation, as the cause of\nthe motions which take place in the solar system, is so entirely\nestablished in our minds, and the fallacy of all the ordinary arguments\nagainst it is so clearly understood among us, that it would undoubtedly\nbe deemed a waste of time to argue such questions in this place, so far\nas physical truth is concerned. But since in other parts of Europe,\nthere are teachers of philosophy whose reputation and influence are\nvery great, and who are sometimes referred to among our own countrymen\nas the authors of new and valuable views of truth, and who yet reject\nthe Newtonian opinions, and deny the validity of the proofs commonly\ngiven of them, it may be worth while to attend for a few minutes to the\ndeclarations of such teachers, as a feature in the present condition\nof European philosophy. I the more readily assume that the Cambridge\nPhilosophical Society will not think a communication on such a subject\ndevoid of interest, in consequence of the favourable reception which it\nhas given to philosophical speculations still more abstract, which I\nhave on previous occasions offered to it. I will therefore proceed to\nmake some remarks on the opinions concerning the Newtonian doctrine of\ngravitation, delivered by the celebrated Hegel, of Berlin, than whom no\nphilosopher in modern, and perhaps hardly any even in ancient times,\nhas had his teaching received with more reverential submission by his\ndisciples, or been followed by a more numerous and zealous band of\nscholars bent upon diffusing and applying his principles.\n\nThe passages to which I shall principally refer are taken from one of\nhis works which is called the _Encyclop\u00e6dia_ (Encyklop\u00e4die), of which\nthe First Part is _the Science of Logic_, the Second, the _Philosophy\nof Nature_, the Third, the _Philosophy of Spirit_. The Second Part,\nwith which I am here concerned, has for an _aliter_ title, _Lectures\non Natural Philosophy_ (Vorlesungen \u00fcber Natur-philosophie), and would\nthrough its whole extent offer abundant material for criticism, by\nreferring it to principles with which we are here familiar: but I\nshall for the present confine myself to that part which refers to the\nsubject which I have mentioned, the Newtonian Doctrine of Gravitation,\n\u00a7 269, 270, of the work. Nor shall I, with regard to this part, think\nit necessary to give a continuous and complete criticism of all the\npassages bearing upon the subject; but only such specimens, and such\nremarks thereon, as may suffice to show in a general manner the value\nand the character of Hegel's declarations on such questions. I do not\npretend to offer here any opinion upon the value and character of\nHegel's philosophy in general: but I think it not unlikely that some\nimpression on that head may be suggested by the examination, here\noffered, of some points in which we can have no doubt where the truth\nlies; and I am not at all persuaded that a like examination of many\nother parts of the Hegelian _Encyclop\u00e6dia_, would not confirm the\nimpression which we shall receive from the parts now to be considered.\n\nHegel both criticises the Newtonian doctrines, or what he states as\nsuch; and also, not denying the truth of the laws of phenomena which he\nrefers to, for instance Kepler's laws, offers his own proof of these\nlaws. I shall make a few brief remarks on each of these portions of the\npages before me. And I would beg it to be understood that where I may\nhappen to put my remarks in a short, and what may seem a peremptory\nform, I do so for the sake of saving time; knowing that among us, upon\nsubjects so familiar, a few words will suffice. For the same reason, I\nshall take passages from Hegel, not in the order in which they occur,\nbut in the order in which they best illustrate what I have to say. I\nshall do Hegel no injustice by this mode of proceeding: for I will\nannex a faithful translation, so far as I can make one, of the whole of\nthe passages referred to, with the context.\n\nNo one will be surprised that a German, or indeed any lover of science,\nshould speak with admiration of the discovery of Kepler's laws, as a\ngreat event in the history of Astronomy, and a glorious distinction to\nthe discoverer. But to say that the glory of the discovery of the proof\nof these laws has been unjustly transferred from Kepler to Newton, is\nquite another matter. This is what Hegel says (_a_)[363]. And we have\nto consider the reasons which he assigns for saying so.\n\nHe says (_b_) that \"it is allowed by mathematicians that the Newtonian\nFormula maybe derived from the Keplerian laws,\" and hence he seems to\ninfer that the Newtonian law is not an additional truth. That is, he\ndoes not allow that the discovery of the cause which produces a certain\nphenomenal law is anything additional to the discovery of the law\nitself.\n\n\"The Newtonian formula may be derived from the Keplerian law.\" It was\nprofessedly so derived; but derived by introducing the Idea of _Force_,\nwhich Idea and its consequences were not introduced and developed till\nafter Kepler's time.\n\n\"The Newtonian formula may be derived from the Keplerian law.\" And the\nKeplerian law may be derived, and was derived, from the observations of\nthe Greek astronomers and their successors; but was not the less a new\nand great discovery on that account.\n\nBut let us see what he says further of this derivation of the Newtonian\n\"formula\" from the Keplerian Law. It is evident that by calling it a\n_formula_, he means to imply, what he also asserts, that it is no new\nlaw, but only a new form (and a bad one) of a previously known truth.\n\nHow is the Newtonian \"formula,\" that is, the law of the inverse squares\nof the central force, derived from the Keplerian law of the cubes of\nthe distances proportional to the squares of the times? This, says\nHegel, is the \"immediate derivation.\" (_c_).--By Kepler's law, _A_\nbeing the distance and _T_ the periodic time, _A_^3/_T_^2 is constant.\nBut Newton _calls_ _A_/_T_^2 universal gravitation; whence it easily\nfollows that gravitation is inversely as _A_^2.\n\nThis is Hegel's way of representing Newton's proof. Reading it, any one\nwho had never read the _Principia_ might suppose that Newton _defined_\ngravitation to be _A_/_T_^2. We, who have read the _Principia_, know\nthat Newton _proves_ that in circles, the _central force_ (not the\n_universal gravitation_) is as _A_/_T_^2: that he proves this, by\nsetting out from the idea of force, as that which deflects a body from\nthe tangent, and makes it describe a curved line: and that in this way,\nhe passes from Kepler's laws of mere motion to his own law of Force.\n\nBut Hegel does not see any value in this. Such a mode of treating the\nsubject he says (_i_) \"offers to us a tangled web, formed of the Lines\nof the mere geometrical construction, to which a physical meaning of\nindependent forces is given.\" That a _measure_ of forces is _found_ in\nsuch lines as the sagitta of the arc described in a given time, (not\nsuch a _meaning_ arbitrarily _given_ to them,) is certainly true, and\nis very distinctly proved in Newton, and in all our elementary books.\n\nBut, says Hegel, as further showing the artificial nature of the\nNewtonian formul\u00e6, (_h_) \"Analysis has long been able to derive the\nNewtonian expression and the laws therewith connected out of the Form\nof the Keplerian Laws;\" an assertion, to verify which he refers to\nFranc\u0153ur's _M\u00e9canique_. This is apparently in order to show that the\n\"lines\" of the Newtonian construction are superfluous. We know very\nwell that analysis does not always refer to visible representations of\nsuch lines: but we know too, (and Franc\u0153ur would testify to this also,)\nthat the analytical proofs contain equivalents to the Newtonian lines.\nWe, in this place, are too familiar with the substitution of analytical\nfor geometrical proofs, to be led to suppose that such a substitution\naffects the substance of the truth proved. The conversion of Newton's\ngeometrical proofs of his discoveries into analytical processes by\nsucceeding writers, has not made them cease to be discoveries: and\naccordingly, those who have taken the most prominent share in such a\nconversion, have been the most ardent admirers of Newton's genius and\ngood fortune.\n\nSo much for Newton's comparison of the Forces in different circular\norbits, and for Hegel's power of understanding and criticising it. Now\nlet us look at the motion in different parts of the same elliptical\norbit, as a further illustration of the value of Hegel's criticism. In\nan elliptical orbit the velocity alternately increases and diminishes.\nThis follows necessarily from Kepler's law of the equal description\nof the areas, and so Newton explains it. Hegel, however, treats of\nthis acceleration and retardation as a separate fact, and talks of\nanother explanation of it, founded upon Centripetal and Centrifugal\nForce (_o_). Where he finds this explanation, I know not; certainly\nnot in Newton, who in the second and third section of the _Principia_\nexplains the variation of the velocity in a quite different manner, as\nI have said; and nowhere, I think, employs centrifugal force in his\nexplanations. However, the notion of centrifugal as acting along with\ncentripetal force is introduced in some treatises, and may undoubtedly\nbe used with perfect truth and propriety. How far Hegel can judge\nwhen it is so used, we may see from what he says of the confusion\nproduced by such an explanation, which is, he says, a maximum. In the\nfirst place, he speaks of the motion being _uniformly_ accelerated and\nretarded in an elliptical orbit, which, in any exact use of the word\n_uniformly_, it is not. But passing by this, he proceeds to criticise\nan explanation, not of the variable velocity of the body in its orbit,\nbut of the alternate access and recess of the body to and from the\ncenter. Let us overlook this confusion also, and see what is the value\nof his criticism on the explanation. He says (_p_), \"according to\nthis explanation, in the motion of a planet from the aphelion to the\nperihelion, the centrifugal is less than the centripetal force; and\nin the perihelion itself the centripetal force is supposed suddenly\nto become greater than the centrifugal;\" and so, of course, the body\nre-ascends to the aphelion.\n\nNow I will not say that this explanation has never been given in a book\nprofessing to be scientific; but I have never seen it given; and it\nnever can have been given but by a very ignorant and foolish person.\nIt goes upon the utterly unmechanical supposition that the approach\nof a body to the center at any moment depends solely upon the excess\nof the centripetal over the centrifugal force; and reversely. But the\nmost elementary knowledge of mechanics shows us that when a body is\nmoving _obliquely_ to the distance from the center, it approaches to\nor recedes from the center in virtue of this obliquity, even if no\nforce at all act. And the total approach to the center is the approach\ndue to this cause, _plus_ the approach due to the centripetal force,\n_minus_ the recess due to the centrifugal force. At the aphelion, the\ncentripetal is greater than the centrifugal force; and _hence_ the\nmotion becomes oblique; and _then_, the body approaches to the center\non _both_ accounts, and approaches on account of the obliquity of the\npath even when the centrifugal has become greater than the centripetal\nforce, which it becomes before the body reaches the perihelion. This\nreasoning is so elementary, that when a person who cannot see this,\nwrites on the subject with an air of authority, I do not see what can\nbe done but to point out the oversight and leave it.\n\nBut there is, says Hegel (_q_), another way of explaining the motion\nby means of centripetal and centrifugal forces. The two forces are\nsupposed to increase and decrease gradually, according to different\nlaws. In this case, there must be a point where they are equal, and in\nequilibrio; and this being the case, they will always continue equal,\nfor there will be no reason for their going out of equilibrium.\n\nThis, which is put as _another_ mode of explanation, is, in fact, the\nsame mode; for, as I have already said, the centrifugal force, which is\nless than the centripetal at the aphelion, becomes the greater of the\ntwo before the perihelion; and there is an intermediate position, at\nwhich the two forces are equal. But at this point, is there no reason\nwhy, being equal, the forces should become unequal? Reason abundant:\nfor the body, being there, moves in a line oblique to the distance, and\nso changes its distance; and the centripetal and centrifugal force,\ndepending upon the distance by different laws, they forthwith become\nunequal.\n\nBut these modes of explanation, by means of the centripetal and\ncentrifugal forces and their relation, are not necessary to Newton's\ndoctrine, and are nowhere used by Newton; and undoubtedly much\nconfusion has been produced in other minds, as well as Hegel's,\nby speaking of the centrifugal force, which is a mere intrinsic\ngeometrical result of a body's curvilinear motion round a center, in\nconjunction with centripetal force, which is an extrinsic force, acting\nupon the body and urging it to the center. Neither Newton, nor any\nintelligent Newtonian, ever spoke of the centripetal and centrifugal\nforce as two distinct forces both extrinsic to the motion, which Hegel\naccuses them of doing. (_n_)\n\nI have spoken of the third and second of Kepler's laws; of Newton's\nexplanations of them, and of Hegel's criticism. Let us now, in the same\nmanner, consider the first law, that the planets move in ellipses.\nNewton's proof that this was the result of a central force varying\ninversely as the square of the distance, was the solution of a problem\nat which his contemporaries had laboured in vain, and is commonly\nlooked upon as an important step. \"But,\" says Hegel, (_d_) \"the proof\ngives a conic section generally, whereas the main point which ought\nto be proved is, that the path of the body is an ellipse only, not a\ncircle or any other conic section.\" Certainly if Newton _had_ proved\nthat a planet cannot move in a circle, (which Hegel says he ought to\nhave done), his system would have perplexed astronomers, since there\nare planets which move in orbits hardly distinguishable from circles,\nand the variation of the extremity from planet to planet shows that\nthere is nothing to prevent the excentricity vanishing and the orbit\nbecoming a circle.\n\n\"But,\" says Hegel again, (_e_) \"the conditions which make the path to\nbe an ellipse rather than any other conic section, are empirical and\nextraneous;--the supposed casual strength of the impulsion originally\nreceived.\" Certainly the circumstances which determine the amount\nof excentricity of a planet's orbit are derived from experience, or\nrather, observation. It is not a part of Newton's system to determine\n_\u00e0 priori_ what the excentricity of a planet's orbit must be. A system\nthat professes to do this will undoubtedly be one very different\nfrom his. And as our knowledge of the excentricity is derived from\nobservation, it is, in that sense, empirical and casual. The strength\nof the original impulsion is a hypothetical and impartial way of\nexpressing this result of observation. And as we see no reason why the\nexcentricity should be of any certain magnitude, we see none why the\nfraction which expresses the excentricity should not become as large\nas unity, that is, why the orbit should not become a parabola; and\naccordingly, some of the bodies which revolve about the same appear to\nmove in orbits of this form: so little is the motion in an ellipse, as\nHegel says, (_f_) \"the only thing to be proved.\"\n\nBut Hegel himself has offered proof of Kepler's laws, to which,\nconsidering his objections to Newton's proofs, we cannot help turning\nwith some curiosity.\n\nAnd first, let us look at the proof of the Proposition which we have\nbeen considering, that the path of a planet is necessarily an ellipse.\nI will translate Hegel's language as well as I can; but without\nanswering for the correctness of my translation, since it does not\nappear to me to conform to the first condition of translation, of\nbeing intelligible. The translation however, such as it is, may help\nus to form some opinion of the validity and value of Hegel's proofs as\ncompared with Newton's. (_r_)\n\n\"For absolutely uniform motion, the circle is the only path.... The\ncircle is the line returning into itself in which all the radii are\nequal; there is, for it, only one determining quantity, the radius.\n\n\"But in free motion, the determination according to space and to\ntime come into view with differences. There must be a difference in\nthe spatial aspect in itself, and therefore the form requires two\ndetermining quantities. Hence the form of the path returning into\nitself is an ellipse.\"\n\nNow even if we could regard this as reasoning, the conclusion does\nnot in the smallest degree follow. A curve returning into itself and\ndetermined by two quantities, may have innumerable forms besides the\nellipse; for instance, any _oval_ form whatever, besides that of the\nconic section.\n\nBut why must the curve be a curve returning into itself? Hegel has\nprofessed to prove this previously (_m_) from \"the determination of\nparticularity and individuality of the bodies in general, so that\nthey have partly a center in themselves, and partly at the same time\ntheir center in another.\" Without seeking to find any precise meaning\nin this, we may ask whether it proves the impossibility of the orbits\nwith moveable apses, (which do not return into themselves,) such as the\nplanets (affected by perturbations) really do describe, and such as\nwe know that bodies must describe in all cases, except when the force\nvaries exactly as the square of the distance? It appears to do so:\nand it proves this impossibility of known facts at least as much as it\nproves anything.\n\nLet us now look at Hegel's proof of Kepler's second law, that the\nelliptical sectors swept by the radius vector are proportional to the\ntime. It is this: (_s_).\n\n\"In the circle, the arc or angle which is included by the two radii is\nindependent of them. But in the motion [of a planet] as determined by\nthe conception, the distance from the center and the arc run over in a\ncertain time must be compounded in one determination, and must make out\na whole. This whole is the sector, a space of two dimensions. And hence\nthe arc is essentially a Function of the radius vector; and the former\n(the arc) being unequal, brings with it the inequality of the radii.\"\n\nAs was said in the former case, if we could regard this as reasoning,\nit would not prove the conclusion, but only, that the arc is _some\nfunction or other_ of the radii.\n\nHegel indeed offers (_t_) a reason why there must be an arc involved.\nThis arises, he says, from \"the determinateness [of the nature of\nmotion], at one while as time in the root, at another while as space in\nthe square. But here the quadratic character of the space is, by the\nreturning of the line of motion into itself, limited to a sector.\"\n\nProbably my readers have had a sufficient specimen of Hegel's mode of\ndealing with these matters. I will however add his proof of Kepler's\nthird law, that the cubes of the distances are as the squares of the\ntimes.\n\nHegel's proof in this case (_u_) has a reference to a previous doctrine\nconcerning falling bodies, in which time and space have, he says, a\nrelation to each other as root and square. Falling bodies however\nare the case of only _half-free_ motion, and the determination is\nincomplete.\n\n\"But in the case of absolute motion, the domain of _free_ masses, the\ndetermination attains its totality. The time as the root is a mere\nempirical magnitude: but as a component of the developed Totality,\nit is a Totality in itself: it produces itself, and therein has a\nreference to itself. And in this process, Time, being itself the\ndimensionless element, only comes to a formal identity with itself and\nreaches the square: Space, on the other hand, as a positive external\nrelation, comes to the full dimensions of the conception of space,\nthat is, the cube. The Realization of the two conceptions (space and\ntime) preserves their original difference. This is the third Keplerian\nlaw, the relation of the Cubes of the distances to the squares of the\ntimes.\"\n\n\"And this,\" he adds, (_v_) with remarkable complacency, \"represents\nsimply and immediately _the reason of the thing_:--while on the\ncontrary, the Newtonian Formula, by means of which the Law is changed\ninto a Law for the Force of Gravity, shows the distortion and inversion\nof _Reflexion_, which stops half-way.\"\n\nI am not able to assign any precise meaning to the _Reflexion_, which\nis here used as a term of condemnation, applicable especially to the\nNewtonian doctrine. It is repeatedly applied in the same manner by\nHegel. Thus he says, (_g_) \"that what Kepler expresses in a simple and\nsublime manner in the form of Laws of the Celestial Motions, Newton has\nmetamorphosed into the _Reflexion-Form_ of the Force of Gravitation.\"\n\nThough Hegel thus denies Newton all merit with regard to the\nexplanation of Kepler's laws by means of the gravitation of the\nplanets to the sun, he allows that to the Keplerian Laws Newton added\nthe Principle of Perturbations (_k_). This Principle he accepts to a\ncertain extent, transforming the expression of it after his peculiar\nfashion. \"It lies,\" he says, (_l_) \"in this: that matter in general\nassigns a center for itself: the collective bodies of the system\nrecognise a reference to their sun, and all the individual bodies,\naccording to the relative positions into which they are brought by\ntheir motions, form a momentary relation of their gravity towards each\nother.\"\n\nThis must appear to us a very loose and insufficient way of stating the\nPrinciple of Perturbations, but loose as it is, it recognises that the\nPerturbations depend upon the gravity of the planets one to another,\nand to the sun. And if the Perturbations depend upon these forces,\none can hardly suppose that any one who allows this will deny that\nthe primary undisturbed motions depend upon these forces, and must be\nexplained by means of them; yet this is what Hegel denies.\n\nIt is evident, on looking at Hegel's mode of reasoning on such\nsubjects, that his views approach towards those of Aristotle and the\nAristotelians; according to which motions were divided into _natural_\nand _unnatural_;--the _celestial motions_ were circular and uniform in\ntheir nature;--and the like. Perhaps it may be worth while to show how\ncompletely Hegel adheres to these ancient views, by an extract from\nthe additions to the Articles on Celestial Motions, made in the last\nedition of the _Encyclop\u00e6dia_. He says (_w_),\n\n\"The motion of the heavenly bodies is not a being pulled this way\nand that, as is imagined (by the Newtonians). _They go along, as the\nancients said, like blessed gods._ The celestial conformity is not\nsuch a one as has the principle of rest or motion external to itself.\nIt is not right to say because a stone is inert, and the whole earth\nconsists of stones, and the other heavenly bodies are of the same\nnature as the earth, therefore the heavenly bodies are inert. This\nconclusion makes the properties of the whole the same as those of the\npart. Impulse, Pressure, Resistance, Friction, Pulling, and the like,\nare valid only for other than celestial matter.\"\n\nThere can be no doubt that this is a very different doctrine from that\nof Newton.\n\nI will only add to these specimens of Hegel's physics, a specimen of\nthe logic by which he refutes the Newtonian argument which has just\nbeen adduced; namely, that the celestial bodies are matter, and that\nmatter, as we see in terrestrial matter, is inert. He says (_x_),\n\n\"Doubtless both are matter, as a good thought and a bad thought are\nboth thoughts; but the bad one is not therefore good, because it is a\nthought.\"\n\n\nAPPENDIX TO THE MEMOIR ON HEGEL'S CRITICISM OF NEWTON'S PRINCIPIA.\n\nHEGEL. _Encyclop\u00e6dia_ (2nd Ed. 1827), Part XI. p. 250.\n\nC. _Absolute Mechanics._\n\n\u00a7 269.\n\nGravitation is the true and determinate conception of material\nCorporeity, which (Conception) is realized to the Idea (zur Idee).\n_General_ Corporeity is separable essentially into _particular_\nBodies, and connects itself with the Element of _Individuality_ or\nsubjectivity, as apparent (phenomenal) presence in the _Motion_, which\nby this means is immediately a system of _several Bodies_.\n\nUniversal gravitation must, as to itself, be recognised as a profound\nthought, although it was principally as apprehended in the sphere\nof Reflexion that it eminently attracted notice and confidence on\naccount of the quantitative determinations therewith connected, and\nwas supposed to find its confirmation in _Experiments_ (Erfahrung)\npursued from the Solar System down to the phenomena of Capillary\nTubes.--But Gravitation contradicts immediately the Law of Inertia,\nfor in virtue of it (Gravitation) matter tends _out of itself_ to the\nother (matter).--In the _Conception of Weight_, there are, as has been\nshown, involved the two elements--Self-existence, and Continuity,\nwhich takes away self-existence. These elements of the Conception,\nhowever, experience a fate, as particular forces, corresponding to\nAttractive and Repulsive Force, and are thereby apprehended in nearer\ndetermination, as _Centripetal_ and _Centrifugal Force_, which (Forces)\nlike weight, _act upon Bodies_, independent of each other, and are\nsupposed to come in contact accidentally in a third thing, Body. By\nthis means, what there is of profound in the thought of universal\nweight is again reduced to nothing; and Conception and Reason cannot\nmake their way into the doctrine of absolute motion, so long as the\nso highly-prized discoveries of Forces are dominant there. In the\nconclusion which contains the _Idea_ of Weight, namely, [contains\nthis Idea] as the Conception which, in the case of motion, enters\ninto external Reality through the particularity of the Bodies, and\nat the same time into this [Reality] and into their Ideality and\nself-regarding Reflexion, (Reflexion-in-sich), the rational identity\nand inseparability of the elements is involved, which at other times\nare represented as independent. Motion itself, as such, has only its\nmeaning and existence in a system of _several_ bodies, and those,\nsuch as stand in relation to each other according to different\ndeterminations.\n\n\u00a7 270.\n\nAs to what concerns bodies in which the conception of gravity\n(weight) is realized free by itself, we say that they have for the\ndeterminations of their different nature the elements (momente) of\ntheir conception. One [conception of this kind] is the _universal_\ncenter of the abstract reference [of a body] to itself. Opposite\nto this [conception] stands the immediate, extrinsic, centerless\n_Individuality_, appearing as _Corporeity_ similarly independent. Those\n[Bodies] however which are particular, which stand in the determination\nof extrinsic, and at the same time of intrinsic relation, are centers\nfor themselves, and [also] have a reference to the first as to their\nessential unity.\n\n    The Planetary Bodies, as the immediately concrete, are in their\n    existence the most complete. Men are accustomed to take the Sun\n    as the most excellent, inasmuch as the understanding prefers the\n    abstract to the concrete, and in like manner the fixed stars are\n    esteemed higher than the Bodies of the Solar System. Centerless\n    Corporeity, as belonging to externality, naturally separates itself\n    into the opposition of the lunar and the cometary Body. The laws\n    of absolutely free motion, as is well known, were discovered by\n    Kepler;--a discovery of immortal fame. Kepler has proved these\n    laws in this sense, that for the empirical data he found their\n(_a_) general expression. Since then, (_a_) it has become a common way\n    of speaking to say that Newton first found out the proof of these\n    Laws. It has rarely happened that fame has been more unjustly\n    transferred from the first discoverer to another person. On this\n    subject I make the following remarks.\n\n    1. That it is allowed by Mathematicians that the Newtonian\n(_b_) Formul\u00e6 may be derived from the Keplerian Laws. The\n    completely immediate derivation is this: In the third Keplerian\n(_c_) Law, _A_^3/_T_^2 is the constant quantity. This being put\n    as _A.A_^2/_T_^2 and calling, with Newton, _A_/_T_^2 universal\n    Gravitation, his expression of the effect of gravity in the\n    reciprocal ratio of the square of the distances is obvious.\n\n(_d_) 2. That the Newtonian proof of the Proposition that a body\n    subjected to the Law of Gravitation moves about the central body\n    in an _Ellipse_, gives a _Conic Section_ generally, while the\n    main Proposition which ought to be proved is that the fall of\n    such a Body is _not_ a _Circle or any other Conic Section_, but\n    an _Ellipse only_. Moreover, there are objections which may be\n    made against this proof in itself (_Princ. Math._ I. 1. Sect. II.\n(_e_) Prop. 1); and although it is the foundation of the Newtonian\n    Theory, analysis has no longer any need of it. The conditions which\n    in the sequel make the path of the Body to a determinate Conic\n    Section, are referred to an _empirical_ circumstance, namely, a\n    particular position of the Body at a determined moment of time, and\n(_f_) the _casual_ strength of an _impulsion_ which it is supposed\n    to have received originally; so that the circumstance which makes\n    the Curve be an Ellipse, which alone ought to be the thing proved,\n    is extraneous to the Formula.\n\n    3. That the Newtonian Law of the so-called Force of Gravitation is\n    in like manner only proved from experience by Induction.\n\n(_g_) The sum of the difference is this, that what Kepler\n    expressed in a simple and sublime manner in the Form of _Laws_\n    _of the Celestial Motions_, Newton has metamorphosed into the\n    _Reflection-Form_ of the _Force of Gravitation_. If the Newtonian\n    Form has not only its convenience but its necessity in reference\n(_h_) to the analytical method, this is only a difference of the\n    mathematical formul\u00e6; Analysis has long been able to derive the\n    Newtonian expression, and the Propositions therewith connected,\n    out of the Form of the Keplerian Laws; (on this subject I refer\n(_i_) to the elegant exposition in _Franc\u0153ur's Trait\u00e9 El\u00e9m. de\n    M\u00e9canique_, Liv. II. Ch. xi. n. 4.)--The old method of so-called\n    proof is conspicuous as offering to us a tangled web, formed of\n    the _Lines_ of the mere geometrical construction, to which a\n    physical meaning of _independent Forces_ is given; and of empty\n    Reflexion-determinations of the already mentioned _Accelerating\n    Force_ and _Vis Inerti\u00e6_, and especially of the relation of\n    the so-called gravitation itself to the centripetal force and\n    centrifugal force, and so on.\n\n    The remarks which are here made would undoubtedly have need of\n    a further explication to show how well founded they are: in a\n    Compendium, propositions of this kind which do not agree with\n    that which is assumed, can only have the shape of assertions.\n    Indeed, since they contradict such high authorities, they must\n    appear as something worse, as presumptuous assertions. I will not,\n    on this subject, support myself by saying, by the bye, that an\n    interest in these subjects has occupied me for 25 years; but it\n    is more precisely to the purpose to remark, that the distinctions\n    and determinations which Mathematical Analysis introduces,\n    and the course which it must take according to its method, is\n    altogether different from that which a physical reality must\n    have. The Presuppositions, the Course, and the Results, which\n    the Analysis necessarily has and gives, remain quite extraneous\n    to the considerations which determine the physical value and the\n    signification of those determinations and of that course. To this\n    it is that attention should be directed. We have to do with a\n    consciousness relative to the deluging of physical Mechanics with\n    an _inconceivable_ (uns\u00e4glichen) _Metaphysic_, which--contrary to\n    experience and conception--has those mathematical determinations\n    alone for its source.\n\n    It is recognized that what Newton--besides the foundation of the\n    analytical treatment, the development of which, by the bye, has\n    of itself rendered superfluous, or indeed rejected much which\n    belonged to Newton's essential Principles and glory--has added\n    to the Keplerian Laws is the Principle of _Perturbations_,--a\n    Principle whose importance we may here accept thus far (hier in\n(_k_) sofern anzuf\u00fchren ist); namely, so far as it rests upon the\n    Proposition that the so-called attraction is an operation of all\n(_l_) the individual parts of bodies, as being material. It lies\n    in this, that matter in general assigns a center for itself (sich\n    das centrum setzt), and the figure of the body is an element in the\n    determination of its place; that collective bodies of the system\n    recognize a reference to their Sun (sich ihre Sonne setzen), but\n    also the individual bodies themselves, according to the relative\n    position with regard to each other into which they come by their\n    general motion, form a momentary relation of their gravity\n    (schwere) _towards each other_, and are related to each other not\n    only in abstract spatial relations, but at the same time assign to\n    themselves a joint center, which however is again resolved [into\n    the general center] in the universal system.\n\n(_m_) As to what concerns the features of the path, to show how\n    the fundamental determinations of Free Motion are connected _with\n    the Conception_, cannot here be undertaken in a satisfactory and\n    detailed manner, and must therefore be left to its fate. The proof\n    from reason of the quantitative determinations of free motion can\n    only rest upon the _determinations_ of _Conceptions_ of space and\n    time, the elements whose relation (intrinsic not extrinsic) motion\n    is.\n\n    That, _in the first place_, the motion in general is a motion\n    _returning into itself_, is founded on the determination of\n    particularity and individuality of the bodies in general (\u00a7 269),\n    so that partly they have a center in themselves, and partly at the\n    same time their center in another. These are the determinations of\n    Conceptions which form the basis of the false representatives of\n(_n_) Centripetal Force and Centrifugal Force, as if each of these\n    were self-existing, extraneous to the other, and independent of\n    it; and as if they only came in contact in their operations and\n    consequently _externally_. They are, as has already been mentioned,\n    the Lines which must be drawn for the mathematical determinations,\n    transformed into physical realities.\n\n    Further, this motion is _uniformly accelerated_, (and--as returning\n    into itself--in turn uniformly retarded). In motion as _free_,\n    Time and Space enter as _different_ things which are to make\n(_o_) themselves effective in the determination of the motion\n    (\u00a7 266, note). In the so-called _Explanation_ of the uniformly\n    accelerated and retarded motion, by means of the alternate\n    decrease and increase of the magnitude of the Centripetal Force\n    and Centrifugal Force, the _confusion_ which the assumption of\n(_p_) such independent Forces produces is at its greatest height.\n    According to this explanation, in the motion of a Planet from the\n    Aphelion to the Perihelion, the centrifugal is _less_ than the\n    centripetal force, and on the contrary, in the Perihelion itself,\n    the centrifugal force is supposed to become greater than the\n    centripetal. For the motion from the Perihelion to the Aphelion,\n    this representation makes the forces pass into the opposite\n    relation in the same manner. It is apparent that such a sudden\n    conversion of the preponderance which a force has obtained over\n    another, into an inferiority to the other, cannot be anything taken\n    out of the nature of Forces. On the contrary it must be concluded,\n    that a preponderance which one Force has obtained over another\n    must not only be preserved, but must go onwards to the complete\n    annihilation of the other Force, and the motion must either, by\n    the Preponderance of the Centripetal Force, proceed till it ends\n    in rest, that is, in the Collision of the Planet with the Central\n(_q_) Body, or till by the Preponderance of the Centrifugal Force\n    it ends in a straight line. But now, if in place of the suddenness\n    of the conversion, we suppose a gradual increase of the Force in\n    question, then, since rather the other Force ought to be assumed as\n    increasing, we lose the opposition which is assumed for the sake\n    of the explanation; and if the increase of the one is assumed to\n    be different from that of the other, (which is the case in some\n    representations,) then there is found at the mean distance between\n    the apsides a point in which the Forces are _in equilibrio_. And\n    the transition of the Forces out of Equilibrium is a thing just as\n    little without any sufficient reason as the aforesaid suddenness\n    of inversion. And in the whole of this kind of explanation, we see\n    that the mode of remedying a bad mode of dealing with a subject\n    leads to newer and greater confusion.--A similar confusion makes\n    its appearance in the explanation of the ph\u00e6nomenon that the\n    pendulum oscillates more slowly at the equator. This ph\u00e6nomenon is\n    ascribed to the Centrifugal Force, which it is asserted must then\n    be greater; but it is easy to see that we may just as well ascribe\n    it to the augmented gravity, inasmuch as that holds the pendulum\n    more strongly to the perpendicular line of rest.\n\n\n    \u00a7 240.\n\n(_r_) And now first, as to what concerns the _Form of the Path_,\n    the _Circle_ only can be conceived as the path of an _absolutely\n    uniform_ motion. _Conceivable_, as people express it, no doubt it\n    is, that an increasing and diminishing motion should take place in\n    a circle. But this conceivableness or possibility means only an\n    abstract capability of being represented, which leaves out of sight\n    that Determinate Thing on which the question turns.\n\n    The Circle is the line returning into itself in which all the radii\n    are _equal_, that is, it is completely determined by means of the\n    radius. There is only _one_ Determination, and that is the _whole_\n    Determination.\n\n    But in free motion, in which the Determinations according to\n    space and according to time come into view with Differences, in a\n    qualitative relation to each other, this Relation appears in the\n    spatial aspect as a _Difference_ thereof in itself, which therefore\n    requires two Determinations. Hereby the Form of the path returning\n    into itself is essentially an _Ellipse_.\n\n(_s_) The abstract Determinations which produces the circle\n    appears also in this way, that the arc or angle which is included\n    by two Radii is independent of them, a magnitude with regard to\n    them completely empirical. But since in the motion as determined\n    by the Conception, the distance from the center, and the arc\n    which is run over in a certain time, must be comprehended in one\n    determinateness, [_and_] make out a whole, this is the sector, a\n    space-determination of two dimensions: in this way, the arc is\n    essentially a Function of the Radius Vector; and the former (the\n    arc) being unequal, brings with it the inequality of the Radii.\n    That the determination with regard to the space by means of the\n(_t_) time appears as a Determination of two Dimensions,--as a\n    Superficies-Determination,--agrees with what was said before (\u00a7\n    266) respecting Falling Bodies, with regard to the exposition of\n    the same Determinateness, at one while as Time in the root, at\n    another while as Space in the Square. Here, however, the Quadratic\n    character of the space is, by the returning of the Line of motion\n    into itself, limited to a Sector. These are, as may be seen, the\n    general principles on which the Keplerian Law, that in equal times\n    equal sectors are cut off, rests.\n\n    This Law becomes, as is clear, only the relation of the arc to\n    the Radius Vector, and the Time enters there as the abstract\n    Unity, in which the different Sectors are compared, because as\n    Unity it is the Determining Element. But the further relation is\n    that of the Time, not as Unity, but as a Quantity in general,--as\n    the time of Revolution--to the magnitude of the Path, or, what is\n    the same thing, the distance from the center. As Root and Square,\n    we saw that Time and Space had a relation to each other, in the\n    case of Falling Bodies, the case of half-free motion--because\n    that [_motion_] is determined on one side by the conception, on\n(_u_) the other by external [_conditions_]. But in the case of\n    absolute motion--the domain of _free_ masses--the determination\n    attains its Totality. The Time as the Root is a mere empirical\n    magnitude; but as a component (moment) of the developed Totality,\n    it is a Totality in itself,--it produces itself, and therein has\n    a reference to itself; as the Dimensionless Element in itself, it\n    only comes to a formal identity with itself, the Square; Space,\n    on the other hand, as the positive Distribution (aussereinander)\n    [_comes_] to the Dimension of the Conception, _the_ CUBE. Their\n(_v_) Realization preserves their original difference. This is the\n    third Keplerian Law, the relation of the _Cubes_ of the _Distances_\n    to the _Squares_ of the _Times_;--a Law which is so great on this\n    account, that it represents so simply and immediately _Reason\n    as belonging to the thing_: while on the contrary the Newtonian\n    Formula, by means of which the Law is changed into a Law for the\n    Force of Gravity, shows the Distortion, Perversion and Inversion of\n    _Reflexion_ which stops half-way.\n\n    Additions to new Edition. \u00a7 269.\n\n    The center has no sense without the circumference, nor the\n    circumference without the center. This makes all physical\n    hypotheses vanish which sometimes proceed from the center,\n    sometimes from the particular bodies, and sometimes assign this,\n    sometimes that, as the original [cause of motion] ... It is silly\n    (l\u00e4ppisch) to suppose that the centrifugal force, as a tendency to\n    fly off in a Tangent, has been produced by a lateral projection, a\n    projectile force, an impulse which they have retained ever since\n    they set out on their journey (von Haus aus). Such casualty of the\n    motion produced by external causes belongs to inert matter; as when\n    a stone fastened to a thread which is thrown transversely tries to\n    fly from the thread. We are not to talk in this way of Forces. If\n    we will speak of Force, there is one Force, whose elements do not\n(_w_) draw bodies to different sides as if they were two Forces.\n    The motion of the heavenly bodies is not a being pulled this way or\n    that, such as is thus imagined; it is free motion: they go along,\n    as the ancients said, as blessed Gods (sie gehen als selige G\u00f6tter\n    einher). The celestial corporeity is not such a one as has the\n    principle of rest or motion external to itself. Because stone is\n    inert, and all the earth consists of stones, and the other heavenly\n    bodies are of the same nature,--is a conclusion which makes the\n    properties of the whole the same as those of the part. Impulse,\n    Pressure, Resistance, Friction, Pulling, and the like, are valid\n(_x_) only for an existence of matter other than the celestial.\n    Doubtless that which is common to the two is matter, as a good\n    thought and a bad thought are both thoughts; but the bad one is not\n    therefore good, because it is a thought.\n\n\nFOOTNOTES:\n\n[Footnote 353: Cartes. _Princip._ iv. 23.]\n\n[Footnote 354: Jac. Bernoulli, _Nouvelles Pens\u00e9es sur le Syst\u00e8me de M.\nDescartes_, op. t. i. p. 239 (1686).]\n\n[Footnote 355: _De la Cause de la Pesanteur_ (1689), p. 135.]\n\n[Footnote 356: _Journal des Savans_, 1703. M\u00e9m. Acad. Par. 1709.\n\nBulfinger, in 1726 (Acad. Petrop.), conceived that by making a sphere\nrevolve at the same time about two axes at right angles to each other,\nevery particle would describe a great circle; but this is not so.]\n\n[Footnote 357: Acad. Par. 1714, _Hist._ p. 106.]\n\n[Footnote 358: Acad. Par. 1733.]\n\n[Footnote 359: Acad. Sc. 1709. If we abandon the clear principles of\nmechanics, the writer says, \"toute la lumi\u00e8re que nous pouvons avoir\nest \u00e9teinte, et nous voil\u00e0 replong\u00e9s de nouveau dans les anciennes\nt\u00e9n\u00e8bres du Peripatetisme, dont le Ciel nous veuille preserver!\"\n\nIt was also objected to the Newtonian system, that it did not account\nfor the remarkable facts, that all the motions of the primary planets,\nall the motions of the satellites, and all the motions of rotation,\nincluding that of the sun, are in the same direction, and nearly in\nthe same plane; facts which have been urged by Laplace as so strongly\nrecommending the Nebular Hypothesis; and that hypothesis is, in truth,\na hypothesis of vortices respecting the _origin_ of the system of the\nworld.]\n\n[Footnote 360: _Nouvelle Physique C\u00e9leste_, Op. t. iii. p. 163.\n\nThe deviation of the orbits of the planets from the plane of the\nsun's equator was of course a difficulty in the system which supposed\nthat they were carried round by the vortices which the sun's rotation\ncaused, or at least rendered evident. Bernoulli's explanation consists\nin supposing the planets to have a sort of _leeway_ (_d\u00e9rive des\nvaisseaux_) in the stream of the vortex.]\n\n[Footnote 361: See _Hist. Sc. Ideas_, b. iii. c. ix. Art. 7.]\n\n[Footnote 362: See Mill's _Logic_, vol. i. p. 311, 2nd ed.]\n\n[Footnote 363: These letters refer to passages in the Translation\nannexed to this Memoir.]\n\n\nAPPENDIX K.\n\nDEMONSTRATION THAT ALL MATTER IS HEAVY.\n\n(_Cam. Phil. Soc._ FEB. 22, 1841.)\n\n\nThe discussion of the nature of the grounds and proofs of the most\ngeneral propositions which the physical sciences include, belongs\nrather to Metaphysics than to that course of experimental and\nmathematical investigation by which the sciences are formed. But such\ndiscussions seem by no means unfitted to occupy the attention of the\ncultivators of physical science. The ideal, as well as the experimental\nside of our knowledge must be carefully studied and scrutinized,\nin order that its true import may be seen; and this province of\nhuman speculation has been perhaps of late unjustly depreciated and\nneglected by men of science. Yet it can be prosecuted in the most\nadvantageous manner by them only: for no one can speculate securely\nand rightly respecting the nature and proofs of the truths of science\nwithout a steady possession of some large and solid portions of such\ntruths. A man must be a mathematician, a mechanical philosopher, a\nnatural historian, in order that he may philosophize well concerning\nmathematics, and mechanics, and natural history; and the mere\nmetaphysician who without such preparation and fitness sets himself\nto determine the grounds of mathematical or mechanical truths, or the\nprinciples of classification, will be liable to be led into error at\nevery step. He must speculate by means of general terms, which he\nwill not be able to use as instruments of discovering and conveying\nphilosophical truth, because he cannot, in his own mind, habitually and\nfamiliarly, embody their import in special examples.\n\nActing upon such views, I have already laid before the Philosophical\nSociety of Cambridge essays on such subjects as I here refer to;\nespecially a memoir \"On the Nature of the Truth of the Laws of Motion,\"\nwhich was printed by the Society in its Transactions. This memoir\nappears to have excited in other places, notice of such a kind as to\nshow that the minds of many speculative persons are ready for and\ninclined towards the discussion of such questions. I am therefore the\nmore willing to bring under consideration another subject of a kind\nclosely related to the one just mentioned.\n\nThe general questions which all such discussions suggest, are (in\nthe existing phase of English philosophy) whether certain proposed\nscientific truths, (as the laws of motion,) be _necessary_ truths;\nand if they are necessary, (which I have attempted to show that in a\ncertain sense they are,) _on what ground_ their necessity rests. These\nquestions may be discussed in a general form, as I have elsewhere\nattempted to show. But it may be instructive also to follow the general\narguments into the form which they assume in special cases; and to\nexhibit, in a distinct shape, the incongruities into which the opposite\nfalse doctrine leads us, when applied to particular examples. This\naccordingly is what I propose to do in the present memoir, with regard\nto the proposition stated at the head of this paper, namely, that _all\nmatter is heavy_.\n\nAt first sight it may appear a doctrine altogether untenable to assert\nthat this proposition is a necessary truth: for, it may be urged, we\nhave no difficulty in conceiving matter which is not heavy; so that\nmatter without weight is a conception not inconsistent with itself;\nwhich it must be if the reverse were a necessary truth. It may be\nadded, that the possibility of conceiving matter without weight\nwas shown in the controversy which ended in the downfall of the\nphlogiston theory of chemical composition; for some of the reasoners\non this subject asserted phlogiston to be a body with positive levity\ninstead of gravity, which hypothesis, however false, shows that such\na supposition is possible. Again, it may be said that _weight_ and\n_inertia_ are two separate properties of matter: that mathematicians\nmeasure the quantity of matter by the inertia, and that we learn\nby experiment only that the weight is proportional to the inertia;\nNewton's experiments with pendulums of different materials having been\nmade with this very object.\n\nI proceed to reply to these arguments. And first, as to the possibility\nof conceiving matter without weight, and the argument thence\ndeduced, that the universal gravity of matter is not a necessary\ntruth, I remark, that it is indeed just, to say that we cannot even\ndistinctly conceive the contrary of a necessary truth to be true;\nbut that this impossibility can be asserted only of those perfectly\ndistinct conceptions which result from a complete development of\nthe fundamental idea and its consequences. Till we reach this stage\nof development, the obscurity and indistinctness may prevent our\nperceiving absolute contradictions, though they exist. We have abundant\nstore of examples of this, even in geometry and arithmetic; where the\ntruths are universally allowed to be necessary, and where the relations\nwhich are impossible, are also inconceivable, that is, not conceivable\ndistinctly. Such relations, though not distinctly conceivable, still\noften appear conceivable and possible, owing to the indistinctness\nof our ideas. Who, at the first outset of his geometrical studies,\nsees any impossibility in supposing the side and the diagonal of a\nsquare to have a common measure? Yet they can be rigorously proved to\nbe incommensurable, and therefore the attempt distinctly to conceive\na common measure of them must fail. The attempts at the geometrical\nduplication of the cube, and the supposed solutions, (as that of\nHobbes,) have involved absolute contradictions; yet this has not\nprevented their being long and obstinately entertained by men, even of\nminds acute and clear in other respects. And the same might be shewn to\nbe the case in arithmetic. It is plain, therefore, that we cannot, from\nthe supposed possibility of conceiving matter without weight, infer\nthat the contrary may not be a necessary truth.\n\nOur power of judging, from the compatibility or incompatibility of our\nconceptions, whether certain propositions respecting the relations of\nideas are true or not, must depend entirely, as I have said, upon the\ndegree of development which such ideas have undergone in our minds.\nSome of the relations of our conceptions on any subject are evident\nupon the first steady contemplation of the fundamental idea by a sound\nmind: these are the _axioms_ of the subject. Other propositions may be\ndeduced from the axioms by strict logical reasoning. These propositions\nare no less _necessary_ than the axioms, though to common minds their\n_evidence_ is very different. Yet as we become familiar with the steps\nby which these ulterior truths are deduced from the axioms, _their_\ntruth also becomes evident, and the contrary becomes inconceivable.\nWhen a person has familiarized himself with the first twenty-six\npropositions of Euclid, and not till then, it becomes evident to him,\nthat parallelograms on the same base and between the same parallels\nare equal; and he cannot even conceive the contrary. When he has a\nlittle further cultivated his geometrical powers, the equality of the\nsquare on the hypothenuse of a right-angled triangle to the squares on\nthe sides, becomes also evident; the steps by which it is demonstrated\nbeing so familiar to the mind as to be apprehended without a conscious\nact. And thus, the contrary of a necessary truth cannot be distinctly\nconceived; but the incapacity of forming such a conception is a\ncondition which depends upon cultivation, being intimately connected\nwith the power of rapidly and clearly perceiving the connection of the\nnecessary truth under consideration with the elementary principles on\nwhich it depends. And thus, again, it may be that there is an absolute\nimpossibility of conceiving matter without weight; but then, this\nimpossibility may not be apparent, till we have traced our fundamental\nconceptions of matter into some of their consequences.\n\nThe question then occurs, whether we can, by any steps of reasoning,\npoint out an inconsistency in the conception of matter without weight.\nThis I conceive we may do, and this I shall attempt to show.\n\nThe general mode of stating the argument is this:--the quantity of\nmatter is measured by those sensible properties of matter which undergo\nquantitative addition, subtraction and division, as the matter is\nadded, subtracted and divided. The quantity of matter cannot be known\nin any other way. But this mode of measuring the quantity of matter,\nin order to be true at all, must be universally true. If it were only\npartially true, the limits within which it is to be applied would be\narbitrary; and therefore the whole procedure would be arbitrary, and,\nas a method of obtaining philosophical truth, altogether futile.\n\nWe may unfold this argument further. Let the contrary be supposed, of\nthat which we assert to be true: namely, let it be supposed that while\nall other kinds of matter are heavy (and of course heavy in proportion\nto the quantity of matter), there is one kind of matter which is\nabsolutely destitute of weight; as, for instance, phlogiston, or any\nother element. Then where this _weightless_ element (as we may term\nit) is mixed with _weighty_ elements, we shall have a compound, in\nwhich the weight is no longer proportional to the quantity of matter.\nIf, for example, 2 measures of heavy matter unite with one measure\nof phlogiston, the weight is as 2, and the quantity of matter as 3.\nIn all such cases, therefore, the weight ceases to be the measure of\nthe quantity of matter. And as the proportion of the weighty and the\nweightless matter may vary in innumerable degrees in such compounds,\nthe weight affords no criterion at all of the quantity of matter\nin them. And the smallest admixture of the weightless element is\nsufficient to prevent the weight from being taken as the measure of the\nquantity of matter.\n\nBut on this hypothesis, how are we to distinguish such compounds from\nbodies consisting purely of heavy matter? How are we to satisfy\nourselves that there is not, in every body, some admixture, small or\ngreat, of the weightless element? If we call this element _phlogiston_,\nhow shall we know that the bodies with which we have to do are, any of\nthem, absolutely free from phlogiston?\n\nWe cannot refer to the weight for any such assurance; for by\nsupposition the presence and absence of phlogiston makes no difference\nin the weight. Nor can any other properties secure us at least from\na very small admixture; for to assert that a mixture of 1 in 100 or\n1 in 10 of phlogiston would always manifest itself in the properties\nof the body, must be an arbitrary procedure, till we have proved this\nassertion by experiment: and we cannot do this till we have learnt\nsome mode of measuring the quantities of matter in bodies and parts of\nbodies; which is exactly what we question the possibility of, in the\npresent hypothesis.\n\nThus, if we assume the existence of an element, _phlogiston_, devoid of\nweight, we cannot be sure that every body does not contain some portion\nof this element; while we see that if there be an admixture of such\nan element, the weight is no longer any criterion of the quantity of\nmatter. And thus we have proved, that if there be any kind of matter\nwhich is not heavy, the weight can no longer avail us, _in any case or\nto any extent_, as a measure of the quantity of matter.\n\nI may remark, that the same conclusion is easily extended to the case\nin which phlogiston is supposed to have absolute levity; for in that\ncase, a certain mixture of phlogiston and of heavy matter would have\nno weight, and might be substituted for phlogiston in the preceding\nreasoning.\n\nI may remark, also, that the same conclusion would follow by the same\nreasoning, if any kind of matter, instead of being void of weight, were\nheavy, indeed, but not _so_ heavy, in proportion to its quantity of\nmatter, as other kinds.\n\nOn all these hypotheses there would be no possibility of measuring\nquantity of matter by weight at all, in any case, or to any extent.\n\nBut it may be urged, that we have not yet reduced the hypothesis of\nmatter without weight to a contradiction; for that mathematicians\nmeasure quantity of matter, not by weight, but by the other property,\nof which we have spoken, inertia.\n\nTo this I reply, that, practically speaking, quantity of matter is\nalways measured by weight, both by mechanicians and chemists: and as\nwe have proved that this procedure is utterly insecure in all cases,\non the hypothesis of weightless matter, the practice rests upon a\nconviction that the hypothesis is false. And yet the practice is\nuniversal. Every experimenter measures quantity of matter by the\nbalance. No one has ever thought of measuring quantity of matter by\nits inertia practically: no one has constructed a measure of quantity\nof matter in which the matter produces its indications of quantity by\nits motion. When we have to take into account the inertia of a body,\nwe inquire what its weight is, and assume this as the measure of the\ninertia; but we never take the contrary course, and ascertain the\ninertia first in order to determine by that means the weight.\n\nBut it may be asked, Is it not then true, and an important scientific\ntruth, that the _quantity of matter_ is measured by the _inertia_?\nIs it not true, and proved by experiment, that the _weight_ is\n_proportional_ to the _inertia_? If this be not the result of Newton's\nexperiments mentioned above, what, it may be demanded, do they prove?\n\nTo these questions I reply: It is true that quantity of matter is\nmeasured by the inertia, for it is true that inertia is as the quantity\nof matter. This truth is indeed one of the laws of motion. That weight\nis proportional to inertia is proved by experiment, as far as the laws\nof motion are so proved: and Newton's experiments prove one of the laws\nof motion, so far as any experiments can prove them, or are needed to\nprove them.\n\nThat inertia is proportional to weight, is a law equivalent to that\nlaw which asserts, that when pressure produces motion in a given body,\nthe velocity produced in a given time is as the pressure. For if the\nvelocity be as the pressure, when the body is given, the velocity will\nbe constant if the inertia also be as the pressure. For the inertia is\nunderstood to be that property of bodies to which, _ceteris paribus_,\nthe velocity impressed is _inversely_ proportional. One body has\ntwice as much inertia as another, if, when the same force acts upon\nit for the same time, it acquires but half the velocity. This is the\nfundamental conception of _inertia_.\n\nIn Newton's pendulum experiments, the pressure producing motion was\na certain resolved part of the weight, and was proportional to the\nweight. It appeared by the experiments, that whatever were the material\nof which the pendulum was formed, the rate of oscillation was the same;\nthat is, the velocity acquired was the same. Hence the inertia of the\ndifferent bodies must have been in each case as the weight: and thus\nthis assertion is true of all different kinds of bodies.\n\nThus it appears that the assertion, that inertia is universally\nproportional to weight, is equivalent to the law of motion, that the\nvelocity is as the pressure. The conception of inertia (of which,\nas we have said, the fundamental conception is, that the velocity\nimpressed is inversely proportional to the inertia,) connects the two\npropositions so as to make them identical.\n\nHence our argument with regard to the universal gravity of matter\nbrings us to the above law of motion, and is proved by Newton's\nexperiments in the same sense in which that law of motion is so proved.\n\nPerhaps some persons might conceive that the identity of weight\nand inertia is obvious at once; for both are merely resistance\nto motion;--inertia, resistance to all motion (or change of\nmotion)--weight, resistance to motion upwards.\n\nBut there is a difference in these two kinds of resistance to motion.\nInertia is instantaneous, weight is continuous resistance. Any\nmomentary impulse which acts upon a free body overcomes its inertia,\nfor it changes its motion; and this change once effected, the inertia\nopposes any return to the former condition, as well as any additional\nchange. The inertia is thus overcome by a momentary force. But the\nweight can only be overcome by a continuous force like itself. If an\nimpulse act in opposition to the weight, it may for a moment neutralize\nor overcome the weight; but if it be not continued, the weight resumes\nits effect, and restores the condition which existed before the impulse\nacted.\n\nBut weight not only produces rest, when it is resisted, but motion,\nwhen it is not resisted. Weight is measured by the reaction which would\nbalance it; but when unbalanced, it produces motion, and the velocity\nof this motion increases constantly. Now what determines the velocity\nthus produced in a given time, or its rate of increase? What determines\nit to have one magnitude rather than another? To this we must evidently\nreply, _the inertia_. When weight produces motion, the inertia is the\nreaction which makes the motion determinate. The accumulated motion\nproduced by the action of unbalanced weight is as determinate a\ncondition as the equilibrium produced by balanced weight. In both cases\nthe condition of the body acted on is determined by the opposition of\nthe action and reaction.\n\nHence inertia is the reaction which opposes the weight, when\nunbalanced. But by the conception of action and reaction, (as mutually\ndetermining and determined,) they are measured by each other: and hence\nthe inertia is necessarily proportional to the weight.\n\nBut when we have reached this conclusion, the original objection may be\nagain urged against it. It may be said, that there must be some fallacy\nin this reasoning, for it proves a state of things to be necessary when\nwe can so easily conceive a contrary state of things. Is it denied,\nthe opponent may ask, that we can readily imagine a state of things in\nwhich bodies have no weight? Is not the uniform tendency of all bodies\nin the same direction not only not necessary, but not even true? For\nthey do in reality tend, not with equal forces in parallel lines, but\nto a center with unequal forces, according to their position: and we\ncan conceive these differences of intensity and direction in the force\nto be greater than they really are; and can with equal ease suppose the\nforce to disappear altogether.\n\nTo this I reply, that certainly we may conceive the weight of bodies\nto vary in intensity and direction, and by an additional effort of\nimagination, may conceive the weight to vanish: but that in all these\nsuppositions, even in the extreme one, we must suppose the rule to be\nuniversal. If _any_ bodies have weight, _all_ bodies must have weight.\nIf the direction of weight be different in different points, this\ndirection must still vary according to the _law of continuity_; and the\nsame is true of the intensity of the weight. For if this were not so,\nthe rest and motion, the velocity and direction, the permanence and\nchange of bodies, as to their mechanical condition, would be arbitrary\nand incoherent: they would not be subject to mechanical ideas; that\nis, not to ideas at all: and hence these conditions of objects would\nin fact be inconceivable. In order that the universe may be possible,\nthat is, may fall under the conditions of intelligible conceptions, we\nmust be able to conceive a body at rest. But the rest of bodies (except\nin the absolute negation of all force) implies the equilibrium of\nopposite forces. And one of these opposite forces must be a _general_\nforce, as weight, in order that the universe may be governed by general\nconditions. And this general force, by the conception of force, may\nproduce motion, as well as equilibrium; and this motion again must\nbe determined, and determined by general conditions; which cannot\nbe, except the communication of motion be regulated by an inertia\nproportional to the weight.\n\nBut it will be asked, Is it then pretended that Newton's experiment,\nby which it was intended to prove inertia proportional to weight,\ndoes really prove nothing but what may be demonstrated _\u00e0 priori_?\nCould we know, without experiment, that all bodies,--gold, iron, wood,\ncork,--have inertia proportional to their weight? And to this we reply,\nthat experiment holds the same place in the establishment of this, as\nof the other fundamental doctrines of mechanics. Intercourse with the\nexternal world is requisite for developing our ideas; measurement of\nphenomena is needed to fix our conceptions and to render them precise:\nbut the result of our experimental studies is, that we reach a\nposition in which our convictions do not rest upon experiment. We learn\nby observation truths of which we afterwards see the necessity. This is\nthe case with the laws of motion, as I have repeatedly endeavoured to\nshow. The same will appear to be the case with the proposition, that\nbodies of different kinds have their inertia proportional to their\nweight.\n\nFor bodies _of the same kind_ have their inertia proportional to their\nweight, both quantities being proportional to the quantity of matter.\nAnd if we compress the same quantity of matter into half the space,\nneither the weight nor the inertia is altered, because these depend\non the quantity of matter alone. But in this way we obtain a body\nof _twice the density_; and in the same manner we obtain a body of\nany other density. Therefore whatever be the density, the inertia is\nproportional to the quantity of matter. But the mechanical relations\nof bodies cannot depend upon any difference of _kind_, _except_ a\ndifference of density. For if we suppose any fundamental difference of\nmechanical nature in the particles or component elements of bodies, we\nare led to the same conclusion, of arbitrary, and therefore impossible,\nresults, which we deduced from this supposition with regard to weight.\nTherefore all bodies of different density, and hence, all bodies\nwhatever, must have their inertia proportional to their weight.\n\nHence we see, that the propositions, that all bodies are heavy, and\nthat inertia is proportional to weight, necessarily follow from those\nfundamental ideas which we unavoidably employ in all attempts to\nreason concerning the mechanical relations of bodies. This conclusion\nmay perhaps appear the more startling to many, because they have\nbeen accustomed to expect that fundamental ideas and their relations\nshould be self-evident at our first contemplation of them. This,\nhowever, is far from being the case, as I have already shown. It is\nnot the _first_, but the most complete and developed condition of our\nconceptions which enables us to see what are axiomatic truths in each\nprovince of human speculation. Our fundamental ideas are necessary\nconditions of knowledge, universal forms of intuition, inherent types\nof mental development; they may even be termed, if any one chooses,\nresults of connate intellectual tendencies; but we cannot term them\n_innate_ ideas, without calling up a large array of false opinions. For\ninnate ideas were considered as capable of composition, but by no means\nof simplification: as most perfect in their original condition; as to\nbe found, if any where, in the most uneducated and most uncultivated\nminds; as the same in all ages, nations, and stages of intellectual\nculture; as capable of being referred to at once, and made the basis\nof our reasonings, without any special acuteness or effort: in all\nwhich circumstances the Fundamental Ideas of which we have spoken, are\nopposed to Innate Ideas so understood.\n\nI shall not, however, here prosecute this subject. I will only remark,\nthat Fundamental Ideas, as we view them, are not only not innate, in\nany usual or useful sense, but they are not necessarily _ultimate_\nelements of our knowledge. They are the results of our analysis so far\nas we have yet prosecuted it; but they may themselves subsequently\nbe analysed. It may hereafter appear, that what we have treated as\ndifferent Fundamental Ideas have, in fact, a connexion, at some point\nbelow the structure which we erect upon them. For instance, we treat of\nthe mechanical ideas of force, matter, and the like, as distinct from\nthe idea of substance. Yet the principle of measuring the quantity of\nmatter by its weight, which we have deduced from mechanical ideas, is\napplied to determine the substances which enter into the composition\nof bodies. The idea of substance supplies the axiom, that the whole\nquantity of matter of a compound body is equal to the sum of the\nquantities of matter of its elements. The mechanical ideas of force\nand matter lead us to infer that the quantity both of the whole and\nits parts must be measured by their weights. _Substance_ may, for some\npurposes, be described as that to which properties belong; _matter_\nin like manner may be described as that which resists force. The\nformer involves the Idea of permanent Being; the latter, the Idea of\nCausation. There may be some elevated point of view from which these\nideas may be seen to run together. But even if this be so, it will by\nno means affect the validity of reasonings founded upon these notions,\nwhen duly determined and developed. If we once adopt a view of the\nnature of knowledge which makes necessary truth possible at all, we\nneed be little embarrassed by finding how closely connected different\nnecessary truths are; and how often, in exploring towards their roots,\ndifferent branches appear to spring from the same stem.\n\n\nEND OF THE APPENDIX.\n\n\n\n\n  Cambridge:\n  PRINTED BY C. J. CLAY, M.A.\n  AT THE UNIVERSITY PRESS.\n\n\n\n\nWORKS BY\n\nWILLIAM WHEWELL, D.D. F.R.S.\n\nMASTER OF TRINITY COLLEGE, CAMBRIDGE.\n\n\n HISTORY OF THE INDUCTIVE SCIENCES. Third and Cheaper Edition. Three\n Volumes, Small Octavo, 24_s._\n\n HISTORY OF SCIENTIFIC IDEAS, being the First Part of a Third Edition\n of the \"Philosophy of the Inductive Sciences,\" with Additions. Two\n Volumes, 14_s._\n\n NOVUM ORGANON RENOVATUM; being the Second Part of a Third Edition of\n the \"Philosophy of the Inductive Sciences.\" With large Additions. 7_s._\n\n INDICATIONS OF THE CREATOR: Theological Extracts from the \"History and\n the Philosophy of the Inductive Sciences.\" Second Edition. 5_s._ 6_d._\n\n ELEMENTS OF MORALITY, INCLUDING POLITY. Third Edition, with a\n Supplement. Two Volumes, 15_s._\n\n LECTURES ON SYSTEMATIC MORALITY. 7_s._ 6_d._\n\n LECTURES ON THE HISTORY OF MORAL PHILOSOPHY IN ENGLAND. 8_s._\n\n OF A LIBERAL EDUCATION IN GENERAL, and with Particular Reference to\n the Studies of the University of Cambridge. Parts I. and II., in One\n Volume, 7_s._ 6_d._ Part III., sewed, 2_s._\n\n ON THE PRINCIPLES OF ENGLISH UNIVERSITY EDUCATION. Second Edition.\n 5_s._\n\n COLLEGE CHAPEL SERMONS. 10_s._ 6_d._\n\n NOTES ON GERMAN CHURCHES. Third Edition. 12_s._\n\n THE MECHANICAL EUCLID. Fifth Edition. 5_s._\n\n THE MECHANICS OF ENGINEERING. 9_s._\n\n THE DOCTRINE OF LIMITS. Octavo, 9_s._\n\n CONIC SECTIONS. 2_s._ 6_d._\n\n\nEDITED BY DR. WHEWELL.\n\n BUTLER'S THREE SERMONS ON HUMAN NATURE, and a Dissertation on Virtue;\n with a Preface and Syllabus. Third Edition. 3_s._ 6_d._\n\n BUTLER'S SIX SERMONS ON MORAL SUBJECTS. With Preface and Syllabus.\n 3_s._ 6_d._\n\n\n  LONDON: JOHN W. PARKER AND SON, WEST STRAND.\n\n\n\n\nNew Books and New Editions,\n\n_Published by John W. Parker and Son, West Strand._\n\n\n History of England, from the Fall of Wolsey to the Death of Elizabeth.\n Fifth and Sixth Volumes, containing the Reigns of Edward the Sixth and\n Mary. By J. ANTHONY FROUDE. _In the Press._\n\n A Second Edition of the First Four Volumes, containing the Reign of\n Henry VIII. 2_l._ 14_s._\n\n History of England, during the Reign of George the Third. By W.\n MASSEY, M.P. Vols. I. and II. 12_s._ each. The Third Volume _in the\n Press_.\n\n History of Civilization in England. By HENRY THOMAS BUCKLE. The First\n Volume. Octavo. Second Edition. 21_s._\n\n Friends in Council. Second Series. The Second Edition. Two Volumes.\n 14_s._\n\n Friends in Council. First Series. New Edition. Two Volumes. 9_s._\n\n On Liberty. BY JOHN STUART MILL. The Second Edition. 7_s._ 6_d._\n\n The Recreations of a Country Parson; Essays Parochial, Architectural,\n \u00c6sthetical, Moral, Social, and Domestic. Being a Selection from the\n Contributions of A. K. H. B. to \"Fraser's Magazine.\" 9_s._\n\n Major Hodson's Twelve Years of a Soldier's Life in India. Edited\n by his Brother, the Rev. GEORGE H. HODSON, M.A. Fellow of Trinity\n College, Cambridge. Third Edition, with Additions, and a Portrait,\n 10_s._ 6_d._\n\n The Saint's Tragedy. By CHARLES KINGSLEY, Chaplain in Ordinary to the\n Queen. The Third Edition. Foolscap Octavo. 5_s._\n\n On the Classification and Geographical Distribution of Mammalia:\n On the Gorilla, On the Extinction and Transmutation of Species. By\n RICHARD OWEN, F.R.S. Octavo. 5_s._\n\n The Odes of Horace. Translated into English Verse, with a Life and\n Notes. By THEODORE MARTIN. 7_s._ 6_d._\n\n Arundines Cami. Edited by the Rev. HENRY DRURY, M.A. Canon of\n Salisbury, Chaplain to the House of Commons. The Fifth and Cheaper\n Edition.\n\n The New Cratylus. By J. W. DONALDSON, D.D. Classical Examiner in\n the University of London. The Third Edition, Revised throughout and\n considerably Enlarged. 20_s._\n\n Night Lessons from Scripture. Compiled by the Author of 'Amy Herbert.'\n Demy, Red Edges. 3_s._\n\n Paley's Evidences of Christianity. With Annotations by the Archbishop\n of Dublin. Octavo. 9_s._\n\n Paley's Moral Philosophy. With Annotations by the Archbishop of\n Dublin. Octavo. 7_s._\n\n The Good News of God. Sermons by CHARLES KINGSLEY, Chaplain in\n Ordinary to the Queen. The Second Edition. 6_s._\n\n Sermons on the Atonement and other Subjects, preached before the\n University of Cambridge. By E. HAROLD BROWNE, M.A. Norrisian Professor\n of Divinity in the University; Canon of Exeter. Octavo. 5_s._\n\n An Exposition of the Thirty-nine Articles, Historical and Doctrinal.\n By Professor HAROLD BROWNE. Fourth Edition. Octavo, 16_s._\n\n Critical and Grammatical Commentary on St. Paul's Epistle to the\n Ephesians. By CHARLES J. ELLICOTT, B.D. Professor of Divinity, King's\n College, London. The Second Edition, Enlarged. 8_s._ 6_d._\n\nLately Published:\n\n  I. Galatians. Second Edition, Enlarged. 8_s._ 6_d._\n  II. Pastoral Epistles. Second Edition. _In the Press._\n  III. Philippians, Colossians, and Philemon. 10_s._ 6_d._\n  IV. Thessalonians. 7_s._ 6_d._\n\n Peloponnesus: Notes of Study and Travel. By W. G. CLARK, M.A. Fellow\n and Tutor of Trinity College, Cambridge. 10_s._ 6_d._\n\n Revolutions in English History. By ROBERT VAUGHAN, D.D. The First\n Volume, Revolutions of Race. 15_s._\n\n History of the Literature of Ancient Greece. From the Manuscripts of\n the late Professor K. O. M\u00fcller. The first half of the Translation by\n the Right Hon. Sir GEORGE CORNEWALL LEWIS, Bart. M.P. The remainder\n of the Translation, and the Completion of the Work, by JOHN WILLIAM\n DONALDSON, D.D. Three Volumes, Octavo. 36_s._ The new portion\n separately, Two Volumes, 20_s._\n\n Soldiers and their Science. By Captain BRABAZON, R.A. 7_s._\n\n Essays written in the Intervals of Business. The Seventh Edition.\n 2_s._ 6_d._\n\n Companions of My Solitude. The Fifth Edition. 3_s._ 6_d._\n\n\n On the Study of Words. By RICHARD CHENEVIX TRENCH, D.D. Dean of\n Westminster. The Ninth Edition, Revised and Enlarged. 4_s._\n\n A Select Glossary of English Words used formerly in Senses different\n from their Present. By RICHARD CHENEVIX TRENCH, D.D. Dean of\n Westminster. The Second Edition, Revised and Improved. 4_s._\n\n Intellectual Education, and its Influence on the Character and\n Happiness of Women. By EMILY SHIRREFF. Octavo. 10_s._\n\n The Cloister Life of the Emperor Charles the Fifth. By WILLIAM\n STIRLING, M.P. The Third Edition. 8_s._\n\n Man and His Dwelling Place. An Essay towards the Interpretation of\n Nature. 9_s._\n\n Dissertations and Discussions, Political, Philosophical and\n Historical. By JOHN STUART MILL. Two Volumes. Octavo. 24_s._\n\n Of the Plurality of Worlds. An Essay. The Fifth Edition. 6_s._\n\n Bacon's Essays. With Annotations by the Archbishop of Dublin. The\n Fourth Edition. 10_s._ 6_d._\n\n Extracts from Jean Paul Richter. Translated by Lady CHATTERTON. 3_s._\n 6_d._\n\n Shipwrecks of the Royal Navy. By W. O. S. GILLY. With Preface by the\n Rev. Dr. Gilly. The Third Edition. 5_s._\n\n The Kingdom and People of Siam; with a Narrative of the Mission\n to that Country. By Sir JOHN BOWRING, F.R.S. Two Volumes, with\n Illustrations and Map. 32_s._\n\n The Spanish Conquest in America, and its Relation to the History of\n Slavery, and to the Government of Colonies. By ARTHUR HELPS. Octavo.\n Volumes I. II. 28_s._ Volume III. 16_s._\n\n Notes on Hospitals. By FLORENCE NIGHTINGALE. The Second Edition. 5_s._\n\n The Mediterranean; A Memoir Historical, Geographical, and Nautical. By\n Admiral W. H. SMYTH, D.C.L., F.R.S. Octavo. 15_s._\n\n Lectures on Astronomy. By HENRY MOSELEY, M.A., F.R.S. Canon of\n Bristol. The Fourth Edition. 3_s._ 6_d._\n\n Elements of Chemistry. By WILLIAM ALLEN MILLER, M.D., F.R.S. Professor\n of Chemistry, King's College, London. Complete in Three Parts, with\n numerous Illustrations. \u00a32. 6_s._ 6_d._\n\n Manual of Human Microscopic Anatomy. By ALBERT K\u00d6LLIKER. With 289\n Illustrations. Octavo.\n\n Lectures on the Principles and Practice of Physic. By THOMAS WATSON, M\n D. Physician Extraordinary to the Queen. Fourth Edition, revised. Two\n Volumes. Octavo. 34_s._\n\n Anatomy, Descriptive and Surgical. By HENRY GRAY, F.R.S. Lecturer\n on Anatomy at St. George's Hospital. With 363 large Woodcuts, from\n Original Drawings. Royal Octavo, 782 pages. 28_s._\n\n Practical Geodesy: Chain Surveying, Surveying Instruments, Levelling,\n Trigonometry, and Mining; Maritime, Estate, Parochial, and Railroad\n Surveying. By BUTLER WILLIAMS, C.E. The Third Edition, revised.\n Octavo. 8_s._ 6_d._\n\n\n Manual of Geographical Science. Part the Second, Descriptive\n Geography, containing\n\n Ancient Geography, by the Rev. W. L. BEVAN, M.A. Vicar of Hay, Brecon.\n\n Maritime Discovery and Modern Geography, by the Rev. C. G. NICOLAY,\n F.R.G.S.\n\nWith Copious Index. Octavo. 15_s._\n\nThe First Part, Octavo, 10_s._ 6_d._ contains:\n\n  Mathematical Geography, by M. O'BRIEN, M.A.\n  Physical Geography, by D. T. ANSTED, M.A., F.R.S.\n  Chartography, by J. JACKSON, F.R.S.\n  Geographical Terminology, by Rev. C. G. NICOLAY.\n\n The Institutes of Justinian; with English Introduction, Translation,\n and Notes. By THOMAS C. SANDARS, M.A. late Fellow of Oriel College,\n Oxford. The Second Edition, revised. Octavo. 15_s._\n\n Principles of Political Economy. By JOHN STUART MILL. Fourth Edition.\n Two Volumes. Octavo. 30_s._\n\n The Senses and the Intellect. The Emotions and the Will: completing\n a Systematic Exposition of the Human Mind. By ALEXANDER BAIN, M.A.,\n Examiner in Logic and Moral Philosophy in the University of London.\n Octavo. 15_s._ each.\n\n Babrii Fabul\u00e6 \u00c6sope\u00e6, e Codice Manuscripto Partem Secundam nunc primum\n edidit GEORGIUS CORNEWALL LEWIS, A.M., \u00c6dis Christi, in Universitate\n Oxoniensi, Alumnus Honorarius. 3_s._ 6_d._\n\n Babrii Fabul\u00e6 \u00c6sope\u00e6, cum Fabularum deperditarum Fragmentis, recensuit\n et breviter illustravit GEORGIUS CORNEWALL LEWIS, M.A. 5_s._ 6_d._\n\n\n The Choephor\u00e6 of \u00c6schylus; with Notes. By JOHN CONINGTON, M.A.\n Professor of Latin, Oxford. 6_s._\n\n Notes upon Thucydides. By JOHN G. SHEPPARD, M.A. Head Master of\n Kidderminster School, and LEWIS EVANS, M.A. Head Master of Sandbach\n School. Books I. and II. 8_s._\n\n The Ethics of Aristotle. By Sir ALEXANDER GRANT, Bart., M.A. The First\n Volume, the Essays, 8_s._ 6_d._ The Second Volume, Books I.--VI., with\n Notes, 12_s._\n\n The Politics of Aristotle; with Introduction, Essays, Notes, and\n Index. By R. CONGREVE, M.A. 16_s._\n\n Platonis Philebus; with Introduction, and Notes, Critical and\n Explanatory. By CHARLES BADHAM, D.D., Head Master of Birmingham and\n Edgbaston Proprietary School. 5_s._\n\n Ph\u00e6drus, Lysis, and Protagoras of Plato, literally translated. By J.\n WRIGHT, M.A. 4_s._ 6_d._\n\n The Greek Testament; with Notes, Grammatical and Exegetical. By W.\n WEBSTER, M.A., of King's College, London; and W. F. WILKINSON, M.A.,\n Vicar of St. Werburgh, Derby. Volume I., containing the Four Gospels\n and the Acts of the Apostles, 20_s._\n\n Synonyms of the New Testament. By R. CHENEVIX TRENCH, D.D. Dean of\n Westminster. Fourth Edition. 5_s._\n\n Select Private Orations of Demosthenes; with English Notes. By C. T.\n PENROSE, M.A. 4_s._\n\n\n The Frogs of Aristophanes; with English Notes. By Rev. H. P.\n COOKESLEY, M.A. 7_s._\n\n Aristophanes. Edited, with Notes and Index, by H. A. HOLDEN, M.A.,\n Head Master of Ipswich School. 15_s._\n\n \u2042 The Plays separately, 1_s._ each; Notul\u00e6 Critic\u00e6 and Onomasticon.\n 4_s._\n\nGreek Verses of Shrewsbury School; with Account of the Iambic Metre,\nand Exercises in Greek Tragic Senarii. Edited by Dr. KENNEDY, Head\nMaster. 8_s._\n\nAntigone of Sophocles, in Greek and English; with Notes. By Dr.\nDONALDSON. 9_s._\n\nAgamemnon of \u00c6schylus, in Greek and English; with Notes. By J.\nCONINGTON, M.A. 7_s._ 6_d._\n\n\u00c6schylus translated into English Verse; with Notes, Life of \u00c6schylus,\nand Discourse on Greek Tragedy. By J. S. BLACKIE, Professor of Greek,\nEdinburgh. Two Volumes, 46_s._\n\nThe Alcestis of Euripides; with Notes. By J. H. MONK, D.D., Bishop of\nGloucester and Bristol. 4_s._ 6_d._\n\nPindar; with Notes. By Dr. DONALDSON. 16_s._\n\nHomeric Ballads. The Text, with Translation in Verse, and Notes. By Dr.\nMAGINN. 6_s._\n\nM\u00fcller's Dissertations on the Eumenides of \u00c6schylus. Second Edition.\n6_s._ 6_d._\n\nC. Cornelii Taciti Opera ad Codices Antiquissimos commentario critico\nedidit FRANCISCUS RITTER, Professor Bonnensis. Four Volumes, Octavo.\n28_s._\n\nPropertius; with English Notes. By F. A. PALEY, Editor of \"\u00c6schylus.\"\nOctavo. 10_s._ 6_d._\n\nPlautus: Aulularia; with Notes. By J. HILDYARD, B.D. 7_s._ 6_d._\n\nPlautus: Men\u00e6chmei; with Notes. By J. HILDYARD, B.D. 7_s._ 6_d._\n\nLonger Exercises in Latin Prose Composition; with a Commentary and\nRemarks on the best mode of forming a correct Latin Style. By Dr.\nDONALDSON. 6_s._ 6_d._\n\nElements of Logic. By RICHARD WHATELY, Archbishop of Dublin. Crown 8vo.\n4_s._ 6_d._ Octavo. 10_s._ 6_d._\n\nElements of Rhetoric. By ARCHBISHOP WHATELY. Crown 8vo. 4_s._ 6_d._\nOctavo. 10_s._ 6_d._\n\nSystem of Logic, Ratiocinative and Inductive. By JOHN STUART MILL.\nFourth Edition. Two Volumes, Octavo. 25_s._\n\nAn Historical and Explanatory Treatise on the Book of Common Prayer. By\nW. G. HUMPHRY, B.D., late Fellow of Trinity College, Cambridge. Second\nEdition, enlarged. 7_s._ 6_d._\n\nChurchman's Guide: A Copious Index of Sermons and other Works, by\neminent Church of England Divines; digested and arranged according to\ntheir subjects. By J. FORSTER, M.A. Octavo. 7_s._\n\nOn Public Reading: Garrick's Mode of Reading the Liturgy; with Notes,\nand a Discourse on Public Reading. By R. CULL, Tutor in Elocution.\n5_s._ 6_d._\n\nThe Churchman's Theological Dictionary. By ROBERT EDEN, M.A., Chaplain\nto the Bishop of Norwich. Demy 12mo. 5_s._\n\n\n  LONDON: JOHN W. PARKER AND SON, WEST STRAND.\n\nAnnotated Edition of the English Poets,\n\nWITH INTRODUCTIONS, NOTES, AND MEMOIRS,\n\nHistorical, Biographical and Critical,\n\nBY ROBERT BELL.\n\nIN VOLUMES, 2s. 6d. EACH, BOUND IN CLOTH.\n\n\n ANCIENT POEMS, BALLADS, AND SONGS OF THE PEASANTRY. 2_s._ 6_d._\n\n GREENE AND MARLOWE. 2_s._ 6_d._\n\n EARLY BALLADS ILLUSTRATIVE OF HISTORY, TRADITIONS, AND CUSTOMS. 2_s._\n 6_d._\n\n BEN JONSON. 2_s._ 6_d._\n\n CHAUCER. Eight Volumes, 20_s._\n\n BUTLER. Three Volumes, 7_s._ 6_d._\n\n THOMSON. Two Volumes, 5_s._\n\n DRYDEN. Three Volumes, 7_s._ 6_d._\n\n SHAKSPEARE. 2_s._ 6_d._\n\n COWPER. Three Volumes. 7_s._ 6_d._\n\n SURREY, MINOR CONTEMPORANEOUS POETS, AND BUCKHURST. 2_s._ 6_d._\n\n SONGS FROM THE DRAMATISTS; from the first regular Comedy to the close\n of the 18th Century. 2_s._ 6_d._\n\n WYATT. 2_s._ 6_d._\n\n OLDHAM. 2_s._ 6_d._\n\n WALLER. 2_s._ 6_d._\n\n\n  LONDON: JOHN W. PARKER AND SON, WEST STRAND.\n\n       *       *       *       *       *\n\nTranscriber's Notes\n\nObvious typographical errors have been silently corrected. Other\nvariations in spelling, punctuation and hyphenation remain unchanged.\n\nIn the Table of Contents Chap. XV. item 3. is not listed.\n\nIn the Table of Contents Chap. XXVIII.  item 5.\nItalics are represented thus _italics_.\n\nThe identification of the appendices skips I and J.","title":"On the Philosophy of Discovery, Chapters Historical and Critical","tradition":"philosophy-ethics","translated_text":null,"word_count":192088}