{"collection":"philosophy-ethics","full_text_available":true,"graph_url":"https://unchartedknowledge.5gfusion.net/v2/api/page/gutenberg_65274/graph","html_url":"https://unchartedknowledge.5gfusion.net/v2/page/gutenberg_65274","id":"gutenberg_65274","license":"Public Domain (US)","rights_basis":"gutenberg_metadata_copyright_false","source":"gutenberg","source_url":"https://www.gutenberg.org/ebooks/65274","summary":null,"tags":["Category: Essays, Letters & Speeches","Category: Philosophy & Ethics","Metaphysics","Peirce, Charles S. (Charles Sanders), 1839-1914 -- Bibliography","Pragmatism","Science -- Philosophy"],"text":"Chance, Love, and Logic\n\n\n\n\n                  International Library of Psychology\n\n                    Philosophy and Scientific Method\n\n\n                        Chance, Love, and Logic\n\n\n\n\nInternational Library of Psychology\n\nPhilosophy and Scientific Method\n\nGENERAL EDITOR: C. K. OGDEN, M.A.\n\n\n_VOLUMES ALREADY PUBLISHED_\n\n    PHILOSOPHICAL STUDIES, _by_ G. E. MOORE, Litt.D.\n\n    THE MISUSE OF MIND, _by_ KARIN STEPHEN. _Prefatory note by Henri\n    Bergson_\n\n    CONFLICT AND DREAM, _by_ W. H. R. RIVERS, F.R.S.\n\n    PSYCHOLOGY AND POLITICS, _by_ W. H. R. RIVERS, F.R.S.\n\n    TRACTATUS LOGICO-PHILOSOPHICUS, _by_ L. WITTGENSTEIN. _Introduction\n    by Bertrand Russell_\n\n    THE MEASUREMENT OF EMOTION, _by_ W. WHATELY SMITH. _Introduction by\n    William Brown_\n\n    PSYCHOLOGICAL TYPES, _by_ C. G. JUNG, M.D., LL.D.\n\n    SCIENTIFIC THOUGHT, _by_ C. D. BROAD, Litt.D.\n\n    THE MEANING OF MEANING, _by_ C. K. OGDEN _and_ I. A. RICHARDS\n\n    CHARACTER AND THE UNCONSCIOUS, _by_ J. H. VAN DER HOOP\n\n\nIN PREPARATION\n\n    SCIENTIFIC METHOD, _by_ A. D. RITCHIE\n\n    THE ANALYSIS OF MATTER, _by_ BERTRAND RUSSELL, F.R.S.\n\n    PSYCHOLOGY AND ETHNOLOGY, _by_ W. H. R. RIVERS, F.R.S.\n\n    INDIVIDUAL PSYCHOLOGY, _by_ ALFRED ADLER\n\n    MATHEMATICS FOR PHILOSOPHERS, _by_ G. H. HARDY, F.R.S.\n\n    THE PSYCHOLOGY OF MYTHS, _by_ G. ELLIOT SMITH, F.R.S.\n\n    THE PHILOSOPHY OF THE UNCONSCIOUS _by_ E. VON HARTMANN.\n    _Introduction by Prof. G. Elliot Smith_\n\n    THE THEORY OF MEDICAL DIAGNOSIS, _by_ F. G. CROOKSHANK, M.D.,\n    F.R.C.P.\n\n    THE ELEMENTS OF PSYCHOTHERAPY, _by_ WILLIAM BROWN, M.D., D.Sc.\n\n    EMOTION AND INSANITY, _by_ S. THALBITZER. _Introduction by Prof. H.\n    H\u00f6ffding_\n\n    THE LAWS OF FEELING, _by_ F. PAULHAN\n\n    THE PSYCHOLOGY OF MUSIC, _by_ EDWARD J. DENT\n\n    COLOUR-HARMONY, _by_ JAMES WOOD\n\n    THE DEVELOPMENT OF CHINESE THOUGHT, _by_ LIANG CHE CHIAO\n\n    THE HISTORY OF MATERIALISM, _by_ F. A. LANGE\n\n    PSYCHE, _by_ E. ROHDE\n\n    THE PRIMITIVE MIND, _by_ P. RADIN, Ph.D.\n\n    THE PSYCHOLOGY OF PRIMITIVE PEOPLES, _by_ B. MALINOWSKI, Ph.D.,\n    D.Sc.\n\n    THE STATISTICAL METHOD IN ECONOMICS, _by_ P. SARGANT FLORENCE\n\n    THE PRINCIPLES OF CRITICISM, _by_ I. A. RICHARDS\n\n    THE PHILOSOPHY OF \u2018AS IF\u2019 _by_ H. VAIHINGER\n\n\n\n\n                        CHANCE, LOVE, AND LOGIC\n\n                          PHILOSOPHICAL ESSAYS\n\n                              BY THE LATE\n                           CHARLES S. PEIRCE\n                       THE FOUNDER OF PRAGMATISM\n\n                      EDITED WITH AN INTRODUCTION\n                                   BY\n                            MORRIS R. COHEN\n\n                     WITH A SUPPLEMENTARY ESSAY ON\n                        THE PRAGMATISM OF PEIRCE\n\n                                   BY\n                               JOHN DEWEY\n\n                                NEW YORK\n                    HARCOURT, BRACE & COMPANY, INC.\n             LONDON: KEGAN PAUL TRENCH, TRUBNER & CO., LTD.\n                                  1923\n\n\n\n\n                          COPYRIGHT, 1923, BY\n                   HARCOURT, BRACE AND COMPANY, INC.\n\n\n                         PRINTED IN THE U.S.A.\n\n\n\n\n                                PREFACE\n\n\nIn the essays gathered together in this volume we have the most\ndeveloped and coherent available account of the philosophy of Charles S.\nPeirce, whom James, Royce, Dewey, and leading thinkers in England,\nFrance, Germany and Italy have placed in the forefront of the great\nseminal minds of recent times. Besides their inherent value as the\nexpression of a highly original and fruitful mind, unusually well\ntrained and informed in the exact sciences, these essays are also\nimportant as giving us the sources of a great deal of contemporary\nAmerican philosophy. Because of this historical importance no omissions\nor changes have been made in the text beyond the correction of some\nobvious slips and the recasting of a few expressions in the interest of\nintelligibility.\n\nIn a subject which bristles with suggestions and difficulties the\ntemptation to add notes of explanation or dissent is almost insuperable.\nBut as such notes might easily have doubled the size of this volume I\nhave refrained from all comment on the text except in a few footnotes\n(indicated, as usual, in brackets). The introduction is intended (and I\nhope it will) help the reader to concatenate the various lines of\nthought contained in these essays. I cannot pretend to have adequately\nindicated their significance. Great minds like those of James and Royce\nhave been nourished by these writings and I am persuaded that they still\noffer mines of fruitful suggestion. Prof. Dewey\u2019s supplementary essay\nindicates their value for the fundamental question of metaphysics, viz.\nthe nature of reality.\n\nGrateful acknowledgment is here made to Mrs. Paul Carus and to the Open\nCourt Publishing Co. for permission to reprint the essays of Part II\nfrom the _Monist_. The late Paul Carus was one of the very few who not\nonly gave Peirce an opportunity to publish, but publicly recognized the\nimportance of his writings.\n\nI must also acknowledge my obligation to Professor Dewey for kind\npermission to reprint his essay on the Pragmatism of Peirce from the\nJournal of Philosophy, and to the editors of that Journal, Professors\nWoodbridge and Bush, for permission to reprint some material of my own.\nPart V of the Bibliography was compiled by Mr. Irving Smith.\n\nMORRIS R. COHEN\n\nTHE COLLEGE OF THE CITY OF NEW YORK.\n\n\n\n\n                           TABLE OF CONTENTS\n\n\nINTRODUCTION vii\n\nPROEM. THE RULES OF PHILOSOPHY 1\n\nPART I. CHANCE AND LOGIC (Illustrations of the Logic of Science.)\n\n1. The Fixation of Belief 7\n\n2. How to Make Our Ideas Clear 32\n\n3. The Doctrine of Chances 61\n\n4. The Probability of Induction 82\n\n5. The Order of Nature 106\n\n6. Deduction, Induction and Hypothesis 131\n\n\nPART II. LOVE AND CHANCE\n\n1. The Architecture of Theories 157\n\n2. The Doctrine of Necessity Examined 179\n\n3. The Law of Mind 202\n\n4. Man\u2019s Glassy Essence 238\n\n5. Evolutionary Love 267\n\n\nSUPPLEMENTARY ESSAY\u2014The Pragmatism of Peirce, by John Dewey 301\n\n\n\n\n                              INTRODUCTION\n\n\nMany and diverse are the minds that form the philosophic community.\nThere are, first and foremost, the great masters, the system builders\nwho rear their stately palaces towering to the moon. These architectonic\nminds are served by a varied host of followers and auxiliaries. Some\nprovide the furnishings to make these mystic mansions of the mind more\ncommodious, while others are engaged in making their fa\u00e7ades more\nimposing. Some are busy strengthening weak places or building\nmuch-needed additions, while many more are engaged in defending these\nstructures against the impetuous army of critics who are ever eager and\nready to pounce down upon and destroy all that is new or bears the\nmortal mark of human imperfection. There are also the philologists,\nthose who are in a more narrow sense scholars, who dig not only for\nfacts or roots, but also for the stones which may serve either for\nbuilding or as weapons of destruction. Remote from all these, however,\nare the intellectual rovers who, in their search for new fields, venture\ninto the thick jungle that surrounds the little patch of cultivated\nscience. They are not gregarious creatures, these lonely pioneers; and\nin their wanderings they often completely lose touch with those who\ntread the beaten paths. Those that return to the community often speak\nstrangely of strange things; and it is not always that they arouse\nsufficient faith for others to follow them and change their trails into\nhigh roads.\n\nFew nowadays question the great value of these pioneer minds; and it is\noften claimed that universities are established to facilitate their\nwork, and to prevent it from being lost. But universities, like other\nwell-managed institutions, can find place only for those who work well\nin harness. The restless, impatient minds, like the socially or\nconventionally unacceptable, are thus kept out, no matter how fruitful\ntheir originality. Charles S. Peirce was certainly one of these restless\npioneer souls with the fatal gift of genuine originality. In his early\npapers, in the _Journal of Speculative Philosophy_, and later, in the\n_Monist_ papers reprinted as Part II of this volume, we get glimpses of\na vast philosophic system on which he was working with an unusual wealth\nof material and apparatus. To a rich imagination and extraordinary\nlearning he added one of the most essential gifts of successful system\nbuilders, the power to coin an apt and striking terminology. But the\nadmitted incompleteness of these preliminary sketches of his philosophic\nsystem is not altogether due to the inherent difficulty of the task and\nto external causes such as neglect and poverty. A certain inner\ninstability or lack of self-mastery is reflected in the outer moral or\nconventional waywardness which, except for a few years at Johns Hopkins,\ncaused him to be excluded from a university career, and thus deprived\nhim of much needed stimulus to ordinary consistency and intelligibility.\nAs the years advanced, bringing little general interest in, or\nrecognition of, the brilliant logical studies of his early years, Peirce\nbecame more and more fragmentary, cryptic, and involved; so that James,\nthe intellectual companion of his youth, later found his lectures on\npragmatism, \u201cflashes of brilliant light relieved against Cimmerian\ndarkness\u201d\u2014a statement not to be entirely discounted by the fact that\nJames had no interest in or aptitude for formal logical or mathematical\nconsiderations.\n\nDespite these limitations, however, Peirce stands out as one of the\ngreat founders of modern scientific logic; and in the realm of general\nphilosophy the development of some of his pregnant ideas has led to the\npragmatism and radical empiricism of James, as well as to the\nmathematical idealism of Royce, and to the anti-nominalism which\ncharacterizes the philosophic movement known as Neo-Realism. At any\nrate, the work of James, Royce, and Russell, as well as that of\nlogicians like Schroeder, brings us of the present generation into a\nbetter position to appreciate the significance of Peirce\u2019s work, than\nwere his contemporaries.\n\n\n                                   I\n\n\nPeirce was by antecedents, training, and occupation a scientist. He was\na son of Benjamin Peirce, the great Harvard mathematician, and his early\nenvironment, together with his training in the Lawrence Scientific\nSchool, justified his favorite claim that he was brought up in a\nlaboratory. He made important contributions not only in mathematical\nlogic but also in photometric astronomy, geodesy, and psychophysics, as\nwell as in philology. For many years Peirce worked on the problems of\ngeodesy, and his contribution to the subject, his researches on the\npendulum, was at once recognized by European investigators in this\nfield. The International Geodetic Congress, to which he was the first\nAmerican representative, gave unusual attention to his paper, and men\nlike Cellerier and Plantamour acknowledged their obligations to him.[1]\n\nThis and other scientific work involving fine measurement, with the\ncorrelative investigations into the theory of probable error, seem to\nhave been a decisive influence in the development of Peirce\u2019s philosophy\nof chance. Philosophers inexperienced in actual scientific measurement\nmay na\u00efvely accept as absolute truth such statements as \u201cevery particle\nof matter attracts every other particle directly as the product of their\nmasses and inversely as the square of the distance,\u201d or \u201cwhen hydrogen\nand oxygen combine to form water the ratio of their weights is 1 : 8.\u201d\nBut to those who are actually engaged in measuring natural phenomena\nwith instruments of precision, nature shows no such absolute constancy\nor simplicity. As every laboratory worker knows, no two observers, and\nno one observer in successive experiments, get absolutely identical\nresults. To the men of the heroic period of science this was no\ndifficulty. They held unquestioningly the Platonic faith that nature was\ncreated on simple geometric lines, and all the minute variations were\nattributable to the fault of the observer or the crudity of his\ninstruments. This heroic faith was, and still is, a most powerful\nstimulus to scientific research and a protection against the incursions\nof supernaturalism. But few would defend it to-day in its explicit form,\nand there is little empirical evidence to show that while the observer\nand his instruments are always varying, the objects which he measures\nnever deviate in the slightest from the simple law. Doubtless, as one\nbecomes more expert in the manipulation of physical instruments, there\nis a noticeable diminution of the range of the personal \u201cerror,\u201d but no\namount of skill and no refinement of our instruments have ever succeeded\nin eliminating irregular, though small, variations. \u201cTry to verify any\nlaw of nature and you will find that the more precise your observations,\nthe more certain they will be to show irregular departure from the\nlaw.\u201d[2] There is certainly nothing in our empirical information to\nprevent us from saying that all the so-called constants of nature are\nmerely instances of variation between limits so near each other that\ntheir differences may be neglected for certain purposes. Moreover, the\napproach to constancy is observed only in mass phenomena, when we are\ndealing with very large numbers of particles; but social statistics also\napproach constant ratios when the numbers are very large. Hence, without\ndenying discrepancies due solely to errors of observation, Peirce\ncontends that \u201cwe must suppose far more minute discrepancies to exist\nowing to the imperfect cogency of the law itself, to a certain swerving\nof the facts from any definite formula.\u201d[3]\n\nIt is usual to associate disbelief in absolute laws of nature with\nsentimental claims for freedom or theological miracles. It is,\ntherefore, well to insist that Peirce\u2019s attack is entirely in the\ninterests of exact logic and a rational account of the physical\nuniverse. As a rigorous logician familiar with the actual procedures by\nwhich our knowledge of the various laws of nature is obtained, he could\nnot admit that experience could prove their claim to absoluteness. All\nthe physical laws actually known, like Boyle\u2019s law or the law of\ngravitation, involve excessive simplification of the phenomenal course\nof events, and thus a large element of empirical inaccuracy. But a more\npositive objection against the traditional assumption of absolute or\ninvariable laws of nature, is the fact that such assumption makes the\nregularities of the universe ultimate, and thus cuts us off from the\npossibility of ever explaining them or how there comes to be as much\nregularity in the universe as there is. But in ordinary affairs, the\noccurrence of any regularity is the very thing to be explained.\nMoreover, modern statistical mechanics and thermodynamics (theory of\ngases, entropy, etc.) suggest that the regularity in the universe is a\nmatter of gradual growth; that the whole of physical nature is a growth\nfrom a chaos of diversity to a maximum of uniformity or entropy. A\nleading physicist of the 19th Century, Boltzmann, has suggested that the\nprocess of the whole physical universe is like that of a continuous\nshaking up of a hap-hazard or chance mixture of things, which thus\ngradually results in a progressively more uniform distribution. Since\nDuns Scotus, students of logic have known that every real entity has its\nindividual character (its _haecceitas_ or _thisness_) which cannot be\nexplained or deduced from that which is uniform. Every explanation, for\nexample, of the moon\u2019s path must take particular existences for granted.\nSuch original or underived individuality and diversity is precisely what\nPeirce means by chance; and from this point of view chance is prior to\nlaw.\n\nAll that is necessary to visualize this is to suppose that there is an\ninfinitesimal tendency in things to acquire habits, a tendency which is\nitself an accidental variation grown habitual. We shall then be on the\nroad to explain the evolution and existence of the limited uniformities\nactually prevailing in the physical world.\n\nA good deal of the foregoing may sound somewhat mythologic. But even if\nit were so it would have the merit of offering a rational alternative to\nthe mechanical mythology according to which all the atoms in the\nuniverse are to-day precisely in the same condition in which they were\non the day of creation, a mythology which is forced to regard all the\nempirical facts of spontaneity and novelty as illusory, or devoid of\nsubstantial truth.\n\nThe doctrine of the primacy of chance naturally suggests the primacy of\nmind. Just as law is a chance habit so is matter inert mind. The\nprincipal law of mind is that ideas literally spread themselves\ncontinuously and become more and more general or inclusive, so that\npeople who form communities of any sort develop general ideas in common.\nWhen this continuous reaching-out of feeling becomes nurturing love,\nsuch, e.g., which parents have for their offspring or thinkers for their\nideas, we have creative evolution.\n\nJames and Royce have called attention to the similarity between Peirce\u2019s\ndoctrine of tychistic-agapism (chance and love) and the creative\nevolution of Bergson. But while both philosophies aim to restore life\nand growth in their account of the nature of things, Peirce\u2019s approach\nseems to me to have marked advantages, owing to its being in closer\ntouch with modern physics. Bergson\u2019s procedure is largely based on the\ncontention that mechanics cannot explain certain empirical facts, such\nas the supposed identity of the vertebrate eye and the eye of the\nscallop. But the fact here is merely one of a certain resemblance of\npattern, which may well be explained by the mechanical principles of\nconvergent evolution. Peirce\u2019s account involves no rejection of the\npossibility of mechanical explanations. Indeed, by carrying chance into\nthe laws of mechanics he is enabled to elaborate a positive and highly\nsuggestive theory of protoplasm to explain the facts of plasticity and\nhabit.[4] Instead of postulating with Spencer and Bergson a continuous\ngrowth of diversity, Peirce allows for growth of habits both in\ndiversity and in uniformity. The Spencerian mechanical philosophy\nreduces all diversity to mere spatial differences. There can be no\nsubstantial novelty; only new forms or combinations can arise in time.\nThe creative evolution of Bergson though intended to support the claims\nof spontaneity is still like the Spencerian in assuming all evolution as\nproceeding from the simple to the complex. Peirce allows for diversity\nand specificity as part of the original character or endowment of\nthings, which in the course of time may increase in some respects and\ndiminish in others. Mind acquires the habit both of taking on, and also\nof laying aside, habits. Evolution may thus lead to homogeneity or\nuniformity as well as to greater heterogeneity.\n\nNot only has Peirce a greater regard than even Bergson for the actual\ndiversity and spontaneity of things, but he is in a much better position\nthan any other modern philosopher to explain the order and coherence of\nthe world. This he effects by uniting the medieval regard for the\nreality of universals with the modern scientific use of the concept of\ncontinuity. The unfortunate war between the pioneers of modern science\nand the adherents of the scholastic doctrine of substantial forms, has\nbeen one of the great misfortunes of human thought, in that it made\nabsolute atomism and nominalism the professed _creed_ of physical\nscience. Now, extreme nominalism, the insistence on the reality of the\nparticular, leaves no room for the genuine reality of law. It leaves, as\nHume had the courage to admit, nothing whereby the present can determine\nthe future; so that anything is as likely to happen as not. From such a\nchaotic world, the _procedure_ of modern natural and mathematical\nscience has saved us by the persistent use of the principle of\ncontinuity; and no one has indicated this more clearly than Peirce who\nwas uniquely qualified to do so by being a close student both of Duns\nScotus and of modern scientific methods.\n\nIt is instructive in this respect to contrast the views of Peirce and\nJames. James, who so generously indicated his indebtedness to Peirce for\nhis pragmatism, was also largely indebted to Peirce for his doctrine of\nradical empiricism.[5] The latter doctrine seeks to rescue the\ncontinuity and fluidity of experience from the traditional British\nempiricism or nominalism, which had resolved everything into a number of\nmutually exclusive mental states. It is curious, however, that while in\nhis psychology James made extensive use of the principle of continuity,\nhe could not free himself from British nominalism in his\nphilosophy\u2014witness the extreme individualism of his social philosophy or\nthe equally extreme anthropomorphism of his religion. Certain of\nPeirce\u2019s suggestions as to the use of continuity in social philosophy\nhave been developed by Royce in his theory of social consciousness and\nthe nature of the community;[6] but much remains to be worked out and we\ncan but repeat Peirce\u2019s own hope: \u201cMay some future student go over this\nground again and have the leisure to give his results to the world.\u201d\n\nIt is well to note, however, that after writing the papers included in\nthis volume Peirce continued to be occupied with the issues here raised.\nThis he most significantly indicated in the articles on logical topics\ncontributed to Baldwin\u2019s Dictionary of Philosophy.[7]\n\nIn these articles it is naturally the logical bearing of the principles\nof tychism (chance), synechism (continuity), and agapism (love) that is\nstressed. To use the Kantian terminology, almost native to Peirce, the\nregulative rather than the constitutive aspect of these principles is\nemphasized. Thus the doctrine of chance is not only what it was for\nJames\u2019 radical empiricism, a release from the blind necessity of a\n\u201cblock universe,\u201d but also a method of keeping open a possible\nexplanation of the genesis of the laws of nature and an interpretation\nof them in accordance with the theorems of probability, so fruitful in\nphysical science as well as in practical life. So the doctrine of love\nis not only a cosmologic one, showing how chance feeling generates order\nor rational diversity through the habit of generality or continuity, but\nit also gives us the meaning of truth in social terms, in showing that\nthe test as to whether any proposition is true postulates an indefinite\nnumber of co-operating investigators. On its logical side the doctrine\nof love (agapism) also recognized the important fact that general ideas\nhave a certain attraction which makes us divine their nature even though\nwe cannot clearly determine their precise meaning before developing\ntheir possible consequences.\n\nOf the doctrine of continuity we are told expressly[8] that \u201csynechism\nis not an ultimate absolute metaphysical doctrine. It is a regulative\nprinciple of logic,\u201d seeking the thread of identity in diverse cases and\navoiding hypotheses that this or that is ultimate and, therefore,\ninexplicable. (Examples of such hypotheses are: the existence of\nabsolutely accurate or uniform laws of nature, the eternity and absolute\nlikeness of all atoms, etc.) To be sure, the synechist cannot deny that\nthere is an element of the inexplicable or ultimate, since it is\ndirectly forced upon him. But he cannot regard it as a source of\nexplanation. The assumption of an inexplicability is a barrier on the\nroad to science. \u201cThe form under which alone anything can be understood\nis the form of generality which is the same thing as continuity.\u201d[9]\nThis insistence on the generality of intelligible form is perfectly\nconsistent with due emphases on the reality of the individual, which to\na Scotist realist connotes an element of will or will-resistence, but in\nlogical procedure means that the test of the truth or falsity of any\nproposition refers us to particular perceptions.[10] But as no multitude\nof individuals can exhaust the meaning of a continuum, which includes\nalso organizing relations of order, the full meaning of a concept cannot\nbe in any individual reaction, but is rather to be sought in the manner\nin which all such reactions contribute to the development of the\nconcrete reasonableness of the whole evolutionary process. In scientific\nprocedure this means that integrity of belief in general is more\nimportant than, because it is the condition of, particular true beliefs.\n\n\n                                   II\n\n\nThis insistence on the continuity so effectually used as a heuristic\nprinciple in natural and mathematical science, distinguishes the\npragmatism of Peirce from that of his follower James. Prof. Dewey has\ndeveloped this point authoritatively in the supplementary essay; but in\nview of the general ignorance as to the sources of pragmatism which\nprevails in this incurious age, some remarks on the actual historical\norigin of pragmatism may be in order.\n\nThere can be little doubt that Peirce was led to the formulation of the\nprinciple of pragmatism through the influence of Chauncey Wright.[11]\nWright who had first hand acquaintance with creative scientific work in\nmathematics, physics, and botany was led by the study of Mill and Bain\nto reflect on the characteristics of scientific method. This reflection\nled him to draw a distinction between the use of popular scientific\nmaterial, by men like Spencer, to construct a myth or picture of the\nworld, and the scientific use of laws by men like Newton as means for\nextending our knowledge of phenomena. Gravitation as a general fact had\ninterested metaphysicians long before Newton. What made Newton\u2019s\ncontribution scientific was the formulation of a mathematical law which\nhas enabled us to deduce all the then known facts of the solar system\nand to anticipate or predict many more facts the existence of which\nwould not otherwise be even suspected, e.g., the existence of the planet\nNeptune. Wright insists, therefore, that the principles of modern\nmathematical and physical science are the means through which nature is\ndiscovered, that scientific laws are the finders rather than merely the\nsummaries of factual truths. This conception of the experimental\nscientist as translating general propositions into prescriptions for\nattaining new experimental truths, is the starting point of Peirce\u2019s\npragmatism. The latter is embodied in the principle that the meaning of\na concept is to be found in \u201call the conceivable experimental phenomena\nwhich the affirmation or denial of the concept could imply.\u201d[12]\n\nIn the earlier statement of the pragmatic maxim,[13] Peirce emphasized\nthe consequences for conduct that follow from the acceptance or\nrejection of an idea; but the stoical maxim that the end of man is\naction did not appeal to him as much at sixty as it did at thirty.[14]\nNaturally also Peirce could not follow the development of pragmatism by\nWm. James who, like almost all modern psychologists, was a thorough\nnominalist and always emphasized particular sensible experience.[15] It\nseemed to Peirce that such emphasis on particular experiences endangered\nthe principle of continuity which in the hands of men like Weierstrass\nhad reformed modern mathematics. For this reason he began to call his\nown doctrine pragmaticism, a sufficiently unattractive name, he thought,\nto save it from kidnappers and from popularity. He never, however,\nabandoned the principle of pragmatism, that the meaning of an idea is\nclarified (because constituted) by its conceivable experimental\nconsequences. Indeed, if we want to clarify the meaning of the idea of\npragmatism, let us apply the pragmatic test to it. What will be the\neffect of accepting it? Obviously it will be to develop certain general\nideas or habits of looking at things.\n\nPeirce\u2019s pragmatism has, therefore, a decidedly intellectual cast. The\nmeaning of an idea or proposition is found not by an intuition of it but\nby working out its implications. It admits that thought does not\nconstitute reality. Categories can have no concrete being without action\nor immediate feeling. But thought is none the less an essential\ningredient of reality; thought is \u201cthe melody running through the\nsuccession of our sensations.\u201d Pragmatism, according to Peirce, seeks to\ndefine the rational purport, not the sensuous quality. It is interested\nnot in the effect of our practical occupations or desires on our ideas,\nbut in the function of ideas as guides of action. Whether a man is to\npay damages in a certain lawsuit may depend, in fact, on a term in the\nAristotelian logic such as proximate cause.\n\nIt is of interest to observe that though Peirce is an ardent admirer of\nDarwin\u2019s method, his scientific caution makes him refuse to apply the\nanalogy of biologic natural selection to the realm of ideas, in the\nwholesale and uncritical manner that has lately become fashionable.\nNatural selection may well favor the triumph of views which directly\ninfluence biologic survival. But the pleasure of entertaining congenial\nillusions may overbalance the inconvenience resulting from their\ndeceptive character. Thus rhetorical appeals may long prevail over\nscientific evidence.\n\n\n                                  III\n\n\nPeirce preferred to call himself a logician, and his contributions to\nlogic have so far proved his most generally recognized achievement. For\na right perspective of these contributions we may well begin with the\nobservation that though few branches of philosophy have been cultivated\nas continuously as logic, Kant was able to affirm that the science of\nlogic had made no substantial progress since the time of Aristotle. The\nreason for this is that Aristotle\u2019s logic, the logic of classes, was\nbased on his own scientific procedure as a zoologist, and is still in\nessence a valid method so far as classification is part of all rational\nprocedure. But when we come to describe the mathematical method of\nphysical science, we cannot cast it into the Aristotelian form without\ninvolving ourselves in such complicated artificialities as to reduce\nalmost to nil the value of Aristotle\u2019s logic as an organon. Aristotle\u2019s\nlogic enables us to make a single inference from two premises. But the\nvast multitude of theorems that modern mathematics has derived from a\nfew premises as to the nature of number, shows the need of formulating a\nlogic or theory of inference that shall correspond to the modern, more\ncomplicated, practice as Aristotle\u2019s logic did to simple classificatory\nzoology. To do this effectively would require the highest constructive\nlogical genius, together with an intimate knowledge of the methods of\nthe great variety of modern sciences. This is in the nature of the case\na very rare combination, since great investigators are not as critical\nin examining their own procedure as they are in examining the subject\nmatter which is their primary scientific interest. Hence, when great\ninvestigators like Poincar\u00e9 come to describe their own work, they fall\nback on the uncritical assumptions of the traditional logic which they\nlearned in their school days. Moreover, \u201cFor the last three centuries\nthought has been conducted in laboratories, in the field, or otherwise\nin the face of the facts, while chairs of logic have been filled by men\nwho breathe the air of the seminary.\u201d[16] The great Leibnitz had the\nqualifications, but here, as elsewhere, his worldly occupations left him\nno opportunity except for very fragmentary contributions. It was not\nuntil the middle of the 19th century that two mathematicians, Boole and\nDeMorgan, laid the foundations for a more generalized logic. Boole\ndeveloped a general logical algorithm or calculus, while DeMorgan called\nattention to non-syllogistic inference and especially to the importance\nof the logic of relations. Peirce\u2019s great achievement is to have\nrecognized the possibilities of both and to have generalized and\ndeveloped them into a general theory of scientific inference. The extent\nand thoroughness of his achievement has been obscured by his fragmentary\nway of writing and by a rather unwieldy symbolism. Still, modern\nmathematical logic, such as that of Russell\u2019s _Principles of\nMathematics_, is but a development of Peirce\u2019s logic of relatives.\n\nThis phase of Peirce\u2019s work is highly technical and an account of it is\nout of place here. Such an account will be found in Lewis\u2019 _Survey of\nSymbolic Logic_.[17] I refer to it here only to remind the reader that\nthe _Illustrations of the Logic of the Sciences_ (Part I of this volume)\nhave a background of patient detailed work which is still being\ndeveloped to-day.\n\nSymbolic logic has been held in rather low esteem by the followers of\nthe old classical methods in philosophy. Their stated objection to it\nhas been mainly that it is concerned with the minutiae of an artificial\nlanguage and is of no value as a guide to the interpretation of reality.\nNow it should be readily admitted that preoccupation with symbolic logic\nis rather apt to retard the irresponsible flight of philosophic fancy.\nYet this is by no means always an evil. By insisting on an accuracy that\nis painful to those impatient to obtain sweeping and comforting, though\nhasty, conclusions, symbolic logic is well calculated to remove the\ngreat scandal of traditional philosophy\u2014the claim of absolutely certain\nresults in fields where there is the greatest conflict of opinion. This\nscandalous situation arises in part from the fact that in popular\nexposition we do not have to make our premises or assumptions explicit;\nhence all sorts of dubious prejudices are implicitly appealed to as\nabsolutely necessary principles. Also, by the use of popular terms which\nhave a variety of meanings, one easily slides from one meaning to\nanother, so that the most improbable conclusions are thus derived from\nseeming truisms. By making assumptions and rules explicit, and by using\ntechnical terms that do not drag wide penumbras of meaning with them,\nthe method of symbolic logic may cruelly reduce the sweeping pretensions\nof philosophy. But there is no reason for supposing that pretentiousness\nrather than humility is the way to philosophic salvation. Man is bound\nto speculate about the universe beyond the range of his knowledge, but\nhe is not bound to indulge the vanity of setting up such speculations as\nabsolutely certain dogmas.\n\nThere is, however, no reason for denying that greater rigor and accuracy\nof exposition can really help us to discern new truth. Modern\nmathematics since Gauss and Weierstrass has actually been led to greater\nfruitfulness by increased rigor which makes such procedure as the old\nproofs of Taylor\u2019s theorem no longer possible. The substitution of\nrigorous analytic procedures for the old Euclidean proofs based on\nintuition, has opened up vast fields of geometry. Nor has this been\nwithout any effect on philosophy. Where formerly concepts like infinity\nand continuity were objects of gaping awe or the recurrent occasions for\nintellectual violence,[18] we are now beginning to use them, thanks to\nPeirce and Royce, in accurate and definable senses. Consider, for\ninstance, the amount of a priori nonsense which Peirce eliminates by\npointing out that the application of the concept of continuity to a span\nof consciousness removes the necessity for assuming a first or last\nmoment; so likewise the range of vision on a large unobstructed ground\nhas no line between the visible and the invisible. These considerations\nwill be found utterly destructive of the force of the old arguments\n(fundamental to Kant and others) as to the necessary infinity of time\nand space. Similar enlightenment is soon likely to result from the more\ncareful use of terms like relative and absolute, which are bones of\ncontention in philosophy but Ariadne threads of exploration in\ntheoretical physics, because of the definite symbolism of mathematics.\nOther important truths made clear by symbolic logic is the hypothetical\ncharacter of universal propositions and the consequent insight that no\nparticulars can be deduced from universals alone, since no number of\nhypotheses can without given data establish an existing fact.\n\nThere is, however, an even more positive direction in which symbolic\nlogic serves the interest of philosophy, and that is in throwing light\non the nature of symbols and on the relation of meaning. Philosophers\nhave light-heartedly dismissed questions as to the nature of significant\nsigns as \u2018merely\u2019 (most fatal word!) a matter of language. But Peirce in\nthe paper on Man\u2019s Glassy [Shakespearian for Mirror-Like] Essence,\nendeavors to exhibit man\u2019s whole nature as symbolic.[19] This is closely\nconnected with his logical doctrine which regards signs or symbols as\none of the fundamental categories or aspects of the universe (Thoughts\nand things are the other two). Independently of Peirce but in line with\nhis thought another great and neglected thinker, Santayana, has shown\nthat the whole life of man that is bound up with the institutions of\ncivilization, is concerned with symbols.\n\nIt is not altogether accidental that, since Boole and DeMorgan, those\nwho have occupied themselves with symbolic logic have felt called upon\nto deal with the problem of probability. The reason is indicated by\nPeirce when he formulates the problem of probable inference in such a\nway as to make the old classic logic of absolutely true or false\nconclusions, a limiting case (i.e., of values 1 and 0) of the logic of\nprobable inference whose values range all the way between these two\nlimits. This technical device is itself the result of applying the\nprinciple of continuity to throw two hitherto distinct types of\nreasoning into the same class. The result is philosophically\nsignificant.\n\nWhere the classical logic spoke of major and minor premises without\nestablishing any really important difference between the two, Peirce\ndraws a distinction between the premises and the guiding principle of\nour argument. All reasoning is from some concrete situation to another.\nThe propositions which represent the first are the premises in the\nstrict sense of the word. But the feeling that certain conclusions\nfollow from these premises is conditioned by an implicit or explicit\nbelief in some guiding principle which connects the premises and the\nconclusions. When such a leading principle results in true conclusions\nin all cases of true premises, we have logical deduction of the orthodox\ntype. If, however, such a principle brings about a true conclusion only\nin a certain proportion of cases, then we have probability.\n\nThis reduction of probability to the relative frequency of true\npropositions in a class of propositions, was suggested to Peirce by\nVenn\u2019s _Logic of Chance_. Peirce uses it to establish some truths of\ngreatest importance to logic and philosophy.\n\nHe eliminates the difficulties of the old conceptualist view, which made\nprobability a measure of our ignorance and yet had to admit that almost\nall fruitfulness of our practical and scientific reasoning depended on\nthe theorems of probability. How could we safely predict phenomena by\nmeasuring our ignorance?\n\nProbability being reduced to a matter of the relative frequency of a\nclass in a larger class or genus, it becomes, strictly speaking,\ninapplicable to single cases by themselves. A single penny will fall\nhead or it will fall tail every time; to-morrow it will rain, or it will\nnot rain at all. The probability of 1/2 or any other fraction means\nnothing in the single case. It is only because we feel the single event\nas representative of a class, as something which repeats itself, that we\nspeak elliptically of the probability of a single event. Hence follows\nthe important corollary that reasoning with respect to the probability\nof this or that arrangement of the universe would be valid only if\nuniverses were as plentiful as blackberries.\n\nTo be useful at all, theories must be simpler than the complex facts\nwhich they seek to explain. Hence, it is often convenient to employ a\nprinciple of certainty where the facts justify only a principle of some\ndegree of probability. In such cases we must be cautious in accepting\nany extreme consequence of these principles, and also be on guard\nagainst apparent refutations based on such extreme consequences.\n\nFinally I should like to emphasize the value of Peirce\u2019s theory of\ninference for a philosophy of civilization. To the old argument that\nlogic is of no importance because people learn to reason, as to walk, by\ninstinct and habit and not by scientific instruction, Peirce admits[20]\nthat \u201call human knowledge up to the highest flights of science is but\nthe development of our inborn animal instincts.\u201d But though logical\nrules are first felt implicitly, bringing them into explicit\nconsciousness helps the process of analysis and thus makes possible the\nrecognition of old principles in novel situations. This increases our\nrange of adaptability to such an extent as to justify a general\ndistinction between the slave of routine or habit and the freeman who\ncan anticipate and control nature through knowledge of principles.\nPeirce\u2019s analysis of the method of science as a method of attaining\nstability of beliefs by free inquiry inviting all possible doubt, in\ncontrast with the methods of iteration (\u201cwill to believe\u201d) and social\nauthority, is one of the best introductions to a theory of liberal or\nHellenic civilization, as opposed to those of despotic societies.\nAuthority has its roots in the force of habit, but it cannot prevent new\nand unorthodox ideas from arising; and in the effort to defend\nauthoritative social views men are apt to be far more ruthless than in\ndefending their own personal convictions.\n\n\n                                   IV\n\n\nNot only the pragmatism and the radical empiricism of James, but the\nidealism of Royce and the more recent movement of neo-realism are\nlargely indebted to Peirce.\n\nIt may seem strange that the same thinker should be claimed as\nfoster-father of both recent idealism and realism, and some may take it\nas another sign of his lack of consistency. But this seeming strangeness\nis really due to the looseness with which the antithesis between realism\nand idealism has generally been put. If by idealism we denote the\nnominalistic doctrine of Berkeley, then Peirce is clearly not an\nidealist; and his work in logic as a study of types of order (in which\nRoyce followed him) is fundamental for a logical realism. But if\nidealism means the old Platonic doctrine that \u201cideas,\u201d genera, or forms\nare not merely mental but the real conditions of existence, we need not\nwonder that Peirce was both idealist and realist.\n\nRoyce\u2019s indebtedness to Peirce is principally in the use of modern\nmathematical material, such as the recent development of the concepts of\ninfinity and continuity, to throw light on fundamental questions of\nphilosophy, such as relation of the individual to God or the Universe.\nAt the end of the nineteenth century mathematics had almost disappeared\nfrom the repertory of philosophy (cf. K\u00fclpe\u2019s _Introduction to\nPhilosophy_), and Peirce\u2019s essay on the _Law of Mind_ opened a new way\nwhich Royce followed in his _World and the Individual_, to the great\nsurprise of his idealistic brethren. In his _Problem of Christianity_\nRoyce has also indicated his indebtedness to Peirce for his doctrine of\nsocial consciousness, the mind of the community, and the process of\ninterpretation. It may be that a great deal of the similarity between\nthe thoughts of these two men is due to common sources, such as the\nworks of Kant and Schelling; but it is well to note that not only in his\nlater writings but also in his lectures and seminars Royce continually\nreferred to Peirce\u2019s views.\n\nThe ground for the neo-realist movement in American philosophy was\nlargely prepared by the mathematical work of Russell and by the\nutilization of mathematics to which Royce was led by Peirce. The logic\nof Mr. Russell is based, as he himself has pointed out, on a combination\nof the work of Peirce and Peano. In this combination the notation of\nPeano has proved of greater technical fluency, but all of Peano\u2019s\nresults can also be obtained by Peirce\u2019s method as developed by\nSchroeder and Mrs. Ladd-Franklin. But philosophically Peirce\u2019s influence\nis far greater in insisting that logic is not a branch of psychology,\nthat it is not concerned with merely mental processes, but with\nobjective relations. To the view that the laws of logic represent \u201cthe\nnecessities of thought,\u201d that propositions are true because \u201cwe can not\nhelp thinking so,\u201d he answers: \u201cExact logic will say that _C_\u2019s\nfollowing logically from _A_ is a state of things which no impotence of\nthought alone can bring about.\u201d[21] \u201cThe question of validity is purely\none of fact and not of thinking.... It is not in the least the question\nwhether, when the premises are accepted by the mind, we feel an impulse\nto accept the conclusion also. The true conclusion would remain true if\nwe had no impulse to accept it, and the false one would remain false\nthough we could not resist the tendency to believe in it.\u201d[22]\n\nSince the days of Locke modern philosophy has been almost entirely\ndominated by the assumption that one must study the process of knowing\nbefore one can find out the nature of things known; in other words, that\npsychology is _the_ central philosophic science. The result of this has\nbeen an almost complete identification of philosophy with mental\nscience. Nor did the influence of biologic studies of the middle of the\nnineteenth century shake the belief in that banal dictum of philosophic\nmediocrity: \u201cThe proper study of mankind is man.\u201d The recent renaissance\nof logical studies, and the remarkable progress of physics in our own\nday bid fair to remind us that while the Lockian way has brought some\ngains to philosophy, the more ancient way of philosophy is by no means\nexhausted of promise. Man cannot lose his interest in the great cosmic\nplay. Those who have faith in the ancient and fruitful approach to\nphilosophy through the doors of mathematics and physics will find the\nwritings of Charles S. Peirce full of suggestions. That such an approach\ncan also throw light on the vexed problem of knowledge needs no\nassurance to those acquainted with Plato and Aristotle. But I may\nconclude by referring to Peirce\u2019s doctrine of ideal as opposed to\nsensible experiment,[23] and to his treatment of the question how it is\nthat in spite of an infinity of possible hypotheses, mankind has managed\nto make so many successful inductions.[24] And for the bearing of\nmathematical studies on the wisdom of life, the following is certainly\nworth serious reflection: \u201cAll human affairs rest upon probabilities. If\nman were immortal [on earth] he could be perfectly sure of seeing the\nday when everything in which he had trusted should betray his trust. He\nwould break down, at last, as every great fortune, as every dynasty, as\nevery civilization does. In place of this we have death.\u201d The\nrecognition that the death of the individual does not destroy the\nlogical meaning of his utterances, that this meaning involves the ideal\nof an unlimited community, carries us into the heart of pure religion.\n\nFootnote 1:\n\n  See Plantamour\u2019s \u201c_Recherches Experimentales sur le mouvement\n  simultan\u00e9 d\u2019un pendule et de ses supports_,\u201d Geneva, 1878, pp. 3-4.\n\nFootnote 2:\n\n  P. 190.\n\nFootnote 3:\n\n  Pp. 162-163.\n\nFootnote 4:\n\n  Pp. 249 ff.\n\nFootnote 5:\n\n  James, _Pluralistic Universe_, pp. 398-400.\n\nFootnote 6:\n\n  Royce, _Studies in Good and Evil_, and _The Problem of Christianity_,\n  esp. Vol. 2. Baldwin (_Mental Development_) is heavily indebted to\n  Royce in this respect.\n\nFootnote 7:\n\n  These articles are by-products or fragments of a comprehensive work on\n  _Logic_ on which Peirce was engaged for many years. For the writing of\n  this book, Royce declared, no greater mind or greater erudition has\n  appeared in America. Only several chapters seem to have been finished,\n  and will doubtless be included with other hitherto unpublished\n  manuscripts in the complete edition of Peirce\u2019s writings that is now\n  being prepared by Harvard University.\n\nFootnote 8:\n\n  Baldwin\u2019s _Dictionary_, article Synechism.\n\nFootnote 9:\n\n  _Ib._\n\nFootnote 10:\n\n  Baldwin\u2019s _Dictionary_, art. Individual: \u201cEverything whose identity\n  consists in a continuity of reactions will be a single logical\n  individual.\u201d\n\nFootnote 11:\n\n  The personal relations between Peirce and Wright were thus described\n  by Peirce in a letter to Mrs. Ladd-Franklin (_Journal of Philosophy_,\n  Vol. 13, p. 719): \u201cIt must have been about 1857 when I first made the\n  acquaintance of Chauncey Wright, a mind about on the level of J. S.\n  Mill. He was a thorough mathematician. He had a most penetrating\n  intellect.\u2014He and I used to have long and very lively and close\n  disputations lasting two or three hours daily for many years. In the\n  sixties I started a little club called \u2018The Metaphysical Club.\u2019\u2014Wright\n  was the strongest member and probably I was next.\u2014Then there were\n  Frank Abbott, William James and others.\u201d \u201cIt was there that the name\n  and the doctrine of pragmatism saw the light.\u201d It might be added that\n  Peirce\u2019s tychism is indebted to Wright\u2019s doctrine of accidents and\n  \u201ccosmic weather,\u201d a doctrine which maintained against LaPlace that a\n  mind knowing nature from moment to moment is bound to encounter\n  genuine novelty in phenomena, which no amount of knowledge would\n  enable us to foresee. See Wright\u2019s _Philosophical Discussions_\u20141876,\n  also Cambridge _Hist. of American Literature_, Vol. 3, p. 234.\n\nFootnote 12:\n\n  _Monist_, Vol. 15, p. 180.\n\nFootnote 13:\n\n  This volume, pp. 43-45.\n\nFootnote 14:\n\n  \u201cTo say that we live for the sake of action would be to say that there\n  is no such thing as a rational purport.\u201d _Monist_, Vol. XV, p. 175.\n\nFootnote 15:\n\n  The letter to Mrs. Ladd-Franklin quoted before, explains why James,\n  though always loyal to Peirce and anxious to give him credit whenever\n  possible, could not understand the latter\u2019s lectures on pragmatism.\n  Peirce\u2019s incidental judgments on others is worth quoting here:\n\n  \u201cModern psychologists are so soaked with sensationalism that they\n  cannot understand anything that does not mean that. How can I, to whom\n  nothing seems so thoroughly real as generals, and who regards Truth\n  and Justice as _literally_ the most powerful powers in the world,\n  expect to be understood by the thoroughgoing Wundtian? But the curious\n  thing is to see absolute idealists tainted with this disease,\u2014or men\n  who, like John Dewey, hover between Absolute Idealism and\n  Sensationalism. Royce\u2019s opinions as developed in his _World and\n  Individualism_ are extremely near to mine. His insistence on the\n  elements of purpose in intellectual concepts is essentially the\n  pragmatic position.\u201d\n\nFootnote 16:\n\n  Baldwin\u2019s _Dictionary_, art. Method.\n\nFootnote 17:\n\n  \u201cPeirce anticipated the most important procedures of his successors\n  even when he did not work them out himself. Again and again one finds\n  the clue to the most recent developments in the writings of Peirce,\u201d\n  Lewis\u2019 _Survey of Symbolic Logic_, p. 79.\n\nFootnote 18:\n\n  Hans Breitmann is symbolic of those who \u201csolved the infinite as one\n  eternal sphere.\u201d\n\nFootnote 19:\n\n  See _Journal of Speculative Philosophy_, Vol. 2, pp. 155-157, article\n  on A New List of Categories in the Proceedings of the American Academy\n  of Arts and Sciences, Vol. 7, 287-298 and article on _Sign_, in\n  Baldwin\u2019s _Dictionary_.\n\nFootnote 20:\n\n  _Studies in Logic_, p. 181.\n\nFootnote 21:\n\n  _Monist_, Vol. 7, p. 27. _Cf._ _Journal of Speculative Philosophy_,\n  Vol. 2, p. 207; _Popular Science Monthly_, Vol. 58, pp. 305-306.\n\nFootnote 22:\n\n  This vol., p. 15.\n\nFootnote 23:\n\n  Suggestive for a theory of the metaphysics of fictions is the\n  suggestion (p. 46) \u201cthat the question of what would occur under\n  circumstances which do not actually arise, is not a question of fact,\n  but only of the most perspicuous arrangement of them.\u201d This\n  arrangement is, of course, not merely subjective.\n\nFootnote 24:\n\n  Pp. 128-129, _cf._ _Monist_, Vol. 7, p. 206, and _Logical Studies_,\n  pp. 175 ff.\n\n\n\n\n                                 PROEM\n                      THE RULES OF PHILOSOPHY[25]\n\n\nDescartes is the father of modern philosophy, and the spirit of\nCartesianism\u2014that which principally distinguishes it from the\nscholasticism which it displaced\u2014may be compendiously stated as follows:\n\n1. It teaches that philosophy must begin with universal doubt; whereas\nscholasticism had never questioned fundamentals.\n\n2. It teaches that the ultimate test of certainty is to be found in the\nindividual consciousness; whereas scholasticism had rested on the\ntestimony of sages and of the Catholic Church.\n\n3. The multiform argumentation of the middle ages is replaced by a\nsingle thread of inference depending often upon inconspicuous premises.\n\n4. Scholasticism had its mysteries of faith, but undertook to explain\nall created things. But there are many facts which Cartesianism not only\ndoes not explain but renders absolutely inexplicable, unless to say that\n\u201cGod makes them so\u201d is to be regarded as an explanation.\n\nIn some, or all of these respects, most modern philosophers have been,\nin effect, Cartesians. Now without wishing to return to scholasticism,\nit seems to me that modern science and modern logic require us to stand\nupon a very different platform from this.\n\n1. We cannot begin with complete doubt. We must begin with all the\nprejudices which we actually have when we enter upon the study of\nphilosophy. These prejudices are not to be dispelled by a maxim, for\nthey are things which it does not occur to us can be questioned. Hence\nthis initial skepticism will be a mere self-deception, and not real\ndoubt; and no one who follows the Cartesian method will ever be\nsatisfied until he has formally recovered all those beliefs which in\nform he has given up. It is, therefore, as useless a preliminary as\ngoing to the North Pole would be in order to get to Constantinople by\ncoming down regularly upon a meridian. A person may, it is true, in the\ncourse of his studies, find reason to doubt what he began by believing;\nbut in that case he doubts because he has a positive reason for it, and\nnot on account of the Cartesian maxim. Let us not pretend to doubt in\nphilosophy what we do not doubt in our hearts.\n\n2. The same formalism appears in the Cartesian criterion, which amounts\nto this: \u201cWhatever I am clearly convinced of, is true.\u201d If I were really\nconvinced, I should have done with reasoning and should require no test\nof certainty. But then to make single individuals absolute judges of\ntruth is most pernicious. The result is that metaphysics has reached a\npitch of certainty far beyond that of the physical sciences;\u2014only they\ncan agree upon nothing else. In sciences in which men come to agreement,\nwhen a theory has been broached it is considered to be on probation\nuntil this agreement is reached. After it is reached, the question of\ncertainty becomes an idle one, because there is no one left who doubts\nit. We individually cannot reasonably hope to attain the ultimate\nphilosophy which we pursue; we can only seek it, therefore, for the\ncommunity of philosophers. Hence, if disciplined and candid minds\ncarefully examine a theory and refuse to accept it, this ought to create\ndoubts in the mind of the author of the theory himself.\n\n3. Philosophy ought to imitate the successful sciences in its methods,\nso far as to proceed only from tangible premises which can be subjected\nto careful scrutiny, and to trust rather to the multitude and variety of\nits arguments than to the conclusiveness of any one. Its reasoning\nshould not form a chain which is no stronger than its weakest link, but\na cable whose fibers may be ever so slender, provided they are\nsufficiently numerous and intimately connected.\n\n4. Every unidealistic philosophy supposes some absolutely inexplicable,\nunanalyzable ultimate; in short, something resulting from mediation\nitself not susceptible of mediation. Now that anything is thus\ninexplicable, can only be known by reasoning from signs. But the only\njustification of an inference from signs is that the conclusion explains\nthe fact. To suppose the fact absolutely inexplicable, is not to explain\nit, and hence this supposition is never allowable.\n\nFootnote 25:\n\n  From the _Journal of Speculative Philosophy_, vol. 2, p. 140.\n\n\n\n\n                                 PART I\n                            CHANCE AND LOGIC\n                (ILLUSTRATIONS OF THE LOGIC OF SCIENCE)\n\n\n\n\n                            CHANCE AND LOGIC\n                              FIRST PAPER\n                       THE FIXATION OF BELIEF[26]\n\n\n                                   I\n\n\nFew persons care to study logic, because everybody conceives himself to\nbe proficient enough in the art of reasoning already. But I observe that\nthis satisfaction is limited to one\u2019s own ratiocination, and does not\nextend to that of other men.\n\nWe come to the full possession of our power of drawing inferences the\nlast of all our faculties, for it is not so much a natural gift as a\nlong and difficult art. The history of its practice would make a grand\nsubject for a book. The medieval schoolman, following the Romans, made\nlogic the earliest of a boy\u2019s studies after grammar, as being very easy.\nSo it was as they understood it. Its fundamental principle, according to\nthem, was, that all knowledge rests on either authority or reason; but\nthat whatever is deduced by reason depends ultimately on a premise\nderived from authority. Accordingly, as soon as a boy was perfect in the\nsyllogistic procedure, his intellectual kit of tools was held to be\ncomplete.\n\nTo Roger Bacon, that remarkable mind who in the middle of the thirteenth\ncentury was almost a scientific man, the schoolmen\u2019s conception of\nreasoning appeared only an obstacle to truth. He saw that experience\nalone teaches anything\u2014a proposition which to us seems easy to\nunderstand, because a distinct conception of experience has been handed\ndown to us from former generations; which to him also seemed perfectly\nclear, because its difficulties had not yet unfolded themselves. Of all\nkinds of experience, the best, he thought, was interior illumination,\nwhich teaches many things about Nature which the external senses could\nnever discover, such as the transubstantiation of bread.\n\nFour centuries later, the more celebrated Bacon, in the first book of\nhis \u201cNovum Organum,\u201d gave his clear account of experience as something\nwhich must be open to verification and re\u00ebxamination. But, superior as\nLord Bacon\u2019s conception is to earlier notions, a modern reader who is\nnot in awe of his grandiloquence is chiefly struck by the inadequacy of\nhis view of scientific procedure. That we have only to make some crude\nexperiments, to draw up briefs of the results in certain blank forms, to\ngo through these by rule, checking off everything disproved and setting\ndown the alternatives, and that thus in a few years physical science\nwould be finished up\u2014what an idea! \u201cHe wrote on science like a Lord\nChancellor,\u201d[27] indeed.\n\nThe early scientists, Copernicus, Tycho Brahe, Kepler, Galileo and\nGilbert, had methods more like those of their modern brethren. Kepler\nundertook to draw a curve through the places of Mars;[28] and his\ngreatest service to science was in impressing on men\u2019s minds that this\nwas the thing to be done if they wished to improve astronomy; that they\nwere not to content themselves with inquiring whether one system of\nepicycles was better than another but that they were to sit down by the\nfigures and find out what the curve, in truth, was. He accomplished this\nby his incomparable energy and courage, blundering along in the most\ninconceivable way (to us), from one irrational hypothesis to another,\nuntil, after trying twenty-two of these, he fell, by the mere exhaustion\nof his invention, upon the orbit which a mind well furnished with the\nweapons of modern logic would have tried almost at the outset.[29]\n\nIn the same way, every work of science great enough to be remembered for\na few generations affords some exemplification of the defective state of\nthe art of reasoning of the time when it was written; and each chief\nstep in science has been a lesson in logic. It was so when Lavoisier and\nhis contemporaries took up the study of Chemistry. The old chemist\u2019s\nmaxim had been, \u201cLege, lege, lege, labora, ora, et relege.\u201d Lavoisier\u2019s\nmethod was not to read and pray, not to dream that some long and\ncomplicated chemical process would have a certain effect, to put it into\npractice with dull patience, after its inevitable failure to dream that\nwith some modification it would have another result, and to end by\npublishing the last dream as a fact: his way was to carry his mind into\nhis laboratory, and to make of his alembics and cucurbits instruments of\nthought, giving a new conception of reasoning as something which was to\nbe done with one\u2019s eyes open, by manipulating real things instead of\nwords and fancies.\n\nThe Darwinian controversy is, in large part, a question of logic. Mr.\nDarwin proposed to apply the statistical method to biology. The same\nthing has been done in a widely different branch of science, the theory\nof gases. Though unable to say what the movement of any particular\nmolecule of gas would be on a certain hypothesis regarding the\nconstitution of this class of bodies, Clausius and Maxwell were yet\nable, by the application of the doctrine of probabilities, to predict\nthat in the long run such and such a proportion of the molecules would,\nunder given circumstances, acquire such and such velocities; that there\nwould take place, every second, such and such a number of collisions,\netc.; and from these propositions they were able to deduce certain\nproperties of gases, especially in regard to their heat-relations. In\nlike manner, Darwin, while unable to say what the operation of variation\nand natural selection in every individual case will be, demonstrates\nthat in the long run they will adapt animals to their circumstances.\nWhether or not existing animal forms are due to such action, or what\nposition the theory ought to take, forms the subject of a discussion in\nwhich questions of fact and questions of logic are curiously interlaced.\n\n\n                                   II\n\n\nThe object of reasoning is to find out, from the consideration of what\nwe already know, something else which we do not know. Consequently,\nreasoning is good if it be such as to give a true conclusion from true\npremises, and not otherwise. Thus, the question of validity is purely\none of fact and not of thinking. A being the premises and B being the\nconclusion, the question is, whether these facts are really so related\nthat if A is B is. If so, the inference is valid; if not, not. It is not\nin the least the question whether, when the premises are accepted by the\nmind, we feel an impulse to accept the conclusion also. It is true that\nwe do generally reason correctly by nature. But that is an accident; the\ntrue conclusion would remain true if we had no impulse to accept it; and\nthe false one would remain false, though we could not resist the\ntendency to believe in it.\n\nWe are, doubtless, in the main logical animals, but we are not perfectly\nso. Most of us, for example, are naturally more sanguine and hopeful\nthan logic would justify. We seem to be so constituted that in the\nabsence of any facts to go upon we are happy and self-satisfied; so that\nthe effect of experience is continually to counteract our hopes and\naspirations. Yet a lifetime of the application of this corrective does\nnot usually eradicate our sanguine disposition. Where hope is unchecked\nby any experience, it is likely that our optimism is extravagant.\nLogicality in regard to practical matters is the most useful quality an\nanimal can possess, and might, therefore, result from the action of\nnatural selection; but outside of these it is probably of more advantage\nto the animal to have his mind filled with pleasing and encouraging\nvisions, independently of their truth; and thus, upon unpractical\nsubjects, natural selection might occasion a fallacious tendency of\nthought.\n\nThat which determines us, from given premises, to draw one inference\nrather than another, is some habit of mind, whether it be constitutional\nor acquired. The habit is good or otherwise, according as it produces\ntrue conclusions from true premises or not; and an inference is regarded\nas valid or not, without reference to the truth or falsity of its\nconclusion specially, but according as the habit which determines it is\nsuch as to produce true conclusions in general or not. The particular\nhabit of mind which governs this or that inference may be formulated in\na proposition whose truth depends on the validity of the inferences\nwhich the habit determines; and such a formula is called a _guiding\nprinciple_ of inference. Suppose, for example, that we observe that a\nrotating disk of copper quickly comes to rest when placed between the\npoles of a magnet, and we infer that this will happen with every disk of\ncopper. The guiding principle is, that what is true of one piece of\ncopper is true of another. Such a guiding principle with regard to\ncopper would be much safer than with regard to many other\nsubstances\u2014brass, for example.\n\nA book might be written to signalize all the most important of these\nguiding principles of reasoning. It would probably be, we must confess,\nof no service to a person whose thought is directed wholly to practical\nsubjects, and whose activity moves along thoroughly beaten paths. The\nproblems which present themselves to such a mind are matters of routine\nwhich he has learned once for all to handle in learning his business.\nBut let a man venture into an unfamiliar field, or where his results are\nnot continually checked by experience, and all history shows that the\nmost masculine intellect will ofttimes lose his orientation and waste\nhis efforts in directions which bring him no nearer to his goal, or even\ncarry him entirely astray. He is like a ship on the open sea, with no\none on board who understands the rules of navigation. And in such a case\nsome general study of the guiding principles of reasoning would be sure\nto be found useful.\n\nThe subject could hardly be treated, however, without being first\nlimited; since almost any fact may serve as a guiding principle. But it\nso happens that there exists a division among facts, such that in one\nclass are all those which are absolutely essential as guiding\nprinciples, while in the other are all those which have any other\ninterest as objects of research. This division is between those which\nare necessarily taken for granted in asking whether a certain conclusion\nfollows from certain premises, and those which are not implied in that\nquestion. A moment\u2019s thought will show that a variety of facts are\nalready assumed when the logical question is first asked. It is implied,\nfor instance, that there are such states of mind as doubt and\nbelief\u2014that a passage from one to the other is possible, the object of\nthought remaining the same, and that this transition is subject to some\nrules which all minds are alike bound by. As these are facts which we\nmust already know before we can have any clear conception of reasoning\nat all, it cannot be supposed to be any longer of much interest to\ninquire into their truth or falsity. On the other hand, it is easy to\nbelieve that those rules of reasoning which are deduced from the very\nidea of the process are the ones which are the most essential; and,\nindeed, that so long as it conforms to these it will, at least, not lead\nto false conclusions from true premises. In point of fact, the\nimportance of what may be deduced from the assumptions involved in the\nlogical question turns out to be greater than might be supposed, and\nthis for reasons which it is difficult to exhibit at the outset. The\nonly one which I shall here mention is, that conceptions which are\nreally products of logical reflections, without being readily seen to be\nso, mingle with our ordinary thoughts, and are frequently the causes of\ngreat confusion. This is the case, for example, with the conception of\nquality. A quality as such is never an object of observation. We can see\nthat a thing is blue or green, but the quality of being blue and the\nquality of being green are not things which we see; they are products of\nlogical reflections. The truth is, that common-sense, or thought as it\nfirst emerges above the level of the narrowly practical, is deeply\nimbued with that bad logical quality to which the epithet _metaphysical_\nis commonly applied; and nothing can clear it up but a severe course of\nlogic.\n\n\n                                  III\n\n\nWe generally know when we wish to ask a question and when we wish to\npronounce a judgment, for there is a dissimilarity between the sensation\nof doubting and that of believing.\n\nBut this is not all which distinguishes doubt from belief. There is a\npractical difference. Our beliefs guide our desires and shape our\nactions. The Assassins, or followers of the Old Man of the Mountain,\nused to rush into death at his least command, because they believed that\nobedience to him would insure everlasting felicity. Had they doubted\nthis, they would not have acted as they did. So it is with every belief,\naccording to its degree. The feeling of believing is a more or less sure\nindication of there being established in our nature some habit which\nwill determine our actions. Doubt never has such an effect.\n\nNor must we overlook a third point of difference. Doubt is an uneasy and\ndissatisfied state from which we struggle to free ourselves and pass\ninto the state of belief; while the latter is a calm and satisfactory\nstate which we do not wish to avoid, or to change to a belief in\nanything else.[30] On the contrary, we cling tenaciously, not merely to\nbelieving, but to believing just what we do believe.\n\nThus, both doubt and belief have positive effects upon us, though very\ndifferent ones. Belief does not make us act at once, but puts us into\nsuch a condition that we shall behave in a certain way, when the\noccasion arises. Doubt has not the least effect of this sort, but\nstimulates us to action until it is destroyed. This reminds us of the\nirritation of a nerve and the reflex action produced thereby; while for\nthe analogue of belief, in the nervous system, we must look to what are\ncalled nervous associations\u2014for example, to that habit of the nerves in\nconsequence of which the smell of a peach will make the mouth water.\n\n\n                                   IV\n\n\nThe irritation of doubt causes a struggle to attain a state of belief. I\nshall term this struggle _inquiry_, though it must be admitted that this\nis sometimes not a very apt designation.\n\nThe irritation of doubt is the only immediate motive for the struggle to\nattain belief. It is certainly best for us that our beliefs should be\nsuch as may truly guide our actions so as to satisfy our desires; and\nthis reflection will make us reject any belief which does not seem to\nhave been so formed as to insure this result. But it will only do so by\ncreating a doubt in the place of that belief. With the doubt, therefore,\nthe struggle begins, and with the cessation of doubt it ends. Hence, the\nsole object of inquiry is the settlement of opinion. We may fancy that\nthis is not enough for us, and that we seek not merely an opinion, but a\ntrue opinion. But put this fancy to the test, and it proves groundless;\nfor as soon as a firm belief is reached we are entirely satisfied,\nwhether the belief be false or true. And it is clear that nothing out of\nthe sphere of our knowledge can be our object, for nothing which does\nnot affect the mind can be a motive for a mental effort. The most that\ncan be maintained is, that we seek for a belief that we shall _think_ to\nbe true. But we think each one of our beliefs to be true, and, indeed,\nit is mere tautology to say so.\n\nThat the settlement of opinion is the sole end of inquiry is a very\nimportant proposition. It sweeps away, at once, various vague and\nerroneous conceptions of proof. A few of these may be noticed here.\n\n1. Some philosophers have imagined that to start an inquiry it was only\nnecessary to utter or question or set it down on paper, and have even\nrecommended us to begin our studies with questioning everything! But the\nmere putting of a proposition into the interrogative form does not\nstimulate the mind to any struggle after belief. There must be a real\nand living doubt, and without all this discussion is idle.\n\n2. It is a very common idea that a demonstration must rest on some\nultimate and absolutely indubitable propositions. These, according to\none school, are first principles of a general nature; according to\nanother, are first sensations. But, in point of fact, an inquiry, to\nhave that completely satisfactory result called demonstration, has only\nto start with propositions perfectly free from all actual doubt. If the\npremises are not in fact doubted at all, they cannot be more\nsatisfactory than they are.\n\n3. Some people seem to love to argue a point after all the world is\nfully convinced of it. But no further advance can be made. When doubt\nceases, mental action on the subject comes to an end; and, if it did go\non, it would be without a purpose.\n\n\n                                   V\n\n\nIf the settlement of opinion is the sole object of inquiry, and if\nbelief is of the nature of a habit, why should we not attain the desired\nend, by taking any answer to a question, which we may fancy, and\nconstantly reiterating it to ourselves, dwelling on all which may\nconduce to that belief, and learning to turn with contempt and hatred\nfrom anything which might disturb it? This simple and direct method is\nreally pursued by many men. I remember once being entreated not to read\na certain newspaper lest it might change my opinion upon free-trade.\n\u201cLest I might be entrapped by its fallacies and misstatements,\u201d was the\nform of expression. \u201cYou are not,\u201d my friend said, \u201ca special student of\npolitical economy. You might, therefore, easily be deceived by\nfallacious arguments upon the subject. You might, then, if you read this\npaper, be led to believe in protection. But you admit that free-trade is\nthe true doctrine; and you do not wish to believe what is not true.\u201d I\nhave often known this system to be deliberately adopted. Still oftener,\nthe instinctive dislike of an undecided state of mind, exaggerated into\na vague dread of doubt, makes men cling spasmodically to the views they\nalready take. The man feels that, if he only holds to his belief without\nwavering, it will be entirely satisfactory. Nor can it be denied that a\nsteady and immovable faith yields great peace of mind. It may, indeed,\ngive rise to inconveniences, as if a man should resolutely continue to\nbelieve that fire would not burn him, or that he would be eternally\ndamned if he received his _ingesta_ otherwise than through a\nstomach-pump. But then the man who adopts this method will not allow\nthat its inconveniences are greater than its advantages. He will say, \u201cI\nhold steadfastly to the truth and the truth is always wholesome.\u201d And in\nmany cases it may very well be that the pleasure he derives from his\ncalm faith overbalances any inconveniences resulting from its deceptive\ncharacter. Thus, if it be true that death is annihilation, then the man\nwho believes that he will certainly go straight to heaven when he dies,\nprovided he have fulfilled certain simple observances in this life, has\na cheap pleasure which will not be followed by the least disappointment.\nA similar consideration seems to have weight with many persons in\nreligious topics, for we frequently hear it said, \u201cOh, I could not\nbelieve so-and-so, because I should be wretched if I did.\u201d When an\nostrich buries its head in the sand as danger approaches, it very likely\ntakes the happiest course. It hides the danger, and then calmly says\nthere is no danger; and, if it feels perfectly sure there is none, why\nshould it raise its head to see? A man may go through life,\nsystematically keeping out of view all that might cause a change in his\nopinions, and if he only succeeds\u2014basing his method, as he does, on two\nfundamental psychological laws\u2014I do not see what can be said against his\ndoing so. It would be an egotistical impertinence to object that his\nprocedure is irrational, for that only amounts to saying that his method\nof settling belief is not ours. He does not propose to himself to be\nrational, and indeed, will often talk with scorn of man\u2019s weak and\nillusive reason. So let him think as he pleases.\n\nBut this method of fixing belief, which may be called the method of\ntenacity, will be unable to hold its ground in practice. The social\nimpulse is against it. The man who adopts it will find that other men\nthink differently from him, and it will be apt to occur to him in some\nsaner moment that their opinions are quite as good as his own, and this\nwill shake his confidence in his belief. This conception, that another\nman\u2019s thought or sentiment may be equivalent to one\u2019s own, is a\ndistinctly new step, and a highly important one. It arises from an\nimpulse too strong in man to be suppressed, without danger of destroying\nthe human species. Unless we make ourselves hermits, we shall\nnecessarily influence each other\u2019s opinions; so that the problem becomes\nhow to fix belief, not in the individual merely, but in the community.\n\nLet the will of the state act, then, instead of that of the individual.\nLet an institution be created which shall have for its object to keep\ncorrect doctrines before the attention of the people, to reiterate them\nperpetually, and to teach them to the young; having at the same time\npower to prevent contrary doctrines from being taught, advocated, or\nexpressed. Let all possible causes of a change of mind be removed from\nmen\u2019s apprehensions. Let them be kept ignorant, lest they should learn\nof some reason to think otherwise than they do. Let their passions be\nenlisted, so that they may regard private and unusual opinions with\nhatred and horror. Then, let all men who reject the established belief\nbe terrified into silence. Let the people turn out and tar-and-feather\nsuch men, or let inquisitions be made into the manner of thinking of\nsuspected persons, and, when they are found guilty of forbidden beliefs,\nlet them be subjected to some signal punishment. When complete agreement\ncould not otherwise be reached, a general massacre of all who have not\nthought in a certain way has proved a very effective means of settling\nopinion in a country. If the power to do this be wanting, let a list of\nopinions be drawn up, to which no man of the least independence of\nthought can assent, and let the faithful be required to accept all these\npropositions, in order to segregate them as radically as possible from\nthe influence of the rest of the world.\n\nThis method has, from the earliest times, been one of the chief means of\nupholding correct theological and political doctrines, and of preserving\ntheir universal or catholic character. In Rome, especially, it has been\npracticed from the days of Numa Pompilius to those of Pius Nonus. This\nis the most perfect example in history; but wherever there is a\npriesthood\u2014and no religion has been without one\u2014this method has been\nmore or less made use of. Wherever there is aristocracy, or a guild, or\nany association of a class of men whose interests depend or are supposed\nto depend on certain propositions, there will be inevitably found some\ntraces of this natural product of social feeling. Cruelties always\naccompany this system; and when it is consistently carried out, they\nbecome atrocities of the most horrible kind in the eyes of any rational\nman. Nor should this occasion surprise, for the officer of a society\ndoes not feel justified in surrendering the interests of that society\nfor the sake of mercy, as he might his own private interests. It is\nnatural, therefore, that sympathy and fellowship should thus produce a\nmost ruthless power.\n\nIn judging this method of fixing belief, which may be called the method\nof authority, we must in the first place, allow its immeasurable mental\nand moral superiority to the method of tenacity. Its success is\nproportionally greater; and in fact it has over and over again worked\nthe most majestic results. The mere structures of stone which it has\ncaused to be put together\u2014in Siam, for example, in Egypt, and in\nEurope\u2014have many of them a sublimity hardly more than rivaled by the\ngreatest works of Nature. And, except the geological epochs, there are\nno periods of time so vast as those which are measured by some of these\norganized faiths. If we scrutinize the matter closely, we shall find\nthat there has not been one of their creeds which has remained always\nthe same; yet the change is so slow as to be imperceptible during one\nperson\u2019s life, so that individual belief remains sensibly fixed. For the\nmass of mankind, then, there is perhaps no better method than this. If\nit is their highest impulse to be intellectual slaves, then slaves they\nought to remain.\n\nBut no institution can undertake to regulate opinions upon every\nsubject. Only the most important ones can be attended to, and on the\nrest men\u2019s minds must be left to the action of natural causes. This\nimperfection will be no source of weakness so long as men are in such a\nstate of culture that one opinion does not influence another\u2014that is, so\nlong as they cannot put two and two together. But in the most\npriest-ridden states some individuals will be found who are raised above\nthat condition. These men possess a wider sort of social feeling; they\nsee that men in other countries and in other ages have held to very\ndifferent doctrines from those which they themselves have been brought\nup to believe; and they cannot help seeing that it is the mere accident\nof their having been taught as they have, and of their having been\nsurrounded with the manners and associations they have, that has caused\nthem to believe as they do and not far differently. And their candor\ncannot resist the reflection that there is no reason to rate their own\nviews at a higher value than those of other nations and other centuries;\nand this gives rise to doubts in their minds.\n\nThey will further perceive that such doubts as these must exist in their\nminds with reference to every belief which seems to be determined by the\ncaprice either of themselves or of those who originated the popular\nopinions. The willful adherence to a belief, and the arbitrary forcing\nof it upon others, must, therefore, both be given up and a new method of\nsettling opinions must be adopted, which shall not only produce an\nimpulse to believe, but shall also decide what proposition it is which\nis to be believed. Let the action of natural preferences be unimpeded,\nthen, and under their influence let men conversing together and\nregarding matters in different lights, gradually develop beliefs in\nharmony with natural causes. This method resembles that by which\nconceptions of art have been brought to maturity. The most perfect\nexample of it is to be found in the history of metaphysical philosophy.\nSystems of this sort have not usually rested upon observed facts, at\nleast not in any great degree. They have been chiefly adopted because\ntheir fundamental propositions seemed \u201cagreeable to reason.\u201d This is an\napt expression; it does not mean that which agrees with experience, but\nthat which we find ourselves inclined to believe. Plato, for example,\nfinds it agreeable to reason that the distances of the celestial spheres\nfrom one another should be proportional to the different lengths of\nstrings which produce harmonious chords. Many philosophers have been led\nto their main conclusions by considerations like this; but this is the\nlowest and least developed form which the method takes, for it is clear\nthat another man might find Kepler\u2019s [earlier] theory, that the\ncelestial spheres are proportional to the inscribed and circumscribed\nspheres of the different regular solids, more agreeable to _his_ reason.\nBut the shock of opinions will soon lead men to rest on preferences of a\nfar more universal nature. Take, for example, the doctrine that man only\nacts selfishly\u2014that is, from the consideration that acting in one way\nwill afford him more pleasure than acting in another. This rests on no\nfact in the world, but it has had a wide acceptance as being the only\nreasonable theory.\n\nThis method is far more intellectual and respectable from the point of\nview of reason than either of the others which we have noticed. But its\nfailure has been the most manifest. It makes of inquiry something\nsimilar to the development of taste; but taste, unfortunately, is always\nmore or less a matter of fashion, and accordingly, meta-physicians have\nnever come to any fixed agreement, but the pendulum has swung backward\nand forward between a more material and a more spiritual philosophy,\nfrom the earliest times to the latest. And so from this, which has been\ncalled the _a priori_ method, we are driven, in Lord Bacon\u2019s phrase, to\na true induction. We have examined into this _a priori_ method as\nsomething which promised to deliver our opinions from their accidental\nand capricious element. But development, while it is a process which\neliminates the effect of some casual circumstances, only magnifies that\nof others. This method, therefore, does not differ in a very essential\nway from that of authority. The government may not have lifted its\nfinger to influence my convictions; I may have been left outwardly quite\nfree to choose, we will say, between monogamy and polygamy, and\nappealing to my conscience only, I may have concluded that the latter\npractice is in itself licentious. But when I come to see that the chief\nobstacle to the spread of Christianity among a people of as high culture\nas the Hindoos has been a conviction of the immorality of our way of\ntreating women, I cannot help seeing that, though governments do not\ninterfere, sentiments in their development will be very greatly\ndetermined by accidental causes. Now, there are some people, among whom\nI must suppose that my reader is to be found, who, when they see that\nany belief of theirs is determined by any circumstance extraneous to the\nfacts, will from that moment not merely admit in words that that belief\nis doubtful, but will experience a real doubt of it, so that it ceases\nto be a belief.\n\nTo satisfy our doubts, therefore, it is necessary that a method should\nbe found by which our beliefs may be caused by nothing human, but by\nsome external permanency\u2014by something upon which our thinking has no\neffect. Some mystics imagine that they have such a method in a private\ninspiration from on high. But that is only a form of the method of\ntenacity, in which the conception of truth as something public is not\nyet developed. Our external permanency would not be external, in our\nsense, if it was restricted in its influence to one individual. It must\nbe something which affects, or might affect, every man. And, though\nthese affections are necessarily as various as are individual\nconditions, yet the method must be such that the ultimate conclusion of\nevery man shall be the same. Such is the method of science. Its\nfundamental hypothesis, restated in more familiar language, is this:\nThere are real things, whose characters are entirely independent of our\nopinions about them; whose realities affect our senses according to\nregular laws, and, though our sensations are as different as our\nrelations to the objects, yet, by taking advantage of the laws of\nperception, we can ascertain by reasoning how things really are, and any\nman, if he have sufficient experience and reason enough about it, will\nbe led to the one true conclusion. The new conception here involved is\nthat of reality. It may be asked how I know that there are any\nrealities. If this hypothesis is the sole support of my method of\ninquiry, my method of inquiry must not be used to support my hypothesis.\nThe reply is this: 1. If investigation cannot be regarded as proving\nthat there are real things, it at least does not lead to a contrary\nconclusion; but the method and the conception on which it is based\nremain ever in harmony. No doubts of the method, therefore, necessarily\narise from its practice, as is the case with all the others. 2. The\nfeeling which gives rise to any method of fixing belief is a\ndissatisfaction at two repugnant propositions. But here already is a\nvague concession that there is some _one_ thing to which a proposition\nshould conform. Nobody, therefore, can really doubt that there are\nrealities, or, if he did, doubt would not be a source of\ndissatisfaction. The hypothesis, therefore, is one which every mind\nadmits. So that the social impulse does not cause me to doubt it. 3.\nEverybody uses the scientific method about a great many things, and only\nceases to use it when he does not know how to apply it. 4. Experience of\nthe method has not led me to doubt it, but, on the contrary, scientific\ninvestigation has had the most wonderful triumphs in the way of settling\nopinion. These afford the explanation of my not doubting the method or\nthe hypothesis which it supposes; and not having any doubt, nor\nbelieving that anybody else whom I could influence has, it would be the\nmerest babble for me to say more about it. If there be anybody with a\nliving doubt upon the subject, let him consider it.\n\nTo describe the method of scientific investigation is the object of this\nseries of papers. At present I have only room to notice some points of\ncontrast between it and other methods of fixing belief.\n\nThis is the only one of the four methods which presents any distinction\nof a right and a wrong way. If I adopt the method of tenacity and shut\nmyself out from all influences, whatever I think necessary to doing this\nis necessary according to that method. So with the method of authority:\nthe state may try to put down heresy by means which, from a scientific\npoint of view, seems very ill-calculated to accomplish its purposes; but\nthe only test _on that method_ is what the state thinks, so that it\ncannot pursue the method wrongly. So with the _a priori_ method. The\nvery essence of it is to think as one is inclined to think. All\nmetaphysicians will be sure to do that, however they may be inclined to\njudge each other to be perversely wrong. The Hegelian system recognizes\nevery natural tendency of thought as logical, although it is certain to\nbe abolished by counter-tendencies. Hegel thinks there is a regular\nsystem in the succession of these tendencies, in consequence of which,\nafter drifting one way and the other for a long time, opinion will at\nlast go right. And it is true that metaphysicians get the right ideas at\nlast; Hegel\u2019s system of Nature represents tolerably the science of that\nday; and one may be sure that whatever scientific investigation has put\nout of doubt will presently receive _a priori_ demonstration on the part\nof the metaphysicians. But with the scientific method the case is\ndifferent. I may start with known and observed facts to proceed to the\nunknown; and yet the rules which I follow in doing so may not be such as\ninvestigation would approve. The test of whether I am truly following\nthe method is not an immediate appeal to my feelings and purposes, but,\non the contrary, itself involves the application of the method. Hence it\nis that bad reasoning as well as good reasoning is possible; and this\nfact is the foundation of the practical side of logic.\n\nIt is not to be supposed that the first three methods of settling\nopinion present no advantage whatever over the scientific method. On the\ncontrary, each has some peculiar convenience of its own. The _a priori_\nmethod is distinguished for its comfortable conclusions. It is the\nnature of the process to adopt whatever belief we are inclined to, and\nthere are certain flatteries to one\u2019s vanities which we all believe by\nnature, until we are awakened from our pleasing dream by rough facts.\nThe method of authority will always govern the mass of mankind; and\nthose who wield the various forms of organized force in the state will\nnever be convinced that dangerous reasoning ought not to be suppressed\nin some way. If liberty of speech is to be untrammeled from the grosser\nforms of constraint, then uniformity of opinion will be secured by a\nmoral terrorism to which the respectability of society will give its\nthorough approval. Following the method of authority is the path of\npeace. Certain non-conformities are permitted; certain others\n(considered unsafe) are forbidden. These are different in different\ncountries and in different ages; but, wherever you are let it be known\nthat you seriously hold a tabooed belief, and you may be perfectly sure\nof being treated with a cruelty no less brutal but more refined than\nhunting you like a wolf. Thus, the greatest intellectual benefactors of\nmankind have never dared, and dare not now, to utter the whole of their\nthought; and thus a shade of _prima facie_ doubt is cast upon every\nproposition which is considered essential to the security of society.\nSingularly enough, the persecution does not all come from without; but a\nman torments himself and is oftentimes most distressed at finding\nhimself believing propositions which he has been brought up to regard\nwith aversion. The peaceful and sympathetic man will, therefore, find it\nhard to resist the temptation to submit his opinions to authority. But\nmost of all I admire the method of tenacity for its strength,\nsimplicity, and directness. Men who pursue it are distinguished for\ntheir decision of character, which becomes very easy with such a mental\nrule. They do not waste time in trying to make up their minds to what\nthey want, but, fastening like lightning upon whatever alternative comes\nfirst, they hold to it to the end, whatever happens, without an\ninstant\u2019s irresolution. This is one of the splendid qualities which\ngenerally accompany brilliant, unlasting success. It is impossible not\nto envy the man who can dismiss reason, although we know how it must\nturn out at last.\n\nSuch are the advantages which the other methods of settling opinions\nhave over scientific investigation. A man should consider well of them;\nand then he should consider that, after all, he wishes his opinions to\ncoincide with the fact, and that there is no reason why the results of\nthese three methods should do so. To bring about this effect is the\nprerogative of the method of science. Upon such considerations he has to\nmake his choice\u2014a choice which is far more than the adoption of any\nintellectual opinion, which is one of the ruling decisions of his life,\nto which when once made he is bound to adhere. The force of habit will\nsometimes cause a man to hold on to old beliefs, after he is in a\ncondition to see that they have no sound basis. But reflection upon the\nstate of the case will overcome these habits, and he ought to allow\nreflection full weight. People sometimes shrink from doing this, having\nan idea that beliefs are wholesome which they cannot help feeling rest\non nothing. But let such persons suppose an analogous though different\ncase from their own. Let them ask themselves what they would say to a\nreformed Mussulman who should hesitate to give up his old notions in\nregard to the relations of the sexes; or to a reformed Catholic who\nshould still shrink from the Bible. Would they not say that these\npersons ought to consider the matter fully, and clearly understand the\nnew doctrine, and then ought to embrace it in its entirety? But, above\nall, let it be considered that what is more wholesome than any\nparticular belief, is integrity of belief; and that to avoid looking\ninto the support of any belief from a fear that it may turn out rotten\nis quite as immoral as it is disadvantageous. The person who confesses\nthat there is such a thing as truth, which is distinguished from\nfalsehood simply by this, that if acted on it will carry us to the point\nwe aim at and not astray, and then though convinced of this, dares not\nknow the truth and seeks to avoid it, is in a sorry state of mind,\nindeed.\n\nYes, the other methods do have their merits: a clear logical conscience\ndoes cost something\u2014just as any virtue, just as all that we cherish,\ncosts us dear. But, we should not desire it to be otherwise. The genius\nof a man\u2019s logical method should be loved and reverenced as his bride,\nwhom he has chosen from all the world. He need not condemn the others;\non the contrary, he may honor them deeply, and in doing so he only\nhonors her the more. But she is the one that he has chosen, and he knows\nthat he was right in making that choice. And having made it, he will\nwork and fight for her, and will not complain that there are blows to\ntake, hoping that there may be as many and as hard to give, and will\nstrive to be the worthy knight and champion of her from the blaze of\nwhose splendors he draws his inspiration and his courage.\n\nFootnote 26:\n\n  _Popular Science Monthly_, November, 1877.\n\nFootnote 27:\n\n  [This is substantially the dictum of Harvey to John Aubrey. See the\n  latter\u2019s _Brief Lives_ (Oxford ed. 1898) I 299.]\n\nFootnote 28:\n\n  Not quite so, but as nearly so as can be told in a few words.\n\nFootnote 29:\n\n  [This modern logic, however, is largely the outcome of Kepler\u2019s work.]\n\nFootnote 30:\n\n  I am not speaking of secondary effects occasionally produced by the\n  interference of other impulses.\n\n\n\n\n                              SECOND PAPER\n                    HOW TO MAKE OUR IDEAS CLEAR[31]\n\n\n                                   I\n\n\nWhoever has looked into a modern treatise on logic of the common sort,\nwill doubtless remember the two distinctions between _clear_ and\n_obscure_ conceptions, and between _distinct_ and _confused_\nconceptions. They have lain in the books now for nigh two centuries,\nunimproved and unmodified, and are generally reckoned by logicians as\namong the gems of their doctrine.\n\nA clear idea is defined as one which is so apprehended that it will be\nrecognized wherever it is met with, and so that no other will be\nmistaken for it. If it fails of this clearness, it is said to be\nobscure.\n\nThis is rather a neat bit of philosophical terminology; yet, since it is\nclearness that they were defining, I wish the logicians had made their\ndefinition a little more plain. Never to fail to recognize an idea, and\nunder no circumstances to mistake another for it, let it come in how\nrecondite a form it may, would indeed imply such prodigious force and\nclearness of intellect as is seldom met with in this world. On the other\nhand, merely to have such an acquaintance with the idea as to have\nbecome familiar with it, and to have lost all hesitancy in recognizing\nit in ordinary cases, hardly seems to deserve the name of clearness of\napprehension, since after all it only amounts to a subjective feeling of\nmastery which may be entirely mistaken. I take it, however, that when\nthe logicians speak of \u201cclearness,\u201d they mean nothing more than such a\nfamiliarity with an idea, since they regard the quality as but a small\nmerit, which needs to be supplemented by another, which they call\n_distinctness_.\n\nA distinct idea is defined as one which contains nothing which is not\nclear. This is technical language; by the _contents_ of an idea\nlogicians understand whatever is contained in its definition. So that an\nidea is _distinctly_ apprehended, according to them, when we can give a\nprecise definition of it, in abstract terms. Here the professional\nlogicians leave the subject; and I would not have troubled the reader\nwith what they have to say, if it were not such a striking example of\nhow they have been slumbering through ages of intellectual activity,\nlistlessly disregarding the enginery of modern thought, and never\ndreaming of applying its lessons to the improvement of logic. It is easy\nto show that the doctrine that familiar use and abstract distinctness\nmake the perfection of apprehension, has its only true place in\nphilosophies which have long been extinct; and it is now time to\nformulate the method of attaining to a more perfect clearness of\nthought, such as we see and admire in the thinkers of our own time.\n\nWhen Descartes set about the reconstruction of philosophy, his first\nstep was to (theoretically) permit skepticism and to discard the\npractice of the schoolmen of looking to authority as the ultimate source\nof truth. That done, he sought a more natural fountain of true\nprinciples, and professed to find it in the human mind; thus passing, in\nthe directest way, from the method of authority to that of apriority, as\ndescribed in my first paper. Self-consciousness was to furnish us with\nour fundamental truths, and to decide what was agreeable to reason. But\nsince, evidently, not all ideas are true, he was led to note, as the\nfirst condition of infallibility, that they must be clear. The\ndistinction between an idea _seeming_ clear and really being so, never\noccurred to him. Trusting to introspection, as he did, even for a\nknowledge of external things, why should he question its testimony in\nrespect to the contents of our own minds? But then, I suppose, seeing\nmen, who seemed to be quite clear and positive, holding opposite\nopinions upon fundamental principles, he was further led to say that\nclearness of ideas is not sufficient, but that they need also to be\ndistinct, i.e., to have nothing unclear about them. What he probably\nmeant by this (for he did not explain himself with precision) was, that\nthey must sustain the test of dialectical examination; that they must\nnot only seem clear at the outset, but that discussion must never be\nable to bring to light points of obscurity connected with them.\n\nSuch was the distinction of Descartes, and one sees that it was\nprecisely on the level of his philosophy. It was somewhat developed by\nLeibnitz. This great and singular genius was as remarkable for what he\nfailed to see as for what he saw. That a piece of mechanism could not do\nwork perpetually without being fed with power in some form, was a thing\nperfectly apparent to him; yet he did not understand that the machinery\nof the mind can only transform knowledge, but never originate it, unless\nit be fed with facts of observation. He thus missed the most essential\npoint of the Cartesian philosophy, which is, that to accept propositions\nwhich seem perfectly evident to us is a thing which, whether it be\nlogical or illogical, we cannot help doing. Instead of regarding the\nmatter in this way, he sought to reduce the first principles of science\nto formulas which cannot be denied without self-contradiction, and was\napparently unaware of the great difference between his position and that\nof Descartes. So he reverted to the old formalities of logic, and, above\nall, abstract definitions played a great part in his philosophy. It was\nquite natural, therefore, that on observing that the method of Descartes\nlabored under the difficulty that we may seem to ourselves to have clear\napprehensions of ideas which in truth are very hazy, no better remedy\noccurred to him than to require an abstract definition of every\nimportant term. Accordingly, in adopting the distinction of _clear_ and\n_distinct_ notions, he described the latter quality as the clear\napprehension of everything contained in the definition; and the books\nhave ever since copied his words. There is no danger that his chimerical\nscheme will ever again be over-valued. Nothing new can ever be learned\nby analyzing definitions. Nevertheless, our existing beliefs can be set\nin order by this process, and order is an essential element of\nintellectual economy, as of every other. It may be acknowledged,\ntherefore, that the books are right in making familiarity with a notion\nthe first step toward clearness of apprehension, and the defining of it\nthe second. But in omitting all mention of any higher perspicuity of\nthought, they simply mirror a philosophy which was exploded a hundred\nyears ago. That much-admired \u201cornament of logic\u201d\u2014the doctrine of\nclearness and distinctness\u2014may be pretty enough, but it is high time to\nrelegate to our cabinet of curiosities the antique _bijou_, and to wear\nabout us something better adapted to modern uses.\n\nThe very first lesson that we have a right to demand that logic shall\nteach us is, how to make our ideas clear; and a most important one it\nis, depreciated only by minds who stand in need of it. To know what we\nthink, to be masters of our own meaning, will make a solid foundation\nfor great and weighty thought. It is most easily learned by those whose\nideas are meagre and restricted; and far happier they than such as\nwallow helplessly in a rich mud of conceptions. A nation, it is true,\nmay, in the course of generations, overcome the disadvantage of an\nexcessive wealth of language and its natural concomitant, a vast,\nunfathomable deep of ideas. We may see it in history, slowly perfecting\nits literary forms, sloughing at length its metaphysics, and, by virtue\nof the untirable patience which is often a compensation, attaining great\nexcellence in every branch of mental acquirement. The page of history is\nnot yet unrolled which is to tell us whether such a people will or will\nnot in the long run prevail over one whose ideas (like the words of\ntheir language) are few, but which possesses a wonderful mastery over\nthose which it has. For an individual, however, there can be no question\nthat a few clear ideas are worth more than many confused ones. A young\nman would hardly be persuaded to sacrifice the greater part of his\nthoughts to save the rest; and the muddled head is the least apt to see\nthe necessity of such a sacrifice. Him we can usually only commiserate,\nas a person with a congenital defect. Time will help him, but\nintellectual maturity with regard to clearness comes rather late, an\nunfortunate arrangement of Nature, inasmuch as clearness is of less use\nto a man settled in life, whose errors have in great measure had their\neffect, than it would be to one whose path lies before him. It is\nterrible to see how a single unclear idea, a single formula without\nmeaning, lurking in a young man\u2019s head, will sometimes act like an\nobstruction of inert matter in an artery, hindering the nutrition of the\nbrain, and condemning its victim to pine away in the fullness of his\nintellectual vigor and in the midst of intellectual plenty. Many a man\nhas cherished for years as his hobby some vague shadow of an idea, too\nmeaningless to be positively false; he has, nevertheless, passionately\nloved it, has made it his companion by day and by night, and has given\nto it his strength and his life, leaving all other occupations for its\nsake, and in short has lived with it and for it, until it has become, as\nit were, flesh of his flesh and bone of his bone; and then he has waked\nup some bright morning to find it gone, clean vanished away like the\nbeautiful Melusina of the fable, and the essence of his life gone with\nit. I have myself known such a man; and who can tell how many histories\nof circle-squarers, metaphysicians, astrologers, and what not, may not\nbe told in the old German story?\n\n\n                                   II\n\n\nThe principles set forth in the first of these papers lead, at once, to\na method of reaching a clearness of thought of a far higher grade than\nthe \u201cdistinctness\u201d of the logicians. We have there found that the action\nof thought is excited by the irritation of doubt, and ceases when belief\nis attained; so that the production of belief is the sole function of\nthought. All these words, however, are too strong for my purpose. It is\nas if I had described the phenomena as they appear under a mental\nmicroscope. Doubt and Belief, as the words are commonly employed, relate\nto religious or other grave discussions. But here I use them to\ndesignate the starting of any question, no matter how small or how\ngreat, and the resolution of it. If, for instance, in a horse-car, I\npull out my purse and find a five-cent nickel and five coppers, I\ndecide, while my hand is going to the purse, in which way I will pay my\nfare. To call such a question Doubt, and my decision Belief, is\ncertainly to use words very disproportionate to the occasion. To speak\nof such a doubt as causing an irritation which needs to be appeased,\nsuggests a temper which is uncomfortable to the verge of insanity. Yet,\nlooking at the matter minutely, it must be admitted that, if there is\nthe least hesitation as to whether I shall pay the five coppers or the\nnickel (as there will be sure to be, unless I act from some previously\ncontracted habit in the matter), though irritation is too strong a word,\nyet I am excited to such small mental activity as may be necessary to\ndeciding how I shall act. Most frequently doubts arise from some\nindecision, however momentary, in our action. Sometimes it is not so. I\nhave, for example, to wait in a railway-station, and to pass the time I\nread the advertisements on the walls, I compare the advantages of\ndifferent trains and different routes which I never expect to take,\nmerely fancying myself to be in a state of hesitancy, because I am bored\nwith having nothing to trouble me. Feigned hesitancy, whether feigned\nfor mere amusement or with a lofty purpose, plays a great part in the\nproduction of scientific inquiry. However the doubt may originate, it\nstimulates the mind to an activity which may be slight or energetic,\ncalm or turbulent. Images pass rapidly through consciousness, one\nincessantly melting into another, until at last, when all is over\u2014it may\nbe in a fraction of a second, in an hour, or after long years\u2014we find\nourselves decided as to how we should act under such circumstances as\nthose which occasioned our hesitation. In other words, we have attained\nbelief.\n\nIn this process we observe two sorts of elements of consciousness, the\ndistinction between which may best be made clear by means of an\nillustration. In a piece of music there are the separate notes, and\nthere is the air. A single tone may be prolonged for an hour or a day,\nand it exists as perfectly in each second of that time as in the whole\ntaken together; so that, as long as it is sounding, it might be present\nto a sense from which everything in the past was as completely absent as\nthe future itself. But it is different with the air, the performance of\nwhich occupies a certain time, during the portions of which only\nportions of it are played. It consists in an orderliness in the\nsuccession of sounds which strike the ear at different times; and to\nperceive it there must be some continuity of consciousness which makes\nthe events of a lapse of time present to us. We certainly only perceive\nthe air by hearing the separate notes; yet we cannot be said to directly\nhear it, for we hear only what is present at the instant, and an\norderliness of succession cannot exist in an instant. These two sorts of\nobjects, what we are _immediately_ conscious of and what we are\n_mediately_ conscious of, are found in all consciousness. Some elements\n(the sensations) are completely present at every instant so long as they\nlast, while others (like thought) are actions having beginning, middle,\nand end, and consist in a congruence in the succession of sensations\nwhich flow through the mind. They cannot be immediately present to us,\nbut must cover some portion of the past or future. Thought is a thread\nof melody running through the succession of our sensations.\n\nWe may add that just as a piece of music may be written in parts, each\npart having its own air, so various systems of relationship of\nsuccession subsist together between the same sensations. These different\nsystems are distinguished by having different motives, ideas, or\nfunctions. Thought is only one such system; for its sole motive, idea,\nand function is to produce belief, and whatever does not concern that\npurpose belongs to some other system of relations. The action of\nthinking may incidentally have other results. It may serve to amuse us,\nfor example, and among _dilettanti_ it is not rare to find those who\nhave so perverted thought to the purposes of pleasure that it seems to\nvex them to think that the questions upon which they delight to exercise\nit may ever get finally settled; and a positive discovery which takes a\nfavorite subject out of the arena of literary debate is met with\nill-concealed dislike. This disposition is the very debauchery of\nthought. But the soul and meaning of thought, abstracted from the other\nelements which accompany it, though it may be voluntarily thwarted, can\nnever be made to direct itself toward anything but the production of\nbelief. Thought in action has for its only possible motive the\nattainment of thought at rest; and whatever does not refer to belief is\nno part of the thought itself.\n\nAnd what, then, is belief? It is the demi-cadence which closes a musical\nphrase in the symphony of our intellectual life. We have seen that it\nhas just three properties: First, it is something that we are aware of;\nsecond, it appeases the irritation of doubt; and, third, it involves the\nestablishment in our nature of a rule of action, or, say for short, a\n_habit_. As it appeases the irritation of doubt, which is the motive for\nthinking, thought relaxes, and comes to rest for a moment when belief is\nreached. But, since belief is a rule for action, the application of\nwhich involves further doubt and further thought, at the same time that\nit is a stopping-place, it is also a new starting-place for thought.\nThat is why I have permitted myself to call it thought at rest, although\nthought is essentially an action. The _final_ upshot of thinking is the\nexercise of volition, and of this thought no longer forms a part; but\nbelief is only a stadium of mental action, an effect upon our nature due\nto thought, which will influence future thinking.\n\n[Illustration: Figure 1.]\n\n[Illustration: Figure 2.]\n\nThe essence of belief is the establishment of a habit, and different\nbeliefs are distinguished by the different modes of action to which they\ngive rise. If beliefs do not differ in this respect, if they appease the\nsame doubt by producing the same rule of action, then no mere\ndifferences in the manner of consciousness of them can make them\ndifferent beliefs, any more than playing a tune in different keys is\nplaying different tunes. Imaginary distinctions are often drawn between\nbeliefs which differ only in their mode of expression;\u2014the wrangling\nwhich ensues is real enough, however. To believe that any objects are\narranged as in Fig. 1, and to believe that they are arranged as in Fig.\n2, are one and the same belief; yet it is conceivable that a man should\nassert one proposition and deny the other. Such false distinctions do as\nmuch harm as the confusion of beliefs really different, and are among\nthe pitfalls of which we ought constantly to beware, especially when we\nare upon metaphysical ground. One singular deception of this sort, which\noften occurs, is to mistake the sensation produced by our own\nunclearness of thought for a character of the object we are thinking.\nInstead of perceiving that the obscurity is purely subjective, we fancy\nthat we contemplate a quality of the object which is essentially\nmysterious; and if our conception be afterward presented to us in a\nclear form we do not recognize it as the same, owing to the absence of\nthe feeling of unintelligibility. So long as this deception lasts, it\nobviously puts an impassable barrier in the way of perspicuous thinking;\nso that it equally interests the opponents of rational thought to\nperpetuate it, and its adherents to guard against it.\n\nAnother such deception is to mistake a mere difference in the\ngrammatical construction of two words for a distinction between the\nideas they express. In this pedantic age, when the general mob of\nwriters attend so much more to words than to things, this error is\ncommon enough. When I just said that thought is an _action_, and that it\nconsists in a _relation_, although a person performs an action but not a\nrelation, which can only be the result of an action, yet there was no\ninconsistency in what I said, but only a grammatical vagueness.\n\nFrom all these sophisms we shall be perfectly safe so long as we reflect\nthat the whole function of thought is to produce habits of action; and\nthat whatever there is connected with a thought, but irrelevant to its\npurpose, is an accretion to it, but no part of it. If there be a unity\namong our sensations which has no reference to how we shall act on a\ngiven occasion, as when we listen to a piece of music, why we do not\ncall that thinking. To develop its meaning, we have, therefore, simply\nto determine what habits it produces, for what a thing means is simply\nwhat habits it involves. Now, the identity of a habit depends on how it\nmight lead us to act, not merely under such circumstances as are likely\nto arise, but under such as might possibly occur, no matter how\nimprobable they may be. What the habit is depends on _when_ and _how_ it\ncauses us to act. As for the _when_, every stimulus to action is derived\nfrom perception; as for the _how_, every purpose of action is to produce\nsome sensible result. Thus, we come down to what is tangible and\npractical, as the root of every real distinction of thought, no matter\nhow subtile it may be; and there is no distinction of meaning so fine as\nto consist in anything but a possible difference of practice.\n\nTo see what this principle leads to, consider in the light of it such a\ndoctrine as that of transubstantiation. The Protestant churches\ngenerally hold that the elements of the sacrament are flesh and blood\nonly in a tropical sense; they nourish our souls as meat and the juice\nof it would our bodies. But the Catholics maintain that they are\nliterally just that; although they possess all the sensible qualities of\nwafer-cakes and diluted wine. But we can have no conception of wine\nexcept what may enter into a belief, either\u2014\n\n1. That this, that, or the other, is wine; or,\n\n2. That wine possesses certain properties.\n\nSuch beliefs are nothing but self-notifications that we should, upon\noccasion, act in regard to such things as we believe to be wine\naccording to the qualities which we believe wine to possess. The\noccasion of such action would be some sensible perception, the motive of\nit to produce some sensible result. Thus our action has exclusive\nreference to what affects the senses, our habit has the same bearing as\nour action, our belief the same as our habit, our conception the same as\nour belief; and we can consequently mean nothing by wine but what has\ncertain effects, direct or indirect, upon our senses; and to talk of\nsomething as having all the sensible characters of wine, yet being in\nreality blood, is senseless jargon. Now, it is not my object to pursue\nthe theological question; and having used it as a logical example I drop\nit, without caring to anticipate the theologian\u2019s reply. I only desire\nto point out how impossible it is that we should have an idea in our\nminds which relates to anything but conceived sensible effects of\nthings. Our idea of anything _is_ our idea of its sensible effects; and\nif we fancy that we have any other we deceive ourselves, and mistake a\nmere sensation accompanying the thought for a part of the thought\nitself. It is absurd to say that thought has any meaning unrelated to\nits only function. It is foolish for Catholics and Protestants to fancy\nthemselves in disagreement about the elements of the sacrament, if they\nagree in regard to all their sensible effects, here or hereafter.\n\nIt appears, then, that the rule for attaining the third grade of\nclearness of apprehension is as follows: Consider what effects, which\nmight conceivably have practical bearings, we conceive the object of our\nconception to have. Then, our conception of these effects is the whole\nof our conception of the object.\n\n\n                                  III\n\n\nLet us illustrate this rule by some examples; and, to begin with the\nsimplest one possible, let us ask what we mean by calling a thing\n_hard_. Evidently that it will not be scratched by many other\nsubstances. The whole conception of this quality, as of every other,\nlies in its conceived effects. There is absolutely no difference between\na hard thing and a soft thing so long as they are not brought to the\ntest. Suppose, then, that a diamond could be crystallized in the midst\nof a cushion of soft cotton, and should remain there until it was\nfinally burned up. Would it be false to say that that diamond was soft?\nThis seems a foolish question, and would be so, in fact, except in the\nrealm of logic. There such questions are often of the greatest utility\nas serving to bring logical principles into sharper relief than real\ndiscussions ever could. In studying logic we must not put them aside\nwith hasty answers, but must consider them with attentive care, in order\nto make out the principles involved. We may, in the present case, modify\nour question, and ask what prevents us from saying that all hard bodies\nremain perfectly soft until they are touched, when their hardness\nincreases with the pressure until they are scratched. Reflection will\nshow that the reply is this: there would be no _falsity_ in such modes\nof speech. They would involve a modification of our present usage of\nspeech with regard to the words hard and soft, but not of their\nmeanings. For they represent no fact to be different from what it is;\nonly they involve arrangements of facts which would be exceedingly\nmaladroit. This leads us to remark that the question of what would occur\nunder circumstances which do not actually arise is not a question of\nfact, but only of the most perspicuous arrangement of them. For example,\nthe question of free-will and fate in its simplest form, stripped of\nverbiage, is something like this: I have done something of which I am\nashamed; could I, by an effort of the will, have resisted the\ntemptation, and done otherwise? The philosophical reply is, that this is\nnot a question of fact, but only of the arrangement of facts. Arranging\nthem so as to exhibit what is particularly pertinent to my\nquestion\u2014namely, that I ought to blame myself for having done wrong\u2014it\nis perfectly true to say that, if I had willed to do otherwise than I\ndid, I should have done otherwise. On the other hand, arranging the\nfacts so as to exhibit another important consideration, it is equally\ntrue that, when a temptation has once been allowed to work, it will, if\nit has a certain force, produce its effect, let me struggle how I may.\nThere is no objection to a contradiction in what would result from a\nfalse supposition. The _reductio ad absurdum_ consists in showing that\ncontradictory results would follow from a hypothesis which is\nconsequently judged to be false. Many questions are involved in the\nfree-will discussion, and I am far from desiring to say that both sides\nare equally right. On the contrary, I am of opinion that one side denies\nimportant facts, and that the other does not. But what I do say is, that\nthe above single question was the origin of the whole doubt; that, had\nit not been for this question, the controversy would never have arisen;\nand that this question is perfectly solved in the manner which I have\nindicated.\n\nLet us next seek a clear idea of Weight. This is another very easy case.\nTo say that a body is heavy means simply that, in the absence of\nopposing force, it will fall. This (neglecting certain specifications of\nhow it will fall, etc., which exist in the mind of the physicist who\nuses the word) is evidently the whole conception of weight. It is a fair\nquestion whether some particular facts may not _account_ for gravity;\nbut what we mean by the force itself is completely involved in its\neffects.\n\nThis leads us to undertake an account of the idea of Force in general.\nThis is the great conception which, developed in the early part of the\nseventeenth century from the rude idea of a cause, and constantly\nimproved upon since, has shown us how to explain all the changes of\nmotion which bodies experience, and how to think about all physical\nphenomena; which has given birth to modern science, and changed the face\nof the globe; and which, aside from its more special uses, has played a\nprincipal part in directing the course of modern thought, and in\nfurthering modern social development. It is, therefore, worth some pains\nto comprehend it. According to our rule, we must begin by asking what is\nthe immediate use of thinking about force; and the answer is, that we\nthus account for changes of motion. If bodies were left to themselves,\nwithout the intervention of forces, every motion would continue\nunchanged both in velocity and in direction. Furthermore, change of\nmotion never takes place abruptly; if its direction is changed, it is\nalways through a curve without angles; if its velocity alters, it is by\ndegrees. The gradual changes which are constantly taking place are\nconceived by geometers to be compounded together according to the rules\nof the parallelogram of forces. If the reader does not already know what\nthis is, he will find it, I hope, to his advantage to endeavor to follow\nthe following explanation; but if mathematics are insupportable to him,\npray let him skip three paragraphs rather than that we should part\ncompany here.\n\nA _path_ is a line whose beginning and end are distinguished. Two paths\nare considered to be equivalent, which, beginning at the same point,\nlead to the same point. Thus the two paths, _A B C D E_ and _A F G H E_\n(Fig. 3), are equivalent. Paths which do _not_ begin at the same point\nare considered to be equivalent, provided that, on moving either of them\nwithout turning it, but keeping it always parallel to its original\nposition, [so that] when its beginning coincides with that of the other\npath, the ends also coincide. Paths are considered as geometrically\nadded together, when one begins where the other ends; thus the path _A\nE_ is conceived to be a sum of _A B_, _B C_, _C D_, and _D E_. In the\nparallelogram of Fig. 4 the diagonal _A C_ is the sum of _A B_ and _B\nC_; or, since _A D_ is geometrically equivalent to _B C_, _A C_ is the\ngeometrical sum of _A B_ and _A D_.\n\n[Illustration: Figure 3.]\n\n[Illustration: Figure 4.]\n\nAll this is purely conventional. It simply amounts to this: that we\nchoose to call paths having the relations I have described equal or\nadded. But, though it is a convention, it is a convention with a good\nreason. The rule for geometrical addition may be applied not only to\npaths, but to any other things which can be represented by paths. Now,\nas a path is determined by the varying direction and distance of the\npoint which moves over it from the starting-point, it follows that\nanything which from its beginning to its end is determined by a varying\ndirection and a varying magnitude is capable of being represented by a\nline. Accordingly, _velocities_ may be represented by lines, for they\nhave only directions and rates. The same thing is true of\n_accelerations_, or changes of velocities. This is evident enough in the\ncase of velocities; and it becomes evident for accelerations if we\nconsider that precisely what velocities are to positions\u2014namely, states\nof change of them\u2014that accelerations are to velocities.\n\n[Illustration: Figure 5.]\n\nThe so-called \u201cparallelogram of forces\u201d is simply a rule for compounding\naccelerations. The rule is, to represent the accelerations by paths, and\nthen to geometrically add the paths. The geometers, however, not only\nuse the \u201cparallelogram of forces\u201d to compound different accelerations,\nbut also to resolve one acceleration into a sum of several. Let _A B_\n(Fig. 5) be the path which represents a certain acceleration\u2014say, such a\nchange in the motion of a body that at the end of one second the body\nwill, under the influence of that change, be in a position different\nfrom what it would have had if its motion had continued unchanged, such\nthat a path equivalent to _A B_ would lead from the latter position to\nthe former. This acceleration may be considered as the sum of the\naccelerations represented by _A C_ and _C B_. It may also be considered\nas the sum of the very different accelerations represented by _A D_ and\n_D B_, where _A D_ is almost the opposite of _A C_. And it is clear that\nthere is an immense variety of ways in which _A B_ might be resolved\ninto the sum of two accelerations.\n\nAfter this tedious explanation, which I hope, in view of the\nextraordinary interest of the conception of force, may not have\nexhausted the reader\u2019s patience, we are prepared at last to state the\ngrand fact which this conception embodies. This fact is that if the\nactual changes of motion which the different particles of bodies\nexperience are each resolved in its appropriate way, each component\nacceleration is precisely such as is prescribed by a certain law of\nNature, according to which bodies in the relative positions which the\nbodies in question actually have at the moment,[32] always receive\ncertain accelerations, which, being compounded by geometrical addition,\ngive the acceleration which the body actually experiences.\n\nThis is the only fact which the idea of force represents, and whoever\nwill take the trouble clearly to apprehend what this fact is, perfectly\ncomprehends what force is. Whether we ought to say that a force _is_ an\nacceleration, or that it _causes_ an acceleration, is a mere question of\npropriety of language, which has no more to do with our real meaning\nthan the difference between the French idiom \u201c_Il fait froid_\u201d and its\nEnglish equivalent \u201c_It is cold_.\u201d Yet it is surprising to see how this\nsimple affair has muddled men\u2019s minds. In how many profound treatises is\nnot force spoken of as a \u201cmysterious entity,\u201d which seems to be only a\nway of confessing that the author despairs of ever getting a clear\nnotion of what the word means! In a recent admired work on _Analytic\nMechanics_ it is stated that we understand precisely the effect of\nforce, but what force itself is we do not understand! This is simply a\nself-contradiction. The idea which the word force excites in our minds\nhas no other function than to affect our actions, and these actions can\nhave no reference to force otherwise than through its effects.\nConsequently, if we know what the effects of force are, we are\nacquainted with every fact which is implied in saying that a force\nexists, and there is nothing more to know. The truth is, there is some\nvague notion afloat that a question may mean something which the mind\ncannot conceive; and when some hair-splitting philosophers have been\nconfronted with the absurdity of such a view, they have invented an\nempty distinction between positive and negative conceptions, in the\nattempt to give their non-idea a form not obviously nonsensical. The\nnullity of it is sufficiently plain from the considerations given a few\npages back; and, apart from those considerations, the quibbling\ncharacter of the distinction must have struck every mind accustomed to\nreal thinking.\n\n\n                                   IV\n\n\nLet us now approach the subject of logic, and consider a conception\nwhich particularly concerns it, that of _reality_. Taking clearness in\nthe sense of familiarity, no idea could be clearer than this. Every\nchild uses it with perfect confidence, never dreaming that he does not\nunderstand it. As for clearness in its second grade, however, it would\nprobably puzzle most men, even among those of a reflective turn of mind,\nto give an abstract definition of the real. Yet such a definition may\nperhaps be reached by considering the points of difference between\nreality and its opposite, fiction. A figment is a product of somebody\u2019s\nimagination; it has such characters as his thought impresses upon it.\nThat those characters are independent of how you or I think is an\nexternal reality. There are, however, phenomena within our own minds,\ndependent upon our thought, which are at the same time real in the sense\nthat we really think them. But though their characters depend on how we\nthink, they do not depend on what we think those characters to be. Thus,\na dream has a real existence as a mental phenomenon, if somebody has\nreally dreamt it; that he dreamt so and so, does not depend on what\nanybody thinks was dreamt, but is completely independent of all opinion\non the subject. On the other hand, considering, not the fact of\ndreaming, but the thing dreamt, it retains its peculiarities by virtue\nof no other fact than that it was dreamt to possess them. Thus we may\ndefine the real as that whose characters are independent of what anybody\nmay think them to be.\n\nBut, however satisfactory such a definition may be found, it would be a\ngreat mistake to suppose that it makes the idea of reality perfectly\nclear. Here, then, let us apply our rules. According to them, reality,\nlike every other quality, consists in the peculiar sensible effects\nwhich things partaking of it produce. The only effect which real things\nhave is to cause belief, for all the sensations which they excite emerge\ninto consciousness in the form of beliefs. The question, therefore, is,\nhow is true belief (or belief in the real) distinguished from false\nbelief (or belief in fiction). Now, as we have seen in the former paper,\nthe ideas of truth and falsehood, in their full development, appertain\nexclusively to the scientific method of settling opinion. A person who\narbitrarily chooses the propositions which he will adopt can use the\nword truth only to emphasize the expression of his determination to hold\non to his choice. Of course, the method of tenacity never prevailed\nexclusively; reason is too natural to men for that. But in the\nliterature of the dark ages we find some fine examples of it. When\nScotus Erigena is commenting upon a poetical passage in which hellebore\nis spoken of as having caused the death of Socrates, he does not\nhesitate to inform the inquiring reader that Helleborus and Socrates\nwere two eminent Greek philosophers, and that the latter having been\novercome in argument by the former took the matter to heart and died of\nit! What sort of an idea of truth could a man have who could adopt and\nteach, without the qualification of a perhaps, an opinion taken so\nentirely at random? The real spirit of Socrates, who I hope would have\nbeen delighted to have been \u201covercome in argument,\u201d because he would\nhave learned something by it, is in curious contrast with the na\u00efve idea\nof the glossist, for whom discussion would seem to have been simply a\nstruggle. When philosophy began to awake from its long slumber, and\nbefore theology completely dominated it, the practice seems to have been\nfor each professor to seize upon any philosophical position he found\nunoccupied and which seemed a strong one, to intrench himself in it, and\nto sally forth from time to time to give battle to the others. Thus,\neven the scanty records we possess of those disputes enable us to make\nout a dozen or more opinions held by different teachers at one time\nconcerning the question of nominalism and realism. Read the opening part\nof the _Historia Calamitatum_ of Abelard, who was certainly as\nphilosophical as any of his contemporaries, and see the spirit of combat\nwhich it breathes. For him, the truth is simply his particular\nstronghold. When the method of authority prevailed, the truth meant\nlittle more than the Catholic faith. All the efforts of the scholastic\ndoctors are directed toward harmonizing their faith in Aristotle and\ntheir faith in the Church, and one may search their ponderous folios\nthrough without finding an argument which goes any further. It is\nnoticeable that where different faiths flourish side by side, renegades\nare looked upon with contempt even by the party whose belief they adopt;\nso completely has the idea of loyalty replaced that of truth-seeking.\nSince the time of Descartes, the defect in the conception of truth has\nbeen less apparent. Still, it will sometimes strike a scientific man\nthat the philosophers have been less intent on finding out what the\nfacts are, than on inquiring what belief is most in harmony with their\nsystem. It is hard to convince a follower of the _a priori_ method by\nadducing facts; but show him that an opinion he is defending is\ninconsistent with what he has laid down elsewhere, and he will be very\napt to retract it. These minds do not seem to believe that disputation\nis ever to cease; they seem to think that the opinion which is natural\nfor one man is not so for another, and that belief will, consequently,\nnever be settled. In contenting themselves with fixing their own\nopinions by a method which would lead another man to a different result,\nthey betray their feeble hold of the conception of what truth is.\n\nOn the other hand, all the followers of science are fully persuaded that\nthe processes of investigation, if only pushed far enough, will give one\ncertain solution to every question to which they can be applied. One man\nmay investigate the velocity of light by studying the transits of Venus\nand the aberration of the stars; another by the oppositions of Mars and\nthe eclipses of Jupiter\u2019s satellites; a third by the method of Fizeau; a\nfourth by that of Foucault; a fifth by the motions of the curves of\nLissajoux; a sixth, a seventh, an eighth, and a ninth, may follow the\ndifferent methods of comparing the measures of statical and dynamical\nelectricity. They may at first obtain different results, but, as each\nperfects his method and his processes, the results will move steadily\ntogether toward a destined center. So with all scientific research.\nDifferent minds may set out with the most antagonistic views, but the\nprogress of investigation carries them by a force outside of themselves\nto one and the same conclusion. This activity of thought by which we are\ncarried, not where we wish, but to a fore-ordained goal, is like the\noperation of destiny. No modification of the point of view taken, no\nselection of other facts for study, no natural bent of mind even, can\nenable a man to escape the predestinate opinion. This great law is\nembodied in the conception of truth and reality. The opinion which is\nfated[33] to be ultimately agreed to by all who investigate, is what we\nmean by the truth, and the object represented in this opinion is the\nreal. That is the way I would explain reality.\n\nBut it may be said that this view is directly opposed to the abstract\ndefinition which we have given of reality, inasmuch as it makes the\ncharacters of the real depend on what is ultimately thought about them.\nBut the answer to this is that, on the one hand, reality is independent,\nnot necessarily of thought in general, but only of what you or I or any\nfinite number of men may think about it; and that, on the other hand,\nthough the object of the final opinion depends on what that opinion is,\nyet what that opinion is does not depend on what you or I or any man\nthinks. Our perversity and that of others may indefinitely postpone the\nsettlement of opinion; it might even conceivably cause an arbitrary\nproposition to be universally accepted as long as the human race should\nlast. Yet even that would not change the nature of the belief, which\nalone could be the result of investigation carried sufficiently far; and\nif, after the extinction of our race, another should arise with\nfaculties and disposition for investigation, that true opinion must be\nthe one which they would ultimately come to. \u201cTruth crushed to earth\nshall rise again,\u201d and the opinion which would finally result from\ninvestigation does not depend on how anybody may actually think. But the\nreality of that which is real does depend on the real fact that\ninvestigation is destined to lead, at last, if continued long enough, to\na belief in it.\n\nBut I may be asked what I have to say to all the minute facts of\nhistory, forgotten never to be recovered, to the lost books of the\nancients, to the buried secrets.\n\n               \u201cFull many a gem of purest ray serene\n                 The dark, unfathomed caves of ocean bear;\n               Full many a flower is born to blush unseen,\n                 And waste its sweetness on the desert air.\u201d\n\nDo these things not really exist because they are hopelessly beyond the\nreach of our knowledge? And then, after the universe is dead (according\nto the prediction of some scientists), and all life has ceased forever,\nwill not the shock of atoms continue though there will be no mind to\nknow it? To this I reply that, though in no possible state of knowledge\ncan any number be great enough to express the relation between the\namount of what rests unknown to the amount of the known, yet it is\nunphilosophical to suppose that, with regard to any given question\n(which has any clear meaning), investigation would not bring forth a\nsolution of it, if it were carried far enough. Who would have said, a\nfew years ago, that we could ever know of what substances stars are made\nwhose light may have been longer in reaching us than the human race has\nexisted? Who can be sure of what we shall not know in a few hundred\nyears? Who can guess what would be the result of continuing the pursuit\nof science for ten thousand years, with the activity of the last\nhundred? And if it were to go on for a million, or a billion, or any\nnumber of years you please, how is it possible to say that there is any\nquestion which might not ultimately be solved?\n\nBut it may be objected, \u201cWhy make so much of these remote\nconsiderations, especially when it is your principle that only practical\ndistinctions have a meaning?\u201d Well, I must confess that it makes very\nlittle difference whether we say that a stone on the bottom of the\nocean, in complete darkness, is brilliant or not\u2014that is to say, that it\n_probably_ makes no difference, remembering always that that stone _may_\nbe fished up to-morrow. But that there are gems at the bottom of the\nsea, flowers in the untraveled desert, etc., are propositions which,\nlike that about a diamond being hard when it is not pressed, concern\nmuch more the arrangement of our language than they do the meaning of\nour ideas.\n\nIt seems to me, however, that we have, by the application of our rule,\nreached so clear an apprehension of what we mean by reality, and of the\nfact which the idea rests on, that we should not, perhaps, be making a\npretension so presumptuous as it would be singular, if we were to offer\na metaphysical theory of existence for universal acceptance among those\nwho employ the scientific method of fixing belief. However, as\nmetaphysics is a subject much more curious than useful, the knowledge of\nwhich, like that of a sunken reef, serves chiefly to enable us to keep\nclear of it, I will not trouble the reader with any more Ontology at\nthis moment. I have already been led much further into that path than I\nshould have desired; and I have given the reader such a dose of\nmathematics, psychology, and all that is most abstruse, that I fear he\nmay already have left me, and that what I am now writing is for the\ncompositor and proofreader exclusively. I trusted to the importance of\nthe subject. There is no royal road to logic, and really valuable ideas\ncan only be had at the price of close attention. But I know that in the\nmatter of ideas the public prefer the cheap and nasty; and in my next\npaper I am going to return to the easily intelligible, and not wander\nfrom it again. The reader who has been at the pains of wading through\nthis paper, shall be rewarded in the next one by seeing how beautifully\nwhat has been developed in this tedious way can be applied to the\nascertainment of the rules of scientific reasoning.\n\nWe have, hitherto, not crossed the threshold of scientific logic. It is\ncertainly important to know how to make our ideas clear, but they may be\never so clear without being true. How to make them so, we have next to\nstudy. How to give birth to those vital and procreative ideas which\nmultiply into a thousand forms and diffuse themselves everywhere,\nadvancing civilization and making the dignity of man, is an art not yet\nreduced to rules, but of the secret of which the history of science\naffords some hints.\n\nFootnote 31:\n\n  _Popular Science Monthly_, January, 1878.\n\nFootnote 32:\n\n  Possibly the velocities also have to be taken into account.\n\nFootnote 33:\n\n  Fate means merely that which is sure to come true, and can nohow be\n  avoided. It is a superstition to suppose that a certain sort of events\n  are ever fated, and it is another to suppose that the word fate can\n  never be freed from its superstitious taint. We are all fated to die.\n\n\n\n\n                              THIRD PAPER\n                      THE DOCTRINE OF CHANCES[34]\n\n\n                                   I\n\n\nIt is a common observation that a science first begins to be exact when\nit is quantitatively treated. What are called the exact sciences are no\nothers than the mathematical ones. Chemists reasoned vaguely until\nLavoisier showed them how to apply the balance to the verification of\ntheir theories, when chemistry leaped suddenly into the position of the\nmost perfect of the classificatory sciences. It has thus become so\nprecise and certain that we usually think of it along with optics,\nthermotics, and electrics. But these are studies of general laws, while\nchemistry considers merely the relations and classification of certain\nobjects; and belongs, in reality, in the same category as systematic\nbotany and zo\u00f6logy. Compare it with these last, however, and the\nadvantage that it derives from its quantitative treatment is very\nevident.\n\nThe rudest numerical scales, such as that by which the mineralogists\ndistinguish the different degrees of hardness, are found useful. The\nmere counting of pistils and stamens sufficed to bring botany out of\ntotal chaos into some kind of form. It is not, however, so much from\n_counting_ as from _measuring_, not so much from the conception of\nnumber as from that of continuous quantity, that the advantage of\nmathematical treatment comes. Number, after all, only serves to pin us\ndown to a precision in our thoughts which, however beneficial, can\nseldom lead to lofty conceptions, and frequently descends to pettiness.\nOf those two faculties of which Bacon speaks, that which marks\ndifferences and that which notes resemblances, the employment of number\ncan only aid the lesser one; and the excessive use of it must tend to\nnarrow the powers of the mind. But the conception of continuous quantity\nhas a great office to fulfill, independently of any attempt at\nprecision. Far from tending to the exaggeration of differences, it is\nthe direct instrument of the finest generalizations. When a naturalist\nwishes to study a species, he collects a considerable number of\nspecimens more or less similar. In contemplating them, he observes\ncertain ones which are more or less alike in some particular respect.\nThey all have, for instance, a certain S-shaped marking. He observes\nthat they are not _precisely_ alike, in this respect; the S has not\nprecisely the same shape, but the differences are such as to lead him to\nbelieve that forms could be found intermediate between any two of those\nhe possesses. He, now, finds other forms apparently quite dissimilar\u2014say\na marking in the form of a C\u2014and the question is, whether he can find\nintermediate ones which will connect these latter with the others. This\nhe often succeeds in doing in cases where it would at first be thought\nimpossible; whereas he sometimes finds those which differ, at first\nglance, much less, to be separated in Nature by the non-occurrence of\nintermediaries. In this way, he builds up from the study of Nature a new\ngeneral conception of the character in question. He obtains, for\nexample, an idea of a leaf which includes every part of the flower, and\nan idea of a vertebra which includes the skull. I surely need not say\nmuch to show what a logical engine there is here. It is the essence of\nthe method of the naturalist.[35] How he applies it first to one\ncharacter, and then to another, and finally obtains a notion of a\nspecies of animals, the differences between whose members, however\ngreat, are confined within limits, is a matter which does not here\nconcern us. The whole method of classification must be considered later;\nbut, at present, I only desire to point out that it is by taking\nadvantage of the idea of continuity, or the passage from one form to\nanother by insensible degrees, that the naturalist builds his\nconceptions. Now, the naturalists are the great builders of conceptions;\nthere is no other branch of science where so much of this work is done\nas in theirs; and we must, in great measure, take them for our teachers\nin this important part of logic. And it will be found everywhere that\nthe idea of continuity is a powerful aid to the formation of true and\nfruitful conceptions. By means of it, the greatest differences are\nbroken down and resolved into differences of degree, and the incessant\napplication of it is of the greatest value in broadening our\nconceptions. I propose to make a great use of this idea in the present\nseries of papers; and the particular series of important fallacies,\nwhich, arising from a neglect of it, have desolated philosophy, must\nfurther on be closely studied. At present, I simply call the reader\u2019s\nattention to the utility of this conception.\n\nIn studies of numbers, the idea of continuity is so indispensable, that\nit is perpetually introduced even where there is no continuity in fact,\nas where we say that there are in the United States 10.7 inhabitants per\nsquare mile, or that in New York 14.72 persons live in the average\nhouse.[36] Another example is that law of the distribution of errors\nwhich Quetelet, Galton, and others, have applied with so much success to\nthe study of biological and social matters. This application of\ncontinuity to cases where it does not really exist illustrates, also,\nanother point which will hereafter demand a separate study, namely, the\ngreat utility which fictions sometimes have in science.\n\n\n                                   II\n\n\nThe theory of probabilities is simply the science of logic\nquantitatively treated. There are two conceivable certainties with\nreference to any hypothesis, the certainty of its truth and the\ncertainty of its falsity. The numbers _one_ and _zero_ are appropriated,\nin this calculus, to marking these extremes of knowledge; while\nfractions having values intermediate between them indicate, as we may\nvaguely say, the degrees in which the evidence leans toward one or the\nother. The general problem of probabilities is, from a given state of\nfacts, to determine the numerical probability of a possible fact. This\nis the same as to inquire how much the given facts are worth, considered\nas evidence to prove the possible fact. Thus the problem of\nprobabilities is simply the general problem of logic.\n\nProbability is a continuous quantity, so that great advantages may be\nexpected from this mode of studying logic. Some writers have gone so far\nas to maintain that, by means of the calculus of chances, every solid\ninference may be represented by legitimate arithmetical operations upon\nthe numbers given in the premises. If this be, indeed, true, the great\nproblem of logic, how it is that the observation of one fact can give us\nknowledge of another independent fact, is reduced to a mere question of\narithmetic. It seems proper to examine this pretension before\nundertaking any more recondite solution of the paradox.\n\nBut, unfortunately, writers on probabilities are not agreed in regard to\nthis result. This branch of mathematics is the only one, I believe, in\nwhich good writers frequently get results entirely erroneous. In\nelementary geometry the reasoning is frequently fallacious, but\nerroneous conclusions are avoided; but it may be doubted if there is a\nsingle extensive treatise on probabilities in existence which does not\ncontain solutions absolutely indefensible. This is partly owing to the\nwant of any regular method of procedure; for the subject involves too\nmany subtilties to make it easy to put its problems into equations\nwithout such an aid. But, beyond this, the fundamental principles of its\ncalculus are more or less in dispute. In regard to that class of\nquestions to which it is chiefly applied for practical purposes, there\nis comparatively little doubt; but in regard to others to which it has\nbeen sought to extend it, opinion is somewhat unsettled.\n\nThis last class of difficulties can only be entirely overcome by making\nthe idea of probability perfectly clear in our minds in the way set\nforth in our last paper.\n\n\n                                  III\n\n\nTo get a clear idea of what we mean by probability, we have to consider\nwhat real and sensible difference there is between one degree of\nprobability and another.\n\nThe character of probability belongs primarily, without doubt, to\ncertain inferences. Locke explains it as follows: After remarking that\nthe mathematician positively knows that the sum of the three angles of a\ntriangle is equal to two right angles because he apprehends the\ngeometrical proof, he thus continues: \u201cBut another man who never took\nthe pains to observe the demonstration, hearing a mathematician, a man\nof credit, affirm the three angles of a triangle to be equal to two\nright ones, _assents_ to it; i.e., receives it for true. In which case\nthe foundation of his assent is the probability of the thing, the proof\nbeing such as, for the most part, carries truth with it; the man on\nwhose testimony he receives it not being wont to affirm anything\ncontrary to, or besides his knowledge, especially in matters of this\nkind.\u201d The celebrated _Essay concerning Human Understanding_ contains\nmany passages which, like this one, make the first steps in profound\nanalyses which are not further developed. It was shown in the first of\nthese papers that the validity of an inference does not depend on any\ntendency of the mind to accept it, however strong such tendency may be;\nbut consists in the real fact that, when premises like those of the\nargument in question are true, conclusions related to them like that of\nthis argument are also true. It was remarked that in a logical mind an\nargument is always conceived as a member of a _genus_ of arguments all\nconstructed in the same way, and such that, when their premises are real\nfacts, their conclusions are so also. If the argument is demonstrative,\nthen this is always so; if it is only probable, then it is for the most\npart so. As Locke says, the probable argument is \u201c_such as_ for the most\npart carries truth with it.\u201d\n\nAccording to this, that real and sensible difference between one degree\nof probability and another, in which the meaning of the distinction\nlies, is that in the frequent employment of two different modes of\ninference, one will carry truth with it oftener than the other. It is\nevident that this is the only difference there is in the existing fact.\nHaving certain premises, a man draws a certain conclusion, and as far as\nthis inference alone is concerned the only possible practical question\nis whether that conclusion is true or not, and between existence and\nnon-existence there is no middle term. \u201cBeing only is and nothing is\naltogether not,\u201d said Parmenides; and this is in strict accordance with\nthe analysis of the conception of reality given in the last paper. For\nwe found that the distinction of reality and fiction depends on the\nsupposition that sufficient investigation would cause one opinion to be\nuniversally received and all others to be rejected. That presupposition,\ninvolved in the very conceptions of reality and figment, involves a\ncomplete sundering of the two. It is the heaven-and-hell idea in the\ndomain of thought. But, in the long run, there is a real fact which\ncorresponds to the idea of probability, and it is that a given mode of\ninference sometimes proves successful and sometimes not, and that in a\nratio ultimately fixed. As we go on drawing inference after inference of\nthe given kind, during the first ten or hundred cases the ratio of\nsuccesses may be expected to show considerable fluctuations; but when we\ncome into the thousands and millions, these fluctuations become less and\nless; and if we continue long enough, the ratio will approximate toward\na fixed limit. We may, therefore, define the probability of a mode of\nargument as the proportion of cases in which it carries truth with it.\n\nThe inference from the premise, A, to the conclusion, B, depends, as we\nhave seen, on the guiding principle, that if a fact of the class A is\ntrue, a fact of the class B is true. The probability consists of the\nfraction whose numerator is the number of times in which both A and B\nare true, and whose denominator is the total number of times in which A\nis true, whether B is so or not. Instead of speaking of this as the\nprobability of the inference, there is not the slightest objection to\ncalling it the probability that, if A happens, B happens. But to speak\nof the probability of the event B, without naming the condition, really\nhas no meaning at all. It is true that when it is perfectly obvious what\ncondition is meant, the ellipsis may be permitted. But we should avoid\ncontracting the habit of using language in this way (universal as the\nhabit is), because it gives rise to a vague way of thinking, as if the\naction of causation might either determine an event to happen or\ndetermine it not to happen, or leave it more or less free to happen or\nnot, so as to give rise to an _inherent_ chance in regard to its\noccurrence.[37] It is quite clear to me that some of the worst and most\npersistent errors in the use of the doctrine of chances have arisen from\nthis vicious mode of expression.[38]\n\n\n                                   IV\n\n\nBut there remains an important point to be cleared up. According to what\nhas been said, the idea of probability essentially belongs to a kind of\ninference which is repeated indefinitely. An individual inference must\nbe either true or false, and can show no effect of probability; and,\ntherefore, in reference to a single case considered in itself,\nprobability can have no meaning. Yet if a man had to choose between\ndrawing a card from a pack containing twenty-five red cards and a black\none, or from a pack containing twenty-five black cards and a red one,\nand if the drawing of a red card were destined to transport him to\neternal felicity, and that of a black one to consign him to everlasting\nwoe, it would be folly to deny that he ought to prefer the pack\ncontaining the larger portion of red cards, although, from the nature of\nthe risk, it could not be repeated. It is not easy to reconcile this\nwith our analysis of the conception of chance. But suppose he should\nchoose the red pack, and should draw the wrong card, what consolation\nwould he have? He might say that he had acted in accordance with reason,\nbut that would only show that his reason was absolutely worthless. And\nif he should choose the right card, how could he regard it as anything\nbut a happy accident? He could not say that if he had drawn from the\nother pack, he might have drawn the wrong one, because an hypothetical\nproposition such as, \u201cif A, then B,\u201d means nothing with reference to a\nsingle case. Truth consists in the existence of a real fact\ncorresponding to the true proposition. Corresponding to the proposition,\n\u201cif A, then B,\u201d there may be the fact that _whenever_ such an event as A\nhappens such an event as B happens. But in the case supposed, which has\nno parallel as far as this man is concerned, there would be no real fact\nwhose existence could give any truth to the statement that, if he had\ndrawn from the other pack, he might have drawn a black card. Indeed,\nsince the validity of an inference consists in the truth of the\nhypothetical proposition that _if_ the premises be true the conclusion\nwill also be true, and since the only real fact which can correspond to\nsuch a proposition is that whenever the antecedent is true the\nconsequent is so also, it follows that there can be no sense in\nreasoning in an isolated case, at all.\n\nThese considerations appear, at first sight, to dispose of the\ndifficulty mentioned. Yet the case of the other side is not yet\nexhausted. Although probability will probably manifest its effect in,\nsay, a thousand risks, by a certain proportion between the numbers of\nsuccesses and failures, yet this, as we have seen, is only to say that\nit certainly will, at length, do so. Now the number of risks, the number\nof probable inferences, which a man draws in his whole life, is a finite\none, and he cannot be absolutely _certain_ that the mean result will\naccord with the probabilities at all. Taking all his risks collectively,\nthen, it cannot be certain that they will not fail, and his case does\nnot differ, except in degree, from the one last supposed. It is an\nindubitable result of the theory of probabilities that every gambler, if\nhe continues long enough, must ultimately be ruined. Suppose he tries\nthe martingale, which some believe infallible, and which is, as I am\ninformed, disallowed in the gambling-houses. In this method of playing,\nhe first bets say $1; if he loses it he bets $2; if he loses that he\nbets $4; if he loses that he bets $8; if he then gains he has lost 1 + 2\n+ 4 = 7, and he has gained $1 more; and no matter how many bets he\nloses, the first one he gains will make him $1 richer than he was in the\nbeginning. In that way, he will probably gain at first; but, at last,\nthe time will come when the run of luck is so against him that he will\nnot have money enough to double, and must, therefore, let his bet go.\nThis will _probably_ happen before he has won as much as he had in the\nfirst place, so that this run against him will leave him poorer than he\nbegan; some time or other it will be sure to happen. It is true that\nthere is always a possibility of his winning any sum the bank can pay,\nand we thus come upon a celebrated paradox that, though he is certain to\nbe ruined, the value of his expectation calculated according to the\nusual rules (which omit this consideration) is large. But, whether a\ngambler plays in this way or any other, the same thing is true, namely,\nthat if he plays long enough he will be sure some time to have such a\nrun against him as to exhaust his entire fortune. The same thing is true\nof an insurance company. Let the directors take the utmost pains to be\nindependent of great conflagrations and pestilences, their actuaries can\ntell them that, according to the doctrine of chances, the time must\ncome, at last, when their losses will bring them to a stop. They may\ntide over such a crisis by extraordinary means, but then they will start\nagain in a weakened state, and the same thing will happen again all the\nsooner. An actuary might be inclined to deny this, because he knows that\nthe expectation of his company is large, or perhaps (neglecting the\ninterest upon money) is infinite. But calculations of expectations leave\nout of account the circumstance now under consideration, which reverses\nthe whole thing. However, I must not be understood as saying that\ninsurance is on this account unsound, more than other kinds of business.\nAll human affairs rest upon probabilities, and the same thing is true\neverywhere. If man were immortal he could be perfectly sure of seeing\nthe day when everything in which he had trusted should betray his trust,\nand, in short, of coming eventually to hopeless misery. He would break\ndown, at last, as every good fortune, as every dynasty, as every\ncivilization does. In place of this we have death.\n\nBut what, without death, would happen to every man, with death must\nhappen to some man. At the same time, death makes the number of our\nrisks, of our inferences, finite, and so makes their mean result\nuncertain. The very idea of probability and of reasoning rests on the\nassumption that this number is indefinitely great. We are thus landed in\nthe same difficulty as before, and I can see but one solution of it. It\nseems to me that we are driven to this, that logicality inexorably\nrequires that our interests shall _not_ be limited. They must not stop\nat our own fate, but must embrace the whole community. This community,\nagain, must not be limited, but must extend to all races of beings with\nwhom we can come into immediate or mediate intellectual relation. It\nmust reach, however vaguely, beyond this geological epoch, beyond all\nbounds. He who would not sacrifice his own soul to save the whole world,\nis, as it seems to me, illogical in all his inferences, collectively.\nLogic is rooted in the social principle.\n\nTo be logical men should not be selfish; and, in point of fact, they are\nnot so selfish as they are thought. The willful prosecution of one\u2019s\ndesires is a different thing from selfishness. The miser is not selfish;\nhis money does him no good, and he cares for what shall become of it\nafter his death. We are constantly speaking of _our_ possessions on the\nPacific, and of _our_ destiny as a republic, where no personal interests\nare involved, in a way which shows that we have wider ones. We discuss\nwith anxiety the possible exhaustion of coal in some hundreds of years,\nor the cooling-off of the sun in some millions, and show in the most\npopular of all religious tenets that we can conceive the possibility of\na man\u2019s descending into hell for the salvation of his fellows.\n\nNow, it is not necessary for logicality that a man should himself be\ncapable of the heroism of self-sacrifice. It is sufficient that he\nshould recognize the possibility of it, should perceive that only that\nman\u2019s inferences who has it are really logical, and should consequently\nregard his own as being only so far valid as they would be accepted by\nthe hero. So far as he thus refers his inferences to that standard, he\nbecomes identified with such a mind.\n\nThis makes logicality attainable enough. Sometimes we can personally\nattain to heroism. The soldier who runs to scale a wall knows that he\nwill probably be shot, but that is not all he cares for. He also knows\nthat if all the regiment, with whom in feeling he identifies himself,\nrush forward at once, the fort will be taken. In other cases we can only\nimitate the virtue. The man whom we have supposed as having to draw from\nthe two packs, who if he is not a logician will draw from the red pack\nfrom mere habit, will see, if he is logician enough, that he cannot be\nlogical so long as he is concerned only with his own fate, but that that\nman who should care equally for what was to happen in all possible cases\nof the sort could act logically, and would draw from the pack with the\nmost red cards, and thus, though incapable himself of such sublimity,\nour logician would imitate the effect of that man\u2019s courage in order to\nshare his logicality.\n\nBut all this requires a conceived identification of one\u2019s interests with\nthose of an unlimited community. Now, there exist no reasons, and a\nlater discussion will show that there can be no reasons, for thinking\nthat the human race, or any intellectual race, will exist forever. On\nthe other hand, there can be no reason against it;[39] and, fortunately,\nas the whole requirement is that we should have certain sentiments,\nthere is nothing in the facts to forbid our having a _hope_, or calm and\ncheerful wish, that the community may last beyond any assignable date.\n\nIt may seem strange that I should put forward three sentiments, namely,\ninterest in an indefinite community, recognition of the possibility of\nthis interest being made supreme, and hope in the unlimited continuance\nof intellectual activity, as indispensable requirements of logic. Yet,\nwhen we consider that logic depends on a mere struggle to escape doubt,\nwhich, as it terminates in action, must begin in emotion, and that,\nfurthermore, the only cause of our planting ourselves on reason is that\nother methods of escaping doubt fail on account of the social impulse,\nwhy should we wonder to find social sentiment presupposed in reasoning?\nAs for the other two sentiments which I find necessary, they are so only\nas supports and accessories of that. It interests me to notice that\nthese three sentiments seem to be pretty much the same as that famous\ntrio of Charity, Faith, and Hope, which, in the estimation of St. Paul,\nare the finest and greatest of spiritual gifts. Neither Old nor New\nTestament is a textbook of the logic of science, but the latter is\ncertainly the highest existing authority in regard to the dispositions\nof heart which a man ought to have.\n\n\n                                   V\n\n\nSuch average statistical numbers as the number of inhabitants per square\nmile, the average number of deaths per week, the number of convictions\nper indictment, or, generally speaking, the numbers of _x_\u2019s per _y_,\nwhere the _x_\u2019s are a class of things some or all of which are connected\nwith another class of things, their _y_\u2019s, I term _relative numbers_. Of\nthe two classes of things to which a relative number refers, that one of\nwhich it is a number may be called its _relate_, and that one _per_\nwhich the numeration is made may be called its _correlate_.\n\nProbability is a kind of relative number; namely, it is the ratio of the\nnumber of arguments of a certain genus which carry truth with them to\nthe total number of arguments of that genus, and the rules for the\ncalculation of probabilities are very easily derived from this\nconsideration. They may all be given here, since they are extremely\nsimple, and it is sometimes convenient to know something of the\nelementary rules of calculation of chances.\n\n\nRULE I. _Direct Calculation._\u2014To calculate, directly, any relative\nnumber, say for instance the number of passengers in the average trip of\na street-car, we must proceed as follows:\n\nCount the number of passengers for each trip; add all these numbers, and\ndivide by the number of trips. There are cases in which this rule may be\nsimplified. Suppose we wish to know the number of inhabitants to a\ndwelling in New York. The same person cannot inhabit two dwellings. If\nhe divide his time between two dwellings he ought to be counted a\nhalf-inhabitant of each. In this case we have only to divide the total\nnumber of the inhabitants of New York by the number of their dwellings,\nwithout the necessity of counting separately those which inhabit each\none. A similar proceeding will apply wherever each individual relate\nbelongs to one individual correlate exclusively. If we want the number\nof _x_\u2019s per _y_, and no _x_ belongs to more than one _y_, we have only\nto divide the whole number of _x_\u2019s of _y_\u2019s by the number of _y_\u2019s.\nSuch a method would, of course, fail if applied to finding the average\nnumber of street-car passengers per trip. We could not divide the total\nnumber of travelers by the number of trips, since many of them would\nhave made many passages.\n\nTo find the probability that from a given class of premises, A, a given\nclass of conclusions, B, follow, it is simply necessary to ascertain\nwhat proportion of the times in which premises of that class are true,\nthe appropriate conclusions are also true. In other words, it is the\nnumber of cases of the occurrence of both the events A and B, divided by\nthe total number of cases of the occurrence of the event A.\n\n\nRULE II. _Addition of Relative Numbers._\u2014Given two relative numbers\nhaving the same correlate, say the number of _x_\u2019s per _y_, and the\nnumber of _z_\u2019s per _y_; it is required to find the number of _x_\u2019s and\n_z_\u2019s together per _y_. If there is nothing which is at once an _x_ and\na _z_ to the same _y_, the sum of the two given numbers would give the\nrequired number. Suppose, for example, that we had given the average\nnumber of friends that men have, and the average number of enemies, the\nsum of these two is the average number of persons interested in a man.\nOn the other hand, it plainly would not do to add the average number of\npersons having constitutional diseases and over military age, to the\naverage number exempted by each special cause from military service, in\norder to get the average number exempt in any way, since many are exempt\nin two or more ways at once.\n\nThis rule applies directly to probabilities, given the probability that\ntwo different and mutually exclusive events will happen under the same\nsupposed set of circumstances. Given, for instance, the probability that\nif A then B, and also the probability that if A then C, then the sum of\nthese two probabilities is the probability that if A then either B or C,\nso long as there is no event which belongs at once to the two classes B\nand C.\n\n\nRULE III. _Multiplication of Relative Numbers._\u2014Suppose that we have\ngiven the relative number of _x_\u2019s per _y_; also the relative number of\n_z_\u2019s per _x_ of _y_; or, to take a concrete example, suppose that we\nhave given, first, the average number of children in families living in\nNew York; and, second, the average number of teeth in the head of a New\nYork child\u2014then the product of these two numbers would give the average\nnumber of children\u2019s teeth in a New York family. But this mode of\nreckoning will only apply in general under two restrictions. In the\nfirst place, it would not be true if the same child could belong to\ndifferent families, for in that case those children who belonged to\nseveral different families might have an exceptionally large or small\nnumber of teeth, which would affect the average number of children\u2019s\nteeth in a family more than it would affect the average number of teeth\nin a child\u2019s head. In the second place, the rule would not be true if\ndifferent children could share the same teeth, the average number of\nchildren\u2019s teeth being in that case evidently something different from\nthe average number of teeth belonging to a child.\n\nIn order to apply this rule to probabilities, we must proceed as\nfollows: Suppose that we have given the probability that the conclusion\nB follows from the premise A, B and A representing as usual certain\nclasses of propositions. Suppose that we also knew the probability of an\ninference in which B should be the premise, and a proposition of a third\nkind, C, the conclusion. Here, then, we have the materials for the\napplication of this rule. We have, first, the relative number of B\u2019s per\nA. We next should have the relative number of C\u2019s per B following from\nA. But the classes of propositions being so selected that the\nprobability of C following from any B in general is just the same as the\nprobability of C\u2019s following from one of those B\u2019s which is deducible\nfrom an A, the two probabilities may be multiplied together, in order to\ngive the probability of C following from A. The same restrictions exist\nas before. It might happen that the probability that B follows from A\nwas affected by certain propositions of the class B following from\nseveral different propositions of the class A. But, practically\nspeaking, all these restrictions are of very little consequence, and it\nis usually recognized as a principle universally true that the\nprobability that, if A is true, B is, multiplied by the probability\nthat, if B is true, C is, gives the probability that, if A is true, C\nis.\n\nThere is a rule supplementary to this, of which great use is made. It is\nnot universally valid, and the greatest caution has to be exercised in\nmaking use of it\u2014a double care, first, never to use it when it will\ninvolve serious error; and, second, never to fail to take advantage of\nit in cases in which it can be employed. This rule depends upon the fact\nthat in very many cases the probability that C is true if B is, is\nsubstantially the same as the probability that C is true if A is.\nSuppose, for example, we have the average number of males among the\nchildren born in New York; suppose that we also have the average number\nof children born in the winter months among those born in New York. Now,\nwe may assume without doubt, at least as a closely approximate\nproposition (and no very nice calculation would be in place in regard to\nprobabilities), that the proportion of males among all the children born\nin New York is the same as the proportion of males born in summer in New\nYork; and, therefore, if the names of all the children born during a\nyear were put into an urn, we might multiply the probability that any\nname drawn would be the name of a male child by the probability that it\nwould be the name of a child born in summer, in order to obtain the\nprobability that it would be the name of a male child born in summer.\nThe questions of probability, in the treatises upon the subject, have\nusually been such as relate to balls drawn from urns, and games of\ncards, and so on, in which the question of the _independence_ of events,\nas it is called\u2014that is to say, the question of whether the probability\nof C, under the hypothesis B, is the same as its probability under the\nhypothesis A, has been very simple; but, in the application of\nprobabilities to the ordinary questions of life, it is often an\nexceedingly nice question whether two events may be considered as\nindependent with sufficient accuracy or not. In all calculations about\ncards it is assumed that the cards are thoroughly shuffled, which makes\none deal quite independent of another. In point of fact the cards seldom\nare, in practice, shuffled sufficiently to make this true; thus, in a\ngame of whist, in which the cards have fallen in suits of four of the\nsame suit, and are so gathered up, they will lie more or less in sets of\nfour of the same suit, and this will be true even after they are\nshuffled. At least some traces of this arrangement will remain, in\nconsequence of which the number of \u201cshort suits,\u201d as they are\ncalled\u2014that is to say, the number of hands in which the cards are very\nunequally divided in regard to suits\u2014is smaller than the calculation\nwould make it to be; so that, when there is a misdeal, where the cards,\nbeing thrown about the table, get very thoroughly shuffled, it is a\ncommon saying that in the hands next dealt out there are generally short\nsuits. A few years ago a friend of mine, who plays whist a great deal,\nwas so good as to count the number of spades dealt to him in 165 hands,\nin which the cards had been, if anything, shuffled better than usual.\nAccording to calculation, there should have been 85 of these hands in\nwhich my friend held either three or four spades, but in point of fact\nthere were 94, showing the influence of imperfect shuffling.\n\nAccording to the view here taken, these are the only fundamental rules\nfor the calculation of chances. An additional one, derived from a\ndifferent conception of probability, is given in some treatises, which\nif it be sound might be made the basis of a theory of reasoning. Being,\nas I believe it is, absolutely absurd, the consideration of it serves to\nbring us to the true theory; and it is for the sake of this discussion,\nwhich must be postponed to the next number, that I have brought the\ndoctrine of chances to the reader\u2019s attention at this early stage of our\nstudies of the logic of science.\n\nFootnote 34:\n\n  _Popular Science Monthly_, March, 1878.\n\nFootnote 35:\n\n  [Later, pp. 170 ff. and 215 ff., it is shown that continuity is also\n  at the basis of mathematical generalization. See also article on\n  Synechism in _Baldwin\u2019s Dictionary of Philosophy_.]\n\nFootnote 36:\n\n  This mode of thought is so familiarly associated with all exact\n  numerical consideration, that the phrase appropriate to it is imitated\n  by shallow writers in order to produce the appearance of exactitude\n  where none exists. Certain newspapers which affect a learned tone talk\n  of \u201cthe average man,\u201d when they simply mean _most men_, and have no\n  idea of striking an average.\n\nFootnote 37:\n\n  _Cf._ pp. 179 ff. below.\n\nFootnote 38:\n\n  The conception of probability here set forth is substantially that\n  first developed by Mr. Venn, in his _Logic of Chance_. Of course, a\n  vague apprehension of the idea had always existed, but the problem was\n  to make it perfectly clear, and to him belongs the credit of first\n  doing this.\n\nFootnote 39:\n\n  I do not here admit an absolutely unknowable. Evidence could show us\n  what would probably be the case after any given lapse of time; and\n  though a subsequent time might be assigned which that evidence might\n  not cover, yet further evidence would cover it.\n\n\n\n\n                              FOURTH PAPER\n                    THE PROBABILITY OF INDUCTION[40]\n\n\n                                   I\n\n\nWe have found that every argument derives its force from the general\ntruth of the class of inferences to which it belongs; and that\nprobability is the proportion of arguments carrying truth with them\namong those of any _genus_. This is most conveniently expressed in the\nnomenclature of the medieval logicians. They called the fact expressed\nby a premise an _antecedent_, and that which follows from it its\n_consequent_; while the leading principle, that every (or almost every)\nsuch antecedent is followed by such a consequent, they termed the\n_consequence_. Using this language, we may say that probability belongs\nexclusively to _consequences_, and the probability of any consequence is\nthe number of times in which antecedent and consequent both occur\ndivided by the number of all the times in which the antecedent occurs.\nFrom this definition are deduced the following rules for the addition\nand multiplication of probabilities:\n\n_Rule for the Addition of Probabilities._\u2014Given the separate\nprobabilities of two consequences having the same antecedent and\nincompatible consequents. Then the sum of these two numbers is the\nprobability of the consequence, that from the same antecedent one or\nother of those consequents follows.\n\n_Rule for the Multiplication of Probabilities._\u2014Given the separate\nprobabilities of the two consequences, \u201cIf A then B,\u201d and \u201cIf both A and\nB, then C.\u201d Then the product of these two numbers is the probability of\nthe consequence, \u201cIf A, then both B and C.\u201d\n\n_Special Rule for the Multiplication of Independent\nProbabilities._\u2014Given the separate probabilities of two consequences\nhaving the same antecedents, \u201cIf A, then B,\u201d and \u201cIf A, then C.\u201d Suppose\nthat these consequences are such that the probability of the second is\nequal to the probability of the consequence, \u201cIf both A and B, then C.\u201d\nThen the product of the two given numbers is equal to the probability of\nthe consequence, \u201cIf A, then both B and C.\u201d\n\nTo show the working of these rules we may examine the probabilities in\nregard to throwing dice. What is the probability of throwing a six with\none die? The antecedent here is the event of throwing a die; the\nconsequent, its turning up a six. As the die has six sides, all of which\nare turned up with equal frequency, the probability of turning up any\none is 1/6. Suppose two dice are thrown, what is the probability of\nthrowing sixes? The probability of either coming up six is obviously the\nsame when both are thrown as when one is thrown\u2014namely, 1/6. The\nprobability that either will come up six when the other does is also the\nsame as that of its coming up six whether the other does or not. The\nprobabilities are, therefore, independent; and, by our rule, the\nprobability that both events will happen together is the product of\ntheir several probabilities, or 1/6 x 1/6. What is the probability of\nthrowing deuce-ace? The probability that the first die will turn up ace\nand the second deuce is the same as the probability that both will turn\nup sixes\u2014namely, 1/36; the probability that the _second_ will turn up\nace and the _first_ deuce is likewise 1/36; these two events\u2014first, ace;\nsecond, deuce; and, second, ace; first, deuce\u2014are incompatible. Hence\nthe rule for addition holds, and the probability that either will come\nup ace and the other deuce is 1/36 + 1/36, or 1/18.\n\nIn this way all problems about dice, etc., may be solved. When the\nnumber of dice thrown is supposed very large, mathematics (which may be\ndefined as the art of making groups to facilitate numeration) comes to\nour aid with certain devices to reduce the difficulties.\n\n\n                                   II\n\n\nThe conception of probability as a matter of _fact_, i.e., as the\nproportion of times in which an occurrence of one kind is accompanied by\nan occurrence of another kind, is termed by Mr. Venn the materialistic\nview of the subject. But probability has often been regarded as being\nsimply the degree of belief which ought to attach to a proposition, and\nthis mode of explaining the idea is termed by Venn the conceptualistic\nview. Most writers have mixed the two conceptions together. They, first,\ndefine the probability of an event as the reason we have to believe that\nit has taken place, which is conceptualistic; but shortly after they\nstate that it is the ratio of the number of cases favorable to the event\nto the total number of cases favorable or contrary, and all equally\npossible. Except that this introduces the thoroughly unclear idea of\ncases equally possible in place of cases equally frequent, this is a\ntolerable statement of the materialistic view. The pure conceptualistic\ntheory has been best expounded by Mr. De Morgan in his _Formal Logic_:\nor, the _Calculus of Inference, Necessary and Probable._\n\nThe great difference between the two analyses is, that the\nconceptualists refer probability to an event, while the materialists\nmake it the ratio of frequency of events of a _species_ to those of a\n_genus_ over that _species_, thus _giving it two terms instead of one_.\nThe opposition may be made to appear as follows:\n\nSuppose that we have two rules of inference, such that, of all the\nquestions to the solution of which both can be applied, the first yields\ncorrect answers to 81/100, and incorrect answers to the remaining\n19/100; while the second yields correct answers to 93/100, and incorrect\nanswers to the remaining 7/100. Suppose, further, that the two rules are\nentirely independent as to their truth, so that the second answers\ncorrectly 93/100 of the questions which the first answers correctly, and\nalso 93/100 of the questions which the first answers incorrectly, and\nanswers incorrectly the remaining 7/100 of the questions which the first\nanswers correctly, and also the remaining 7/100 of the questions which\nthe first answers incorrectly. Then, of all the questions to the\nsolution of which both rules can be applied\u2014\n\n    both answer correctly 93/100 of 81/100 or 93/100 x 81/100;\n\n    the second answers correctly and the first incorrectly 93/100 of\n    19/100 or 93/100 x 19/100;\n\n    the second answers incorrectly and the first correctly 7/100 of\n    81/100 or 7/100 x 81/100;\n\n    and both answer incorrectly 7/100 of 19/100 or 7/100 x 19/100;\n\nSuppose, now, that, in reference to any question, both give the same\nanswer. Then (the questions being always such as are to be answered by\n_yes_ or _no_), those in reference to which their answers agree are the\nsame as those which both answer correctly together with those which both\nanswer falsely, or 93/100 x 81/100 + 7/100 x 19/100 of all. The\nproportion of those which both answer correctly out of those their\nanswers to which agree is, therefore\u2014\n\n    ((93 \u00d7 81)/(100 \u00d7 100))/((93 \u00d7 81)/(100 \u00d7 100)) + ((7 \u00d7 19)/(100 \u00d7\n    100)) or (93 \u00d7 81)/((93 \u00d7 81) + (7 \u00d7 19)).\n\nThis is, therefore, the probability that, if both modes of inference\nyield the same result, that result is correct. We may here conveniently\nmake use of another mode of expression. _Probability_ is the ratio of\nthe favorable cases to all the cases. Instead of expressing our result\nin terms of this ratio, we may make use of another\u2014the ratio of\nfavorable to unfavorable cases. This last ratio may be called the\n_chance_ of an event. Then the chance of a true answer by the first mode\nof inference is 81/19 and by the second is 93/7; and the chance of a\ncorrect answer from both, when they agree, is\u2014\n\n    (81 \u00d7 93)/(19 \u00d7 7) or 81/19 \u00d7 93/7,\n\nor the product of the chances of each singly yielding a true answer.\n\nIt will be seen that a chance is a quantity which may have any\nmagnitude, however great. An event in whose favor there is an even\nchance, or 1/1, has a probability of 1/2. An argument having an even\nchance can do nothing toward re-enforcing others, since according to the\nrule its combination with another would only multiply the chance of the\nlatter by 1.\n\nProbability and chance undoubtedly belong primarily to consequences, and\nare relative to premises; but we may, nevertheless, speak of the chance\nof an event absolutely, meaning by that the chance of the combination of\nall arguments in reference to it which exist for us in the given state\nof our knowledge. Taken in this sense it is incontestable that the\nchance of an event has an intimate connection with the degree of our\nbelief in it. Belief is certainly something more than a mere feeling;\nyet there is a feeling of believing, and this feeling does and ought to\nvary with the chance of the thing believed, as deduced from all the\narguments. Any quantity which varies with the chance might, therefore,\nit would seem, serve as a thermometer for the proper intensity of\nbelief. Among all such quantities there is one which is peculiarly\nappropriate. When there is a very great chance, the feeling of belief\nought to be very intense. Absolute certainty, or an infinite chance, can\nnever be attained by mortals, and this may be represented appropriately\nby an infinite belief. As the chance diminishes the feeling of believing\nshould diminish, until an even chance is reached, where it should\ncompletely vanish and not incline either toward or away from the\nproposition. When the chance becomes less, then a contrary belief should\nspring up and should increase in intensity as the chance diminishes, and\nas the chance almost vanishes (which it can never quite do) the contrary\nbelief should tend toward an infinite intensity. Now, there is one\nquantity which, more simply than any other, fulfills these conditions;\nit is the _logarithm_ of the chance. But there is another consideration\nwhich must, if admitted, fix us to this choice for our thermometer. It\nis that our belief ought to be proportional to the weight of evidence,\nin this sense, that two arguments which are entirely independent,\nneither weakening nor strengthening each other, ought, when they concur,\nto produce a belief equal to the sum of the intensities of belief which\neither would produce separately. Now, we have seen that the chances of\nindependent concurrent arguments are to be multiplied together to get\nthe chance of their combination, and, therefore, the quantities which\nbest express the intensities of belief should be such that they are to\nbe _added_ when the _chances_ are multiplied in order to produce the\nquantity which corresponds to the combined chance. Now, the logarithm is\nthe only quantity which fulfills this condition. There is a general law\nof sensibility, called Fechner\u2019s psychophysical law. It is that the\nintensity of any sensation is proportional to the logarithm of the\nexternal force which produces it. It is entirely in harmony with this\nlaw that the feeling of belief should be as the logarithm of the chance,\nthis latter being the expression of the state of facts which produces\nthe belief.\n\nThe rule for the combination of independent concurrent arguments takes a\nvery simple form when expressed in terms of the intensity of belief,\nmeasured in the proposed way. It is this: Take the sum of all the\nfeelings of belief which would be produced separately by all the\narguments _pro_, subtract from that the similar sum for arguments _con_,\nand the remainder is the feeling of belief which we ought to have on the\nwhole. This is a proceeding which men often resort to, under the name of\n_balancing reasons_.\n\nThese considerations constitute an argument in favor of the\nconceptualistic view. The kernel of it is that the conjoint probability\nof all the arguments in our possession, with reference to any fact, must\nbe intimately connected with the just degree of our belief in that fact;\nand this point is supplemented by various others showing the consistency\nof the theory with itself and with the rest of our knowledge.\n\nBut probability, to have any value at all, must express a fact. It is,\ntherefore, a thing to be inferred upon evidence. Let us, then, consider\nfor a moment the formation of a belief of probability. Suppose we have a\nlarge bag of beans from which one has been secretly taken at random and\nhidden under a thimble. We are now to form a probable judgment of the\ncolor of that bean, by drawing others singly from the bag and looking at\nthem, each one to be thrown back, and the whole well mixed up after each\ndrawing. Suppose the first drawing is white and the next black. We\nconclude that there is not an immense preponderance of either color, and\nthat there is something like an even chance that the bean under the\nthimble is black. But this judgment may be altered by the next few\ndrawings. When we have drawn ten times, if 4, 5, or 6, are white, we\nhave more confidence that the chance is even. When we have drawn a\nthousand times, if about half have been white, we have great confidence\nin this result. We now feel pretty sure that, if we were to make a large\nnumber of bets upon the color of single beans drawn from the bag, we\ncould approximately insure ourselves in the long run by betting each\ntime upon the white, a confidence which would be entirely wanting if,\ninstead of sampling the bag by 1,000 drawings, we had done so by only\ntwo. Now, as the whole utility of probability is to insure us in the\nlong run, and as that assurance depends, not merely on the value of the\nchance, but also on the accuracy of the evaluation, it follows that we\nought not to have the same feeling of belief in reference to all events\nof which the chance is even. In short, to express the proper state of\nour belief, not _one_ number but _two_ are requisite, the first\ndepending on the inferred probability, the second on the amount of\nknowledge on which that probability is based.[41] It is true that when\nour knowledge is very precise, when we have made many drawings from the\nbag, or, as in most of the examples in the books, when the total\ncontents of the bag are absolutely known, the number which expresses the\nuncertainty of the assumed probability and its liability to be changed\nby further experience may become insignificant, or utterly vanish. But,\nwhen our knowledge is very slight, this number may be even more\nimportant than the probability itself; and when we have no knowledge at\nall this completely overwhelms the other, so that there is no sense in\nsaying that the chance of the totally unknown event is even (for what\nexpresses absolutely no fact has absolutely no meaning), and what ought\nto be said is that the chance is entirely indefinite. We thus perceive\nthat the conceptualistic view, though answering well enough in some\ncases, is quite inadequate.\n\nSuppose that the first bean which we drew from our bag were black. That\nwould constitute an argument, no matter how slender, that the bean under\nthe thimble was also black. If the second bean were also to turn out\nblack, that would be a second independent argument re\u00ebnforcing the\nfirst. If the whole of the first twenty beans drawn should prove black,\nour confidence that the hidden bean was black would justly attain\nconsiderable strength. But suppose the twenty-first bean were to be\nwhite and that we were to go on drawing until we found that we had drawn\n1,010 black beans and 990 white ones. We should conclude that our first\ntwenty beans being black was simply an extraordinary accident, and that\nin fact the proportion of white beans to black was sensibly equal, and\nthat it was an even chance that the hidden bean was black. Yet according\nto the rule of _balancing reasons_, since all the drawings of black\nbeans are so many independent arguments in favor of the one under the\nthimble being black, and all the white drawings so many against it, an\nexcess of twenty black beans ought to produce the same degree of belief\nthat the hidden bean was black, whatever the total number drawn.\n\nIn the conceptualistic view of probability, complete ignorance, where\nthe judgment ought not to swerve either toward or away from the\nhypothesis, is represented by the probability 1/2.[42]\n\nBut let us suppose that we are totally ignorant what colored hair the\ninhabitants of Saturn have. Let us, then, take a color-chart in which\nall possible colors are shown shading into one another by imperceptible\ndegrees. In such a chart the relative areas occupied by different\nclasses of colors are perfectly arbitrary. Let us inclose such an area\nwith a closed line, and ask what is the chance on conceptualistic\nprinciples that the color of the hair of the inhabitants of Saturn falls\nwithin that area? The answer cannot be indeterminate because we must be\nin some state of belief; and, indeed, conceptualistic writers do not\nadmit indeterminate probabilities. As there is no certainty in the\nmatter, the answer lies between _zero_ and _unity_. As no numerical\nvalue is afforded by the data, the number must be determined by the\nnature of the scale of probability itself, and not by calculation from\nthe data. The answer can, therefore, only be one-half, since the\njudgment should neither favor nor oppose the hypothesis. What is true of\nthis area is true of any other one; and it will equally be true of a\nthird area which embraces the other two. But the probability for each of\nthe smaller areas being one-half, that for the larger should be at least\nunity, which is absurd.\n\n\n                                  III\n\n\nAll our reasonings are of two kinds: 1. _Explicative_, _analytic_, or\n_deductive_; 2. _Amplifiative_, _synthetic_, or (loosely speaking)\n_inductive_. In explicative reasoning, certain facts are first laid down\nin the premises. These facts are, in every case, an inexhaustible\nmultitude, but they may often be summed up in one simple proposition by\nmeans of some regularity which runs through them all. Thus, take the\nproposition that Socrates was a man; this implies (to go no further)\nthat during every fraction of a second of his whole life (or, if you\nplease, during the greater part of them) he was a man. He did not at one\ninstant appear as a tree and at another as a dog; he did not flow into\nwater, or appear in two places at once; you could not put your finger\nthrough him as if he were an optical image, etc. Now, the facts being\nthus laid down, some order among some of them, not particularly made use\nof for the purpose of stating them, may perhaps be discovered; and this\nwill enable us to throw part or all of them into a new statement, the\npossibility of which might have escaped attention. Such a statement will\nbe the conclusion of an analytic inference. Of this sort are all\nmathematical demonstrations. But synthetic reasoning is of another kind.\nIn this case the facts summed up in the conclusion are not among those\nstated in the premises. They are different facts, as when one sees that\nthe tide rises _m_ times and concludes that it will rise the next time.\nThese are the only inferences which increase our real knowledge, however\nuseful the others may be.\n\nIn any problem in probabilities, we have given the relative frequency of\ncertain events, and we perceive that in these facts the relative\nfrequency of another event is given in a hidden way. This being stated\nmakes the solution. This is, therefore, mere explicative reasoning, and\nis evidently entirely inadequate to the representation of synthetic\nreasoning, which goes out beyond the facts given in the premises. There\nis, therefore, a manifest impossibility in so tracing out any\nprobability for a synthetic conclusion.\n\nMost treatises on probability contain a very different doctrine. They\nstate, for example, that if one of the ancient denizens of the shores of\nthe Mediterranean, who had never heard of tides, had gone to the bay of\nBiscay, and had there seen the tide rise, say _m_ times, he could know\nthat there was a probability equal to\n\n    (m + 1)/(m + 2)\n\nthat it would rise the next time. In a well-known work by Quetelet, much\nstress is laid on this, and it is made the foundation of a theory of\ninductive reasoning.\n\nBut this solution betrays its origin if we apply it to the case in which\nthe man has never seen the tide rise at all; that is, if we put _m_ = 0.\nIn this case, the probability that it will rise the next time comes out\n1/2, or, in other words, the solution involves the conceptualistic\nprinciple that there is an even chance of a totally unknown event. The\nmanner in which it has been reached has been by considering a number of\nurns all containing the same number of balls, part white and part black.\nOne urn contains all white balls, another one black and the rest white,\na third two black and the rest white, and so on, one urn for each\nproportion, until an urn is reached containing only black balls. But the\nonly possible reason for drawing any analogy between such an arrangement\nand that of Nature is the principle that alternatives of which we know\nnothing must be considered as equally probable. But this principle is\nabsurd. There is an indefinite variety of ways of enumerating the\ndifferent possibilities, which, on the application of this principle,\nwould give different results. If there be any way of enumerating the\npossibilities so as to make them all equal, it is not that from which\nthis solution is derived, but is the following: Suppose we had an\nimmense granary filled with black and white balls well mixed up; and\nsuppose each urn were filled by taking a fixed number of balls from this\ngranary quite at random. The relative number of white balls in the\ngranary might be anything, say one in three. Then in one-third of the\nurns the first ball would be white, and in two-thirds black. In\none-third of those urns of which the first ball was white, and also in\none-third of those in which the first ball was black, the second ball\nwould be white. In this way, we should have a distribution like that\nshown in the following table, where _w_ stands for a white ball and _b_\nfor a black one. The reader can, if he chooses, verify the table for\nhimself.\n\n    wwww.\n\n    wwwb.   wwbw.   wbww.   bwww.\n    wwwb.   wwbw.   wbww.   bwww.\n\n    wwbb.   wbwb.   bwwb.   wbbw.   bwbw.   bbww.\n    wwbb.   wbwb.   bwwb.   wbbw.   bwbw.   bbww.\n    wwbb.   wbwb.   bwwb.   wbbw.   bwbw.   bbww.\n    wwbb.   wbwb.   bwwb.   wbbw.   bwbw.   bbww.\n\n    wbbb.   bwbb.   bbwb.   bbbw.\n    wbbb.   bwbb.   bbwb.   bbbw.\n    wbbb.   bwbb.   bbwb.   bbbw.\n    wbbb.   bwbb.   bbwb.   bbbw.\n    wbbb.   bwbb.   bbwb.   bbbw.\n    wbbb.   bwbb.   bbwb.   bbbw.\n    wbbb.   bwbb.   bbwb.   bbbw.\n    wbbb.   bwbb.   bbwb.   bbbw.\n\n    bbbb.\n    bbbb.\n    bbbb.\n    bbbb.\n    bbbb.\n    bbbb.\n    bbbb.\n    bbbb.\n    bbbb.\n    bbbb.\n    bbbb.\n    bbbb.\n    bbbb.\n    bbbb.\n    bbbb.\n    bbbb.\n\nIn the second group, where there is one b, there are two sets just\nalike; in the third there are 4, in the fourth 8, and in the fifth 16,\ndoubling every time. This is because we have supposed twice as many\nblack balls in the granary as white ones; had we supposed 10 times as\nmany, instead of\n\n           1, 2, 4, 8, 16\n\nsets we should have had\n\n           1, 10, 100, 1000, 10000\n\nsets; on the other hand, had the numbers of black and white balls in the\ngranary been even, there would have been but one set in each group. Now\nsuppose two balls were drawn from one of these urns and were found to be\nboth white, what would be the probability of the next one being white?\nIf the two drawn out were the first two put into the urns, and the next\nto be drawn out were the third put in, then the probability of this\nthird being white would be the same whatever the colors of the first\ntwo, for it has been supposed that just the same proportion of urns has\nthe third ball white among those which have the first two _white-white_,\n_white-black_, _black-white_, and _black-black_. Thus, in this case, the\nchance of the third ball being white would be the same whatever the\nfirst two were. But, by inspecting the table, the reader can see that in\neach group all orders of the balls occur with equal frequency, so that\nit makes no difference whether they are drawn out in the order they were\nput in or not. Hence the colors of the balls already drawn have no\ninfluence on the probability of any other being white or black.\n\nNow, if there be any way of enumerating the possibilities of Nature so\nas to make them equally probable, it is clearly one which should make\none arrangement or combination of the elements of Nature as probable as\nanother, that is, a distribution like that we have supposed, and it,\ntherefore, appears that the assumption that any such thing can be done,\nleads simply to the conclusion that reasoning from past to future\nexperience is absolutely worthless. In fact, the moment that you assume\nthat the chances in favor of that of which we are totally ignorant are\neven, the problem about the tides does not differ, in any arithmetical\nparticular, from the case in which a penny (known to be equally likely\nto come up heads and tails) should turn up heads _m_ times successively.\nIn short, it would be to assume that Nature is a pure chaos, or chance\ncombination of independent elements, in which reasoning from one fact to\nanother would be impossible; and since, as we shall hereafter see, there\nis no judgment of pure observation without reasoning, it would be to\nsuppose all human cognition illusory and no real knowledge possible. It\nwould be to suppose that if we have found the order of Nature more or\nless regular in the past, this has been by a pure run of luck which we\nmay expect is now at an end. Now, it may be we have no scintilla of\nproof to the contrary, but reason is unnecessary in reference to that\nbelief which is of all the most settled, which nobody doubts or can\ndoubt, and which he who should deny would stultify himself in so doing.\n\nThe relative probability of this or that arrangement of Nature is\nsomething which we should have a right to talk about if universes were\nas plenty as blackberries, if we could put a quantity of them in a bag,\nshake them well up, draw out a sample, and examine them to see what\nproportion of them had one arrangement and what proportion another. But,\neven in that case, a higher universe would contain us, in regard to\nwhose arrangements the conception of probability could have no\napplicability.\n\n\n                                   IV\n\n\nWe have examined the problem proposed by the conceptualists, which,\ntranslated into clear language, is this: Given a synthetic conclusion;\nrequired to know out of all possible states of things how many will\naccord, to any assigned extent, with this conclusion; and we have found\nthat it is only an absurd attempt to reduce synthetic to analytic\nreason, and that no definite solution is possible.\n\nBut there is another problem in connection with this subject. It is\nthis: Given a certain state of things, required to know what proportion\nof all synthetic inferences relating to it will be true within a given\ndegree of approximation. Now, there is no difficulty about this problem\n(except for its mathematical complication); it has been much studied,\nand the answer is perfectly well known. And is not this, after all, what\nwe want to know much rather than the other? Why should we want to know\nthe probability that the fact will accord with our conclusion? That\nimplies that we are interested in all possible worlds, and not merely\nthe one in which we find ourselves placed. Why is it not much more to\nthe purpose to know the probability that our conclusion will accord with\nthe fact? One of these questions is the first above stated and the other\nthe second, and I ask the reader whether, if people, instead of using\nthe word probability without any clear apprehension of their own\nmeaning, had always spoken of relative frequency, they could have failed\nto see that what they wanted was not to follow along the synthetic\nprocedure with an analytic one, in order to find the probability of the\nconclusion; but, on the contrary, to begin with the fact at which the\nsynthetic inference aims, and follow back to the facts it uses for\npremises in order to see the probability of their being such as will\nyield the truth.\n\nAs we cannot have an urn with an infinite number of balls to represent\nthe inexhaustibleness of Nature, let us suppose one with a finite\nnumber, each ball being thrown back into the urn after being drawn out,\nso that there is no exhaustion of them. Suppose one ball out of three is\nwhite and the rest black, and that four balls are drawn. Then the table\non pages 95-96 represents the relative frequency of the different ways\nin which these balls might be drawn. It will be seen that if we should\njudge by these four balls of the proportion in the urn, 32 times out of\n81 we should find it 1/4, and 24 times out of 81 we should find it 1/2,\nthe truth being 1/3. To extend this table to high numbers would be great\nlabor, but the mathematicians have found some ingenious ways of\nreckoning what the numbers would be. It is found that, if the true\nproportion of white balls is _p_, and _s_ balls are drawn, then the\nerror of the proportion obtained by the induction will be\u2014\n\n    half the time within 0.477 \u221a((2p(1-p))/s)\n    9 times out of 10 within 1.163 \u221a((2p(1-p))/s)\n    99 times out of 100 within 1.821 \u221a((2p(1-p))/s)\n    999 times out of 1,000 within 2.328 \u221a((2p(1-p))/s)\n    9,999 times out of 10,000 within 2.751 \u221a((2p(1-p))/s)\n    9,999,999,999 times out of 10,000,000,000 within 4.77 \u221a((2p(1-p))/s)\n\nThe use of this may be illustrated by an example. By the census of 1870,\nit appears that the proportion of males among native white children\nunder one year old was 0.5082, while among colored children of the same\nage the proportion was only 0.4977. The difference between these is\n0.0105, or about one in a 100. Can this be attributed to chance, or\nwould the difference always exist among a great number of white and\ncolored children under like circumstances? Here _p_ may be taken at 1/2;\nhence 2_p_(1-_p_) is also 1/2. The number of white children counted was\nnear 1,000,000; hence the fraction whose square-root is to be taken is\nabout 1/2000000. The root is about 1/1400, and this multiplied by 0.477\ngives about 0.0003 as the probable error in the ratio of males among the\nwhites as obtained from the induction. The number of black children was\nabout 150,000, which gives 0.0008 for the probable error. We see that\nthe actual discrepancy is ten times the sum of these, and such a result\nwould happen, according to our table, only once out of 10,000,000,000\ncensuses, in the long run.\n\nIt may be remarked that when the real value of the probability sought\ninductively is either very large or very small, the reasoning is more\nsecure. Thus, suppose there were in reality one white ball in 100 in a\ncertain urn, and we were to judge of the number by 100 drawings. The\nprobability of drawing no white ball would be 366/1000; that of drawing\none white ball would be 370/1000; that of drawing two would be 185/1000;\nthat of drawing three would be 61/1000; that of drawing four would be\n15/1000; that of drawing five would be only 3/1000, etc. Thus we should\nbe tolerably certain of not being in error by more than one ball in 100.\n\nIt appears, then, that in one sense we can, and in another we cannot,\ndetermine the probability of synthetic inference. When I reason in this\nway:\n\n                Ninety-nine Cretans in a hundred are liars;\n                But Epimenides is a Cretan;\n                Therefore, Epimenides is a liar:\u2014\n\nI know that reasoning similar to that would carry truth 99 times in 100.\nBut when I reason in the opposite direction:\n\n         Minos, Sarpedon, Rhadamanthus, Deucalion, and Epimenides,\n         are all the Cretans I can think of;\n         But these were all atrocious liars,\n         Therefore, pretty much all Cretans must have been liars;\n\nI do not in the least know how often such reasoning would carry me\nright. On the other hand, what I do know is that some definite\nproportion of Cretans must have been liars, and that this proportion can\nbe probably approximated to by an induction from five or six instances.\nEven in the worst case for the probability of such an inference, that in\nwhich about half the Cretans are liars, the ratio so obtained would\nprobably not be in error by more than 1/6. So much I know; but, then, in\nthe present case the inference is that pretty much all Cretans are\nliars, and whether there may not be a special improbability in that I do\nnot know.\n\n\n                                   V\n\n\nLate in the last century, Immanuel Kant asked the question, \u201cHow are\nsynthetical judgments _a priori_ possible?\u201d By synthetical judgments he\nmeant such as assert positive fact and are not mere affairs of\narrangement; in short, judgments of the kind which synthetical reasoning\nproduces, and which analytic reasoning cannot yield. By _a priori_\njudgments he meant such as that all outward objects are in space, every\nevent has a cause, etc., propositions which according to him can never\nbe inferred from experience. Not so much by his answer to this question\nas by the mere asking of it, the current philosophy of that time was\nshattered and destroyed, and a new epoch in its history was begun. But\nbefore asking _that_ question he ought to have asked the more general\none, \u201cHow are any synthetical judgments at all possible?\u201d How is it that\na man can observe one fact and straightway pronounce judgment concerning\nanother different fact not involved in the first? Such reasoning, as we\nhave seen, has, at least in the usual sense of the phrase, no definite\nprobability; how, then, can it add to our knowledge? This is a strange\nparadox; the Abb\u00e9 Gratry says it is a miracle, and that every true\ninduction is an immediate inspiration from on high.[43] I respect this\nexplanation far more than many a pedantic attempt to solve the question\nby some juggle with probabilities, with the forms of syllogism, or what\nnot. I respect it because it shows an appreciation of the depth of the\nproblem, because it assigns an adequate cause, and because it is\nintimately connected\u2014as the true account should be\u2014with a general\nphilosophy of the universe. At the same time, I do not accept this\nexplanation, because an explanation should tell _how_ a thing is done,\nand to assert a perpetual miracle seems to be an abandonment of all hope\nof doing that, without sufficient justification.\n\nIt will be interesting to see how the answer which Kant gave to his\nquestion about synthetical judgments _a priori_ will appear if extended\nto the question of synthetical judgments in general. That answer is,\nthat synthetical judgments _a priori_ are possible because whatever is\nuniversally true is involved in the conditions of experience. Let us\napply this to a general synthetical reasoning. I take from a bag a\nhandful of beans; they are all purple, and I infer that all the beans in\nthe bag are purple. How can I do that? Why, upon the principle that\nwhatever is universally true of my experience (which is here the\nappearance of these different beans) is involved in the condition of\nexperience. The condition of this special experience is that all these\nbeans were taken from that bag. According to Kant\u2019s principle, then,\nwhatever is found true of all the beans drawn from the bag must find its\nexplanation in some peculiarity of the contents of the bag. This is a\nsatisfactory statement of the principle of induction.\n\nWhen we draw a deductive or analytic conclusion, our rule of inference\nis that facts of a certain general character are either invariably or in\na certain proportion of cases accompanied by facts of another general\ncharacter. Then our premise being a fact of the former class, we infer\nwith certainty or with the appropriate degree of probability the\nexistence of a fact of the second class. But the rule for synthetic\ninference is of a different kind. When we sample a bag of beans we do\nnot in the least assume that the fact of some beans being purple\ninvolves the necessity or even the probability of other beans being so.\nOn the contrary, the conceptualistic method of treating probabilities,\nwhich really amounts simply to the deductive treatment of them, when\nrightly carried out leads to the result that a synthetic inference has\njust an even chance in its favor, or in other words is absolutely\nworthless. The color of one bean is entirely independent of that of\nanother. But synthetic inference is founded upon a classification of\nfacts, not according to their characters, but according to the manner of\nobtaining them. Its rule is, that a number of facts obtained in a given\nway will in general more or less resemble other facts obtained in the\nsame way; or, _experiences whose conditions are the same will have the\nsame general characters_.\n\nIn the former case, we know that premises precisely similar in form to\nthose of the given ones will yield true conclusions, just once in a\ncalculable number of times. In the latter case, we only know that\npremises obtained under circumstances similar to the given ones (though\nperhaps themselves very different) will yield true conclusions, at least\nonce in a calculable number of times. We may express this by saying that\nin the case of analytic inference we know the probability of our\nconclusion (if the premises are true), but in the case of synthetic\ninferences we only know the degree of trustworthiness of our proceeding.\nAs all knowledge comes from synthetic inference, we must equally infer\nthat all human certainty consists merely in our knowing that the\nprocesses by which our knowledge has been derived are such as must\ngenerally have led to true conclusions.\n\nThough a synthetic inference cannot by any means be reduced to\ndeduction, yet that the rule of induction will hold good in the long run\nmay be deduced from the principle that reality is only the object of the\nfinal opinion to which sufficient investigation would lead. That belief\ngradually tends to fix itself under the influence of inquiry is, indeed,\none of the facts with which logic sets out.\n\nFootnote 40:\n\n  _Popular Science Monthly_, April, 1878.\n\nFootnote 41:\n\n  Strictly we should need an infinite series of numbers each depending\n  on the probable error of the last.\n\nFootnote 42:\n\n  \u201cPerfect indecision, belief inclining neither way, an even chance.\u201d\u2014DE\n  MORGAN, p. 182.\n\nFootnote 43:\n\n  _Logique_. The same is true, according to him, of every performance of\n  a differentiation, but not of integration. He does not tell us whether\n  it is the supernatural assistance which makes the former process so\n  much the easier.\n\n\n\n\n                              FIFTH PAPER\n                        THE ORDER OF NATURE[44]\n\n\n                                   I\n\n\nAny proposition whatever concerning the order of Nature must touch more\nor less upon religion. In our day, belief, even in these matters,\ndepends more and more upon the observation of facts. If a remarkable and\nuniversal orderliness be found in the universe, there must be some cause\nfor this regularity, and science has to consider what hypotheses might\naccount for the phenomenon. One way of accounting for it, certainly,\nwould be to suppose that the world is ordered by a superior power. But\nif there is nothing in the universal subjection of phenomena to laws,\nnor in the character of those laws themselves (as being benevolent,\nbeautiful, economical, etc.), which goes to prove the existence of a\ngovernor of the universe, it is hardly to be anticipated that any other\nsort of evidence will be found to weigh very much with minds emancipated\nfrom the tyranny of tradition.\n\nNevertheless, it cannot truly be said that even an absolutely negative\ndecision of that question could altogether destroy religion, inasmuch as\nthere are faiths in which, however much they differ from our own, we\nrecognize those essential characters which make them worthy to be called\nreligions, and which, nevertheless, do not postulate an actually\nexisting Deity. That one, for instance, which has had the most numerous\nand by no means the least intelligent following of any on earth, teaches\nthat the Divinity in his highest perfection is wrapped away from the\nworld in a state of profound and eternal sleep, which really does not\ndiffer from non-existence, whether it be called by that name or not. No\ncandid mind who has followed the writings of M. Vacherot can well deny\nthat his religion is as earnest as can be. He worships the Perfect, the\nSupreme Ideal; but he conceives that the very notion of the Ideal is\nrepugnant to its real existence.[45] In fact, M. Vacherot finds it\nagreeable to his reason to assert that non-existence is an essential\ncharacter of the perfect, just as St. Anselm and Descartes found it\nagreeable to theirs to assert the extreme opposite. I confess that there\nis one respect in which either of these positions seems to me more\ncongruous with the religious attitude than that of a theology which\nstands upon evidences; for as soon as the Deity presents himself to\neither Anselm or Vacherot, and manifests his glorious attributes,\nwhether it be in a vision of the night or day, either of them recognizes\nhis adorable God, and sinks upon his knees at once; whereas the\ntheologian of evidences will first demand that the divine apparition\nshall identify himself, and only after having scrutinized his\ncredentials and weighed the probabilities of his being found among the\ntotality of existences, will he finally render his circumspect homage,\nthinking that no characters can be adorable but those which belong to a\nreal thing.\n\nIf we could find out any general characteristic of the universe, any\nmannerism in the ways of Nature, any law everywhere applicable and\nuniversally valid, such a discovery would be of such singular assistance\nto us in all our future reasoning, that it would deserve a place almost\nat the head of the principles of logic. On the other hand, if it can be\nshown that there is nothing of the sort to find out, but that every\ndiscoverable regularity is of limited range, this again will be of\nlogical importance. What sort of a conception we ought to have of the\nuniverse, how to think of the _ensemble_ of things, is a fundamental\nproblem in the theory of reasoning.\n\n\n                                   II\n\n\nIt is the legitimate endeavor of scientific men now, as it was\ntwenty-three hundred years ago, to account for the formation of the\nsolar system and of the cluster of stars which forms the galaxy, by the\nfortuitous concourse of atoms. The greatest expounder of this theory,\nwhen asked how he could write an immense book on the system of the world\nwithout one mention of its author, replied, very logically, \u201cJe n\u2019avais\npas besoin de cette hypoth\u00e8se-l\u00e0.\u201d But, in truth, there is nothing\natheistical in the theory, any more than there was in this answer.\nMatter is supposed to be composed of molecules which obey the laws of\nmechanics and exert certain attractions upon one another; and it is to\nthese regularities (which there is no attempt to account for) that\ngeneral arrangement of the solar system would be due, and not to hazard.\n\nIf any one has ever maintained that the universe is a pure throw of the\ndice, the theologians have abundantly refuted him. \u201cHow often,\u201d says\nArchbishop Tillotson, \u201cmight a man, after he had jumbled a set of\nletters in a bag, fling them out upon the ground before they would fall\ninto an exact poem, yea, or so much as make a good discourse in prose!\nAnd may not a little book be as easily made by chance as this great\nvolume of the world?\u201d The chance world here shown to be so different\nfrom that in which we live would be one in which there were no laws, the\ncharacters of different things being entirely independent; so that,\nshould a sample of any kind of objects ever show a prevalent character,\nit could only be by accident, and no general proposition could ever be\nestablished. Whatever further conclusions we may come to in regard to\nthe order of the universe, thus much may be regarded as solidly\nestablished, that the world is not a mere chance-medley.\n\nBut whether the world makes an exact poem or not, is another question.\nWhen we look up at the heavens at night, we readily perceive that the\nstars are not simply splashed on to the celestial vault; but there does\nnot seem to be any precise system in their arrangement either. It will\nbe worth our while, then, to inquire into the degree of orderliness in\nthe universe; and, to begin, let us ask whether the world we live in is\nany more orderly than a purely chance-world would be.\n\nAny uniformity, or law of Nature, may be stated in the form, \u201cEvery A is\nB\u201d; as, every ray of light is a non-curved line, every body is\naccelerated toward the earth\u2019s center, etc. This is the same as to say,\n\u201cThere does not exist any A which is not B\u201d; there is no curved ray;\nthere is no body not accelerated toward the earth; so that the\nuniformity consists in the non-occurrence in Nature of a certain\ncombination of characters (in this case, the combination of being A with\nbeing non-B).[46] And, conversely, every case of the non-occurrence of a\ncombination of characters would constitute a uniformity in Nature. Thus,\nsuppose the quality A is never found in combination with the quality C:\nfor example, suppose the quality of idiocy is never found in combination\nwith that of having a well-developed brain. Then nothing of the sort A\nis of the sort C, or everything of the sort A is of the sort non-C (or\nsay, every idiot has an ill-developed brain), which, being something\nuniversally true of the A\u2019s, is a uniformity in the world. Thus we see\nthat, in a world where there were no uniformities, no logically possible\ncombination of characters would be excluded, but every combination would\nexist in some object. But two objects not identical must differ in some\nof their characters, though it be only in the character of being in\nsuch-and-such a place. Hence, precisely the same combination of\ncharacters could not be found in two different objects; and,\nconsequently, in a chance-world every combination involving either the\npositive or negative of every character would belong to just one thing.\nThus, if there were but five simple characters in such a world,[47] we\nmight denote them by A, B, C, D, E, and their negatives by a, b, c, d,\ne; and then, as there would be 2^5 or 32 different combinations of these\ncharacters, completely determinate in reference to each of them, that\nworld would have just 32 objects in it, their characters being as in the\nfollowing table:\n\n\nTABLE I.\n\n    ABCDE   AbCDE   aBCDE   abCDE\n    ABCDe   AbCDe   aBCDe   abCDe\n    ABCdE   AbCdE   aBCdE   abCdE\n    ABCde   AbCde   aBCde   abCde\n    ABcDE   AbcDE   aBcDE   abcDE\n    ABcDe   AbcDe   aBcDe   abcDe\n    ABcdE   AbcdE   aBcdE   abcdE\n    ABcde   Abcde   aBcde   abcde\n\nFor example, if the five primary characters were _hard_, _sweet_,\n_fragrant_, _green_, _bright_, there would be one object which reunited\nall these qualities, one which was hard, sweet, fragrant, and green, but\nnot bright; one which was hard, sweet, fragrant, and bright, but not\ngreen; one which was hard, sweet, and fragrant, but neither green nor\nbright; and so on through all the combinations.\n\nThis is what a thoroughly chance-world would be like, and certainly\nnothing could be imagined more systematic. When a quantity of letters\nare poured out of a bag, the appearance of disorder is due to the\ncircumstance that the phenomena are only partly fortuitous. The laws of\nspace are supposed, in that case, to be rigidly preserved, and there is\nalso a certain amount of regularity in the formation of the letters. The\nresult is that some elements are orderly and some are disorderly, which\nis precisely what we observe in the actual world. Tillotson, in the\npassage of which a part has been quoted, goes on to ask, \u201cHow long might\n20,000 blind men which should be sent out from the several remote parts\nof England, wander up and down before they would all meet upon Salisbury\nPlains, and fall into rank and file in the exact order of an army? And\nyet this is much more easy to be imagined than how the innumerable blind\nparts of matter should rendezvous themselves into a world.\u201d This is very\ntrue, but in the actual world the _blind men_ are, as far as we can see,\n_not_ drawn up in any particular order at all. And, in short, while a\ncertain amount of order exists in the world, it would seem that the\nworld is not so orderly as it might be, and, for instance, not so much\nso as a world of pure chance would be.\n\nBut we can never get to the bottom of this question until we take\naccount of a highly-important logical principle[48] which I now proceed\nto enounce. This principle is that any plurality or lot of objects\nwhatever have some character in common (no matter how insignificant)\nwhich is peculiar to them and not shared by anything else. The word\n\u201ccharacter\u201d here is taken in such a sense as to include negative\ncharacters, such as incivility, inequality, etc., as well as their\npositives, civility, equality, etc. To prove the theorem, I will show\nwhat character any two things, A and B, have in common, not shared by\nanything else. The things, A and B, are each distinguished from all\nother things by the possession of certain characters which may be named\nA-ness and B-ness. Corresponding to these positive characters, are the\nnegative characters un-A-ness, which is possessed by everything except\nA, and un-B-ness, which is possessed by everything except B. These two\ncharacters are united in everything except A and B; and this union of\nthe characters un-A-ness and un-B-ness makes a compound character which\nmay be termed A-B-lessness. This is not possessed by either A or B, but\nit is possessed by everything else. This character, like every other,\nhas its corresponding negative un-A-B-lessness, and this last is the\ncharacter possessed by both A and B, and by nothing else. It is obvious\nthat what has thus been shown true of two things is _mutatis mutandis_,\ntrue of any number of things. Q. E. D.\n\nIn any world whatever, then, there must be a character peculiar to each\npossible group of objects. If, as a matter of nomenclature, characters\npeculiar to the same group be regarded as only different aspects of the\nsame character, then we may say that there will be precisely one\ncharacter for each possible group of objects. Thus, suppose a world to\ncontain five things, \u03b1, \u03b2, \u03b3, \u03b4, \u03b5. Then it will have a separate\ncharacter for each of the 31 groups (with _non-existence_ making up 32\nor 2^5) shown in the following table:\n\n\nTABLE II.\n\n         \u03b1\u03b2    \u03b1\u03b2\u03b3    \u03b1\u03b2\u03b3\u03b4    \u03b1\u03b2\u03b3\u03b4\u03b5\n    \u03b1    \u03b1\u03b3    \u03b1\u03b2\u03b4    \u03b1\u03b2\u03b3\u03b5\n    \u03b2    \u03b1\u03b4    \u03b1\u03b2\u03b5    \u03b1\u03b2\u03b4\u03b5\n    \u03b3    \u03b1\u03b5    \u03b1\u03b3\u03b4    \u03b1\u03b3\u03b4\u03b5\n    \u03b4    \u03b2\u03b3    \u03b1\u03b3\u03b5    \u03b2\u03b3\u03b4\u03b5\n    \u03b5    \u03b2\u03b4    \u03b1\u03b4\u03b5\n         \u03b2\u03b5    \u03b2\u03b3\u03b4\n         \u03b3\u03b4    \u03b2\u03b3\u03b5\n         \u03b3\u03b5    \u03b2\u03b4\u03b5\n         \u03b4\u03b5    \u03b3\u03b4\u03b5\n\nThis shows that a contradiction is involved in the very idea[49] of a\nchance-world, for in a world of 32 things, instead of there being only\n3^5 or 243 characters, as we have seen that the notion of a chance-world\nrequires, there would, in fact, be no less than 2^{32}, or 4,294,967,296\ncharacters, which would not be all independent, but would have all\npossible relations with one another.\n\nWe further see that so long as we regard characters abstractly, without\nregard to their relative importance, etc., there is no possibility of a\nmore or less degree of orderliness in the world, the whole system of\nrelationship between the different characters being given by mere logic;\nthat is, being implied in those facts which are tacitly admitted as soon\nas we admit that there is any such thing as reasoning.\n\nIn order to descend from this abstract point of view, it is requisite to\nconsider the characters of things as relative to the perceptions and\nactive powers of living beings. Instead, then, of attempting to imagine\na world in which there should be no uniformities, let us suppose one in\nwhich none of the uniformities should have reference to characters\ninteresting or important to us. In the first place, there would be\nnothing to puzzle us in such a world. The small number of qualities\nwhich would directly meet the senses would be the ones which would\nafford the key to everything which could possibly interest us. The whole\nuniverse would have such an air of system and perfect regularity that\nthere would be nothing to ask. In the next place, no action of ours, and\nno event of Nature, would have important consequences in such a world.\nWe should be perfectly free from all responsibility, and there would be\nnothing to do but to enjoy or suffer whatever happened to come along.\nThus there would be nothing to stimulate or develop either the mind or\nthe will, and we consequently should neither act nor think. We should\nhave no memory, because that depends on a law of our organization. Even\nif we had any senses, we should be situated toward such a world\nprecisely as inanimate objects are toward the present one, provided we\nsuppose that these objects have an absolutely transitory and\ninstantaneous consciousness without memory\u2014a supposition which is a mere\nmode of speech, for that would be no consciousness at all. We may,\ntherefore, say that a world of chance is simply our actual world viewed\nfrom the standpoint of an animal at the very vanishing-point of\nintelligence. The actual world is almost a chance-medley to the mind of\na polyp. The interest which the uniformities of Nature have for an\nanimal measures his place in the scale of intelligence.\n\nThus, nothing can be made out from the orderliness of Nature in regard\nto the existence of a God, unless it be maintained that the existence of\na finite mind proves the existence of an infinite one.\n\n\n                                  III\n\n\nIn the last of these papers we examined the nature of inductive or\nsynthetic reasoning. We found it to be a process of sampling. A number\nof specimens of a class are taken, not by selection within that class,\nbut at random. These specimens will agree in a great number of respects.\nIf, now, it were likely that a second lot would agree with the first in\nthe majority of these respects, we might base on this consideration an\ninference in regard to any one of these characters. But such an\ninference would neither be of the nature of induction, nor would it\n(except in special cases) be valid, because the vast majority of points\nof agreement in the first sample drawn would generally be entirely\naccidental, as well as insignificant. To illustrate this, I take the\nages at death of the first five poets given in Wheeler\u2019s _Biographical\nDictionary_. They are:\n\n                               Aagard, 48.\n                               Abeille, 70.\n                               Abulola, 84.\n                               Abunowas, 48.\n                               Accords, 45.\n\nThese five ages have the following characters in common:\n\n1. The difference of the two digits composing the number, divided by\nthree, leaves a remainder of _one_.\n\n2. The first digit raised to the power indicated by the second, and\ndivided by three, leaves a remainder of _one_.\n\n3. The sum of the prime factors of each age, including one, is divisible\nby three.\n\nIt is easy to see that the number of accidental agreements of this sort\nwould be quite endless. But suppose that, instead of considering a\ncharacter because of its prevalence in the sample, we designate a\ncharacter before taking the sample, selecting it for its importance,\nobviousness, or other point of interest. Then two considerable samples\ndrawn at random are extremely likely to agree approximately in regard to\nthe proportion of occurrences of a character so chosen. _The inference\nthat a previously designated character has nearly the same frequency of\noccurrence in the whole of a class that it has in a sample drawn at\nrandom out of that class is induction._ If the character be not\npreviously designated, then a sample in which it is found to be\nprevalent can only serve to suggest that it _may be_ prevalent in the\nwhole class. We may consider this surmise as an inference if we\nplease\u2014an inference of possibility; but a second sample must be drawn to\ntest the question of whether the character actually is prevalent.\nInstead of designating beforehand a single character in reference to\nwhich we will examine a sample, we may designate two, and use the same\nsample to determine the relative frequencies of both. This will be\nmaking two inductive inferences at once; and, of course, we are less\ncertain that both will yield correct conclusions than we should be that\neither separately would do so. What is true of two characters is true of\nany limited number. Now, the number of characters which have any\nconsiderable interest for us in reference to any class of objects is\nmore moderate than might be supposed. As we shall be sure to examine any\nsample with reference to these characters, they may be regarded not\nexactly as predesignated, but as predetermined (which amounts to the\nsame thing); and we may infer that the sample represents the class in\nall these respects if we please, remembering only that this is not so\nsecure an inference as if the particular quality to be looked for had\nbeen fixed upon beforehand.\n\nThe demonstration of this theory of induction rests upon principles and\nfollows methods which are accepted by all those who display in other\nmatters the particular knowledge and force of mind which qualify them to\njudge of this. The theory itself, however, quite unaccountably seems\nnever to have occurred to any of the writers who have undertaken to\nexplain synthetic reasoning. The most widely-spread opinion in the\nmatter is one which was much promoted by Mr. John Stuart Mill\u2014namely,\nthat induction depends for its validity upon the uniformity of\nNature\u2014that is, on the principle that what happens once will, under a\nsufficient degree of similarity of circumstances, happen again as often\nas the same circumstances recur. The application is this: The fact that\ndifferent things belong to the same class constitutes the similarity of\ncircumstances, and the induction is good, provided this similarity is\n\u201csufficient.\u201d What happens once is, that a number of these things are\nfound to have a certain character; what may be expected, then, to happen\nagain as often as the circumstances recur consists in this, that all\nthings belonging to the same class should have the same character.\n\nThis analysis of induction has, I venture to think, various\nimperfections, to some of which it may be useful to call attention. In\nthe first place, when I put my hand in a bag and draw out a handful of\nbeans, and, finding three-quarters of them black, infer that about\nthree-quarters of all in the bag are black, my inference is obviously of\nthe same kind as if I had found any larger proportion, or the whole, of\nthe sample black, and had assumed that it represented in that respect\nthe rest of the contents of the bag. But the analysis in question hardly\nseems adapted to the explanation of this _proportionate_ induction,\nwhere the conclusion, instead of being that a certain event uniformly\nhappens under certain circumstances, is precisely that it does not\nuniformly occur, but only happens in a certain proportion of cases. It\nis true that the whole sample may be regarded as a single object, and\nthe inference may be brought under the formula proposed by considering\nthe conclusion to be that any similar sample will show a similar\nproportion among its constituents. But this is to treat the induction as\nif it rested on a single instance, which gives a very false idea of its\nprobability.\n\nIn the second place, if the uniformity of Nature were the sole warrant\nof induction, we should have no right to draw one in regard to a\ncharacter whose constancy we knew nothing about. Accordingly, Mr. Mill\nsays that, though none but white swans were known to Europeans for\nthousands of years, yet the inference that all swans were white was \u201cnot\na good induction,\u201d because it was not known that color was a usual\ngeneric character (it, in fact, not being so by any means). But it is\nmathematically demonstrable that an inductive inference may have as high\na degree of probability as you please independent of any antecedent\nknowledge of the constancy of the character inferred. Before it was\nknown that color is not usually a character of _genera_, there was\ncertainly a considerable probability that all swans were white. But the\nfurther study of the _genera_ of animals led to the induction of their\nnon-uniformity in regard to color. A deductive application of this\ngeneral proposition would have gone far to overcome the probability of\nthe universal whiteness of swans before the black species was\ndiscovered. When we do know anything in regard to the general constancy\nor inconstancy of a character, the application of that general knowledge\nto the particular class to which any induction relates, though it serves\nto increase or diminish the force of the induction, is, like every\napplication of general knowledge to particular cases, deductive in its\nnature and not inductive.\n\nIn the third place, to say that inductions are true because similar\nevents happen in similar circumstances\u2014or, what is the same thing,\nbecause objects similar in some respects are likely to be similar in\nothers\u2014is to overlook those conditions which really are essential to the\nvalidity of inductions. When we take all the characters into account,\nany pair of objects resemble one another in just as many particulars as\nany other pair. If we limit ourselves to such characters as have for us\nany importance, interest, or obviousness, then a synthetic conclusion\nmay be drawn, but only on condition that the specimens by which we judge\nhave been taken at random from the class in regard to which we are to\nform a judgment, and not selected as belonging to any sub-class. The\ninduction only has its full force when the character concerned has been\ndesignated before examining the sample. These are the essentials of\ninduction, and they are not recognized in attributing the validity of\ninduction to the uniformity of Nature. The explanation of induction by\nthe doctrine of probabilities, given in the last of these papers, is not\na mere metaphysical formula, but is one from which all the rules of\nsynthetic reasoning can be deduced systematically and with mathematical\ncogency. But the account of the matter by a principle of Nature, even if\nit were in other respects satisfactory, presents the fatal disadvantage\nof leaving us quite as much afloat as before in regard to the proper\nmethod of induction. It does not surprise me, therefore, that those who\nadopt this theory have given erroneous rules for the conduct of\nreasoning, nor that the greater number of examples put forward by Mr.\nMill in his first edition, as models of what inductions should be,\nproved in the light of further scientific progress so particularly\nunfortunate that they had to be replaced by others in later editions.\nOne would have supposed that Mr. Mill might have based an induction on\n_this_ circumstance, especially as it is his avowed principle that, if\nthe conclusion of an induction turns out false, it cannot have been a\ngood induction. Nevertheless, neither he nor any of his scholars seem to\nhave been led to suspect, in the least, the perfect solidity of the\nframework which he devised for securely supporting the mind in its\npassage from the known to the unknown, although at its first trial it\ndid not answer quite so well as had been expected.\n\n\n                                   IV\n\n\nWhen we have drawn any statistical induction\u2014such, for instance, as that\none-half of all births are of male children\u2014it is always possible to\ndiscover, by investigation sufficiently prolonged, a class of which the\nsame predicate may be affirmed universally; to find out, for instance,\n_what sort of_ births are of male children. The truth of this principle\nfollows immediately from the theorem that there is a character peculiar\nto every possible group of objects. The form in which the principle is\nusually stated is, that _every event must have a cause_.\n\nBut, though there exists a cause for every event, and that of a kind\nwhich is capable of being discovered, yet if there be nothing to guide\nus to the discovery; if we have to hunt among all the events in the\nworld without any scent; if, for instance, the sex of a child might\nequally be supposed to depend on the configuration of the planets, on\nwhat was going on at the antipodes, or on anything else\u2014then the\ndiscovery would have no chance of ever getting made.\n\nThat we ever do discover the precise causes of things, that any\ninduction whatever is absolutely without exception, is what we have no\nright to assume. On the contrary, it is an easy corollary, from the\ntheorem just referred to, that every empirical rule has an\nexception.[50] But there are certain of our inductions which present an\napproach to universality so extraordinary that, even if we are to\nsuppose that they are not strictly universal truths, we cannot possibly\nthink that they have been reached merely by accident. The most\nremarkable laws of this kind are those of _time_ and _space_. With\nreference to space, Bishop Berkeley first showed, in a very conclusive\nmanner, that it was not a thing _seen_, but a thing _inferred_. Berkeley\nchiefly insists on the impossibility of directly seeing the third\ndimension of space, since the retina of the eye is a surface. But, in\npoint of fact, the retina is not even a surface; it is a conglomeration\nof nerve-needles directed toward the light and having only their extreme\npoints sensitive, these points lying at considerable distances from one\nanother compared with their areas. Now, of these points, certainly the\nexcitation of no one singly can produce the perception of a surface, and\nconsequently not the aggregate of all the sensations can amount to this.\nBut certain relations subsist between the excitations of different\nnerve-points, and these constitute the premises upon which the\nhypothesis of space is founded, and from which it is inferred. That\nspace is not immediately perceived is now universally admitted; and a\nmediate cognition is what is called an inference, and is subject to the\ncriticism of logic. But what are we to say to the fact of every chicken\nas soon as it is hatched solving a problem whose data are of a\ncomplexity sufficient to try the greatest mathematical powers? It would\nbe insane to deny that the tendency to light upon the conception of\nspace is inborn in the mind of the chicken and of every animal. The same\nthing is equally true of time. That time is not directly perceived is\nevident, since no lapse of time is present, and we only perceive what is\npresent. That, not having the idea of time, we should never be able to\nperceive the flow in our sensations without some particular aptitude for\nit, will probably also be admitted. The idea of force\u2014at least, in its\nrudiments\u2014is another conception so early arrived at, and found in\nanimals so low in the scale of intelligence, that it must be supposed\ninnate. But the innateness of an idea admits of degree, for it consists\nin the tendency of that idea to present itself to the mind. Some ideas,\nlike that of space, do so present themselves irresistibly at the very\ndawn of intelligence, and take possession of the mind on small\nprovocation, while of other conceptions we are prepossessed, indeed, but\nnot so strongly, down a scale which is greatly extended. The tendency to\npersonify every thing, and to attribute human characters to it, may be\nsaid to be innate; but it is a tendency which is very soon overcome by\ncivilized man in regard to the greater part of the objects about him.\nTake such a conception as that of gravitation varying inversely as the\nsquare of the distance. It is a very simple law. But to say that it is\nsimple is merely to say that it is one which the mind is particularly\nadapted to apprehend with facility. Suppose the idea of a quantity\nmultiplied into another had been no more easy to the mind than that of a\nquantity raised to the power indicated by itself\u2014should we ever have\ndiscovered the law of the solar system?\n\nIt seems incontestable, therefore, that the mind of man is strongly\nadapted to the comprehension of the world; at least, so far as this\ngoes, that certain conceptions, highly important for such a\ncomprehension, naturally arise in his mind; and, without such a\ntendency, the mind could never have had any development at all.\n\nHow are we to explain this adaptation? The great utility and\nindispensableness of the conceptions of time, space, and force, even to\nthe lowest intelligence, are such as to suggest that they are the\nresults of natural selection. Without something like geometrical,\nkinetical, and mechanical conceptions, no animal could seize his food or\ndo anything which might be necessary for the preservation of the\nspecies. He might, it is true, be provided with an instinct which would\ngenerally have the same effect; that is to say, he might have\nconceptions different from those of time, space, and force, but which\ncoincided with them in regard to the ordinary cases of the animal\u2019s\nexperience. But, as that animal would have an immense advantage in the\nstruggle for life whose mechanical conceptions did not break down in a\nnovel situation (such as development must bring about), there would be a\nconstant selection in favor of more and more correct ideas of these\nmatters. Thus would be attained the knowledge of that fundamental law\nupon which all science rolls; namely, that forces depend upon relations\nof time, space, and mass. When this idea was once sufficiently clear, it\nwould require no more than a comprehensible degree of genius to discover\nthe exact nature of these relations. Such an hypothesis naturally\nsuggests itself, but it must be admitted that it does not seem\nsufficient to account for the extraordinary accuracy with which these\nconceptions apply to the phenomena of Nature, and it is probable that\nthere is some secret here which remains to be discovered.\n\n\n                                   V\n\n\nSome important questions of logic depend upon whether we are to consider\nthe material universe as of limited extent and finite age, or quite\nboundless in space and in time. In the former case, it is conceivable\nthat a general plan or design embracing the whole universe should be\ndiscovered, and it would be proper to be on the alert for some traces of\nsuch a unity. In the latter case, since the proportion of the world of\nwhich we can have any experience is less than the smallest assignable\nfraction, it follows that we never could discover any _pattern_ in the\nuniverse except a repeating one; any design embracing the whole would be\nbeyond our powers to discern, and beyond the united powers of all\nintellects during all time. Now, what is absolutely incapable of being\nknown is, as we have seen in a former paper, not real at all. An\nabsolutely incognizable existence is a nonsensical phrase. If,\ntherefore, the universe is infinite, the attempt to find in it any\ndesign embracing it as a whole is futile, and involves a false way of\nlooking at the subject. If the universe never had any beginning, and if\nin space world stretches beyond world without limit, there is no _whole_\nof material things, and consequently no general character to the\nuniverse, and no need or possibility of any governor for it. But if\nthere was a time before which absolutely no matter existed, if there are\ncertain absolute bounds to the region of things outside of which there\nis a mere void, then we naturally seek for an explanation of it, and,\nsince we cannot look for it among material things, the hypothesis of a\ngreat disembodied animal, the creator and governor of the world, is\nnatural enough.\n\nThe actual state of the evidence as to the limitation of the universe is\nas follows: As to time, we find on our earth a constant progress of\ndevelopment since the planet was a red-hot ball; the solar system seems\nto have resulted from the condensation of a nebula, and the process\nappears to be still going on. We sometimes see stars (presumably with\nsystems of worlds) destroyed and apparently resolved back into the\nnebulous condition, but we have no evidence of any existence of the\nworld previous to the nebulous stage from which it seems to have been\nevolved. All this rather favors the idea of a beginning than otherwise.\nAs for limits in space, we cannot be sure that we see anything outside\nof the system of the Milky Way. Minds of theological predilections have\ntherefore no need of distorting the facts to reconcile them with their\nviews.\n\nBut the only scientific presumption is, that the unknown parts of space\nand time are like the known parts, occupied; that, as we see cycles of\nlife and death in all development which we can trace out to the end, the\nsame holds good in regard to solar systems; that as enormous distances\nlie between the different planets of our solar system, relatively to\ntheir diameters, and as still more enormous distances lie between our\nsystem relatively to its diameter and other systems, so it may be\nsupposed that other galactic clusters exist so remote from ours as not\nto be recognized as such with certainty. I do not say that these are\nstrong inductions; I only say that they are the presumptions which, in\nour ignorance of the facts, should be preferred to hypotheses which\ninvolve conceptions of things and occurrences totally different in their\ncharacter from any of which we have had any experience, such as\ndisembodied spirits, the creation of matter, infringements of the laws\nof mechanics, etc.\n\nThe universe ought to be presumed too vast to have any character. When\nit is claimed that the arrangements of Nature are benevolent, or just,\nor wise, or of any other peculiar kind, we ought to be prejudiced\nagainst such opinions, as being the offspring of an ill-founded notion\nof the finitude of the world. And examination has hitherto shown that\nsuch beneficences, justice, etc., are of a most limited kind\u2014limited in\ndegree and limited in range.\n\nIn like manner, if any one claims to have discovered a plan in the\nstructure of organized beings, or a scheme in their classification, or a\nregular arrangement among natural objects, or a system of\nproportionality in the human form, or an order of development, or a\ncorrespondence between conjunctions of the planets and human events, or\na significance in numbers, or a key to dreams, the first thing we have\nto ask is whether such relations are susceptible of explanation on\nmechanical principles, and if not they should be looked upon with\ndisfavor as having already a strong presumption against them; and\nexamination has generally exploded all such theories.\n\nThere are minds to whom every prejudice, every presumption, seems\nunfair. It is easy to say what minds these are. They are those who never\nhave known what it is to draw a well-grounded induction, and who imagine\nthat other people\u2019s knowledge is as nebulous as their own. That all\nscience rolls upon presumption (not of a formal but of a real kind) is\nno argument with them, because they cannot imagine that there is\nanything solid in human knowledge. These are the people who waste their\ntime and money upon perpetual motions and other such rubbish.\n\nBut there are better minds who take up mystical theories (by which I\nmean all those which have no possibility of being mechanically\nexplained). These are persons who are strongly prejudiced in favor of\nsuch theories. We all have natural tendencies to believe in such things;\nour education often strengthens this tendency; and the result is, that\nto many minds nothing seems so antecedently probable as a theory of this\nkind. Such persons find evidence enough in favor of their views, and in\nthe absence of any recognized logic of induction they cannot be driven\nfrom their belief.\n\nBut to the mind of a physicist there ought to be a strong presumption\nagainst every mystical theory; and, therefore, it seems to me that those\nscientific men who have sought to make out that science was not hostile\nto theology have not been so clear-sighted as their opponents.\n\nIt would be extravagant to say that science can at present disprove\nreligion; but it does seem to me that the spirit of science is hostile\nto any religion except such a one as that of M. Vacherot. Our appointed\nteachers inform us that Buddhism is a miserable and atheistical faith,\nshorn of the most glorious and needful attributes of a religion; that\nits priests can be of no use to agriculture by praying for rain, nor to\nwar by commanding the sun to stand still. We also hear the remonstrances\nof those who warn us that to shake the general belief in the living God\nwould be to shake the general morals, public and private. This, too,\nmust be admitted; such a revolution of thought could no more be\naccomplished without waste and desolation than a plantation of trees\ncould be transferred to new ground, however wholesome in itself, without\nall of them languishing for a time, and many of them dying. Nor is it,\nby-the-way, a thing to be presumed that a man would have taken part in a\nmovement having a possible atheistical issue without having taken\nserious and adequate counsel in regard to that responsibility. But, let\nthe consequences of such a belief be as dire as they may, one thing is\ncertain: that the state of the facts, whatever it may be, will surely\nget found out, and no human prudence can long arrest the triumphal car\nof truth\u2014no, not if the discovery were such as to drive every individual\nof our race to suicide!\n\nBut it would be folly to suppose that any metaphysical theory in regard\nto the mode of being of the perfect is to destroy that aspiration toward\nthe perfect which constitutes the essence of religion. It is true that,\nif the priests of any particular form of religion succeed in making it\ngenerally believed that religion cannot exist without the acceptance of\ncertain formulas, or if they succeed in so interweaving certain dogmas\nwith the popular religion that the people can see no essential analogy\nbetween a religion which accepts these points of faith and one which\nrejects them, the result may very well be to render those who cannot\nbelieve these things irreligious. Nor can we ever hope that any body of\npriests should consider themselves more teachers of religion in general\nthan of the particular system of theology advocated by their own party.\nBut no man need be excluded from participation in the common feelings,\nnor from so much of the public expression of them as is open to all the\nlaity, by the unphilosophical narrowness of those who guard the\nmysteries of worship. Am I to be prevented from joining in that common\njoy at the revelation of enlightened principles of religion, which we\ncelebrate at Easter and Christmas, because I think that certain\nscientific, logical, and metaphysical ideas which have been mixed up\nwith these principles are untenable? No; to do so would be to estimate\nthose errors as of more consequence than the truth\u2014an opinion which few\nwould admit. People who do not believe what are really the fundamental\nprinciples of Christianity are rare to find, and all but these few ought\nto feel at home in the churches.\n\nFootnote 44:\n\n  _Popular Science Monthly_, June, 1878.\n\nFootnote 45:\n\n  [See Santayana, _Reason in Religion_.]\n\nFootnote 46:\n\n  For the present purpose, the negative of a character is to be\n  considered as much a character as the positive, for a uniformity may\n  either be affirmative or negative. I do not say that no distinction\n  can be drawn between positive and negative uniformities.\n\nFootnote 47:\n\n  There being 5 simple characters, with their negatives, they could be\n  compounded in various ways so as to make 241 characters in all,\n  without counting the characters _existence_ and _non-existence_, which\n  make up 243 or 3^5.\n\nFootnote 48:\n\n  This principle was, I believe, first stated by Mr. De Morgan.\n\nFootnote 49:\n\n  Not in every idea but only in the one so formulated.\n\nFootnote 50:\n\n  [Note that this corollary is itself a theoretical inference and not an\n  empirical rule.]\n\n\n\n\n                              SIXTH PAPER\n                DEDUCTION, INDUCTION, AND HYPOTHESIS[51]\n\n\n                                   I\n\n\nThe chief business of the logician is to classify arguments; for all\ntesting clearly depends on classification. The classes of the logicians\nare defined by certain typical forms called syllogisms. For example, the\nsyllogism called _Barbara_ is as follows:\n\n                              S is M; M is P:\n                              Hence, S is P.\n\nOr, to put words for letters\u2014\n\n                  Enoch and Elijah were men; all men die:\n                  Hence, Enoch and Elijah must have died.\n\nThe \u201cis P\u201d of the logicians stands for any verb, active or neuter. It is\ncapable of strict proof (with which, however, I will not trouble the\nreader) that all arguments whatever can be put into this form; but only\nunder the condition that the _is_ shall mean \u201c_is_ for the purposes of\nthe argument\u201d or \u201cis represented by.\u201d Thus, an induction will appear in\nthis form something like this:\n\nThese beans are two-thirds white;\n\nBut, the beans in this bag are (represented by) these beans;\n\n\u2234 The beans in the bag are two-thirds white.\n\nBut, because all inference may be reduced in some way to _Barbara_, it\ndoes not follow that this is the most appropriate form in which to\nrepresent every kind of inference. On the contrary, to show the\ndistinctive characters of different sorts of inference, they must\nclearly be exhibited in different forms peculiar to each. _Barbara_\nparticularly typifies deductive reasoning; and so long as the _is_ is\ntaken literally, no inductive reasoning can be put into this form.\n_Barbara_ is, in fact, nothing but the application of a rule. The\nso-called major premise lays down this rule; as, for example, _All men\nare mortal._ The other or minor premise states a case under the rule;\nas, _Enoch was a man._ The conclusion applies the rule to the case and\nstates the result: _Enoch is mortal._ All deduction is of this\ncharacter; it is merely the application of general rules to particular\ncases. Sometimes this is not very evident, as in the following:\n\n                 All quadrangles are figures,\n                 But no triangle is a quadrangle;\n                 Therefore, some figures are not triangles.\n\nBut here the reasoning is really this:\n\n             _Rule._\u2014Every quadrangle is other than a triangle.\n             _Case._\u2014Some figures are quadrangles.\n             _Result._\u2014Some figures are not triangles.\n\nInductive or synthetic reasoning, being something more than the mere\napplication of a general rule to a particular case, can never be reduced\nto this form.\n\nIf, from a bag of beans of which we know that 2/3 are white, we take one\nat random, it is a deductive inference that this bean is probably white,\nthe probability being 2/3. We have, in effect, the following syllogism:\n\n_Rule._\u2014The beans in this bag are 2/3 white.\n\n_Case._\u2014This bean has been drawn in such a way that in the long run the\nrelative number of white beans so drawn would be equal to the relative\nnumber in the bag.\n\n_Result._\u2014This bean has been drawn in such a way that in the long run it\nwould turn out white 2/3 of the time.\n\nIf instead of drawing one bean we draw a handful at random and conclude\nthat about 2/3 of the handful are probably white, the reasoning is of\nthe same sort. If, however, not knowing what proportion of white beans\nthere are in the bag, we draw a handful at random and, finding 2/3 of\nthe beans in the handful white, conclude that about 2/3 of those in the\nbag are white, we are rowing up the current of deductive sequence, and\nare concluding a rule from the observation of a result in a certain\ncase. This is particularly clear when all the handful turn out one\ncolor. The induction then is:\n\n              These beans were in this bag.\u2014\u2014\u2014\u2014\u2014\u2014\u2014-\n              These beans are white.\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014\n              All the beans in the bag were white.             | |\n                                                             | | |\n          Which is but an inversion of the deductive         | | |\n            syllogism.                                       | | |\n                                                             | | |\n              _Rule._\u2014All the beans in the bag were white.\u2014+ | |\n              _Case._\u2014These beans were in the bag.\u2014\u2014\u2014\u2014\u2014\u2014+-+\n              _Result._\u2014These beans are white.\u2014\u2014\u2014\u2014\u2014\u2014\u2014\u2014+\n\nSo that induction is the inference of the _rule_ from the _case_ and\n_result_.\n\nBut this is not the only way of inverting a deductive syllogism so as to\nproduce a synthetic inference. Suppose I enter a room and there find a\nnumber of bags, containing different kinds of beans. On the table there\nis a handful of white beans; and, after some searching, I find one of\nthe bags contains white beans only. I at once infer as a probability, or\nas a fair guess, that this handful was taken out of that bag. This sort\nof inference is called _making an hypothesis_.[52] It is the inference\nof a _case_ from a _rule_ and _result_. We have, then\u2014\n\n               DEDUCTION.\n\n               _Rule._\u2014All the beans from this bag are white.\n\n               _Case._\u2014These beans are from this bag.\n\n               \u2234 _Result._\u2014These beans are white.\n\n              INDUCTION.\n\n              _Case._\u2014These beans are from this bag.\n\n              _Result._\u2014These beans are white.\n\n              \u2234 _Rule._\u2014All the beans from this bag are white.\n\n               HYPOTHESIS.\n\n               _Rule._\u2014All the beans from this bag are white.\n\n               _Result._\u2014These beans are white.\n\n               \u2234 _Case._\u2014These beans are from this bag.\n\nWe, accordingly, classify all inference as follows:\n\n                              Inference.\n                        /\u2014\u2014\u2014\u2014\u2014\u2014\u2014^\u2014\u2014\u2014\u2014\u2014\u2014\u2014-|\n             Deductive or Analytic.       Synthetic.\n                                        /\u2014\u2014\u2014\u2014^\u2014\u2014\u2014\u2014\u2014|\n                                   Induction.      Hypothesis.\n\nInduction is where we generalize from a number of cases of which\nsomething is true, and infer that the same thing is true of a whole\nclass. Or, where we find a certain thing to be true of a certain\nproportion of cases and infer that it is true of the same proportion of\nthe whole class. Hypothesis is where we find some very curious\ncircumstance, which would be explained by the supposition that it was a\ncase of a certain general rule, and thereupon adopt that supposition.\nOr, where we find that in certain respects two objects have a strong\nresemblance, and infer that they resemble one another strongly in other\nrespects.\n\nI once landed at a seaport in a Turkish province; and, as I was walking\nup to the house which I was to visit, I met a man upon horseback,\nsurrounded by four horsemen holding a canopy over his head. As the\ngovernor of the province was the only personage I could think of who\nwould be so greatly honored, I inferred that this was he. This was an\nhypothesis.\n\nFossils are found; say, remains like those of fishes, but far in the\ninterior of the country. To explain the phenomenon, we suppose the sea\nonce washed over this land. This is another hypothesis.\n\nNumberless documents and monuments refer to a conqueror called Napoleon\nBonaparte. Though we have not seen the man, yet we cannot explain what\nwe have seen, namely, all these documents and monuments, without\nsupposing that he really existed. Hypothesis again.\n\nAs a general rule, hypothesis is a weak kind of argument. It often\ninclines our judgment so slightly toward its conclusion that we cannot\nsay that we believe the latter to be true; we only surmise that it may\nbe so. But there is no difference except one of degree between such an\ninference and that by which we are led to believe that we remember the\noccurrences of yesterday from our feeling as if we did so.\n\n\n                                   II\n\n\nBesides the way just pointed out of inverting a deductive syllogism to\nproduce an induction or hypothesis, there is another. If from the truth\nof a certain premise the truth of a certain conclusion would necessarily\nfollow, then from the falsity of the conclusion the falsity of the\npremise would follow. Thus, take the following syllogism in _Barbara_:\n\n                 _Rule._\u2014All men are mortal.\n\n                 _Case._\u2014Enoch and Elijah were men.\n\n                 \u2234 _Result._\u2014Enoch and Elijah were mortal.\n\nNow, a person who denies this result may admit the rule, and, in that\ncase, he must deny the case. Thus:\n\n           _Denial of Result._\u2014Enoch and Elijah were not mortal.\n\n           _Rule._\u2014All men are mortal.\n\n           \u2234 _Denial of Case._\u2014Enoch and Elijah were not men.\n\nThis kind of syllogism is called _Baroco_, which is the typical mood of\nthe second figure. On the other hand, the person who denies the result\nmay admit the case, and in that case he must deny the rule. Thus:\n\n         _Denial of the Result._\u2014Enoch and Elijah were not mortal.\n\n         _Case._\u2014Enoch and Elijah were men.\n\n         \u2234 _Denial of the Rule._\u2014Some men are not mortal.\n\nThis kind of syllogism is called _Bocardo_, which is the typical mood of\nthe third figure.\n\n_Baroco_ and _Bocardo_ are, of course, deductive syllogisms; but of a\nvery peculiar kind. They are called by logicians indirect moods, because\nthey need some transformation to appear as the application of a rule to\na particular case. But if, instead of setting out as we have here done\nwith a necessary deduction in _Barbara_, we take a probable deduction of\nsimilar form, the indirect moods which we shall obtain will be\u2014\n\n                    Corresponding to _Baroco_, an hypothesis;\n               and, Corresponding to _Bocardo_, an induction.\n\nFor example, let us begin with this probable deduction in _Barbara_:\n\n       _Rule._\u2014Most of the beans in this bag are white.\n\n       _Case._\u2014This handful of beans are from this bag.\n\n       \u2234 _Result._\u2014Probably, most of this handful of beans are white.\n\nNow, deny the result, but accept the rule:\n\n    _Denial of Result._\u2014Few beans of this handful are white.\n\n    _Rule._\u2014Most beans in this bag are white.\n\n    \u2234 _Denial of Case._\u2014Probably, these beans were taken from another\n       bag.\n\nThis is an hypothetical inference. Next, deny the result, but accept the\ncase:\n\n       _Denial of Result._\u2014Few beans of this handful are white.\n\n       _Case._\u2014These beans came from this bag.\n\n       \u2234 _Denial of Rule._\u2014Probably, few beans in the bag are white.\n\nThis is an induction.\n\nThe relation thus exhibited between synthetic and deductive reasoning is\nnot without its importance. When we adopt a certain hypothesis, it is\nnot alone because it will explain the observed facts, but also because\nthe contrary hypothesis would probably lead to results contrary to those\nobserved. So, when we make an induction, it is drawn not only because it\nexplains the distribution of characters in the sample, but also because\na different rule would probably have led to the sample being other than\nit is.\n\nBut the advantage of this way of considering the subject might easily be\noverrated. An induction is really the inference of a rule, and to\nconsider it as the denial of a rule is an artificial conception, only\nadmissible because, when statistical or proportional propositions are\nconsidered as rules, the denial of a rule is itself a rule. So, an\nhypothesis is really a subsumption of a case under a class and not the\ndenial of it, except for this, that to deny a subsumption under one\nclass is to admit a subsumption under another.\n\n_Bocardo_ may be considered as an induction, so timid as to lose its\namplificative character entirely. Enoch and Elijah are specimens of a\ncertain kind of men. All that kind of men are shown by these instances\nto be immortal. But instead of boldly concluding that all very pious\nmen, or all men favorites of the Almighty, etc., are immortal, we\nrefrain from specifying the description of men, and rest in the merely\nexplicative inference that _some_ men are immortal. So _Baroco_ might be\nconsidered as a very timid hypothesis. Enoch and Elijah are not mortal.\nNow, we might boldly suppose them to be gods or something of that sort,\nbut instead of that we limit ourselves to the inference that they are of\n_some_ nature different from that of man.\n\nBut, after all, there is an immense difference between the relation of\n_Baroco_ and _Bocardo_ to _Barbara_ and that of Induction and Hypothesis\nto Deduction. _Baroco_ and _Bocardo_ are based upon the fact that if the\ntruth of a conclusion necessarily follows from the truth of a premise,\nthen the falsity of the premise follows from the falsity of the\nconclusion. This is always true. It is different when the inference is\nonly probable. It by no means follows that, because the truth of a\ncertain premise would render the truth of a conclusion probable,\ntherefore the falsity of the conclusion renders the falsity of the\npremise probable. At least, this is only true, as we have seen in a\nformer paper, when the word probable is used in one sense in the\nantecedent and in another in the consequent.\n\n\n                                  III\n\n\nA certain anonymous writing is upon a torn piece of paper. It is\nsuspected that the author is a certain person. His desk, to which only\nhe has had access, is searched, and in it is found a piece of paper, the\ntorn edge of which exactly fits, in all its irregularities, that of the\npaper in question. It is a fair hypothetic inference that the suspected\nman was actually the author. The ground of this inference evidently is\nthat two torn pieces of paper are extremely unlikely to fit together by\naccident. Therefore, of a great number of inferences of this sort, but a\nvery small proportion would be deceptive. The analogy of hypothesis with\ninduction is so strong that some logicians have confounded them.\nHypothesis has been called an induction of characters. A number of\ncharacters belonging to a certain class are found in a certain object;\nwhence it is inferred that all the characters of that class belong to\nthe object in question. This certainly involves the same principle as\ninduction; yet in a modified form. In the first place, characters are\nnot susceptible of simple enumeration like objects; in the next place,\ncharacters run in categories. When we make an hypothesis like that about\nthe piece of paper, we only examine a single line of characters, or\nperhaps two or three, and we take no specimen at all of others. If the\nhypothesis were nothing but an induction, all that we should be\njustified in concluding, in the example above, would be that the two\npieces of paper which matched in such irregularities as have been\nexamined would be found to match in other, say slighter, irregularities.\nThe inference from the shape of the paper to its ownership is precisely\nwhat distinguishes hypothesis from induction, and makes it a bolder and\nmore perilous step.\n\nThe same warnings that have been given against imagining that induction\nrests upon the uniformity of Nature might be repeated in regard to\nhypothesis. Here, as there, such a theory not only utterly fails to\naccount for the validity of the inference, but it also gives rise to\nmethods of conducting it which are absolutely vicious. There are, no\ndoubt, certain uniformities in Nature, the knowledge of which will\nfortify an hypothesis very much. For example, we suppose that iron,\ntitanium, and other metals exist in the sun, because we find in the\nsolar spectrum many lines coincident in position with those which these\nmetals would produce; and this hypothesis is greatly strengthened by our\nknowledge of the remarkable distinctiveness of the particular line of\ncharacters observed. But such a fortification of hypothesis is of a\ndeductive kind, and hypothesis may still be probable when such\nre\u00ebnforcement is wanting.\n\nThere is no greater nor more frequent mistake in practical logic than to\nsuppose that things which resemble one another strongly in some respects\nare any the more likely for that to be alike in others. That this is\nabsolutely false, admits of rigid demonstration; but, inasmuch as the\nreasoning is somewhat severe and complicated (requiring, like all such\nreasoning, the use of A, B, C, etc., to set it forth), the reader would\nprobably find it distasteful, and I omit it. An example, however, may\nillustrate the proposition: The comparative mythologists occupy\nthemselves with finding points of resemblance between solar phenomena\nand the careers of the heroes of all sorts of traditional stories; and\nupon the basis of such resemblances they infer that these heroes are\nimpersonations of the sun. If there be anything more in their\nreasonings, it has never been made clear to me. An ingenious logician,\nto show how futile all that is, wrote a little book, in which he\npretended to prove, in the same manner, that Napoleon Bonaparte is only\nan impersonation of the sun. It was really wonderful to see how many\npoints of resemblance he made out. The truth is, that any two things\nresemble one another just as strongly as any two others, if recondite\nresemblances are admitted. But, in order that the process of making an\nhypothesis should lead to a probable result, the following rules must be\nfollowed:\n\n1. The hypothesis should be distinctly put as a question, before making\nthe observations which are to test its truth. In other words, we must\ntry to see what the result of predictions from the hypothesis will be.\n\n2. The respect in regard to which the resemblances are noted must be\ntaken at random. We must not take a particular kind of predictions for\nwhich the hypothesis is known to be good.\n\n3. The failures as well as the successes of the predictions must be\nhonestly noted. The whole proceeding must be fair and unbiased.\n\nSome persons fancy that bias and counter-bias are favorable to the\nextraction of truth\u2014that hot and partisan debate is the way to\ninvestigate. This is the theory of our atrocious legal procedure. But\nLogic puts its heel upon this suggestion. It irrefragably demonstrates\nthat knowledge can only be furthered by the real desire for it, and that\nthe methods of obstinacy, of authority, and every mode of trying to\nreach a foregone conclusion, are absolutely of no value. These things\nare proved. The reader is at liberty to think so or not as long as the\nproof is not set forth, or as long as he refrains from examining it.\nJust so, he can preserve, if he likes, his freedom of opinion in regard\nto the propositions of geometry; only, in that case, if he takes a fancy\nto read Euclid, he will do well to skip whatever he finds with A, B, C,\netc., for, if he reads attentively that disagreeable matter, the freedom\nof his opinion about geometry may unhappily be lost forever.\n\nHow many people there are who are incapable of putting to their own\nconsciences this question, \u201cDo I want to know how the fact stands, or\nnot?\u201d\n\nThe rules which have thus far been laid down for induction and\nhypothesis are such as are absolutely essential. There are many other\nmaxims expressing particular contrivances for making synthetic\ninferences strong, which are extremely valuable and should not be\nneglected. Such are, for example, Mr. Mill\u2019s four methods. Nevertheless,\nin the total neglect of these, inductions and hypotheses may and\nsometimes do attain the greatest force.\n\n\n                                   IV\n\n\nClassifications in all cases perfectly satisfactory hardly exist. Even\nin regard to the great distinction between explicative and ampliative\ninferences, examples could be found which seem to lie upon the border\nbetween the two classes, and to partake in some respects of the\ncharacters of either. The same thing is true of the distinction between\ninduction and hypothesis. In the main, it is broad and decided. By\ninduction, we conclude that facts, similar to observed facts, are true\nin cases not examined. By hypothesis, we conclude the existence of a\nfact quite different from anything observed, from which, according to\nknown laws, something observed would necessarily result. The former, is\nreasoning from particulars to the general law; the latter, from effect\nto cause. The former classifies, the latter explains. It is only in some\nspecial cases that there can be more than a momentary doubt to which\ncategory a given inference belongs. One exception is where we observe,\nnot facts similar under similar circumstances, but facts different under\ndifferent circumstances\u2014the difference of the former having, however, a\ndefinite relation to the difference of the latter. Such inferences,\nwhich are really inductions, sometimes present nevertheless some\nindubitable resemblances to hypotheses.\n\nKnowing that water expands by heat, we make a number of observations of\nthe volume of a constant mass of water at different temperatures. The\nscrutiny of a few of these suggests a form of algebraical formula which\nwill approximately express the relation of the volume to the\ntemperature. It may be, for instance, that _v_ being the relative\nvolume, and _t_ the temperature, a few observations examined indicate a\nrelation of the form\u2014\n\n                     _v_ = 1 + _at_ + _bt_^2 + _ct_^3.\n\nUpon examining observations at other temperatures taken at random, this\nidea is confirmed; and we draw the inductive conclusion that all\nobservations within the limits of temperature from which we have drawn\nour observations could equally be so satisfied. Having once ascertained\nthat such a formula is possible, it is a mere affair of arithmetic to\nfind the values of _a_, _b_, and _c_, which will make the formula\nsatisfy the observations best. This is what physicists call an empirical\nformula, because it rests upon mere induction, and is not explained by\nany hypothesis.\n\nSuch formul\u00e6, though very useful as means of describing in general terms\nthe results of observations, do not take any high rank among scientific\ndiscoveries. The induction which they embody, that expansion by heat (or\nwhatever other phenomenon is referred to) takes place in a perfectly\ngradual manner without sudden leaps or inummerable fluctuations,\nalthough really important, attracts no attention, because it is what we\nnaturally anticipate. But the defects of such expressions are very\nserious. In the first place, as long as the observations are subject to\nerror, as all observations are, the formula cannot be expected to\nsatisfy the observations exactly. But the discrepancies cannot be due\nsolely to the errors of the observations, but must be partly owing to\nthe error of the formula which has been deducted from erroneous\nobservations. Moreover, we have no right to suppose that the real facts,\nif they could be had free from error, could be expressed by such a\nformula at all. They might, perhaps, be expressed by a similar formula\nwith an infinite number of terms; but of what use would that be to us,\nsince it would require an infinite number of coefficients to be written\ndown? When one quantity varies with another, if the corresponding values\nare exactly known, it is a mere matter of mathematical ingenuity to find\nsome way of expressing their relation in a simple manner. If one\nquantity is of one kind\u2014say, a specific gravity\u2014and the other of another\nkind\u2014say, a temperature\u2014we do not desire to find an expression for their\nrelation which is wholly free from numerical constants, since if it were\nfree from them when, say, specific gravity as compared with water, and\ntemperature as expressed by the Centigrade thermometer, were in\nquestion, numbers would have to be introduced when the scales of\nmeasurement were changed. We may, however, and do desire to find\nformulas expressing the relations of physical phenomena which shall\ncontain no more arbitrary numbers than changes in the scales of\nmeasurement might require.\n\nWhen a formula of this kind is discovered, it is no longer called an\nempirical formula, but a law of Nature; and is sooner or later made the\nbasis of an hypothesis which is to explain it. These simple formul\u00e6 are\nnot usually, if ever, exactly true, but they are none the less important\nfor that; and the great triumph of the hypothesis comes when it explains\nnot only the formula, but also the deviations from the formula. In the\ncurrent language of the physicists, an hypothesis of this importance is\ncalled a theory, while the term hypothesis is restricted to suggestions\nwhich have little evidence in their favor. There is some justice in the\ncontempt which clings to the word hypothesis. To think that we can\nstrike out of our own minds a true preconception of how Nature acts, in\na vain fancy. As Lord Bacon well says: \u201cThe subtlety of Nature far\nexceeds the subtlety of sense and intellect: so that these fine\nmeditations, and speculations, and reasonings of men are a sort of\ninsanity, only there is no one at hand to remark it.\u201d The successful\ntheories are not pure guesses, but are guided by reasons.\n\nThe kinetical theory of gases is a good example of this. This theory is\nintended to explain certain simple formul\u00e6, the chief of which is called\nthe law of Boyle. It is, that if air or any other gas be placed in a\ncylinder with a piston, and if its volume be measured under the pressure\nof the atmosphere, say fifteen pounds on the square inch, and if then\nanother fifteen pounds per square inch be placed on the piston, the gas\nwill be compressed to one-half its bulk, and in similar inverse ratio\nfor other pressures. The hypothesis which has been adopted to account\nfor this law is that the molecules of a gas are small, solid particles\nat great distances from each other (relatively to their dimensions), and\nmoving with great velocity, without sensible attractions or repulsions,\nuntil they happen to approach one another very closely. Admit this, and\nit follows that when a gas is under pressure what prevents it from\ncollapsing is not the incompressibility of the separate molecules, which\nare under no pressure at all, since they do not touch, but the pounding\nof the molecules against the piston. The more the piston falls, and the\nmore the gas is compressed, the nearer together the molecules will be;\nthe greater number there will be at any moment within a given distance\nof the piston, the shorter the distance which any one will go before its\ncourse is changed by the influence of another, the greater number of new\ncourses of each in a given time, and the oftener each, within a given\ndistance of the piston, will strike it. This explains Boyle\u2019s law. The\nlaw is not exact; but the hypothesis does not lead us to it exactly.\nFor, in the first place, if the molecules are large, they will strike\neach other oftener when their mean distances are diminished, and will\nconsequently strike the piston oftener, and will produce more pressure\nupon it. On the other hand, if the molecules have an attraction for one\nanother, they will remain for a sensible time within one another\u2019s\ninfluence, and consequently they will not strike the wall so often as\nthey otherwise would, and the pressure will be less increased by\ncompression.\n\nWhen the kinetical theory of gases was first proposed by Daniel\nBernoulli, in 1738, it rested only on the law of Boyle, and was\ntherefore pure hypothesis. It was accordingly quite naturally and\ndeservedly neglected. But, at present, the theory presents quite another\naspect; for, not to speak of the considerable number of observed facts\nof different kinds with which it has been brought into relation, it is\nsupported by the mechanical theory of heat. That bringing together\nbodies which attract one another, or separating bodies which repel one\nanother, when sensible motion is not produced nor destroyed, is always\naccompanied by the evolution of heat, is little more than an induction.\nNow, it has been shown by experiment that, when a gas is allowed to\nexpand without doing work, a very small amount of heat disappears. This\nproves that the particles of the gas attract one another slightly, and\nbut very slightly. It follows that, when a gas is under pressure, what\nprevents it from collapsing is not any repulsion between the particles,\nsince there is none. Now, there are only two modes of force known to us,\nforce of position or attractions and repulsions, and force of motion.\nSince, therefore, it is not the force of position which gives a gas its\nexpansive force, it must be the force of motion. In this point of view,\nthe kinetical theory of gases appears as a deduction from the mechanical\ntheory of heat. It is to be observed, however, that it supposes the same\nlaw of mechanics (that there are only those two modes of force) which\nholds in regard to bodies such as we can see and examine, to hold also\nfor what are very different, the molecules of bodies. Such a supposition\nhas but a slender support from induction. Our belief in it is greatly\nstrengthened by its connection with the law of Boyle, and it is,\ntherefore, to be considered as an hypothetical inference. Yet it must be\nadmitted that the kinetical theory of gases would deserve little\ncredence if it had not been connected with the principles of mechanics.\n\nThe great difference between induction and hypothesis is, that the\nformer infers the existence of phenomena such as we have observed in\ncases which are similar, while hypothesis supposes something of a\ndifferent kind from what we have directly observed, and frequently\nsomething which it would be impossible for us to observe directly.\nAccordingly, when we stretch an induction quite beyond the limits of our\nobservation, the inference partakes of the nature of hypothesis. It\nwould be absurd to say that we have no inductive warrant for a\ngeneralization extending a little beyond the limits of experience, and\nthere is no line to be drawn beyond which we cannot push our inference;\nonly it becomes weaker the further it is pushed. Yet, if an induction be\npushed very far, we cannot give it much credence unless we find that\nsuch an extension explains some fact which we can and do observe. Here,\nthen, we have a kind of mixture of induction and hypothesis supporting\none another; and of this kind are most of the theories of physics.\n\n\n                                   V\n\n\nThat synthetic inferences may be divided into induction and hypothesis\nin the manner here proposed,[53] admits of no question. The utility and\nvalue of the distinction are to be tested by their applications.\n\nInduction is, plainly, a much stronger kind of inference than\nhypothesis; and this is the first reason for distinguishing between\nthem. Hypotheses are sometimes regarded as provisional resorts, which in\nthe progress of science are to be replaced by inductions. But this is a\nfalse view of the subject. Hypothetic reasoning infers very frequently a\nfact not capable of direct observation. It is an hypothesis that\nNapoleon Bonaparte once existed. How is that hypothesis ever to be\nreplaced by an induction? It may be said that from the premise that such\nfacts as we have observed are as they would be if Napoleon existed, we\nare to infer by induction that _all_ facts that are hereafter to be\nobserved will be of the same character. There is no doubt that every\nhypothetic inference may be distorted into the appearance of an\ninduction in this way. But the essence of an induction is that it infers\nfrom one set of facts another set of similar facts, whereas hypothesis\ninfers from facts of one kind to facts of another. Now, the facts which\nserve as grounds for our belief in the historic reality of Napoleon are\nnot by any means necessarily the only kind of facts which are explained\nby his existence. It may be that, at the time of his career, events were\nbeing recorded in some way not now dreamed of, that some ingenious\ncreature on a neighboring planet was photographing the earth, and that\nthese pictures on a sufficiently large scale may some time come into our\npossession, or that some mirror upon a distant star will, when the light\nreaches it, reflect the whole story back to earth. Never mind how\nimprobable these suppositions are; everything which happens is\ninfinitely improbable. I am not saying that _these_ things are likely to\noccur, but that _some_ effect of Napoleon\u2019s existence which now seems\nimpossible is certain nevertheless to be brought about. The hypothesis\nasserts that such facts, when they do occur, will be of a nature to\nconfirm, and not to refute, the existence of the man. We have, in the\nimpossibility of inductively inferring hypothetical conclusions, a\nsecond reason for distinguishing between the two kinds of inference.\n\nA third merit of the distinction is, that it is associated with an\nimportant psychological or rather physiological difference in the mode\nof apprehending facts. Induction infers a rule. Now, the belief of a\nrule is a habit. That a habit is a rule active in us, is evident. That\nevery belief is of the nature of a habit, in so far as it is of a\ngeneral character, has been shown in the earlier papers of this series.\nInduction, therefore, is the logical formula which expresses the\nphysiological process of formation of a habit. Hypothesis substitutes,\nfor a complicated tangle of predicates attached to one subject, a single\nconception. Now, there is a peculiar sensation belonging to the act of\nthinking that each of these predicates inheres in the subject. In\nhypothetic inference this complicated feeling so produced is replaced by\na single feeling of greater intensity, that belonging to the act of\nthinking the hypothetic conclusion. Now, when our nervous system is\nexcited in a complicated way, there being a relation between the\nelements of the excitation, the result is a single harmonious\ndisturbance which I call an emotion. Thus, the various sounds made by\nthe instruments of an orchestra strike upon the ear, and the result is a\npeculiar musical emotion, quite distinct from the sounds themselves.\nThis emotion is essentially the same thing as an hypothetic inference,\nand every hypothetic inference involves the formation of such an\nemotion. We may say, therefore, that hypothesis produces the _sensuous_\nelement of thought, and induction the _habitual_ element. As for\ndeduction, which adds nothing to the premises, but only out of the\nvarious facts represented in the premises selects one and brings the\nattention down to it, this may be considered as the logical formula for\npaying attention, which is the _volitional_ element of thought, and\ncorresponds to nervous discharge in the sphere of physiology.\n\nAnother merit of the distinction between induction and hypothesis is,\nthat it leads to a very natural classification of the sciences and of\nthe minds which prosecute them. What must separate different kinds of\nscientific men more than anything else are the differences of their\n_techniques_. We cannot expect men who work with books chiefly to have\nmuch in common with men whose lives are passed in laboratories. But,\nafter differences of this kind, the next most important are differences\nin the modes of reasoning. Of the natural sciences, we have, first, the\nclassificatory sciences, which are purely inductive\u2014systematic botany\nand zo\u00f6logy, mineralogy, and chemistry. Then, we have the sciences of\ntheory, as above explained\u2014astronomy, pure physics, etc. Then, we have\nsciences of hypothesis\u2014geology, biology, etc.\n\nThere are many other advantages of the distinction in question which I\nshall leave the reader to find out by experience. If he will only take\nthe custom of considering whether a given inference belongs to one or\nother of the two forms of synthetic inference given on page 134, I can\npromise him that he will find his advantage in it, in various ways.\n\nFootnote 51:\n\n  _Popular Science Monthly_, August, 1878.\n\nFootnote 52:\n\n  [Later Pierce called it _presumptive inference_. See Baldwin\u2019s\n  _Dictionary_ art. _Probable Inference_.]\n\nFootnote 53:\n\n  This division was first made in a course of lectures by the author\n  before the Lowell Institute, Boston, in 1866, and was printed in the\n  _Proceedings of the American Academy of Arts and Sciences_, for April\n  9, 1867.\n\n\n\n\n                                PART II\n                            LOVE AND CHANCE\n\n\n\n\n                  I. THE ARCHITECTURE OF THEORIES[54]\n\n\nOf the fifty or hundred systems of philosophy that have been advanced at\ndifferent times of the world\u2019s history, perhaps the larger number have\nbeen, not so much results of historical evolution, as happy thoughts\nwhich have accidently occurred to their authors. An idea which has been\nfound interesting and fruitful has been adopted, developed, and forced\nto yield explanations of all sorts of phenomena. The English have been\nparticularly given to this way of philosophizing; witness, Hobbes,\nHartley, Berkeley, James Mill. Nor has it been by any means useless\nlabor; it shows us what the true nature and value of the ideas developed\nare, and in that way affords serviceable materials for philosophy. Just\nas if a man, being seized with the conviction that paper was a good\nmaterial to make things of, were to go to work to build a _papier m\u00e2ch\u00e9_\nhouse, with roof of roofing-paper, foundations of pasteboard, windows of\nparaffined paper, chimneys, bath tubs, locks, etc., all of different\nforms of paper, his experiment would probably afford valuable lessons to\nbuilders, while it would certainly make a detestable house, so those\none-idea\u2019d philosophies are exceedingly interesting and instructive, and\nyet are quite unsound.\n\nThe remaining systems of philosophy have been of the nature of reforms,\nsometimes amounting to radical revolutions, suggested by certain\ndifficulties which have been found to beset systems previously in vogue;\nand such ought certainly to be in large part the motive of any new\ntheory. This is like partially rebuilding a house. The faults that have\nbeen committed are, first, that the repairs of the dilapidations have\ngenerally not been sufficiently thorough-going, and second, that not\nsufficient pains had been taken to bring the additions into deep harmony\nwith the really sound parts of the old structure.\n\nWhen a man is about to build a house, what a power of thinking he has to\ndo, before he can safely break ground! With what pains he has to\nexcogitate the precise wants that are to be supplied! What a study to\nascertain the most available and suitable materials, to determine the\nmode of construction to which those materials are best adapted, and to\nanswer a hundred such questions! Now without riding the metaphor too\nfar, I think we may safely say that the studies preliminary to the\nconstruction of a great theory should be at least as deliberate and\nthorough as those that are preliminary to the building of a\ndwelling-house.\n\nThat systems ought to be constructed architectonically has been preached\nsince Kant, but I do not think the full import of the maxim has by any\nmeans been apprehended. What I would recommend is that every person who\nwishes to form an opinion concerning fundamental problems, should first\nof all make a complete survey of human knowledge, should take note of\nall the valuable ideas in each branch of science, should observe in just\nwhat respect each has been successful and where it has failed, in order\nthat in the light of the thorough acquaintance so attained of the\navailable materials for a philosophical theory and of the nature and\nstrength of each, he may proceed to the study of what the problem of\nphilosophy consists in, and of the proper way of solving it. I must not\nbe understood as endeavoring to state fully all that these preparatory\nstudies should embrace; on the contrary, I purposely slur over many\npoints, in order to give emphasis to one special recommendation, namely,\nto make a systematic study of the conceptions out of which a\nphilosophical theory may be built, in order to ascertain what place each\nconception may fitly occupy in such a theory, and to what uses it is\nadapted.\n\nThe adequate treatment of this single point would fill a volume, but I\nshall endeavor to illustrate my meaning by glancing at several sciences\nand indicating conceptions in them serviceable for philosophy. As to the\nresults to which long studies thus commenced have led me, I shall just\ngive a hint at their nature.\n\nWe may begin with dynamics,\u2014field in our day of perhaps the grandest\nconquest human science has ever made,\u2014I mean the law of the conservation\nof energy. But let us revert to the first step taken by modern\nscientific thought,\u2014and a great stride it was,\u2014the inauguration of\ndynamics by Galileo. A modern physicist on examining Galileo\u2019s works is\nsurprised to find how little experiment had to do with the establishment\nof the foundations of mechanics. His principal appeal is to common sense\nand _il lume naturale_. He always assumes that the true theory will be\nfound to be a simple and natural one. And we can see why it should\nindeed be so in dynamics. For instance, a body left to its own inertia,\nmoves in a straight line, and a straight line appears to us the simplest\nof curves. In _itself_, no curve is simpler than another. A system of\nstraight lines has intersections precisely corresponding to those of a\nsystem of like parabolas similarly placed, or to those of any one of an\ninfinity of systems of curves. But the straight line appears to us\nsimple, because, as Euclid says, it lies evenly between its extremities;\nthat is, because viewed endwise it appears as a point. That is, again,\nbecause light moves in straight lines. Now, light moves in straight\nlines because of the part which the straight line plays in the laws of\ndynamics. Thus it is that our minds having been formed under the\ninfluence of phenomena governed by the laws of mechanics, certain\nconceptions entering into those laws become implanted in our minds, so\nthat we readily guess at what the laws are. Without such a natural\nprompting, having to search blindfold for a law which would suit the\nphenomena, our chance of finding it would be as one to infinity. The\nfurther physical studies depart from phenomena which have directly\ninfluenced the growth of the mind, the less we can expect to find the\nlaws which govern them \u201csimple,\u201d that is, composed of a few conceptions\nnatural to our minds.\n\nThe researches of Galileo, followed up by Huygens and others, led to\nthose modern conceptions of _Force_ and _Law_, which have revolutionized\nthe intellectual world. The great attention given to mechanics in the\nseventeenth century soon so emphasized these conceptions as to give rise\nto the Mechanical Philosophy, or doctrine that all the phenomena of the\nphysical universe are to be explained upon mechanical principles.\nNewton\u2019s great discovery imparted a new impetus to this tendency. The\nold notion that heat consists in an agitation of corpuscles was now\napplied to the explanation of the chief properties of gases. The first\nsuggestion in this direction was that the pressure of gases is explained\nby the battering of the particles against the walls of the containing\nvessel, which explained Boyle\u2019s law of the compressibility of air.\nLater, the expansion of gases, Avogadro\u2019s chemical law, the diffusion\nand viscosity of gases, and the action of Crookes\u2019s radiometer were\nshown to be consequences of the same kinetical theory; but other\nphenomena, such as the ratio of the specific heat at constant volume to\nthat at constant pressure, require additional hypotheses, which we have\nlittle reason to suppose are simple, so that we find ourselves quite\nafloat. In like manner with regard to light. That it consists of\nvibrations was almost proved by the phenomena of diffraction, while\nthose of polarization showed the excursions of the particles to be\nperpendicular to the line of propagation; but the phenomena of\ndispersion, etc., require additional hypotheses which may be very\ncomplicated. Thus, the further progress of molecular speculation appears\nquite uncertain. If hypotheses are to be tried haphazard, or simply\nbecause they will suit certain phenomena, it will occupy the\nmathematical physicists of the world say half a century on the average\nto bring each theory to the test, and since the number of possible\ntheories may go up into the trillions, only one of which can be true, we\nhave little prospect of making further solid additions to the subject in\nour time. When we come to atoms, the presumption in favor of a simple\nlaw seems very slender. There is room for serious doubt whether the\nfundamental laws of mechanics hold good for single atoms, and it seems\nquite likely that they are capable of motion in more than three\ndimensions.\n\nTo find out much more about molecules and atoms, we must search out a\nnatural history of laws of nature, which may fulfil that function which\nthe presumption in favor of simple laws fulfilled in the early days of\ndynamics, by showing us what kind of laws we have to expect and by\nanswering such questions as this: Can we with reasonable prospect of not\nwasting time, try the supposition that atoms attract one another\ninversely as the seventh power of their distances, or can we not? To\nsuppose universal laws of nature capable of being apprehended by the\nmind and yet having no reason for their special forms, but standing\ninexplicable and irrational, is hardly a justifiable position.\nUniformities are precisely the sort of facts that need to be accounted\nfor. That a pitched coin should sometimes turn up heads and sometimes\ntails calls for no particular explanation; but if it shows heads every\ntime, we wish to know how this result has been brought about. Law is\n_par excellence_ the thing that wants a reason.\n\nNow the only possible way of accounting for the laws of nature and for\nuniformity in general is to suppose them results of evolution. This\nsupposes them not to be absolute, not to be obeyed precisely. It makes\nan element of indeterminacy, spontaneity, or absolute chance in nature.\nJust as, when we attempt to verify any physical law, we find our\nobservations cannot be precisely satisfied by it, and rightly attribute\nthe discrepancy to errors of observation, so we must suppose far more\nminute discrepancies to exist owing to the imperfect cogency of the law\nitself, to a certain swerving of the facts from any definite formula.\n\nMr. Herbert Spencer wishes to explain evolution upon mechanical\nprinciples. This is illogical, for four reasons. First, because the\nprinciple of evolution requires no extraneous cause; since the tendency\nto growth can be supposed itself to have grown from an infinitesimal\ngerm accidentally started. Second, because law ought more than anything\nelse to be supposed a result of evolution. Third, because exact law\nobviously never can produce heterogeneity out of homogeneity; and\narbitrary heterogeneity is the feature of the universe the most manifest\nand characteristic. Fourth, because the law of the conservation of\nenergy is equivalent to the proposition that all operations governed by\nmechanical laws are reversible; so that an immediate corollary from it\nis that growth is not explicable by those laws, even if they be not\nviolated in the process of growth. In short, Spencer is not a\nphilosophical evolutionist, but only a half-evolutionist,\u2014or, if you\nwill, only a semi-Spencerian. Now philosophy requires thoroughgoing\nevolutionism or none.\n\nThe theory of Darwin was that evolution had been brought about by the\naction of two factors: first, heredity, as a principle making offspring\nnearly resemble their parents, while yet giving room for \u201csporting,\u201d or\naccidental variations,\u2014for very slight variations often, for wider ones\nrarely; and, second, the destruction of breeds or races that are unable\nto keep the birth rate up to the death rate. This Darwinian principle is\nplainly capable of great generalization. Wherever there are large\nnumbers of objects, having a tendency to retain certain characters\nunaltered, this tendency, however, not being absolute but giving room\nfor chance variations, then, if the amount of variation is absolutely\nlimited in certain directions by the destruction of everything which\nreaches those limits, there will be a gradual tendency to change in\ndirections of departure from them. Thus, if a million players sit down\nto bet at an even game, since one after another will get ruined, the\naverage wealth of those who remain will perpetually increase. Here is\nindubitably a genuine formula of possible evolution, whether its\noperation accounts for much or little in the development of animal and\nvegetable species.\n\nThe Lamarckian theory also supposes that the development of species has\ntaken place by a long series of insensible changes, but it supposes that\nthose changes have taken place during the lives of the individuals, in\nconsequence of effort and exercise, and that reproduction plays no part\nin the process except in preserving these modifications. Thus, the\nLamarckian theory only explains the development of characters for which\nindividuals strive, while the Darwinian theory only explains the\nproduction of characters really beneficial to the race, though these may\nbe fatal to individuals.[55] But more broadly and philosophically\nconceived, Darwinian evolution is evolution by the operation of chance,\nand the destruction of bad results, while Lamarckian evolution is\nevolution by the effect of habit and effort.\n\nA third theory of evolution is that of Mr. Clarence King. The testimony\nof monuments and of rocks is that species are unmodified or scarcely\nmodified, under ordinary circumstances, but are rapidly altered after\ncataclysms or rapid geological changes. Under novel circumstances, we\noften see animals and plants sporting excessively in reproduction, and\nsometimes even undergoing transformations during individual life,\nphenomena no doubt due partly to the enfeeblement of vitality from the\nbreaking up of habitual modes of life, partly to changed food, partly to\ndirect specific influence of the element in which the organism is\nimmersed. If evolution has been brought about in this way, not only have\nits single steps not been insensible, as both Darwinians and Lamarckians\nsuppose, but they are furthermore neither haphazard on the one hand, nor\nyet determined by an inward striving on the other, but on the contrary\nare effects of the changed environment, and have a positive general\ntendency to adapt the organism to that environment, since variation will\nparticularly affect organs at once enfeebled and stimulated. This mode\nof evolution, by external forces and the breaking up of habits, seems to\nbe called for by some of the broadest and most important facts of\nbiology and paleontology; while it certainly has been the chief factor\nin the historical evolution of institutions as in that of ideas; and\ncannot possibly be refused a very prominent place in the process of\nevolution of the universe in general.\n\nPassing to psychology, we find the elementary phenomena of mind fall\ninto three categories. First, we have Feelings, comprising all that is\nimmediately present, such as pain, blue, cheerfulness, the feeling that\narises when we contemplate a consistent theory, etc. A feeling is a\nstate of mind having its own living quality, independent of any other\nstate of mind. Or, a feeling is an element of consciousness which might\nconceivably override every other state until it monopolized the mind,\nalthough such a rudimentary state cannot actually be realized, and would\nnot properly be consciousness. Still, it is conceivable, or supposable,\nthat the quality of blue should usurp the whole mind, to the exclusion\nof the ideas of shape, extension, contrast, commencement and cessation,\nand all other ideas, whatsoever. A feeling is necessarily perfectly\nsimple, _in itself_, for if it had parts these would also be in the\nmind, whenever the whole was present, and thus the whole could not\nmonopolize the mind.[56]\n\nBesides Feelings, we have Sensations of reaction; as when a person\nblindfold suddenly runs against a post, when we make a muscular effort,\nor when any feeling gives way to a new feeling. Suppose I had nothing in\nmy mind but a feeling of blue, which were suddenly to give place to a\nfeeling of red; then, at the instant of transition there would be a\nshock, a sense of reaction, my blue life being transmuted into red life.\nIf I were further endowed with a memory, that sense would continue for\nsome time, and there would also be a peculiar feeling or sentiment\nconnected with it. This last feeling might endure (conceivably I mean)\nafter the memory of the occurrence and the feelings of blue and red had\npassed away. But the _sensation_ of reaction cannot exist except in the\nactual presence of the two feelings blue and red to which it relates.\nWherever we have two feelings and pay attention to a relation between\nthem of whatever kind, there is the sensation of which I am speaking.\nBut the sense of action and reaction has two types: it may either be a\nperception of relation between two ideas, or it may be a sense of action\nand reaction between feeling and something out of feeling. And this\nsense of external reaction again has two forms; for it is either a sense\nof something happening to us, by no act of ours, we being passive in the\nmatter, or it is a sense of resistance, that is, of our expending\nfeeling upon something without. The sense of reaction is thus a sense of\nconnection or comparison between feelings, either, _A_, between one\nfeeling and another, or _B_, between feeling and its absence or lower\ndegree; and under _B_ we have, First, the sense of the access of\nfeeling, and Second, the sense of remission of feeling.\n\nVery different both from feelings and from reaction-sensations or\ndisturbances of feeling are general conceptions. When we think, we are\nconscious that a connection between feelings is determined by a general\nrule, we are aware of being governed by a habit. Intellectual power is\nnothing but facility in taking habits and in following them in cases\nessentially analogous to, but in non-essentials widely remote from, the\nnormal cases of connections of feelings under which those habits were\nformed.\n\nThe one primary and fundamental law of mental action consists in a\ntendency to generalization. Feeling tends to spread; connections between\nfeelings awaken feelings; neighboring feelings become assimilated; ideas\nare apt to reproduce themselves. These are so many formulations of the\none law of the growth of mind. When a disturbance of feeling takes\nplace, we have a consciousness of gain, the gain of experience; and a\nnew disturbance will be apt to assimilate itself to the one that\npreceded it. Feelings, by being excited, become more easily excited,\nespecially in the ways in which they have previously been excited. The\nconsciousness of such a habit constitutes a general conception.\n\nThe cloudiness of psychological notions may be corrected by connecting\nthem with physiological conceptions. Feeling may be supposed to exist,\nwherever a nerve-cell is in an excited condition. The disturbance of\nfeeling, or sense of reaction, accompanies the transmission of\ndisturbance between nerve-cells or from a nerve-cell to a muscle-cell or\nthe external stimulation of a nerve-cell. General conceptions arise upon\nthe formation of habits in the nerve-matter, which are molecular changes\nconsequent upon its activity and probably connected with its nutrition.\n\nThe law of habit exhibits a striking contrast to all physical laws in\nthe character of its commands. A physical law is absolute. What it\nrequires is an exact relation. Thus, a physical force introduces into a\nmotion a component motion to be combined with the rest by the\nparallelogram of forces; but the component motion must actually take\nplace exactly as required by the law of force. On the other hand, no\nexact conformity is required by the mental law. Nay, exact conformity\nwould be in downright conflict with the law; since it would instantly\ncrystallize thought and prevent all further formation of habit. The law\nof mind only makes a given feeling _more likely_ to arise. It thus\nresembles the \u201cnon-conservative\u201d forces of physics, such as viscosity\nand the like, which are due to statistical uniformities in the chance\nencounters of trillions of molecules.\n\nThe old dualistic notion of mind and matter, so prominent in\nCartesianism, as two radically different kinds of substance, will hardly\nfind defenders to-day. Rejecting this, we are driven to some form of\nhylopathy, otherwise called monism. Then the question arises whether\nphysical laws on the one hand, and the psychical law on the other are to\nbe taken\u2014\n\n(_A_) as independent, a doctrine often called _monism_, but which I\nwould name _neutralism_; or,\n\n(_B_) the psychical law as derived and special, the physical law alone\nas primordial, which is _materialism_; or,\n\n(_C_) the physical law as derived and special, the psychical law alone\nas primordial, which is _idealism_.\n\nThe materialistic doctrine seems to me quite as repugnant to scientific\nlogic as to common sense; since it requires us to suppose that a certain\nkind of mechanism will feel, which would be a hypothesis absolutely\nirreducible to reason,\u2014an ultimate, inexplicable regularity; while the\nonly possible justification of any theory is that it should make things\nclear and reasonable.\n\nNeutralism is sufficiently condemned by the logical maxim known as\nOckham\u2019s razor, i.e., that not more independent elements are to be\nsupposed than necessary. By placing the inward and outward aspects of\nsubstance on a par, it seems to render both primordial.\n\nThe one intelligible theory of the universe is that of objective\nidealism, that matter is effete mind, inveterate habits becoming\nphysical laws. But before this can be accepted it must show itself\ncapable of explaining the tridimensionality of space, the laws of\nmotion, and the general characteristics of the universe, with\nmathematical clearness and precision; for no less should be demanded of\nevery Philosophy.\n\n[Illustration: Figure 6.]\n\nModern mathematics is replete with ideas which may be applied to\nphilosophy. I can only notice one or two. The manner in which\nmathematicians generalize is very instructive. Thus, painters are\naccustomed to think of a picture as consisting geometrically of the\nintersections of its plane by rays of light from the natural objects to\nthe eye. But geometers use a generalized perspective.[57] For instance\nin the figure let _O_ be the eye, let _A_ _B_ _C_ _D_ _E_ be the\nedgewise view of any plane, and let _a_ _f_ _e_ _D_ _c_ be the edgewise\nview of another plane. The geometers draw rays through _O_ cutting both\nthese planes, and treat the points of intersection of each ray with one\nplane as representing the point of intersection of the same ray with the\nother plane. Thus, _e_ represents _E_, in the painter\u2019s way. _D_\nrepresents itself. _C_ is represented by _c_, which is further from the\neye; and _A_ is represented by _a_ which is on the other side of the\neye. Such generalization is not bound down to sensuous images. Further,\naccording to this mode of representation every point on one plane\nrepresents a point on the other, and every point on the latter is\nrepresented by a point on the former. But how about the point _f_ which\nis in a direction from _O_ parallel to the represented plane, and how\nabout the point _B_ which is in a direction parallel to the representing\nplane? Some will say that these are exceptions; but modern mathematics\ndoes not allow exceptions which can be annulled by generalization.[58]\nAs a point moves from _C_ to _D_ and thence to _E_ and off toward\ninfinity, the corresponding point on the other plane moves from _c_ to\n_D_ and thence to _e_ and toward _f_. But this second point can pass\nthrough _f_ to _a_; and when it is there the first point has arrived at\n_A_. We therefore say that the first point has passed _through\ninfinity_, and that every line joins in to itself somewhat like an oval.\nGeometers talk of the parts of lines at an infinite distance as points.\nThis is a kind of generalization very efficient in mathematics.\n\nModern views of measurement have a philosophical aspect. There is an\nindefinite number of systems of measuring along a line; thus, a\nperspective representation of a scale on one line may be taken to\nmeasure another, although of course such measurements will not agree\nwith what we call the distances of points on the latter line. To\nestablish a system of measurement on a line we must assign a distinct\nnumber to each point of it, and for this purpose we shall plainly have\nto suppose the numbers carried out into an infinite number of places of\ndecimals. These numbers must be ranged along the line in unbroken\nsequence. Further, in order that such a scale of numbers should be of\nany use, it must be capable of being shifted into new positions, each\nnumber continuing to be attached to a single distinct point. Now it is\nfound that if this is true for \u201cimaginary\u201d as well as for real points\n(an expression which I cannot stop to elucidate), any such shifting will\nnecessarily leave two numbers attached to the same points as before. So\nthat when the scale is moved over the line by any continuous series of\nshiftings of one kind, there are two points which no numbers on the\nscale can ever reach, except the numbers fixed there. This pair of\npoints, thus unattainable in measurement, is called the Absolute. These\ntwo points may be distinct and real, or they may coincide, or they may\nbe both imaginary. As an example of a linear quantity with a double\nabsolute we may take probability, which ranges from an unattainable\nabsolute certainty _against_ a proposition to an equally unattainable\nabsolute certainty _for_ it. A line, according to ordinary notions, we\nhave seen is a linear quantity where the two points at infinity\ncoincide. A velocity is another example. A train going with infinite\nvelocity from Chicago to New York would be at all the points on the line\nat the very same instant, and if the time of transit were reduced to\nless than nothing it would be moving in the other direction. An angle is\na familiar example of a mode of magnitude with no real immeasurable\nvalues. One of the questions philosophy has to consider is whether the\ndevelopment of the universe is like the increase of an angle, so that it\nproceeds forever without tending toward anything unattained, which I\ntake to be the Epicurean view, or whether the universe sprang from a\nchaos in the infinitely distant past to tend toward something different\nin the infinitely distant future, or whether the universe sprang from\nnothing in the past to go on indefinitely toward a point in the\ninfinitely distant future, which, were it attained, would be the mere\nnothing from which it set out.\n\nThe doctrine of the absolute applied to space comes to this, that\neither\u2014\n\nFirst, space is, as Euclid teaches, both _unlimited_ and _immeasurable_,\nso that the infinitely distant parts of any plane seen in perspective\nappear as a straight line, in which case the sum of the three angles of\na triangle amounts to 180\u00b0; or,\n\nSecond, space is _immeasurable_ but _limited_, so that the infinitely\ndistant parts of any plane seen in perspective appear as a circle,\nbeyond which all is blackness, and in this case the sum of the three\nangles of a triangle is less than 180\u00b0 by an amount proportional to the\narea of the triangle; or,\n\nThird, space is _unlimited_ but _finite_, (like the surface of a\nsphere), so that it has no infinitely distant parts; but a finite\njourney along any straight line would bring one back to his original\nposition, and looking off with an unobstructed view one would see the\nback of his own head enormously magnified, in which case the sum of the\nthree angles of a triangle exceeds 180\u00b0 by an amount proportional to the\narea.\n\nWhich of these three hypotheses is true we know not. The largest\ntriangles we can measure are such as have the earth\u2019s orbit for base,\nand the distance of a fixed star for altitude. The angular magnitude\nresulting from subtracting the sum of the two angles at the base of such\na triangle from 180\u00b0 is called the star\u2019s _parallax_. The parallaxes of\nonly about forty stars have been measured as yet. Two of them come out\nnegative, that of Arided (\u03b1 Cycni), a star of magnitude 1-1/2, which is\n\u20140.\u201c082, according to C. A. F. Peters, and that of a star of magnitude\n7-3/4, known as Piazzi III 422, which is \u20140.\u201d045, according to R. S.\nBall. But these negative parallaxes are undoubtedly to be attributed to\nerrors of observation; for the probable error of such a determination is\nabout \u00b1 0.\u201c075, and it would be strange indeed if we were to be able to\nsee, as it were, more than half way round space, without being able to\nsee stars with larger negative parallaxes. Indeed, the very fact that of\nall the parallaxes measured only two come out negative would be a strong\nargument that the smallest parallaxes really amount to +0.\u201d1, were it\nnot for the reflection that the publication of other negative parallaxes\nmay have been suppressed. I think we may feel confident that the\nparallax of the furthest star lies somewhere between -0.\u201d05 and +0.\u201d15,\nand within another century our grandchildren will surely know whether\nthe three angles of a triangle are greater or less than 180\u00b0,\u2014that they\nare _exactly_ that amount is what nobody ever can be justified in\nconcluding. It is true that according to the axioms of geometry the sum\nof the three sides of a triangle are precisely 180\u00b0; but these axioms\nare now exploded, and geometers confess that they, as geometers, know\nnot the slightest reason for supposing them to be precisely true. They\nare expressions of our inborn conception of space, and as such are\nentitled to credit, so far as their truth could have influenced the\nformation of the mind. But that affords not the slightest reason for\nsupposing them exact.\n\nNow, metaphysics has always been the ape of mathematics. Geometry\nsuggested the idea of a demonstrative system of absolutely certain\nphilosophical principles; and the ideas of the metaphysicians have at\nall times been in large part drawn from mathematics. The metaphysical\naxioms are imitations of the geometrical axioms; and now that the latter\nhave been thrown overboard, without doubt the former will be sent after\nthem. It is evident, for instance, that we can have no reason to think\nthat every phenomenon in all its minutest details is precisely\ndetermined by law. That there is an arbitrary element in the universe we\nsee,\u2014namely, its variety. This variety must be attributed to spontaneity\nin some form.\n\nHad I more space, I now ought to show how important for philosophy is\nthe mathematical conception of continuity. Most of what is true in Hegel\nis a darkling glimmer of a conception which the mathematicians had long\nbefore made pretty clear, and which recent researches have still further\nillustrated.\n\nAmong the many principles of Logic which find their application in\nPhilosophy, I can here only mention one. Three conceptions are\nperpetually turning up at every point in every theory of logic, and in\nthe most rounded systems they occur in connection with one another. They\nare conceptions so very broad and consequently indefinite that they are\nhard to seize and may be easily overlooked. I call them the conceptions\nof First, Second, Third. First is the conception of being or existing\nindependent of anything else. Second is the conception of being relative\nto, the conception of reaction with, something else. Third is the\nconception of mediation, whereby a first and second are brought into\nrelation. To illustrate these ideas, I will show how they enter into\nthose we have been considering. The origin of things, considered not as\nleading to anything, but in itself, contains the idea of First, the end\nof things that of Second, the process mediating between them that of\nThird. A philosophy which emphasizes the idea of the One, is generally a\ndualistic philosophy in which the conception of Second receives\nexaggerated attention; for this One (though of course involving the idea\nof First) is always the other of a manifold which is not one. The idea\nof the Many, because variety is arbitrariness and arbitrariness is\nrepudiation of any Secondness, has for its principal component the\nconception of First. In psychology Feeling is First, Sense of reaction\nSecond, General conception Third, or mediation. In biology, the idea of\narbitrary sporting is First, heredity is Second, the process whereby the\naccidental characters become fixed is Third. Chance is First, Law is\nSecond, the tendency to take habits is Third. Mind is First, Matter is\nSecond, Evolution is Third.\n\nSuch are the materials out of which chiefly a philosophical theory ought\nto be built, in order to represent the state of knowledge to which the\nnineteenth century has brought us. Without going into other important\nquestions of philosophical architectonic, we can readily foresee what\nsort of a metaphysics would appropriately be constructed from those\nconceptions. Like some of the most ancient and some of the most recent\nspeculations it would be a Cosmogonic Philosophy. It would suppose that\nin the beginning,\u2014infinitely remote,\u2014there was a chaos of unpersonalized\nfeeling, which being without connection or regularity would properly be\nwithout existence. This feeling, sporting here and there in pure\narbitrariness, would have started the germ of a generalizing tendency.\nIts other sportings would be evanescent, but this would have a growing\nvirtue. Thus, the tendency to habit would be started; and from this with\nthe other principles of evolution all the regularities of the universe\nwould be evolved. At any time, however, an element of pure chance\nsurvives and will remain until the world becomes an absolutely perfect,\nrational, and symmetrical system, in which mind is at last crystallized\nin the infinitely distant future.\n\nThat idea has been worked out by me with elaboration. It accounts for\nthe main features of the universe as we know it,\u2014the characters of time,\nspace, matter, force, gravitation, electricity, etc. It predicts many\nmore things which new observations can alone bring to the test. May some\nfuture student go over this ground again, and have the leisure to give\nhis results to the world.\n\nFootnote 54:\n\n  _The Monist_, January, 1891.\n\nFootnote 55:\n\n  The neo-Darwinian, Weismann, has shown that mortality would almost\n  necessarily result from the action of the Darwinian principle.\n\nFootnote 56:\n\n  A feeling may certainly be compound, but only in virtue of a\n  perception which is not that feeling nor any feeling at all.\n\nFootnote 57:\n\n  [The reader will find further light on the following illustration in\n  any text-book of projective geometry, e.g., Reye, _Geometry of\n  Position_, I, pp. 17-24, or _Encyc. Britannica_, XI, p. 689.]\n\nFootnote 58:\n\n  [A more familiar example of this is the introduction of irrational or\n  absurd numbers like \u221a2. After it was proved that no ratio of two\n  integers could possibly equal \u221a2 the idea of number was generalized to\n  include the latter. Fractions and the so-called imaginary numbers\n  illustrate the same process of generalization for the sake of making\n  certain operations (i.e. division and finding the root) continuously\n  applicable.]\n\n\n\n\n               II. THE DOCTRINE OF NECESSITY EXAMINED[59]\n\n\nIn _The Monist_ for January, 1891, I endeavored to show what elementary\nideas ought to enter into our view of the universe. I may mention that\non those considerations I had already grounded a cosmical theory, and\nfrom it had deduced a considerable number of consequences capable of\nbeing compared with experience. This comparison is now in progress, but\nunder existing circumstances must occupy many years.\n\nI propose here to examine the common belief that every single fact in\nthe universe is precisely determined by law. It must not be supposed\nthat this is a doctrine accepted everywhere and at all times by all\nrational men. Its first advocate appears to have been Democritus, the\natomist, who was led to it, as we are informed, by reflecting upon the\n\u201cimpenetrability, translation, and impact of matter (\u1f00\u03bd\u03c4\u03b9\u03c4\u03c5\u03c0\u03af\u03b1 \u03ba\u03b1\u1f76 \u03c6\u03bf\u03c1\u1f70\n\u03ba\u03b1\u1f76 \u03c0\u03bb\u03b7\u03b3\u1f74 \u03c4\u1fc6\u03c2 \u1f55\u03bb\u03b7\u03c2).\u201d That is to say, having restricted his attention to\na field where no influence other than mechanical constraint could\npossibly come before his notice, he straightway jumped to the conclusion\nthat throughout the universe that was the sole principle of action,\u2014a\nstyle of reasoning so usual in our day with men not unreflecting as to\nbe more than excusable in the infancy of thought. But Epicurus, in\nrevising the atomic doctrine and repairing its defences, found himself\nobliged to suppose that atoms swerve from their courses by spontaneous\nchance; and thereby he conferred upon the theory life and entelechy. For\nwe now see clearly that the peculiar function of the molecular\nhypothesis in physics is to open an entry for the calculus of\nprobabilities. Already, the prince of philosophers had repeatedly and\nemphatically condemned the dictum of Democritus (especially in the\n\u201cPhysics,\u201d Book II, chapters iv, v, vi), holding that events come to\npass in three ways, namely, (1) by external compulsion, or the action of\nefficient causes, (2) by virtue of an inward nature, or the influence of\nfinal causes, and (3) irregularly without definite cause, but just by\nabsolute chance; and this doctrine is of the inmost essence of\nAristotelianism. It affords, at any rate, a valuable enumeration of the\npossible ways in which anything can be supposed to have come about. The\nfreedom of the will, too, was admitted both by Aristotle and by\nEpicurus. But the Stoa, which in every department seized upon the most\ntangible, hard, and lifeless element, and blindly denied the existence\nof every other, which, for example, impugned the validity of the\ninductive method and wished to fill its place with the _reductio ad\nabsurdum_, very naturally became the one school of ancient philosophy to\nstand by a strict necessitarianism, thus returning to a single principle\nof Democritus that Epicurus had been unable to swallow. Necessitarianism\nand materialism with the Stoics went hand in hand, as by affinity they\nshould. At the revival of learning, Stoicism met with considerable\nfavor, partly because it departed just enough from Aristotle to give it\nthe spice of novelty, and partly because its superficialities well\nadapted it for acceptance by students of literature and art who wanted\ntheir philosophy drawn mild. Afterwards, the great discoveries in\nmechanics inspired the hope that mechanical principles might suffice to\nexplain the universe; and though without logical justification, this\nhope has since been continually stimulated by subsequent advances in\nphysics. Nevertheless, the doctrine was in too evident conflict with the\nfreedom of the will and with miracles to be generally acceptable, at\nfirst. But meantime there arose that most widely spread of philosophical\nblunders, the notion that associationalism belongs intrinsically to the\nmaterialistic family of doctrines; and thus was evolved the theory of\nmotives; and libertarianism became weakened. At present, historical\ncriticism has almost exploded the miracles, great and small; so that the\ndoctrine of necessity has never been in so great vogue as now.\n\nThe proposition in question is that the state of things existing at any\ntime, together with certain immutable laws, completely determine the\nstate of things at every other time (for a limitation to _future_ time\nis indefensible). Thus, given the state of the universe in the original\nnebula, and given the laws of mechanics, a sufficiently powerful mind\ncould deduce from these data the precise form of every curlicue of every\nletter I am now writing.\n\nWhoever holds that every act of the will as well as every idea of the\nmind is under the rigid governance of a necessity co-ordinated with that\nof the physical world, will logically be carried to the proposition that\nminds are part of the physical world in such a sense that the laws of\nmechanics determine everything that happens according to immutable\nattractions and repulsions. In that case, that instantaneous state of\nthings from which every other state of things is calculable consists in\nthe positions and velocities of all the particles at any instant. This,\nthe usual and most logical form of necessitarianism, is called the\nmechanical philosophy.\n\nWhen I have asked thinking men what reason they had to believe that\nevery fact in the universe is precisely determined by law, the first\nanswer has usually been that the proposition is a \u201cpresupposition\u201d or\npostulate of scientific reasoning. Well, if that is the best that can be\nsaid for it, the belief is doomed. Suppose it be \u201cpostulated\u201d: that does\nnot make it true, nor so much as afford the slightest rational motive\nfor yielding it any credence. It is as if a man should come to borrow\nmoney, and when asked for his security, should reply he \u201cpostulated\u201d the\nloan. To \u201cpostulate\u201d a proposition is no more than to hope it is true.\nThere are, indeed, practical emergencies in which we act upon\nassumptions of certain propositions as true, because if they are not so,\nit can make no difference how we act. But all such propositions I take\nto be hypotheses of individual facts. For it is manifest that no\nuniversal principle can in its universality be comprised in a special\ncase or can be requisite for the validity of any ordinary inference. To\nsay, for instance, that the demonstration by Archimedes of the property\nof the lever would fall to the ground if men were endowed with\nfree-will, is extravagant; yet this is implied by those who make a\nproposition incompatible with the freedom of the will the postulate of\nall inference. Considering, too, that the conclusions of science make no\npretence to being more than probable, and considering that a probable\ninference can at most only suppose something to be most frequently, or\notherwise approximately, true, but never that anything is precisely true\nwithout exception throughout the universe, we see how far this\nproposition in truth is from being so postulated.\n\nBut the whole notion of a postulate being involved in reasoning\nappertains to a by-gone and false conception of logic. Non-deductive, or\nampliative inference, is of three kinds: induction, hypothesis, and\nanalogy. If there be any other modes, they must be extremely unusual and\nhighly complicated, and may be assumed with little doubt to be of the\nsame nature as those enumerated. For induction, hypothesis, and analogy,\nas far as their ampliative character goes, that is, so far as they\nconclude something not implied in the premises, depend upon one\nprinciple and involve the same procedure. All are essentially inferences\nfrom sampling. Suppose a ship arrives at Liverpool laden with wheat in\nbulk. Suppose that by some machinery the whole cargo be stirred up with\ngreat thoroughness. Suppose that twenty-seven thimblefuls be taken\nequally from the forward, midships, and aft parts, from the starboard,\ncenter, and larboard parts, and from the top, half depth, and lower\nparts of her hold, and that these being mixed and the grains counted,\nfour-fifths of the latter are found to be of quality _A_. Then we infer,\nexperientially and provisionally, that approximately four-fifths of all\nthe grain in the cargo is of the same quality. I say we infer this\n_experientially_ and _provisionally_. By saying that we infer it\n_experientially_, I mean that our conclusion makes no pretension to\nknowledge of wheat-in-itself, our \u1f00\u03bb\u03ae\u03b8\u03b5\u03b9\u03b1, as the derivation of that\nword implies, has nothing to do with _latent_ wheat. We are dealing only\nwith the matter of possible experience,\u2014experience in the full\nacceptation of the term as something not merely affecting the senses but\nalso as the subject of thought. If there be any wheat hidden on the\nship, so that it can neither turn up in the sample nor be heard of\nsubsequently from purchasers,\u2014or if it be half-hidden, so that it may,\nindeed, turn up, but is less likely to do so than the rest,\u2014or if it can\naffect our senses and our pockets, but from some strange cause or\ncauselessness cannot be reasoned about,\u2014all such wheat is to be excluded\n(or have only its proportional weight) in calculating that true\nproportion of quality _A_, to which our inference seeks to approximate.\nBy saying that we draw the inference _provisionally_, I mean that we do\nnot hold that we have reached any assigned degree of approximation as\nyet, but only hold that if our experience be indefinitely extended, and\nif every fact of whatever nature, as fast as it presents itself, be duly\napplied, according to the inductive method, in correcting the inferred\nratio, then our approximation will become indefinitely close in the long\nrun; that is to say, close to the experience _to come_ (not merely close\nby the exhaustion of a finite collection) so that if experience in\ngeneral is to fluctuate irregularly to and fro, in a manner to deprive\nthe ratio sought of all definite value, we shall be able to find out\napproximately within what limits it fluctuates, and if, after having one\ndefinite value, it changes and assumes another, we shall be able to find\nthat out, and in short, whatever may be the variations of this ratio in\nexperience, experience indefinitely extended will enable us to detect\nthem, so as to predict rightly, at last, what its ultimate value may be,\nif it have any ultimate value, or what the ultimate law of succession of\nvalues may be, if there be any such ultimate law, or that it ultimately\nfluctuates irregularly within certain limits, if it do so ultimately\nfluctuate. Now our inference, claiming to be no more than thus\nexperiential and provisional, manifestly involves no postulate whatever.\n\nFor what is a postulate? It is the formulation of a material fact which\nwe are not entitled to assume as a premise, but the truth of which is\nrequisite to the validity of an inference. Any fact, then, which might\nbe supposed postulated, must either be such that it would ultimately\npresent itself in experience, or not. If it will present itself, we need\nnot postulate it now in our provisional inference, since we shall\nultimately be entitled to use it as a premise. But if it never would\npresent itself in experience, our conclusion is valid but for the\npossibility of this fact being otherwise than assumed, that is, it is\nvalid as far as possible experience goes, and that is all that we claim.\nThus, every postulate is cut off, either by the provisionality or by the\nexperientiality of our inference. For instance, it has been said that\ninduction postulates that, if an indefinite succession of samples be\ndrawn, examined, and thrown back each before the next is drawn, then in\nthe long run every grain will be drawn as often as any other, that is to\nsay, postulates that the ratio of the numbers of times in which any two\nare drawn will indefinitely approximate to unity. But no such postulate\nis made; for if, on the one hand, we are to have no other experience of\nthe wheat than from such drawings, it is the ratio that presents itself\nin those drawings and not the ratio which belongs to the wheat in its\nlatent existence that we are endeavoring to determine; while if, on the\nother hand, there is some other mode by which the wheat is to come under\nour knowledge, equivalent to another kind of sampling, so that after all\nour care in stirring up the wheat, some experiential grains will present\nthemselves in the first sampling operation more often than others in the\nlong run, this very singular fact will be sure to get discovered by the\ninductive method, which must avail itself of every sort of experience;\nand our inference, which was only provisional, corrects itself at last.\nAgain, it has been said, that induction postulates that under like\ncircumstances like events will happen, and that this postulate is at\nbottom the same as the principle of universal causation. But this is a\nblunder, or _bevue_, due to thinking exclusively of inductions where the\nconcluded ratio is either 1 or 0. If any such proposition were\npostulated, it would be that under like circumstances (the circumstances\nof drawing the different samples) different events occur in the same\nproportions in all the different sets,\u2014a proposition which is false and\neven absurd. But in truth no such thing is postulated, the experiential\ncharacter of the inference reducing the condition of validity to this,\nthat if a certain result does not occur, the opposite result will be\nmanifested, a condition assured by the provisionality of the inference.\nBut it may be asked whether it is not conceivable that every instance of\na certain class destined to be ever employed as a datum of induction\nshould have one character, while every instance destined not to be so\nemployed should have the opposite character. The answer is that in that\ncase, the instances excluded from being subjects of reasoning would not\nbe experienced in the full sense of the word, but would be among these\n_latent_ individuals of which our conclusion does not pretend to speak.\n\nTo this account of the rationale of induction I know of but one\nobjection worth mention: it is that I thus fail to deduce the full\ndegree of force which this mode of inference in fact possesses; that\naccording to my view, no matter how thorough and elaborate the stirring\nand mixing process had been, the examination of a single handful of\ngrain would not give me any assurance, sufficient to risk money upon\nthat the next handful would not greatly modify the concluded value of\nthe ratio under inquiry, while, in fact, the assurance would be very\nhigh that this ratio was not greatly in error. If the true ratio of\ngrains of quality _A_ were 0.80 and the handful contained a thousand\ngrains, nine such handfuls out of every ten would contain from 780 to\n820 grains of quality _A_. The answer to this is that the calculation\ngiven is correct when we know that the units of this handful and the\nquality inquired into have the normal independence of one another, if\nfor instance the stirring has been complete and the character sampled\nfor has been settled upon in advance of the examination of the sample.\nBut in so far as these conditions are not known to be complied with, the\nabove figures cease to be applicable. Random sampling and predesignation\nof the character sampled for should always be striven after in inductive\nreasoning, but when they cannot be attained, so long as it is conducted\nhonestly, the inference retains some value. When we cannot ascertain how\nthe sampling has been done or the sample-character selected, induction\nstill has the essential validity which my present account of it shows it\nto have.\n\nI do not think a man who combines a willingness to be convinced with a\npower of appreciating an argument upon a difficult subject can resist\nthe reasons which have been given to show that the principle of\nuniversal necessity cannot be defended as being a postulate of\nreasoning. But then the question immediately arises whether it is not\nproved to be true, or at least rendered highly probable, by observation\nof nature.\n\nStill, this question ought not long to arrest a person accustomed to\nreflect upon the force of scientific reasoning. For the essence of the\nnecessitarian position is that certain continuous quantities have\ncertain exact values. Now, how can observation determine the value of\nsuch a quantity with a probable error absolutely _nil_? To one who is\nbehind the scenes, and knows that the most refined comparisons of\nmasses, lengths, and angles, far surpassing in precision all other\nmeasurements, yet fall behind the accuracy of bank-accounts, and that\nthe ordinary determinations of physical constants, such as appear from\nmonth to month in the journals, are about on a par with an upholsterer\u2019s\nmeasurements of carpets and curtains, the idea of mathematical\nexactitude being demonstrated in the laboratory will appear simply\nridiculous. There is a recognized method of estimating the probable\nmagnitudes of errors in physics,\u2014the method of least squares. It is\nuniversally admitted that this method makes the errors smaller than they\nreally are; yet even according to that theory an error indefinitely\nsmall is indefinitely improbable; so that any statement to the effect\nthat a certain continuous quantity has a certain exact value, if\nwell-founded at all, must be founded on something other than\nobservation.\n\nStill, I am obliged to admit that this rule is subject to a certain\nqualification. Namely, it only applies to continuous[60] quantity. Now,\ncertain kinds of continuous quantity are discontinuous at one or at two\nlimits, and for such limits the rule must be modified. Thus, the length\nof a line cannot be less than zero. Suppose, then, the question arises\nhow long a line a certain person had drawn from a marked point on a\npiece of paper. If no line at all can be seen, the observed length is\nzero; and the only conclusion this observation warrants is that the\nlength of the line is less than the smallest length visible with the\noptical power employed. But indirect observations,\u2014for example, that the\nperson supposed to have drawn the line was never within fifty feet of\nthe paper,\u2014may make it probable that no line at all was made, so that\nthe concluded length will be strictly zero. In like manner, experience\nno doubt would warrant the conclusion that there is absolutely _no_\nindigo in a given ear of wheat, and absolutely _no_ attar in a given\nlichen. But such inferences can only be rendered valid by positive\nexperiential evidence, direct or remote, and cannot rest upon a mere\ninability to detect the quantity in question. We have reason to think\nthere is no indigo in the wheat, because we have remarked that wherever\nindigo is produced it is produced in considerable quantities, to mention\nonly one argument. We have reason to think there is no attar in the\nlichen, because essential oils seem to be in general peculiar to single\nspecies. If the question had been whether there was iron in the wheat or\nthe lichen, though chemical analysis should fail to detect its presence,\nwe should think some of it probably was there, since iron is almost\neverywhere. Without any such information, one way or the other, we could\nonly abstain from any opinion as to the presence of the substance in\nquestion. It cannot, I conceive, be maintained that we are in any\n_better_ position than this in regard to the presence of the element of\nchance or spontaneous departures from law in nature.\n\nThose observations which are generally adduced in favor of mechanical\ncausation simply prove that there is an element of regularity in nature,\nand have no bearing whatever upon the question of whether such\nregularity is exact and universal, or not. Nay, in regard to this\n_exactitude_, all observation is directly _opposed_ to it; and the most\nthat can be said is that a good deal of this observation can be\nexplained away. Try to verify any law of nature, and you will find that\nthe more precise your observations, the more certain they will be to\nshow irregular departures from the law. We are accustomed to ascribe\nthese, and I do not say wrongly, to errors of observation; yet we cannot\nusually account for such errors in any antecedently probable way. Trace\ntheir causes back far enough, and you will be forced to admit they are\nalways due to arbitrary determination, or chance.\n\nBut it may be asked whether if there were an element of real chance in\nthe universe it must not occasionally be productive of signal effects\nsuch as could not pass unobserved. In answer to this question, without\nstopping to point out that there is an abundance of great events which\none might be tempted to suppose were of that nature, it will be simplest\nto remark that physicists hold that the particles of gases are moving\nabout irregularly, substantially as if by real chance, and that by the\nprinciples of probabilities there must occasionally happen to be\nconcentrations of heat in the gases contrary to the second law of\nthermodynamics, and these concentrations, occurring in explosive\nmixtures, must sometimes have tremendous effects. Here, then, is in\nsubstance the very situation supposed; yet no phenomena ever have\nresulted which we are forced to attribute to such chance concentration\nof heat, or which anybody, wise or foolish, has ever dreamed of\naccounting for in that manner.\n\nIn view of all these considerations, I do not believe that anybody, not\nin a state of case-hardened ignorance respecting the logic of science,\ncan maintain that the precise and universal conformity of facts to law\nis clearly proved, or even rendered particularly probable, by any\nobservations hitherto made. In this way, the determined advocate of\nexact regularity will soon find himself driven to _a priori_ reasons to\nsupport his thesis. These received such a socdolager from Stuart Mill in\nhis Examination of Hamilton, that holding to them now seems to me to\ndenote a high degree of imperviousness to reason; so that I shall pass\nthem by with little notice.\n\nTo say that we cannot help believing a given proposition is no argument,\nbut it is a conclusive fact if it be true; and with the substitution of\n\u201cI\u201d for \u201cwe,\u201d it is true in the mouths of several classes of minds, the\nblindly passionate, the unreflecting and ignorant, and the person who\nhas overwhelming evidence before his eyes. But that which has been\ninconceivable to-day has often turned out indisputable on the morrow.\nInability to conceive is only a stage through which every man must pass\nin regard to a number of beliefs,\u2014unless endowed with extraordinary\nobstinacy and obtuseness. His understanding is enslaved to some blind\ncompulsion which a vigorous mind is pretty sure soon to cast off.\n\nSome seek to back up the _a priori_ position with empirical arguments.\nThey say that the exact regularity of the world is a natural belief, and\nthat natural beliefs have generally been confirmed by experience. There\nis some reason in this. Natural beliefs, however, if they generally have\na foundation of truth, also require correction and purification from\nnatural illusions. The principles of mechanics are undoubtedly natural\nbeliefs; but, for all that, the early formulations of them were\nexceedingly erroneous. The general approximation to truth in natural\nbeliefs is, in fact, a case of the general adaptation of genetic\nproducts to recognizable utilities or ends. Now, the adaptations of\nnature, beautiful and often marvelous as they verily are, are never\nfound to be quite perfect; so that the argument is quite _against_ the\nabsolute exactitude of any natural belief, including that of the\nprinciple of causation.\n\nAnother argument, or convenient commonplace, is that absolute chance is\n_inconceivable_. (This word has eight current significations. The\n_Century Dictionary_ enumerates six.) Those who talk like this will\nhardly be persuaded to say in what sense they mean that chance is\ninconceivable. Should they do so, it would easily be shown either that\nthey have no sufficient reason for the statement or that the\ninconceivability is of a kind which does not prove that chance is\nnon-existent.\n\nAnother _a priori_ argument is that chance is unintelligible; that is to\nsay, while it may perhaps be conceivable, it does not disclose to the\neye of reason the how or why of things; and since a hypothesis can only\nbe justified so far as it renders some phenomenon intelligible, we never\ncan have any right to suppose absolute chance to enter into the\nproduction of anything in nature. This argument may be considered in\nconnection with two others. Namely, instead of going so far as to say\nthat the supposition of chance can _never_ properly be used to explain\nany observed fact, it may be alleged merely that no facts are known\nwhich such a supposition could in any way help in explaining. Or again,\nthe allegation being still further weakened, it may be said that since\ndepartures from law are not unmistakably observed, chance is not a _vera\ncausa_, and ought not unnecessarily to be introduced into a hypothesis.\n\nThese are no mean arguments, and require us to examine the matter a\nlittle more closely. Come, my superior opponent, let me learn from your\nwisdom. It seems to me that every throw of sixes with a pair of dice is\na manifest instance of chance.\n\n\u201cWhile you would hold a throw of deuce-ace to be brought about by\nnecessity?\u201d (The opponent\u2019s supposed remarks are placed in quotation\nmarks.)\n\nClearly one throw is as much chance as another.\n\n\u201cDo you think throws of dice are of a different nature from other\nevents?\u201d\n\nI see that I must say that _all_ the diversity and specificalness of\nevents is attributable to chance.\n\n\u201cWould you, then, deny that there is any regularity in the world?\u201d\n\nThat is clearly undeniable. I must acknowledge there is an approximate\nregularity, and that every event is influenced by it. But the\ndiversification, specificalness, and irregularity of things I suppose is\nchance. A throw of sixes appears to me a case in which this element is\nparticularly obtrusive.\n\n\u201cIf you reflect more deeply, you will come to see that _chance_ is only\na name for a cause that is unknown to us.\u201d\n\nDo you mean that we have no idea whatever what kind of causes could\nbring about a throw of sixes?\n\n\u201cOn the contrary, each die moves under the influence of precise\nmechanical laws.\u201d\n\nBut it appears to me that it is not these _laws_ which made the die turn\nup sixes; for these laws act just the same when other throws come up.\nThe chance lies in the diversity of throws; and this diversity cannot be\ndue to laws which are immutable.\n\n\u201cThe diversity is due to the diverse circumstances under which the laws\nact. The dice lie differently in the box, and the motion given to the\nbox is different. These are the unknown causes which produce the throws,\nand to which we give the name of chance; not the mechanical law which\nregulates the operation of these causes. You see you are already\nbeginning to think more clearly about this subject.\u201d\n\nDoes the operation of mechanical law not increase the diversity?\n\n\u201cProperly not. You must know that the instantaneous state of a system of\nparticles is defined by six times as many numbers as there are\nparticles, three for the co-ordinates of each particle\u2019s position, and\nthree more for the components of its velocity. This number of numbers,\nwhich expresses the amount of diversity in the system, remains the same\nat all times. There may be, to be sure, some kind of relation between\nthe co-ordinates and component velocities of the different particles, by\nmeans of which the state of the system might be expressed by a smaller\nnumber of numbers. But, if this is the case, a precisely corresponding\nrelationship must exist between the co-ordinates and component\nvelocities at any other time, though it may doubtless be a relation less\nobvious to us. Thus, the intrinsic complexity of the system is the same\nat all times.\u201d\n\nVery well, my obliging opponent, we have now reached an issue. You think\nall the arbitrary specifications of the universe were introduced in one\ndose, in the beginning, if there was a beginning, and that the variety\nand complication of nature has always been just as much as it is now.\nBut I, for my part, think that the diversification, the specification,\nhas been continually taking place. Should you condescend to ask me why I\nso think, I should give my reasons as follows:\n\n(1) Question any science which deals with the course of time. Consider\nthe life of an individual animal or plant, or of a mind. Glance at the\nhistory of states, of institutions, of language, of ideas. Examine the\nsuccessions of forms shown by paleontology, the history of the globe as\nset forth in geology, of what the astronomer is able to make out\nconcerning the changes of stellar systems. Everywhere the main fact is\ngrowth and increasing complexity. Death and corruption are mere\naccidents or secondary phenomena. Among some of the lower organisms, it\nis a moot point with biologists whether there be anything which ought to\nbe called death. Races, at any rate, do not die out except under\nunfavorable circumstances. From these broad and ubiquitous facts we may\nfairly infer, by the most unexceptionable logic, that there is probably\nin nature some agency by which the complexity and diversity of things\ncan be increased; and that consequently the rule of mechanical necessity\nmeets in some way with interference.\n\n(2) By thus admitting pure spontaneity or life as a character of the\nuniverse, acting always and everywhere though restrained within narrow\nbounds by law, producing infinitesimal departures from law continually,\nand great ones with infinite infrequency, I account for all the variety\nand diversity of the universe, in the only sense in which the really\n_sui generis_ and new can be said to be accounted for. The ordinary view\nhas to admit the inexhaustible multitudinous variety of the world, has\nto admit that its mechanical law cannot account for this in the least,\nthat variety can spring only from spontaneity, and yet denies without\nany evidence or reason the existence of this spontaneity, or else shoves\nit back to the beginning of time and supposes it dead ever since. The\nsuperior logic of my view appears to me not easily controverted.\n\n(3) When I ask the necessitarian how he would explain the diversity and\nirregularity of the universe, he replies to me out of the treasury of\nhis wisdom that irregularity is something which from the nature of\nthings we must not seek to explain. Abashed at this, I seek to cover my\nconfusion by asking how he would explain the uniformity and regularity\nof the universe, whereupon he tells me that the laws of nature are\nimmutable and ultimate facts, and no account is to be given of them. But\nmy hypothesis of spontaneity does explain irregularity, in a certain\nsense; that is, it explains the general fact of irregularity, though\nnot, of course, what each lawless event is to be. At the same time, by\nthus loosening the bond of necessity, it gives room for the influence of\nanother kind of causation, such as seems to be operative in the mind in\nthe formation of associations, and enables us to understand how the\nuniformity of nature could have been brought about. That single events\nshould be hard and unintelligible, logic will permit without difficulty:\nwe do not expect to make the shock of a personally experienced\nearthquake appear natural and reasonable by any amount of cogitation.\nBut logic does expect things _general_ to be understandable. To say that\nthere is a universal law, and that it is a hard, ultimate,\nunintelligible fact, the why and wherefore of which can never be\ninquired into, at this a sound logic will revolt; and will pass over at\nonce to a method of philosophizing which does not thus barricade the\nroad of discovery.\n\n(4) Necessitarianism cannot logically stop short of making the whole\naction of the mind a part of the physical universe. Our notion that we\ndecide what we are going to do, if as the necessitarian says, it has\nbeen calculable since the earliest times, is reduced to illusion.\nIndeed, consciousness in general thus becomes a mere illusory aspect of\na material system. What we call red, green, and violet are in reality\nonly different rates of vibration. The sole reality is the distribution\nof qualities of matter in space and time. Brain-matter is protoplasm in\na certain degree and kind of complication,\u2014a certain arrangement of\nmechanical particles. Its feeling is but an inward aspect, a phantom.\nFor, from the positions and velocities of the particles at any one\ninstant, and the knowledge of the immutable forces, the positions at all\nother times are calculable; so that the universe of space, time, and\nmatter is a rounded system uninterfered with from elsewhere. But from\nthe state of feeling at any instant, there is no reason to suppose the\nstates of feeling at all other instants are thus exactly calculable; so\nthat feeling is, as I said, a mere fragmentary and illusive aspect of\nthe universe. This is the way, then, that necessitarianism has to make\nup its accounts. It enters consciousness under the head of sundries, as\na forgotten trifle; its scheme of the universe would be more\nsatisfactory if this little fact could be dropped out of sight. On the\nother hand, by supposing the rigid exactitude of causation to yield, I\ncare not how little,\u2014be it but by a strictly infinitesimal amount,\u2014we\ngain room to insert mind into our scheme, and to put it into the place\nwhere it is needed, into the position which, as the sole\nself-intelligible thing, it is entitled to occupy, that of the fountain\nof existence; and in so doing we resolve the problem of the connection\nof soul and body.\n\n(5) But I must leave undeveloped the chief of my reasons, and can only\nadumbrate it. The hypothesis of chance-spontaneity is one whose\ninevitable consequences are capable of being traced out with\nmathematical precision into considerable detail. Much of this I have\ndone and find the consequences to agree with observed facts to an extent\nwhich seems to me remarkable. But the matter and methods of reasoning\nare novel, and I have no right to promise that other mathematicians\nshall find my deductions as satisfactory as I myself do, so that the\nstrongest reason for my belief must for the present remain a private\nreason of my own, and cannot influence others. I mention it to explain\nmy own position; and partly to indicate to future mathematical\nspeculators a veritable goldmine, should time and circumstances and the\nabridger of all joys prevent my opening it to the world.\n\nIf now I, in my turn, inquire of the necessitarian why he prefers to\nsuppose that all specification goes back to the beginning of things, he\nwill answer me with one of those last three arguments which I left\nunanswered.\n\nFirst, he may say that chance is a thing absolutely unintelligible, and,\ntherefore, that we never can be entitled to make such a supposition. But\ndoes not this objection smack of na\u00efve impudence? It is not mine, it is\nhis own conception of the universe which leads abruptly up to hard,\nultimate, inexplicable, immutable law, on the one hand, and to\ninexplicable specification and diversification of circumstances on the\nother. My view, on the contrary, hypothetises nothing at all, unless it\nbe hypothesis to say that all specification came about in some sense,\nand is not to be accepted as unaccountable. To undertake to account for\nanything by saying boldly that it is due to chance would, indeed, be\nfutile. But this I do not do. I make use of chance chiefly to make room\nfor a principle of generalization, or tendency to form habits, which I\nhold has produced all regularities. The mechanical philosopher leaves\nthe whole specification of the world utterly unaccounted for, which is\npretty nearly as bad as to boldly attribute it to chance. I attribute it\naltogether to chance, it is true, but to chance in the form of a\nspontaneity which is to some degree regular. It seems to me clear at any\nrate that one of these two positions must be taken, or else\nspecification must be supposed due to a spontaneity which develops\nitself in a certain and not in a chance way, by an objective logic like\nthat of Hegel. This last way I leave as an open possibility, for the\npresent; for it is as much opposed to the necessitarian scheme of\nexistence as my own theory is.\n\nSecondly, the necessitarian may say there are, at any rate, no observed\nphenomena which the hypothesis of chance could aid in explaining. In\nreply, I point first to the phenomenon of growth and developing\ncomplexity, which appears to be universal, and which though it may\npossibly be an affair of mechanism perhaps, certainly presents all the\nappearance of increasing diversification. Then, there is variety itself,\nbeyond comparison the most obtrusive character of the universe: no\nmechanism can account for this. Then, there is the very fact the\nnecessitarian most insists upon, the regularity of the universe which\nfor him serves only to block the road of inquiry. Then, there are the\nregular relationships between the laws of nature,\u2014similarities and\ncomparative characters, which appeal to our intelligence as its cousins,\nand call upon us for a reason. Finally, there is consciousness, feeling,\na patent fact enough, but a very inconvenient one to the mechanical\nphilosopher.\n\nThirdly, the necessitarian may say that chance is not a _vera causa_,\nthat we cannot know positively there is any such element in the\nuniverse. But the doctrine of the _vera causa_ has nothing to do with\nelementary conceptions. Pushed to that extreme, it at once cuts off\nbelief in the existence of a material universe; and without that\nnecessitarianism could hardly maintain its ground. Besides, variety is a\nfact which must be admitted; and the theory of chance merely consists in\nsupposing this diversification does not antedate all time. Moreover, the\navoidance of hypotheses involving causes nowhere positively known to\nact\u2014is only a recommendation of logic, not a positive command. It cannot\nbe formulated in any precise terms without at once betraying its\nuntenable character,\u2014I mean as rigid rule, for as a recommendation it is\nwholesome enough.\n\nI believe I have thus subjected to fair examination all the important\nreasons for adhering to the theory of universal necessity, and have\nshown their nullity. I earnestly beg that whoever may detect any flaw in\nmy reasoning will point it out to me, either privately or publicly; for\nif I am wrong, it much concerns me to be set right speedily. If my\nargument remains unrefuted, it will be time, I think, to doubt the\nabsolute truth of the principle of universal law; and when once such a\ndoubt has obtained a living root in any man\u2019s mind, my cause with him, I\nam persuaded, is gained.\n\nFootnote 59:\n\n  _The Monist_, April, 1892.\n\nFootnote 60:\n\n  _Continuous_ is not exactly the right word, but I let it go to avoid a\n  long and irrelevant discussion.\n\n\n\n\n                        III. THE LAW OF MIND[61]\n\n\nIn an article published in _The Monist_ for January, 1891, I endeavored\nto show what ideas ought to form the warp of a system of philosophy, and\nparticularly emphasized that of absolute chance. In the number of April,\n1892, I argued further in favor of that way of thinking, which it will\nbe convenient to christen _tychism_ (from \u03c4\u03cd\u03c7\u03b7, chance). A serious\nstudent of philosophy will be in no haste to accept or reject this\ndoctrine; but he will see in it one of the chief attitudes which\nspeculative thought may take, feeling that it is not for an individual,\nnor for an age, to pronounce upon a fundamental question of philosophy.\nThat is a task for a whole era to work out. I have begun by showing that\n_tychism_ must give birth to an evolutionary cosmology, in which all the\nregularities of nature and of mind are regarded as products of growth,\nand to a Schelling-fashioned idealism which holds matter to be mere\nspecialized and partially deadened mind. I may mention, for the benefit\nof those who are curious in studying mental biographies, that I was born\nand reared in the neighborhood of Concord,\u2014I mean in Cambridge,\u2014at the\ntime when Emerson, Hedge, and their friends were disseminating the ideas\nthat they had caught from Schelling, and Schelling from Plotinus, from\nBoehm, or from God knows what minds stricken with the monstrous\nmysticism of the East. But the atmosphere of Cambridge held many an\nantiseptic against Concord transcendentalism; and I am not conscious of\nhaving contracted any of that virus. Nevertheless, it is probable that\nsome cultured bacilli, some benignant form of the disease was implanted\nin my soul, unawares, and that now, after long incubation, it comes to\nthe surface, modified by mathematical conceptions and by training in\nphysical investigations.\n\nThe next step in the study of cosmology must be to examine the general\nlaw of mental action. In doing this, I shall for the time drop my\ntychism out of view, in order to allow a free and independent expansion\nto another conception signalized in my first _Monist_ paper as one of\nthe most indispensable to philosophy, though it was not there dwelt\nupon; I mean the idea of continuity. The tendency to regard continuity,\nin the sense in which I shall define it, as an idea of prime importance\nin philosophy may conveniently be termed _synechism_. The present paper\nis intended chiefly to show what synechism is, and what it leads to. I\nattempted, a good many years ago, to develop this doctrine in the\n_Journal of Speculative Philosophy_ (Vol. II.); but I am able now to\nimprove upon that exposition, in which I was a little blinded by\nnominalistic prepossessions. I refer to it, because students may\npossibly find that some points not sufficiently explained in the present\npaper are cleared up in those earlier ones.\n\n\n                            WHAT THE LAW IS\n\n\nLogical analysis applied to mental phenomena shows that there is but one\nlaw of mind, namely, that ideas tend to spread continuously and to\naffect certain others which stand to them in a peculiar relation of\naffectibility. In this spreading they lose intensity, and especially the\npower of affecting others, but gain generality and become welded with\nother ideas.\n\nI set down this formula at the beginning, for convenience; and now\nproceed to comment upon it.\n\n\n                         INDIVIDUALITY OF IDEAS\n\n\nWe are accustomed to speak of ideas as reproduced, as passed from mind\nto mind, as similar or dissimilar to one another, and, in short, as if\nthey were substantial things; nor can any reasonable objection be raised\nto such expressions. But taking the word \u201cidea\u201d in the sense of an event\nin an individual consciousness, it is clear that an idea once past is\ngone forever, and any supposed recurrence of it is another idea. These\ntwo ideas are not present in the same state of consciousness, and\ntherefore cannot possibly be compared. To say, therefore, that they are\nsimilar can only mean that an occult power from the depths of the soul\nforces us to connect them in our thoughts after they are both no more.\nWe may note, here, in passing, that of the two generally recognized\nprinciples of association, contiguity and similarity, the former is a\nconnection due to a power without, the latter a connection due to a\npower within.\n\nBut what can it mean to say that ideas wholly past are thought of at\nall, any longer? They are utterly unknowable. What distinct meaning can\nattach to saying that an idea in the past in any way affects an idea in\nthe future, from which it is completely detached? A phrase between the\nassertion and the denial of which there can in no case be any sensible\ndifference is mere gibberish.\n\nI will not dwell further upon this point, because it is a commonplace of\nphilosophy.\n\n\n                          CONTINUITY OF IDEAS\n\n\nWe have here before us a question of difficulty, analogous to the\nquestion of nominalism and realism. But when once it has been clearly\nformulated, logic leaves room for one answer only. How can a past idea\nbe present? Can it be present vicariously? To a certain extent, perhaps;\nbut not merely so; for then the question would arise how the past idea\ncan be related to its vicarious representation. The relation, being\nbetween ideas, can only exist in some consciousness: now that past idea\nwas in no consciousness but that past consciousness that alone contained\nit; and that did not embrace the vicarious idea.\n\nSome minds will here jump to the conclusion that a past idea cannot in\nany sense be present. But that is hasty and illogical. How extravagant,\ntoo, to pronounce our whole knowledge of the past to be mere delusion!\nYet it would seem that the past is as completely beyond the bounds of\npossible experience as a Kantian thing-in-itself.\n\nHow can a past idea be present? Not vicariously. Then, only by direct\nperception. In other words, to be present, it must be _ipso facto_\npresent. That is, it cannot be wholly past; it can only be going,\ninfinitesimally past, less past than any assignable past date. We are\nthus brought to the conclusion that the present is connected with the\npast by a series of real infinitesimal steps.\n\nIt has already been suggested by psychologists that consciousness\nnecessarily embraces an interval of time. But if a finite time be meant,\nthe opinion is not tenable. If the sensation that precedes the present\nby half a second were still immediately before me, then, on the same\nprinciple the sensation preceding that would be immediately present, and\nso on _ad infinitum_. Now, since there is a time, say a year, at the end\nof which an idea is no longer _ipso facto_ present, it follows that this\nis true of any finite interval, however short.\n\nBut yet consciousness must essentially cover an interval of time; for if\nit did not, we could gain no knowledge of time, and not merely no\nveracious cognition of it, but no conception whatever. We are,\ntherefore, forced to say that we are immediately conscious through an\ninfinitesimal interval of time.\n\nThis is all that is requisite. For, in this infinitesimal interval, not\nonly is consciousness continuous in a subjective sense, that is,\nconsidered as a subject or substance having the attribute of duration;\nbut also, because it is immediate consciousness, its object is _ipso\nfacto_ continuous. In fact, this infinitesimally spread-out\nconsciousness is a direct feeling of its contents as spread out. This\nwill be further elucidated below. In an infinitesimal interval we\ndirectly perceive the temporal sequence of its beginning, middle, and\nend,\u2014not, of course, in the way of recognition, for recognition is only\nof the past, but in the way of immediate feeling. Now upon this interval\nfollows another, whose beginning is the middle of the former, and whose\nmiddle is the end of the former. Here, we have an immediate perception\nof the temporal sequence of its beginning, middle, and end, or say of\nthe second, third, and fourth instants. From these two immediate\nperceptions, we gain a mediate, or inferential, perception of the\nrelation of all four instants. This mediate perception is objectively,\nor as to the object represented, spread over the four instants; but\nsubjectively, or as itself the subject of duration, it is completely\nembraced in the second moment. (The reader will observe that I use the\nword _instant_ to mean a point of time, and _moment_ to mean an\ninfinitesimal duration.) If it is objected that, upon the theory\nproposed, we must have more than a mediate perception of the succession\nof the four instants, I grant it; for the sum of the two infinitesimal\nintervals is itself infinitesimal, so that it is immediately perceived.\nIt is immediately perceived in the whole interval, but only mediately\nperceived in the last two-thirds of the interval. Now, let there be an\nindefinite succession of these inferential acts of comparative\nperception; and it is plain that the last moment will contain\nobjectively the whole series. Let there be, not merely an indefinite\nsuccession, but a continuous flow of inference through a finite time;\nand the result will be a mediate objective consciousness of the whole\ntime in the last moment. In this last moment, the whole series will be\nrecognized, or known as known before, except only the last moment, which\nof course will be absolutely unrecognizable to itself. Indeed, even this\nlast moment will be recognized like the rest, or, at least, be just\nbeginning to be so. There is a little _elenchus_, or appearance of\ncontradiction, here, which the ordinary logic of reflection quite\nsuffices to resolve.\n\n\n                  INFINITY AND CONTINUITY, IN GENERAL\n\n\nMost of the mathematicians who during the last two generations have\ntreated the differential calculus have been of the opinion that an\ninfinitesimal quantity is an absurdity; although, with their habitual\ncaution, they have often added \u201cor, at any rate, the conception of an\ninfinitesimal is so difficult, that we practically cannot reason about\nit with confidence and security.\u201d Accordingly, the doctrine of limits\nhas been invented to evade the difficulty, or, as some say, to explain\nthe signification of the word \u201cinfinitesimal.\u201d This doctrine, in one\nform or another, is taught in all the text-books, though in some of them\nonly as an alternative view of the matter; it answers well enough the\npurposes of calculation, though even in that application it has its\ndifficulties.\n\nThe illumination of the subject by a strict notation for the logic of\nrelatives had shown me clearly and evidently that the idea of an\ninfinitesimal involves no contradiction, before I became acquainted with\nthe writings of Dr. Georg Cantor (though many of these had already\nappeared in the _Mathematische Annalen_ and in _Borchardt\u2019s Journal_, if\nnot yet in the _Acta Mathematica_, all mathematical journals of the\nfirst distinction), in which the same view is defended with\nextraordinary genius and penetrating logic.\n\nThe prevalent opinion is that finite numbers are the only ones that we\ncan reason about, at least, in any ordinary mode of reasoning, or, as\nsome authors express it, they are the only numbers that can be reasoned\nabout mathematically. But this is an irrational prejudice. I long ago\nshowed that finite collections are distinguished from infinite ones only\nby one circumstance and its consequences, namely, that to them is\napplicable a peculiar and unusual mode of reasoning called by its\ndiscoverer, De Morgan, the \u201csyllogism of transposed quantity.\u201d\n\nBalzac, in the introduction of his _Physiologie du mariage_, remarks\nthat every young Frenchman boasts of having seduced some Frenchwoman.\nNow, as a woman can only be seduced once, and there are no more\nFrenchwomen than Frenchmen, it follows, if these boasts are true, that\nno French women escape seduction. If their number be finite, the\nreasoning holds. But since the population is continually increasing, and\nthe seduced are on the average younger than the seducers, the conclusion\nneed not be true. In like manner, De Morgan, as an actuary, might have\nargued that if an insurance company pays to its insured on an average\nmore than they have ever paid it, including interest, it must lose\nmoney. But every modern actuary would see a fallacy in that, since the\nbusiness is continually on the increase. But should war, or other\ncataclysm, cause the class of insured to be a finite one, the conclusion\nwould turn out painfully correct, after all. The above two reasonings\nare examples of the syllogism of transposed quantity.\n\nThe proposition that finite and infinite collections are distinguished\nby the applicability to the former of the syllogism of transposed\nquantity ought to be regarded as the basal one of scientific arithmetic.\n\nIf a person does not know how to reason logically, and I must say that a\ngreat many fairly good mathematicians,\u2014yea, distinguished ones,\u2014fall\nunder this category, but simply uses a rule of thumb in blindly drawing\ninferences like other inferences that have turned out well, he will, of\ncourse, be continually falling into error about infinite numbers. The\ntruth is such people do not reason, at all. But for the few who do\nreason, reasoning about infinite numbers is easier than about finite\nnumbers, because the complicated syllogism of transposed quantity is not\ncalled for. For example, that the whole is greater than its part is not\nan axiom, as that eminently bad reasoner, Euclid, made it to be. It is a\ntheorem readily proved by means of a syllogism of transposed quantity,\nbut not otherwise. Of finite collections it is true, of infinite\ncollections false. Thus, a part of the whole numbers are even numbers.\nYet the even numbers are no fewer than all the numbers; an evident\nproposition since if every number in the whole series of whole numbers\nbe doubled, the result will be the series of even numbers.\n\n                          1, 2, 3, 4, 5, 6, etc.\n                          2, 4, 6, 8, 10, 12, etc.\n\nSo for every number there is a distinct even number. In fact, there are\nas many distinct doubles of numbers as there are of distinct numbers.\nBut the doubles of numbers are all even numbers.\n\nIn truth, of infinite collections there are but two grades of magnitude,\nthe _endless_ and the _innumerable_. Just as a finite collection is\ndistinguished from an infinite one by the applicability to it of a\nspecial mode of reasoning, the syllogism of transposed quantity, so, as\nI showed in the paper last referred to, a numerable collection is\ndistinguished from an innumerable one by the applicability to it of a\ncertain mode of reasoning, the Fermatian inference, or, as it is\nsometimes improperly termed, \u201cmathematical induction.\u201d\n\nAs an example of this reasoning, Euler\u2019s demonstration of the binomial\ntheorem for integral powers may be given. The theorem is that (_x_ +\n_y_)^n, where _n_ is a whole number, may be expanded into the sum of a\nseries of terms of which the first is _x_^n_y_^o and each of the others\nis derived from the next preceding by diminishing the exponent of _x_ by\n1 and multiplying by that exponent and at the same time increasing the\nexponent of _y_ by 1 and dividing by that increased exponent. Now,\nsuppose this proposition to be true for a certain exponent, _n_ = _M_,\nthen it must also be true for _n_ = _M_ + 1. For let one of the terms in\nthe expansion of (_x_ + _y_)^M be written A_x^p__y^q_. Then, this term\nwith the two following will be\n\n    A_x^p__y^q_ + A _p_/(_q_ + 1) _x_^{_p_ - 1} _y_^{_q_ + 1} + A\n       _p_/(_q_ + 1) (_p_ - 1)/(_q_ + 2) _x_^{_p_ - 2} _y_^{_q_ + 2}\n\nNow, when (_x_ + _y_)^M is multiplied by _x_ + _y_ to give (_x_ +\n_y_)^{M + 1}, we multiply first by _x_ and then by _y_ instead of by _x_\nand add the two results. When we multiply by _x_, the second of the\nabove three terms will be the only one giving a term involving\n_x^p__y_^{_q_ + 1} and the third will be the only one giving a term in\n_x_^{_p_ - 1}_y_^{_q_ + 2}; and when we multiply by y the first will be\nthe only term giving a term in _x^p__y_^{_q_ + 1}, and the second will\nbe the only term giving a term in _x_^{_p_ - 1}_y_^{_q_ + 2}. Hence,\nadding like terms, we find that the coefficient of _x^p__y_^{_q_ + 1} in\nthe expansion of (_x_ + _y_)^{M + 1} will be the sum of the coefficients\nof the first two of the above three terms, and that the coefficient of\n_x_^{_p_ - 1}_y_^{_q_ + 2} will be the sum of the coefficients of the\nlast two terms. Hence, two successive terms in the expansion of (_x_ +\n_y_)^{M + 1} will be\n\n    A[1 + (_p_/(_q_ + 1))]_x^p__y_^{_q_+1} + A(_p_/(_q_ + 1))[1+ ((_p_ -\n       1)/(_q_ + 2))]_x_^{_p_-1}_y_^{_q_+2}\n    = A((_p_ + _q_ + 1)/(_q_ + 1))_x^p__y_^{_q_+1} + A((_p_ + _q_ +\n       1)/(_q_ + 1))(_p_/(_q_ + 2))_x_^{_p_-1}_y_{_q_+2}\n\nIt is, thus, seen that the succession of terms follows the rule. Thus if\nany integral power follows the rule, so also does the next higher power.\nBut the first power obviously follows the rule. Hence, all powers do so.\n\nSuch reasoning holds good of any collection of objects capable of being\nranged in a series which though it may be endless, can be numbered so\nthat each member of it receives a definite integral number. For\ninstance, all the whole numbers constitute such a numerable collection.\nAgain, all numbers resulting from operating according to any definite\nrule with any finite number of whole numbers form such a collection. For\nthey may be arranged in a series thus. Let F be the symbol of operation.\nFirst operate on 1, giving F(1). Then, operate on a second 1, giving\nF(1,1). Next, introduce 2, giving 3rd, F(2); 4th F(2,1); 5th, F(1,2);\n6th, F(2,2). Next use a third variable giving 7th, F(1,1,1); 8th,\nF(2,1,1); 9th, F(1,2,1); 10th, F(2,2,1); 11th, F(1,1,2); 12th, F(2,1,2);\n13th, F(1,2,2); 14th, F(2,2,2). Next introduce 3, and so on, alternately\nintroducing new variables and new figures; and in this way it is plain\nthat every arrangement of integral values of the variables will receive\na numbered place in the series.[62]\n\nThe class of endless but numerable collections (so called because they\ncan be so ranged that to each one corresponds a distinct whole number)\nis very large. But there are collections which are certainly\ninnumerable. Such is the collection of all numbers to which endless\nseries of decimals are capable of approximating. It has been recognized\nsince the time of Euclid that certain numbers are surd or\nincommensurable, and are not exactly expressible by any finite series of\ndecimals, nor by a circulating decimal. Such is the ratio of the\ncircumference of a circle to its diameter, which we know is nearly\n3.1415926. The calculation of this number has been carried to over 700\nfigures without the slightest appearance of regularity in their\nsequence. The demonstrations that this and many other numbers are\nincommensurable are perfect. That the entire collection of\nincommensurable numbers is innumerable has been clearly proved by\nCantor. I omit the demonstration; but it is easy to see that to\ndiscriminate one from some other would, in general, require the use of\nan endless series of numbers. Now if they cannot be exactly expressed\nand discriminated, clearly they cannot be ranged in a linear series.\n\nIt is evident that there are as many points on a line or in an interval\nof time as there are of real numbers in all. These are, therefore,\ninnumerable collections. Many mathematicians have incautiously assumed\nthat the points on a surface or in a solid are more than those on a\nline. But this has been refuted by Cantor. Indeed, it is obvious that\nfor every set of values of co\u00f6rdinates there is a single distinct\nnumber. Suppose, for instance, the values of the coordinates all lie\nbetween 0 and + 1. Then if we compose a number by putting in the first\ndecimal place the first figure of the first co\u00f6rdinate, in the second\nthe first figure of the second co\u00f6rdinate, and so on, and when the first\nfigures are all dealt out go on to the second figures in like manner, it\nis plain that the values of the co\u00f6rdinates can be read off from the\nsingle resulting number, so that a triad or tetrad of numbers, each\nhaving innumerable values, has no more values than a single\nincommensurable number.\n\nWere the number of dimensions infinite, this would fail; and the\ncollection of infinite sets of numbers having each innumerable\nvariations, might, therefore, be greater than the simple innumerable\ncollection, and might be called _endlessly infinite_. The single\nindividuals of such a collection could not, however, be designated, even\napproximately, so that this is indeed a magnitude concerning which it\nwould be possible to reason only in the most general way, if at all.\n\nAlthough there are but two grades of magnitudes of infinite collections,\nyet when certain conditions are imposed upon the order in which\nindividuals are taken, distinctions of magnitude arise from that cause.\nThus, if a simply endless series be doubled by separating each unit into\ntwo parts, the successive first parts and also the second parts being\ntaken in the same order as the units from which they are derived, this\ndouble endless series will, so long as it is taken in that order, appear\nas twice as large as the original series. In like manner the product of\ntwo innumerable collections, that is, the collection of possible pairs\ncomposed of one individual of each, if the order of continuity is to be\nmaintained, is, by virtue of that order, infinitely greater than either\nof the component collections.\n\nWe now come to the difficult question. What is continuity? Kant\nconfounds it with infinite divisibility, saying that the essential\ncharacter of a continuous series is that between any two members of it a\nthird can always be found. This is an analysis beautifully clear and\ndefinite; but unfortunately, it breaks down under the first test. For\naccording to this, the entire series of rational fractions arranged in\nthe order of their magnitude, would be an infinite series, although the\nrational fractions are numerable, while the points of a line are\ninnumerable. Nay, worse yet, if from that series of fractions any two\nwith all that lie between them be excised, and any number of such finite\ngaps be made, Kant\u2019s definition is still true of the series, though it\nhas lost all appearance of continuity.\n\nCantor defines a continuous series as one which is _concatenated_ and\n_perfect_. By a concatenated series, he means such a one that if any two\npoints are given in it, and any finite distance, however small, it is\npossible to proceed from the first point to the second through a\nsuccession of points of the series each at a distance from the preceding\none less than the given distance. This is true of the series of rational\nfractions ranged in the order of their magnitude. By a perfect series,\nhe means one which contains every point such that there is no distance\nso small that this point has not an infinity of points of the series\nwithin that distance of it. This is true of the series of numbers\nbetween 0 and 1 capable of being expressed by decimals in which only the\ndigits 0 and 1 occur.\n\nIt must be granted that Cantor\u2019s definition includes every series that\nis continuous; nor can it be objected that it includes any important or\nindubitable case of a series not continuous. Nevertheless, it has some\nserious defects. In the first place, it turns upon metrical\nconsiderations; while the distinction between a continuous and a\ndiscontinuous series is manifestly non-metrical. In the next place, a\nperfect series is defined as one containing \u201cevery point\u201d of a certain\ndescription. But no positive idea is conveyed of what all the points\nare: that is definition by negation, and cannot be admitted. If that\nsort of thing were allowed, it would be very easy to say, at once, that\nthe continuous linear series of points is one which contains every point\nof the line between its extremities. Finally, Cantor\u2019s definition does\nnot convey a distinct notion of what the components of the conception of\ncontinuity are. It ingeniously wraps up its properties in two separate\nparcels, but does not display them to our intelligence.\n\nKant\u2019s definition expresses one simple property of a continuum; but it\nallows of gaps in the series. To mend the definition, it is only\nnecessary to notice how these gaps can occur. Let us suppose, then, a\nlinear series of points extending from a point, _A_, to a point, _B_,\nhaving a gap from _B_ to a third point, _C_, and thence extending to a\nfinal limit, _D_; and let us suppose this series conforms to Kant\u2019s\ndefinition. Then, of the two points, _B_ and _C_, one or both must be\nexcluded from the series; for otherwise, by the definition, there would\nbe points between them. That is, if the series contains _C_, though it\ncontains all the points up to _B_, it cannot contain _B_. What is\nrequired, therefore, is to state in non-metrical terms that if a series\nof points up to a limit is included in a continuum the limit is\nincluded. It may be remarked that this is the property of a continuum to\nwhich Aristotle\u2019s attention seems to have been directed when he defines\na continuum as something whose parts have a common limit. The property\nmay be exactly stated as follows: If a linear series of points is\ncontinuous between two points, _A_ and _D_, and if an endless series of\npoints be taken, the first of them between _A_ and _D_ and each of the\nothers between the last preceding one and _D_, then there is a point of\nthe continuous series between all that endless series of points and _D_,\nand such that every other point of which this is true lies between this\npoint and _D_. For example, take any number between 0 and 1, as 0.1;\nthen, any number between 0.1 and 1, as 0.11; then any number between\n0.11 and 1, as 0.111; and so on, without end. Then, because the series\nof real numbers between 0 and 1 is continuous, there must be a _least_\nreal number, greater than every number of that endless series. This\nproperty, which may be called the Aristotelicity of the series, together\nwith Kant\u2019s property, or its Kanticity, completes the definition of a\ncontinuous series.\n\nThe property of Aristotelicity may be roughly stated thus: a continuum\ncontains the end point belonging to every endless series of points which\nit contains. An obvious corollary is that every continuum contains its\nlimits. But in using this principle it is necessary to observe that a\nseries may be continuous except in this, that it omits one or both of\nthe limits.\n\nOur ideas will find expression more conveniently if, instead of points\nupon a line, we speak of real numbers. Every real number is, in one\nsense, the limit of a series, for it can be indefinitely approximated\nto. Whether every real number is a limit of a _regular_ series may\nperhaps be open to doubt. But the series referred to in the definition\nof Aristotelicity must be understood as including all series whether\nregular or not. Consequently, it is implied that between any two points\nan innumerable series of points can be taken.\n\nEvery number whose expression in decimals requires but a finite number\nof places of decimals is commensurable. Therefore, incommensurable\nnumbers suppose an infinitieth place of decimals. The word infinitesimal\nis simply the Latin form of infinitieth; that is, it is an ordinal\nformed from _infinitum_, as centesimal from _centum_. Thus, continuity\nsupposes infinitesimal quantities. There is nothing contradictory about\nthe idea of such quantities. In adding and multiplying them the\ncontinuity must not be broken up, and consequently they are precisely\nlike any other quantities, except that neither the syllogism of\ntransposed quantity, nor the Fermatian inference applies to them.\n\nIf A is a finite quantity and _i_ an infinitesimal, then in a certain\nsense we may write A + _i_ = A. That is to say, this is so for all\npurposes of measurement. But this principle must not be applied except\nto get rid of _all_ the terms in the highest order of infinitesimals\npresent. As a mathematician, I prefer the method of infinitesimals to\nthat of limits, as far easier and less infested with snares. Indeed, the\nlatter, as stated in some books, involves propositions that are false;\nbut this is not the case with the forms of the method used by Cauchy,\nDuhamel, and others. As they understand the doctrine of limits, it\ninvolves the notion of continuity, and, therefore, contains in another\nshape the very same ideas as the doctrine of infinitesimals.\n\nLet us now consider an aspect of the Aristotelical principle which is\nparticularly important in philosophy. Suppose a surface to be part red\nand part blue; so that every point on it is either red or blue, and, of\ncourse, no part can be both red and blue. What, then, is the color of\nthe boundary line between the red and the blue? The answer is that red\nor blue, to exist at all, must be spread over a surface; and the color\nof the surface is the color of the surface in the immediate neighborhood\nof the point. I purposely use a vague form of expression. Now, as the\nparts of the surface in the immediate neighborhood of any ordinary point\nupon a curved boundary are half of them red and half blue, it follows\nthat the boundary is half red and half blue. In like manner, we find it\nnecessary to hold that consciousness essentially occupies time; and what\nis present to the mind at any ordinary instant, is what is present\nduring a moment in which that instant occurs. Thus, the present is half\npast and half to come. Again, the color of the parts of a surface at any\nfinite distance from a point, has nothing to do with its color just at\nthat point; and, in the parallel, the feeling at any finite interval\nfrom the present has nothing to do with the present feeling, except\nvicariously. Take another case: the velocity of a particle at any\ninstant of time is its mean velocity during an infinitesimal instant in\nwhich that time is contained. Just so my immediate feeling is my feeling\nthrough an infinitesimal duration containing the present instant.\n\n\n                            ANALYSIS OF TIME\n\n\nOne of the most marked features about the law of mind is that it makes\ntime to have a definite direction of flow from past to future. The\nrelation of past to future is, in reference to the law of mind,\ndifferent from the relation of future to past. This makes one of the\ngreat contrasts between the law of mind and the law of physical force,\nwhere there is no more distinction between the two opposite directions\nin time than between moving northward and moving southward.\n\nIn order, therefore, to analyze the law of mind, we must begin by asking\nwhat the flow of time consists in. Now, we find that in reference to any\nindividual state of feeling, all others are of two classes, those which\naffect this one (or have a tendency to affect it, and what this means we\nshall inquire shortly), and those which do not. The present is\naffectible by the past but not by the future.\n\nMoreover, if state _A_ is affected by state _B_, and state _B_ by state\n_C_, then _A_ is affected by state _C_, though not so much so. It\nfollows, that if _A_ is affectible by _B_, _B_ is not affectible by _A_.\n\nIf, of two states, each is absolutely unaffectible by the other, they\nare to be regarded as parts of the same state. They are contemporaneous.\n\nTo say that a state is _between_ two states means that it affects one\nand is affected by the other. Between any two states in this sense lies\nan innumerable series of states affecting one another; and if a state\nlies between a given state and any other state which can be reached by\ninserting states between this state and any third state, these inserted\nstates not immediately affecting or being affected by either, then the\nsecond rate mentioned, immediately affects or is affected by the first,\nin the sense that in the one the other is _ipso facto_ present in a\nreduced degree.\n\nThese propositions involve a definition of time and of its flow. Over\nand above this definition they involve a doctrine, namely, that every\nstate of feeling is affectible by every earlier state.\n\n\n                THAT FEELINGS HAVE INTENSIVE CONTINUITY\n\n\nTime with its continuity logically involves some other kind of\ncontinuity than its own. Time, as the universal form of change, cannot\nexist unless there is something to undergo change, and to undergo a\nchange continuous in time, there must be a continuity of changeable\nqualities. Of the continuity of intrinsic qualities of feeling we can\nnow form but a feeble conception. The development of the human mind has\npractically extinguished all feelings, except a few sporadic kinds,\nsound, colors, smells, warmth, etc., which now appear to be disconnected\nand disparate. In the case of colors, there is a tridimensional spread\nof feelings. Originally, all feelings may have been connected in the\nsame way, and the presumption is that the number of dimensions was\nendless. For development essentially involves a limitation of\npossibilities. But given a number of dimensions of feeling, all possible\nvarieties are obtainable by varying the intensities of the different\nelements. Accordingly, time logically supposes a continuous range of\nintensity in feeling. It follows, then, from the definition of\ncontinuity, that when any particular kind of feeling is present, an\ninfinitesimal continuum of all feelings differing infinitesimally from\nthat is present.\n\n\n                  THAT FEELINGS HAVE SPATIAL EXTENSION\n\n\nConsider a gob of protoplasm, say an am\u0153ba or a slime-mould. It does not\ndiffer in any radical way from the contents of a nerve-cell, though its\nfunctions may be less specialized. There is no doubt that this\nslime-mould, or this am\u0153ba, or at any rate some similar mass of\nprotoplasm feels. That is to say, it feels when it is in its excited\ncondition. But note how it behaves. When the whole is quiescent and\nrigid, a place upon it is irritated. Just at this point, an active\nmotion is set up, and this gradually spreads to other parts. In this\naction, no unity nor relation to a nucleus, or other unitary organ can\nbe discerned. It is a mere amorphous continuum of protoplasm, with\nfeeling passing from one part to another. Nor is there anything like a\nwave-motion. The activity does not advance to new parts, just as fast as\nit leaves old parts. Rather, in the beginning, it dies out at a slower\nrate than that at which it spreads. And while the process is going on,\nby exciting the mass at another point, a second quite independent state\nof excitation will be set up. In some places, neither excitation will\nexist, in others each separately, in still other places, both effects\nwill be added together. Whatever there is in the whole phenomenon to\nmake us think there is feeling in such a mass of protoplasm,\u2014_feeling_,\nbut plainly no _personality_,\u2014goes logically to show that that feeling\nhas a subjective, or substantial, spatial extension, as the excited\nstate has. This is, no doubt, a difficult idea to seize, for the reason\nthat it is a subjective, not an objective, extension. It is not that we\nhave a feeling of bigness; though Professor James, perhaps rightly,\nteaches that we have. It is that the feeling, as a subject of inhesion,\nis big. Moreover, our own feelings are focused in attention to such a\ndegree that we are not aware that ideas are not brought to an absolute\nunity; just as nobody not instructed by special experiment has any idea\nhow very, very little of the field of vision is distinct. Still, we all\nknow how the attention wanders about among our feelings; and this fact\nshows that those feelings that are not co-ordinated in attention have a\nreciprocal externality, although they are present at the same time. But\nwe must not tax introspection to make a phenomenon manifest which\nessentially involves externality.\n\nSince space is continuous, it follows that there must be an immediate\ncommunity of feeling between parts of mind infinitesimally near\ntogether. Without this, I believe it would have been impossible for\nminds external to one another, ever to become co-ordinated, and equally\nimpossible for any co\u00f6rdination to be established in the action of the\nnerve-matter of one brain.\n\n\n                          AFFECTIONS OF IDEAS\n\n\nBut we are met by the question what is meant by saying that one idea\naffects another. The unravelment of this problem requires us to trace\nout phenomena a little further.\n\nThree elements go to make up an idea. The first is its intrinsic quality\nas a feeling. The second is the energy with which it affects other\nideas, an energy which is infinite in the here-and-nowness of immediate\nsensation, finite and relative in the recency of the past. The third\nelement is the tendency of an idea to bring along other ideas with it.\n\nAs an idea spreads, its power of affecting other ideas gets rapidly\nreduced; but its intrinsic quality remains nearly unchanged. It is long\nyears now since I last saw a cardinal in his robes; and my memory of\ntheir color has become much dimmed. The color itself, however, is not\nremembered as dim. I have no inclination to call it a dull red. Thus,\nthe intrinsic quality remains little changed; yet more accurate\nobservation will show a slight reduction of it. The third element, on\nthe other hand, has increased. As well as I can recollect, it seems to\nme the cardinals I used to see wore robes more scarlet than vermillion\nis, and highly luminous. Still, I know the color commonly called\ncardinal is on the crimson side of vermillion and of quite moderate\nluminosity, and the original idea calls up so many other hues with it,\nand asserts itself so feebly, that I am unable any longer to isolate it.\n\nA finite interval of time generally contains an innumerable series of\nfeelings; and when these become welded together in association, the\nresult is a general idea. For we have just seen how by continuous\nspreading an idea becomes generalised.\n\nThe first character of a general idea so resulting is that it is living\nfeeling. A continuum of this feeling, infinitesimal in duration, but\nstill embracing innumerable parts, and also, though infinitesimal,\nentirely unlimited, is immediately present. And in its absence of\nboundedness a vague possibility of more than is present is directly\nfelt.\n\nSecond, in the presence of this continuity of feeling, nominalistic\nmaxims appear futile. There is no doubt about one idea affecting\nanother, when we can directly perceive the one gradually modified and\nshaping itself into the other. Nor can there any longer be any\ndifficulty about one idea resembling another, when we can pass along the\ncontinuous field of quality from one to the other and back again to the\npoint which we had marked.\n\n[Illustration: Figure 7.]\n\nThird, consider the insistency of an idea. The insistency of a past idea\nwith reference to the present is a quantity which is less the further\nback that past idea is, and rises to infinity as the past idea is\nbrought up into coincidence with the present. Here we must make one of\nthose inductive applications of the law of continuity which have\nproduced such great results in all the positive sciences. We must extend\nthe law of insistency into the future. Plainly, the insistency of a\nfuture idea with reference to the present is a quantity affected by the\nminus sign; for it is the present that affects the future, if there be\nany effect, not the future that affects the present. Accordingly, the\ncurve of insistency is a sort of equilateral hyperbola. (See the\nfigure.) Such a conception is none the less mathematical, that its\nquantification cannot now be exactly specified.\n\nNow consider the induction which we have here been led into. This curve\nsays that feeling which has not yet emerged into immediate consciousness\nis already affectible and already affected. In fact, this is habit, by\nvirtue of which an idea is brought up into present consciousness by a\nbond that had already been established between it and another idea while\nit was still _in futuro_.\n\nWe can now see what the affection of one idea by another consists in. It\nis that the affected idea is attached as a logical predicate to the\naffecting idea as subject. So when a feeling emerges into immediate\nconsciousness, it always appears as a modification of a more or less\ngeneral object already in the mind. The word suggestion is well adapted\nto expressing this relation. The future is suggested by, or rather is\ninfluenced by the suggestions of, the past.\n\n\n             IDEAS CANNOT BE CONNECTED EXCEPT BY CONTINUITY\n\n\nThat ideas can nowise be connected without continuity is sufficiently\nevident to one who reflects upon the matter. But still the opinion may\nbe entertained that after continuity has once made the connection of\nideas possible, then they may get to be connected in other modes than\nthrough continuity. Certainly, I cannot see how anyone can deny that the\ninfinite diversity of the universe, which we call chance, may bring\nideas into proximity which are not associated in one general idea. It\nmay do this many times. But then the law of continuous spreading will\nproduce a mental association; and this I suppose is an abridged\nstatement of the way the universe has been evolved. But if I am asked\nwhether a blind \u1f00\u03bd\u03ac\u03b3\u03ba\u03b7 cannot bring ideas together, first I point out\nthat it would not remain blind. There being a continuous connection\nbetween the ideas, they would infallibly become associated in a living,\nfeeling, and perceiving general idea. Next, I cannot see what the\nmustness or necessity of this \u1f01\u03bd\u03ac\u03b3\u03ba\u03b7 would consist in. In the absolute\nuniformity of the phenomenon, says the nominalist. Absolute is well put\nin; for if it merely happened so three times in succession, or three\nmillion times in succession, in the absence of any reason, the\ncoincidence could only be attributed to chance. But absolute uniformity\nmust extend over the whole infinite future; and it is idle to talk of\nthat except as an idea. No; I think we can only hold that wherever ideas\ncome together they tend to weld into general ideas; and wherever they\nare generally connected, general ideas govern the connection; and these\ngeneral ideas are living feelings spread out.\n\n\n                 MENTAL LAW FOLLOWS THE FORMS OF LOGIC\n\n\nThe three main classes of logical inference are Deduction, Induction,\nand Hypothesis. These correspond to three chief modes of action of the\nhuman soul. In deduction the mind is under the dominion of a habit or\nassociation by virtue of which a general idea suggests in each case a\ncorresponding reaction. But a certain sensation is seen to involve that\nidea. Consequently, that sensation is followed by that reaction. That is\nthe way the hind legs of a frog, separated from the rest of the body,\nreason, when you pinch them. It is the lowest form of psychical\nmanifestation.\n\nBy induction, a habit becomes established. Certain sensations, all\ninvolving one general idea, are followed each by the same reaction; and\nan association becomes established, whereby that general idea gets to be\nfollowed uniformly by that reaction.\n\nHabit is that specialization of the law of mind whereby a general idea\ngains the power of exciting reactions. But in order that the general\nidea should attain all its functionality, it is necessary, also, that it\nshould become suggestible by sensations. That is accomplished by a\npsychical process having the form of hypothetic inference. By hypothetic\ninference, I mean, as I have explained in other writings, an induction\nfrom qualities. For example, I know that the kind of man known and\nclassed as a \u201cmugwump\u201d has certain characteristics. He has a high\nself-respect and places great value upon social distinction. He laments\nthe great part that rowdyism and unrefined good-fellowship play in the\ndealings of American politicians with their constituency. He thinks that\nthe reform which would follow from the abandonment of the system by\nwhich the distribution of offices is made to strengthen party\norganizations and a return to the original and essential conception of\noffice-filling would be found an unmixed good. He holds that monetary\nconsiderations should usually be the decisive ones in questions of\npublic policy. He respects the principle of individualism and of\n_laissez-faire_ as the greatest agency of civilization. These views,\namong others, I know to be obtrusive marks of a \u201cmugwump.\u201d Now, suppose\nI casually meet a man in a railway-train, and falling into conversation\nfind that he holds opinions of this sort; I am naturally led to suppose\nthat he is a \u201cmugwump.\u201d That is hypothetic inference. That is to say, a\nnumber of readily verifiable marks of a mugwump being selected, I find\nthis man has these, and infer that he has all the other characters which\ngo to make a thinker of that stripe. Or let us suppose that I meet a man\nof a semi-clerical appearance and a sub-pharisaical sniff, who appears\nto look at things from the point of view of a rather wooden dualism. He\ncites several texts of scripture and always with particular attention to\ntheir logical implications; and he exhibits a sternness, almost\namounting to vindictiveness, toward evil-doers, in general. I readily\nconclude that he is a minister of a certain denomination. Now the mind\nacts in a way similar to this, every time we acquire a power of\nco-ordinating reactions in a peculiar way, as in performing any act\nrequiring skill. Thus, most persons have a difficulty in moving the two\nhands simultaneously and in opposite directions through two parallel\ncircles nearly in the medial plane of the body. To learn to do this, it\nis necessary to attend, first, to the different actions in different\nparts of the motion, when suddenly a general conception of the action\nsprings up and it becomes perfectly easy. We think the motion we are\ntrying to do involves this action, and this, and this. Then, the general\nidea comes which unites all those actions, and thereupon the desire to\nperform the motion calls up the general idea. The same mental process is\nmany times employed whenever we are learning to speak a language or are\nacquiring any sort of skill.\n\nThus, by induction, a number of sensations followed by one reaction\nbecome united under one general idea followed by the same reaction;\nwhile by the hypothetic process, a number of reactions called for by one\noccasion get united in a general idea which is called out by the same\noccasion. By deduction, the habit fulfils its function of calling out\ncertain reactions on certain occasions.\n\n\n                      UNCERTAINTY OF MENTAL ACTION\n\n\nThe inductive and hypothetic forms of inference are essentially probable\ninferences, not necessary; while deduction may be either necessary or\nprobable.\n\nBut no mental action seems to be necessary or invariable in its\ncharacter. In whatever manner the mind has reacted under a given\nsensation, in that manner it is the more likely to react again; were\nthis, however, an absolute necessity, habits would become wooden and\nineradicable, and no room being left for the formation of new habits,\nintellectual life would come to a speedy close. Thus, the uncertainty of\nthe mental law is no mere defect of it, but is on the contrary of its\nessence. The truth is, the mind is not subject to \u201claw,\u201d in the same\nrigid sense that matter is. It only experiences gentle forces which\nmerely render it more likely to act in a given way than it otherwise\nwould be. There always remains a certain amount of arbitrary spontaneity\nin its action, without which it would be dead.\n\nSome psychologists think to reconcile the uncertainty of reactions with\nthe principle of necessary causation by means of the law of fatigue.\nTruly for a _law_, this law of fatigue is a little lawless. I think it\nis merely a case of the general principle that an idea in spreading\nloses its insistency. Put me tarragon into my salad, when I have not\ntasted it for years, and I exclaim \u201cWhat nectar is this!\u201d But add it to\nevery dish I taste for week after week, and a habit of expectation has\nbeen created; and in thus spreading into habit, the sensation makes\nhardly any more impression upon me; or, if it be noticed, it is on a new\nside from which it appears as rather a bore. The doctrine that fatigue\nis one of the primordial phenomena of mind I am much disposed to doubt.\nIt seems a somewhat little thing to be allowed as an exception to the\ngreat principle of mental uniformization. For this reason, I prefer to\nexplain it in the manner here indicated, as a special case of that great\nprinciple. To consider it as something distinct in its nature, certainly\nsomewhat strengthens the necessitarian position; but even if it be\ndistinct, the hypothesis that all the variety and apparent arbitrariness\nof mental action ought to be explained away in favor of absolute\ndeterminism does not seem to me to recommend itself to a sober and sound\njudgment, which seeks the guidance of observed facts and not that of\nprepossessions.\n\n\n                         RESTATEMENT OF THE LAW\n\n\nLet me now try to gather up all these odds and ends of commentary and\nrestate the law of mind, in a unitary way.\n\nFirst, then, we find that when we regard ideas from a nominalistic,\nindividualistic, sensualistic way, the simplest facts of mind become\nutterly meaningless. That one idea should resemble another or influence\nanother, or that one state of mind should so much as be thought of in\nanother is, from that standpoint, sheer nonsense.\n\nSecond, by this and other means we are driven to perceive, what is quite\nevident of itself, that instantaneous feelings flow together into a\ncontinuum of feeling, which has in a modified degree the peculiar\nvivacity of feeling and has gained generality. And in reference to such\ngeneral ideas, or continua of feeling, the difficulties about\nresemblance and suggestion and reference to the external, cease to have\nany force.\n\nThird, these general ideas are not mere words, nor do they consist in\nthis, that certain concrete facts will every time happen under certain\ndescriptions of conditions; but they are just as much, or rather far\nmore, living realities than the feelings themselves out of which they\nare concreted. And to say that mental phenomena are governed by law does\nnot mean merely that they are describable by a general formula; but that\nthere is a living idea, a conscious continuum of feeling, which pervades\nthem, and to which they are docile.\n\nFourth, this supreme law, which is the celestial and living harmony,\ndoes not so much as demand that the special ideas shall surrender their\npeculiar arbitrariness and caprice entirely; for that would be\nself-destructive. It only requires that they shall influence and be\ninfluenced by one another.\n\nFifth, in what measure this unification acts, seems to be regulated only\nby special rules; or, at least, we cannot in our present knowledge say\nhow far it goes. But it may be said that, judging by appearances, the\namount of arbitrariness in the phenomena of human minds is neither\naltogether trifling nor very prominent.\n\n\n                              PERSONALITY\n\n\nHaving thus endeavored to state the law of mind, in general, I descend\nto the consideration of a particular phenomenon which is remarkably\nprominent in our own consciousnesses, that of personality. A strong\nlight is thrown upon this subject by recent observations of double and\nmultiple personality. The theory which at one time seemed plausible that\ntwo persons in one body corresponded to the two halves of the brain\nwill, I take it, now be universally acknowledged to be insufficient. But\nthat which these cases make quite manifest is that personality is some\nkind of co-ordination or connection of ideas. Not much to say, this,\nperhaps. Yet when we consider that, according to the principle which we\nare tracing out, a connection between ideas is itself a general idea,\nand that a general idea is a living feeling, it is plain that we have at\nleast taken an appreciable step toward the understanding of personality.\nThis personality, like any general idea, is not a thing to be\napprehended in an instant. It has to be lived in time; nor can any\nfinite time embrace it in all its fullness. Yet in each infinitesimal\ninterval it is present and living, though specially colored by the\nimmediate feelings of that moment. Personality, so far as it is\napprehended in a moment, is immediate self-consciousness.\n\nBut the word co-ordination implies somewhat more than this; it implies a\nteleological harmony in ideas, and in the case of personality this\nteleology is more than a mere purposive pursuit of a predeterminate end;\nit is a developmental teleology. This is personal character. A general\nidea, living and conscious now, it is already determinative of acts in\nthe future to an extent to which it is not now conscious.\n\nThis reference to the future is an essential element of personality.\nWere the ends of a person already explicit, there would be no room for\ndevelopment, for growth, for life; and consequently there would be no\npersonality. The mere carrying out of predetermined purposes is\nmechanical. This remark has an application to the philosophy of\nreligion. It is that a genuine evolutionary philosophy, that is, one\nthat makes the principle of growth a primordial element of the universe,\nis so far from being antagonistic to the idea of a personal creator,\nthat it is really inseparable from that idea; while a necessitarian\nreligion is in an altogether false position and is destined to become\ndisintegrated. But a pseudo-evolutionism which enthrones mechanical law\nabove the principle of growth, is at once scientifically unsatisfactory,\nas giving no possible hint of how the universe has come about, and\nhostile to all hopes of personal relations to God.\n\n\n                             COMMUNICATION\n\n\nConsistently with the doctrine laid down in the beginning of this paper,\nI am bound to maintain that an idea can only be affected by an idea in\ncontinuous connection with it. By anything but an idea, it cannot be\naffected at all. This obliges me to say, as I do say, on other grounds,\nthat what we call matter is not completely dead, but is merely mind\nhide-bound with habits. It still retains the element of diversification;\nand in that diversification there is life. When an idea is conveyed from\none mind to another, it is by forms of combination of the diverse\nelements of nature, say by some curious symmetry, or by some union of a\ntender color with a refined odor. To such forms the law of mechanical\nenergy has no application. If they are eternal, it is in the spirit they\nembody; and their origin cannot be accounted for by any mechanical\nnecessity. They are embodied ideas; and so only can they convey ideas.\nPrecisely how primary sensations, as colors and tones, are excited, we\ncannot tell, in the present state of psychology. But in our ignorance, I\nthink that we are at liberty to suppose that they arise in essentially\nthe same manner as the other feelings, called secondary. As far as sight\nand hearing are in question, we know that they are only excited by\nvibrations of inconceivable complexity; and the chemical senses are\nprobably not more simple. Even the least psychical of peripheral\nsensations, that of pressure, has in its excitation conditions which,\nthough apparently simple, are seen to be complicated enough when we\nconsider the molecules and their attractions. The principle with which I\nset out requires me to maintain that these feelings are communicated to\nthe nerves by continuity, so that there must be something like them in\nthe excitants themselves. If this seems extravagant, it is to be\nremembered that it is the sole possible way of reaching any explanation\nof sensation, which otherwise must be pronounced a general fact,\nabsolutely inexplicable and ultimate. Now absolute inexplicability is a\nhypothesis which sound logic refuses under any circumstances to justify.\n\nI may be asked whether my theory would be favorable or otherwise to\ntelepathy. I have no decided answer to give to this. At first sight, it\nseems unfavorable. Yet there may be other modes of continuous connection\nbetween minds other than those of time and space.\n\nThe recognition by one person of another\u2019s personality takes place by\nmeans to some extent identical with the means by which he is conscious\nof his own personality. The idea of the second personality, which is as\nmuch as to say that second personality itself, enters within the field\nof direct consciousness of the first person, and is as immediately\nperceived as his ego, though less strongly. At the same time, the\nopposition between the two persons is perceived, so that the externality\nof the second is recognized.\n\nThe psychological phenomena of intercommunication between two minds have\nbeen unfortunately little studied. So that it is impossible to say, for\ncertain, whether they are favorable to this theory or not. But the very\nextraordinary insight which some persons are able to gain of others from\nindications so slight that it is difficult to ascertain what they are,\nis certainly rendered more comprehensible by the view here taken.\n\nA difficulty which confronts the synechistic philosophy is this. In\nconsidering personality, that philosophy is forced to accept the\ndoctrine of a personal God; but in considering communication, it cannot\nbut admit that if there is a personal God, we must have a direct\nperception of that person and indeed be in personal communication with\nhim. Now, if that be the case, the question arises how it is possible\nthat the existence of this being should ever have been doubted by\nanybody. The only answer that I can at present make is that facts that\nstand before our face and eyes and stare us in the face are far from\nbeing, in all cases, the ones most easily discerned. That has been\nremarked from time immemorial.\n\n\n                               CONCLUSION\n\n\nI have thus developed as well as I could in a little space the\n_synechistic_ philosophy, as applied to mind. I think that I have\nsucceeded in making it clear that this doctrine gives room for\nexplanations of many facts which without it are absolutely and\nhopelessly inexplicable; and further that it carries along with it the\nfollowing doctrines: 1st, a logical realism of the most pronounced type;\n2nd, objective idealism; 3rd, tychism, with its consequent thoroughgoing\nevolutionism. We also notice that the doctrine presents no hindrances to\nspiritual influences, such as some philosophies are felt to do.\n\nFootnote 61:\n\n  _The Monist_, July, 1892.\n\nFootnote 62:\n\n  This proposition is substantially the same as a theorem of Cantor,\n  though it is enunciated in a much more general form.\n\n\n\n\n                      IV. MAN\u2019S GLASSY ESSENCE[63]\n\n\nIn _The Monist_ for January, 1891, I tried to show what conceptions\nought to form the brick and mortar of a philosophical system. Chief\namong these was that of absolute chance for which I argued again in last\nApril\u2019s number.[64] In July, I applied another fundamental idea, that of\ncontinuity, to the law of mind. Next in order, I have to elucidate, from\nthe point of view chosen, the relation between the psychical and\nphysical aspects of a substance.\n\nThe first step towards this ought, I think, to be the framing of a\nmolecular theory of protoplasm. But before doing that, it seems\nindispensable to glance at the constitution of matter, in general. We\nshall, thus, unavoidably make a long detour; but, after all, our pains\nwill not be wasted, for the problems of the papers that are to follow in\nthe series will call for the consideration of the same question.\n\nAll physicists are rightly agreed the evidence is overwhelming which\nshows all sensible matter is composed of molecules in swift motion and\nexerting enormous mutual attractions, and perhaps repulsions, too. Even\nSir William Thomson, Lord Kelvin, who wishes to explode action at a\ndistance and return to the doctrine of a plenum, not only speaks of\nmolecules, but undertakes to assign definite magnitudes to them. The\nbrilliant Judge Stallo, a man who did not always rightly estimate his\nown qualities in accepting tasks for himself, declared war upon the\natomic theory in a book well worth careful perusal. To the old arguments\nin favor of atoms which he found in Fechner\u2019s monograph, he was able to\nmake replies of considerable force, though they were not sufficient to\ndestroy those arguments. But against modern proofs he made no headway at\nall. These set out from the mechanical theory of heat. Rumford\u2019s\nexperiments showed that heat is not a substance. Joule demonstrated that\nit was a form of energy. The heating of gases under constant volume, and\nother facts instanced by Rankine, proved that it could not be an energy\nof strain. This drove physicists to the conclusion that it was a mode of\nmotion. Then it was remembered that John Bernoulli had shown that the\npressure of gases could be accounted for by assuming their molecules to\nbe moving uniformly in rectilinear paths. The same hypothesis was now\nseen to account for Avogadro\u2019s law, that in equal volumes of different\nkinds of gases exposed to the same pressure and temperature are\ncontained equal numbers of molecules. Shortly after, it was found to\naccount for the laws of diffusion and viscosity of gases, and for the\nnumerical relation between these properties. Finally, Crookes\u2019s\nradiometer furnished the last link in the strongest chain of evidence\nwhich supports any physical hypothesis.\n\nSuch being the constitution of gases, liquids must clearly be bodies in\nwhich the molecules wander in curvilinear paths, while in solids they\nmove in orbits or quasi-orbits. (See my definition _solid_ II, 1, in the\n_Century Dictionary_.)\n\nWe see that the resistance to compression and to inter-penetration\nbetween sensible bodies is, by one of the prime propositions of the\nmolecular theory, due in large measure to the kinetical energy of the\nparticles, which must be supposed to be quite remote from one another,\non the average, even in solids. This resistance is no doubt influenced\nby finite attractions and repulsions between the molecules. All the\nimpenetrability of bodies which we can observe is, therefore, a limited\nimpenetrability due to kinetic and positional energy. This being the\ncase, we have no logical right to suppose that absolute impenetrability,\nor the exclusive occupancy of space, belongs to molecules or to atoms.\nIt is an unwarranted hypothesis, not a _vera causa_.[65] Unless we are\nto give up the theory of energy, finite positional attractions and\nrepulsions between molecules must be admitted. Absolute impenetrability\nwould amount to an infinite repulsion at a certain distance. No analogy\nof known phenomena exists to excuse such a wanton violation of the\nprinciple of continuity as such a hypothesis is. In short, we are\nlogically bound to adopt the Boscovichian idea that an atom is simply a\ndistribution of component potential energy throughout space (this\ndistribution being absolutely rigid), combined with inertia. The\npotential energy belongs to two molecules, and is to be conceived as\ndifferent between molecules _A_ and _B_ from what it is between\nmolecules _A_ and _C_. The distribution of energy is not necessarily\nspherical. Nay, a molecule may conceivably have more than one center; it\nmay even have a central curve, returning into itself. But I do not think\nthere are any observed facts pointing to such multiple or linear\ncenters. On the other hand, many facts relating to crystals, especially\nthose observed by Voigt,[66] go to show that the distribution of energy\nis harmonical but not concentric. We can easily calculate the forces\nwhich such atoms must exert upon one another by considering[67] that\nthey are equivalent to aggregations of pairs of electrically positive\nand negative points infinitely near to one another. About such an atom\nthere would be regions of positive and of negative potential, and the\nnumber and distribution of such regions would determine the valency of\nthe atom, a number which it is easy to see would in many cases be\nsomewhat indeterminate. I must not dwell further upon this hypothesis,\nat present. In another paper, its consequences will be further\nconsidered.\n\nI cannot assume that the students of philosophy who read this magazine\nare thoroughly versed in modern molecular physics, and, therefore, it is\nproper to mention that the governing principle in this branch of science\nis Clausius\u2019s law of the virial. I will first state the law, and then\nexplain the peculiar terms of the statement. This statement is that the\ntotal kinetic energy of the particles of a system in stationary motion\nis equal to the total virial. By a _system_ is here meant a number of\nparticles acting upon one another.[68] Stationary motion is a\nquasi-orbital motion among a system of particles so that none of them\nare removed to indefinitely great distances nor acquire indefinitely\ngreat velocities. The kinetic energy of a particle is the work which\nwould be required to bring it to rest, independently of any forces which\nmay be acting upon it. The virial of a pair of particles is half the\nwork which the force which actually operates between them would do if,\nbeing independent of the distance, it were to bring them together. The\nequation of the virial is\n\n                          1/2\u2211_mv_^2 = 1/2\u2211\u2211_Rr_.\n\nHere _m_ is the mass of a particle, _v_ its velocity, _R_ is the\nattraction between two particles, and _r_ is the distance between them.\nThe sign \u2211 on the left hand side signifies that the values of _mv_^2 are\nto be summed for all the particles, and \u2211\u2211 on the right hand side\nsignifies that the values of _Rr_ are to be summed for all the pairs of\nparticles. If there is an external pressure _P_ (as from the atmosphere)\nupon the system, and the volume of vacant space within the boundary of\nthat pressure is _V_, then the virial must be understood as including\n3/2_PV_, so that the equation is\n\n                     1/2\u2211_mv_^2 = 3/2_PV_ + 1/2\u2211\u2211_Rr_.\n\nThere is strong (if not demonstrative) reason for thinking that the\ntemperature of any body above the absolute zero (-273\u00b0 C.), is\nproportional to the average kinetic energy of its molecules, or say\n_a_\u03b8, where _a_ is a constant and \u03b8 is the absolute temperature. Hence,\nwe may write the equation\n\n       _a_\u03b8 = (1/2)avg(_mv_^2) = (3/2)_P_ avg(_V_) + (1/2)\u2211 avg(_Rr_)\n\nwhere the heavy lines above the different expressions signify that the\naverage values for single molecules are to be taken. In 1872, a student\nin the University of Leyden, Van der Waals, propounded in his thesis for\nthe doctorate a specialization of the equation of the virial which has\nsince attracted great attention. Namely, he writes it\n\n                    _a_\u03b8 = (_P_ + _c_/_V_^2)(_V_ - _b_.)\n\nThe quantity _b_ is the volume of a molecule, which he supposes to be an\nimpenetrable body, and all the virtue of the equation lies in this term\nwhich makes the equation a cubic in _V_, which is required to account\nfor the shape of certain isothermal curves.[69] But if the idea of an\nimpenetrable atom is illogical, that of an impenetrable molecule is\nalmost absurd. For the kinetical theory of matter teaches us that a\nmolecule is like a solar system or star-cluster in miniature. Unless we\nsuppose that in all heating of gases and vapors internal work is\nperformed upon the molecules, implying that their atoms are at\nconsiderable distances, the whole kinetical theory of gases falls to the\nground. As for the term added to _P_, there is no more than a partial\nand roughly approximative justification for it. Namely, let us imagine\ntwo spheres described round a particle as their center, the radius of\nthe larger being so great as to include all the particles whose action\nupon the center is sensible, while the radius of the smaller is so large\nthat a good many molecules are included within it. The possibility of\ndescribing such a sphere as the outer one implies that the attraction of\nthe particles varies at some distances inversely as some higher power of\nthe distance than the cube, or, to speak more clearly, that the\nattraction multiplied by the cube of the distance diminishes as the\ndistance increases; for the number of particles at a given distance from\nany one particle is proportionate to the square of that distance and\neach of these gives a term of the virial which is the product of the\nattraction into the distance. Consequently, unless the attraction\nmultiplied by the cube of the distance diminished so rapidly with the\ndistance as soon to become insensible, no such outer sphere as is\nsupposed could be described. However, ordinary experience shows that\nsuch a sphere is possible; and consequently there must be distances at\nwhich the attraction does thus rapidly diminish as the distance\nincreases. The two spheres, then, being so drawn, consider the virial of\nthe central particle due to the particles between them. Let the density\nof the substance be increased, say, _N_ times. Then, for every turn,\n_Rr_, of the virial before the condensation, there will be _N_ terms of\nthe same magnitude after the condensation. Hence, the virial of each\nparticle will be proportional to the density, and the equation of the\nvirial becomes\n\n                    _a_\u03b8 = _P_ avg(_V_) + _c_/avg(_V_).\n\nThis omits the virial within the inner sphere, the radius of which is so\ntaken that within that distance the number of particles is not\nproportional to the number in a large sphere. For Van der Waals this\nradius is the diameter of his hard molecules, which assumption gives his\nequation. But it is plain that the attraction between the molecules must\nto a certain extent modify their distribution, unless some peculiar\nconditions are fulfilled. The equation of Van der Waals can be\napproximately true, therefore, only for a gas. In a solid or liquid\ncondition, in which the removal of a small amount of pressure has little\neffect on the volume, and where consequently the virial must be much\ngreater than _P_ avg(_V_), the virial must increase with the volume. For\nsuppose we had a substance in a critical condition in which an increase\nof the volume would diminish the virial more than it would increase\n(3/2)_P_ avg(_V_). If we were forcibly to diminish the volume of such a\nsubstance, when the temperature became equalized, the pressure which it\ncould withstand would be less than before, and it would be still further\ncondensed, and this would go on indefinitely until a condition were\nreached in which an increase of volume would increase (3/2)_P_ avg(_V_)\nmore than it would decrease the virial. In the case of solids, at least,\n_P_ may be zero; so that the state reached would be one in which the\nvirial increases with the volume, or the attraction between the\nparticles does not increase so fast with a diminution of their distance\nas it would if the attraction were inversely as the distance.\n\nAlmost contemporaneously with Van der Waals\u2019s paper, another remarkable\nthesis for the doctorate was presented at Paris by Amagat. It related to\nthe elasticity and expansion of gases, and to this subject the superb\nexperimenter, its author, has devoted his whole subsequent life.\nEspecially interesting are his observations of the volumes of ethylene\nand of carbonic acid at temperatures from 20\u00b0 to 100\u00b0 and at pressures\nranging from an ounce to 5000 pounds to the square inch. As soon as\nAmagat had obtained these results, he remarked that the \u201ccoefficient of\nexpansion at constant volume,\u201d as it is absurdly called, that is, the\nrate of variation of the pressure with the temperature, was very nearly\nconstant for each volume. This accords with the equation of the virial,\nwhich gives\n\n              _dp_/_d_\u03b8 = _a_/avg(_V_) - _d_\u2211 avg(_Rr_)/_d_\u03b8.\n\nNow, the virial must be nearly independent of the temperature, and,\ntherefore, the last term almost disappears. The virial would not be\nquite independent of the temperature, because if the temperature (i.e.,\nthe square of the velocity of the molecules) is lowered, and the\npressure correspondingly lowered, so as to make the volume the same, the\nattractions of the molecules will have more time to produce their\neffects, and consequently, the pairs of molecules the closest together\nwill be held together longer and closer; so that the virial will\ngenerally be increased by a decrease of temperature. Now, Amagat\u2019s\nexperiments do show an excessively minute effect of this sort, at least,\nwhen the volumes are not too small. However, the observations are well\nenough satisfied by assuming the \u201ccoefficient of expansion at constant\nvolume\u201d to consist wholly of the first term, _a_/avg(_V_). Thus,\nAmagat\u2019s experiments enable us to determine the values of a and thence\nto calculate the virial; and this we find varies for carbonic acid gas\nnearly inversely to avg(_V_)^{0.9}. There is, thus, a rough\napproximation to satisfying Van der Waals\u2019s equation. But the most\ninteresting result of Amagat\u2019s experiments, for our purpose at any rate,\nis that the quantity _a_, though nearly constant for any one volume,\ndiffers considerably with the volume, nearly doubling when the volume is\nreduced fivefold. This can only indicate that the mean kinetic energy of\na given mass of the gas for a given temperature is greater the more the\ngas is compressed. But the laws of mechanics appear to enjoin that the\nmean kinetic energy of a moving particle shall be constant at any given\ntemperature. The only escape from contradiction, then, is to suppose\nthat the mean mass of a moving particle diminishes upon the condensation\nof the gas. In other words, many of the molecules are dissociated, or\nbroken up into atoms or sub-molecules. The idea that dissociation should\nbe favored by diminishing the volume will be pronounced by physicists,\nat first blush, as contrary to all our experience. But it must be\nremembered that the circumstances we are speaking of, that of a gas\nunder fifty or more atmospheres pressure, are also unusual. That the\n\u201ccoefficient of expansion under constant volume\u201d when multiplied by the\nvolumes should increase with a decrement of the volume is also quite\ncontrary to ordinary experience; yet it undoubtedly takes place in all\ngases under great pressure. Again, the doctrine of Arrhenius[70] is now\ngenerally accepted, that the molecular conductivity of an electrolyte is\nproportional to the dissociation of ions. Now the molecular conductivity\nof a fused electrolyte is usually superior to that of a solution. Here\nis a case, then, in which diminution of volume is accompanied by\nincreased dissociation.\n\nThe truth is that several different kinds of dissociation have to be\ndistinguished. In the first place, there is the dissociation of a\nchemical molecule to form chemical molecules under the regular action of\nchemical laws. This may be a double decomposition, as when iodhydric\nacid is dissociated, according to the formula\n\n                         _HI_ + _HI_ = _HH_ + _II_;\n\nor, it may be a simple decomposition, as when pentachloride of\nphosphorus is dissociated according to the formula\n\n                      _PCl__{5} = _PCl__{3} + _ClCl_.\n\nAll these dissociations require, according to the laws of\nthermo-chemistry, an elevated temperature. In the second place, there is\nthe dissociation of a physically polymerous molecule, that is, of\nseveral chemical molecules joined by physical attractions. This I am\ninclined to suppose is a common concomitant of the heating of solids and\nliquids; for in these bodies there is no increase of compressibility\nwith the temperature at all comparable with the increase of the\nexpansibility. But, in the third place, there is the dissociation with\nwhich we are now concerned, which must be supposed to be a throwing off\nof unsaturated sub-molecules or atoms from the molecule. The molecule\nmay, as I have said, be roughly likened to a solar system. As such,\nmolecules are able to produce perturbations of one another\u2019s internal\nmotions; and in this way a planet, i.e., a sub-molecule, will\noccasionally get thrown off and wander about by itself, till it finds\nanother unsaturated sub-molecule with which it can unite. Such\ndissociation by perturbation will naturally be favored by the proximity\nof the molecules to one another.\n\nLet us now pass to the consideration of that special substance, or\nrather class of substances, whose properties form the chief subject of\nbotany and of zo\u00f6logy, as truly as those of the silicates form the chief\nsubject of mineralogy: I mean the life-slimes, or protoplasm. Let us\nbegin by cataloguing the general characters of these slimes. They one\nand all exist in two states of aggregation, a solid or nearly solid\nstate and a liquid or nearly liquid state; but they do not pass from the\nformer to the latter by ordinary fusion. They are readily decomposed by\nheat, especially in the liquid state; nor will they bear any\nconsiderable degree of cold. All their vital actions take place at\ntemperatures very little below the point of decomposition. This extreme\ninstability is one of numerous facts which demonstrate the chemical\ncomplexity of protoplasm. Every chemist will agree that they are far\nmore complicated than the albumens. Now, albumen is estimated to contain\nin each molecule about a thousand atoms; so that it is natural to\nsuppose that the protoplasms contain several thousands. We know that\nwhile they are chiefly composed of oxygen, hydrogen, carbon, and\nnitrogen, a large number of other elements enter into living bodies in\nsmall proportions; and it is likely that most of these enter into the\ncomposition of protoplasms. Now, since the numbers of chemical varieties\nincrease at an enormous rate with the number of atoms per molecule, so\nthat there are certainly hundreds of thousands of substances whose\nmolecules contain twenty atoms or fewer, we may well suppose that the\nnumber of protoplasmic substances runs into the billions or trillions.\nProfessor Cayley has given a mathematical theory of \u201ctrees,\u201d with a view\nof throwing a light upon such questions; and in that light the estimate\nof trillions (in the English sense) seems immoderately moderate. It is\ntrue that an opinion has been emitted, and defended among biologists,\nthat there is but one kind of protoplasm; but the observations of\nbiologists, themselves, have almost exploded that hypothesis, which from\na chemical standpoint appears utterly incredible. The anticipation of\nthe chemist would decidedly be that enough different chemical substances\nhaving protoplasmic characters might be formed to account, not only for\nthe differences between nerve-slime and muscle-slime, between\nwhale-slime and lion-slime, but also for those minuter pervasive\nvariations which characterize different breeds and single individuals.\n\nProtoplasm, when quiescent, is, broadly speaking, solid; but when it is\ndisturbed in an appropriate way, or sometimes even spontaneously without\nexternal disturbance, it becomes, broadly speaking, liquid. A moner in\nthis state is seen under the microscope to have streams within its\nmatter; a slime-mould slowly flows by force of gravity. The liquefaction\nstarts from the point of disturbance and spreads through the mass. This\nspreading, however, is not uniform in all directions; on the contrary,\nit takes at one time one course, at another another, through the\nhomogeneous mass, in a manner that seems a little mysterious. The cause\nof disturbance being removed, these motions gradually (with higher kinds\nof protoplasm, quickly) cease, and the slime returns to its solid\ncondition.\n\nThe liquefaction of protoplasm is accompanied by a mechanical\nphenomenon. Namely, some kinds exhibit a tendency to draw themselves up\ninto a globular form. This happens particularly with the contents of\nmuscle-cells. The prevalent opinion, founded on some of the most\nexquisite experimental investigations that the history of science can\nshow, is undoubtedly that the contraction of muscle-cells is due to\nosmotic pressure; and it must be allowed that that is a factor in\nproducing the effect. But it does not seem to me that it satisfactorily\naccounts even for the phenomena of muscular contraction; and besides,\neven naked slimes often draw up in the same way. In this case, we seem\nto recognize an increase of the surface-tension. In some cases, too, the\nreverse action takes place, extraordinary pseudopodia being put forth,\nas if the surface-tension were diminished in spots. Indeed, such a slime\nalways has a sort of skin, due no doubt to surface-tension, and this\nseems to give way at the point where a pseudopodium is put forth.\n\nLong-continued or frequently repeated liquefaction of the protoplasm\nresults in an obstinate retention of the solid state, which we call\nfatigue. On the other hand, repose in this state, if not too much\nprolonged, restores the liquefiability. These are both important\nfunctions.\n\nThe life-slimes have, further, the peculiar property of growing.\nCrystals also grow; their growth, however, consists merely in attracting\nmatter like their own from the circumambient fluid. To suppose the\ngrowth of protoplasm of the same nature, would be to suppose this\nsubstance to be spontaneously generated in copious supplies wherever\nfood is in solution. Certainly, it must be granted that protoplasm is\nbut a chemical substance, and that there is no reason why it should not\nbe formed synthetically like any other chemical substance. Indeed,\nClifford has clearly shown that we have overwhelming evidence that it is\nso formed. But to say that such formation is as regular and frequent as\nthe assimilation of food is quite another matter. It is more consonant\nwith the facts of observation to suppose that assimilated protoplasm is\nformed at the instant of assimilation, under the influence of the\nprotoplasm already present. For each slime in its growth preserves its\ndistinctive characters with wonderful truth, nerve-slime growing\nnerve-slime and muscle-slime muscle-slime, lion-slime growing\nlion-slime, and all the varieties of breeds and even individual\ncharacters being preserved in the growth. Now it is too much to suppose\nthere are billions of different kinds of protoplasm floating about\nwherever there is food.\n\nThe frequent liquefaction of protoplasm increases its power of\nassimilating food; so much so, indeed, that it is questionable whether\nin the solid form it possesses this power.\n\nThe life-slime wastes as well as grows; and this too takes place chiefly\nif not exclusively in its liquid phases.\n\nClosely connected with growth is reproduction; and though in higher\nforms this is a specialized function, it is universally true that\nwherever there is protoplasm, there is, will be, or has been a power of\nreproducing that same kind of protoplasm in a separated organism.\nReproduction seems to involve the union of two sexes; though it is not\ndemonstrable that this is always requisite.\n\nAnother physical property of protoplasm is that of taking habits. The\ncourse which the spread of liquefaction has taken in the past is\nrendered thereby more likely to be taken in the future; although there\nis no absolute certainly that the same path will be followed again.\n\nVery extraordinary, certainly, are all these properties of protoplasm;\nas extraordinary as indubitable. But the one which has next to be\nmentioned, while equally undeniable, is infinitely more wonderful. It is\nthat protoplasm feels. We have no direct evidence that this is true of\nprotoplasm universally, and certainly some kinds feel far more than\nothers. But there is a fair analogical inference that all protoplasm\nfeels. It not only feels but exercises all the functions of mind.\n\nSuch are the properties of protoplasm. The problem is to find a\nhypothesis of the molecular constitution of this compound which will\naccount for these properties, one and all.\n\nSome of them are obvious results of the excessively complicated\nconstitution of the protoplasm molecule. All very complicated substances\nare unstable; and plainly a molecule of several thousand atoms may be\nseparated in many ways into two parts in each of which the polar\nchemical forces are very nearly saturated. In the solid protoplasm, as\nin other solids, the molecules must be supposed to be moving as it were\nin orbits, or, at least, so as not to wander indefinitely. But this\nsolid cannot be melted, for the same reason that starch cannot be\nmelted; because an amount of heat insufficient to make the entire\nmolecules wander is sufficient to break them up completely and cause\nthem to form new and simpler molecules. But when one of the molecules is\ndisturbed, even if it be not quite thrown out of its orbit at first,\nsub-molecules of perhaps several hundred atoms each are thrown off from\nit. These will soon acquire the same mean kinetic energy as the others,\nand, therefore, velocities several times as great. They will naturally\nbegin to wander, and in wandering will perturb a great many other\nmolecules and cause them in their turn to behave like the one originally\nderanged. So many molecules will thus be broken up, that even those that\nare intact will no longer be restrained within orbits, but will wander\nabout freely. This is the usual condition of a liquid, as modern\nchemists understand it; for in all electrolytic liquids there is\nconsiderable dissociation.\n\nBut this process necessarily chills the substance, not merely on account\nof the heat of chemical combination, but still more because the number\nof separate particles being greatly increased, the mean kinetic energy\nmust be less. The substance being a bad conductor, this heat is not at\nonce restored. Now the particles moving more slowly, the attractions\nbetween them have time to take effect, and they approach the condition\nof equilibrium. But their dynamic equilibrium is found in the\nrestoration of the solid condition, which, therefore, takes place, if\nthe disturbance is not kept up.\n\nWhen a body is in the solid condition, most of its molecules must be\nmoving at the same rate, or, at least, at certain regular sets of rates;\notherwise the orbital motion would not be preserved. The distances of\nneighboring molecules must always be kept between a certain maximum and\na certain minimum value. But if, without absorption of heat, the body be\nthrown into a liquid condition, the distances of neighboring molecules\nwill be far more unequally distributed, and an effect upon the virial\nwill result. The chilling of protoplasm upon its liquefaction must also\nbe taken into account. The ordinary effect will no doubt be to increase\nthe cohesion and with that the surface-tension, so that the mass will\ntend to draw itself up. But in special cases, the virial will be\nincreased so much that the surface-tension will be diminished at points\nwhere the temperature is first restored. In that case, the outer film\nwill give way and the tension at other places will aid in causing the\ngeneral fluid to be poured out at those points, forming pseudopodia.\n\nWhen the protoplasm is in a liquid state, and then only, a solution of\nfood is able to penetrate its mass by diffusion. The protoplasm is then\nconsiderably dissociated; and so is the food, like all dissolved matter.\nIf then the separated and unsaturated sub-molecules of the food happen\nto be of the same chemical species as sub-molecules of the protoplasm,\nthey may unite with other sub-molecules of the protoplasm to form new\nmolecules, in such a fashion that when the solid state is resumed, there\nmay be more molecules of protoplasm than there were at the beginning. It\nis like the jackknife whose blade and handle, after having been\nseverally lost and replaced, were found and put together to make a new\nknife.\n\nWe have seen that protoplasm is chilled by liquefaction, and that this\nbrings it back to the solid state, when the heat is recovered. This\nseries of operations must be very rapid in the case of nerve-slime and\neven of muscle-slime, and may account for the unsteady or vibratory\ncharacter of their action. Of course, if assimilation takes place, the\nheat of combination, which is probably trifling, is gained. On the other\nhand, if work is done, whether by nerve or by muscle, loss of energy\nmust take place. In the case of the muscle, the mode by which the\ninstantaneous part of the fatigue is brought about is easily traced out.\nIf when the muscle contracts it be under stress, it will contract less\nthan it otherwise would do, and there will be a loss of heat. It is like\nan engine which should work by dissolving salt in water and using the\ncontraction during the solution to lift a weight, the salt being\nrecovered afterwards by distillation. But the major part of fatigue has\nnothing to do with the correlation of forces. A man must labor hard to\ndo in a quarter of an hour the work which draws from him enough heat to\ncool his body by a single degree. Meantime, he will be getting heated,\nhe will be pouring out extra products of combustion, perspiration, etc.,\nand he will be driving the blood at an accelerated rate through minute\ntubes at great expense. Yet all this will have little to do with his\nfatigue. He may sit quietly at his table writing, doing practically no\nphysical work at all, and yet in a few hours be terribly fagged. This\nseems to be owing to the deranged sub-molecules of the nerve-slime not\nhaving had time to settle back into their proper combinations. When such\nsub-molecules are thrown out, as they must be from time to time, there\nis so much waste of material.\n\nIn order that a sub-molecule of food may be thoroughly and firmly\nassimilated into a broken molecule of protoplasm, it is necessary not\nonly that it should have precisely the right chemical composition, but\nalso that it should be at precisely the right spot at the right time and\nshould be moving in precisely the right direction with precisely the\nright velocity. If all these conditions are not fulfilled, it will be\nmore loosely retained than the other parts of the molecule; and every\ntime it comes round into the situation in which it was drawn in,\nrelatively to the other parts of that molecule and to such others as\nwere near enough to be factors in the action, it will be in special\ndanger of being thrown out again. Thus, when a partial liquefaction of\nthe protoplasm takes place many times to about the same extent, it will,\neach time, be pretty nearly the same molecules that were last drawn in\nthat are now thrown out. They will be thrown out, too, in about the same\nway, as to position, direction of motion, and velocity, in which they\nwere drawn in; and this will be in about the same course that the ones\nlast before them were thrown out. Not exactly, however; for the very\ncause of their being thrown off so easily is their not having fulfilled\nprecisely the conditions of stable retention. Thus, the law of habit is\naccounted for, and with it its peculiar characteristic of not acting\nwith exactitude.\n\nIt seems to me that this explanation of habit, aside from the question\nof its truth or falsity, has a certain value as an addition to our\nlittle store of mechanical examples of actions analogous to habit. All\nthe others, so far as I know, are either statical or else involve forces\nwhich, taking only the sensible motions into account, violate the law of\nenergy. It is so with the stream that wears its own bed. Here, the sand\nis carried to its most stable situation and left there. The law of\nenergy forbids this; for when anything reaches a position of stable\nequilibrium, its momentum will be at a maximum, so that it can according\nto this law only be left at rest in an unstable situation. In all the\nstatical illustrations, too, things are brought into certain states and\nleft there. A garment receives folds and keeps them; that is, its limit\nof elasticity is exceeded. This failure to spring back is again an\napparent violation of the law of energy; for the substance will not only\nnot spring back of itself (which might be due to an unstable equilibrium\nbeing reached) but will not even do so when an impulse that way is\napplied to it. Accordingly, Professor James says, \u201cthe phenomena of\nhabit ... are due to the plasticity of the ... materials.\u201d Now,\nplasticity of materials means the having of a low limit of elasticity.\n(See the _Century Dictionary_, under _solid_.) But the hypothetical\nconstitution of protoplasm here proposed involves no forces but\nattractions and repulsions strictly following the law of energy. The\naction here, that is, the throwing of an atom out of its orbit in a\nmolecule, and the entering of a new atom into nearly, but not quite the\nsame orbit, is somewhat similar to the molecular actions which may be\nsupposed to take place in a solid strained beyond its limit of\nelasticity. Namely, in that case certain molecules must be thrown out of\ntheir orbits, to settle down again shortly after into new orbits. In\nshort, the plastic solid resembles protoplasm in being partially and\ntemporarily liquefied by a slight mechanical force. But the taking of a\nset by a solid body has but a moderate resemblance to the taking of a\nhabit, inasmuch as the characteristic feature of the latter, its\ninexactitude and want of complete determinacy, is not so marked in the\nformer, if it can be said to be present there, at all.\n\nThe truth is that though the molecular explanation of habit is pretty\nvague on the mathematical side, there can be no doubt that systems of\natoms having polar forces would act substantially in that manner, and\nthe explanation is even too satisfactory to suit the convenience of an\nadvocate of tychism. For it may fairly be urged that since the phenomena\nof habit may thus result from a purely mechanical arrangement, it is\nunnecessary to suppose that habit-taking is a primordial principle of\nthe universe. But one fact remains unexplained mechanically, which\nconcerns not only the facts of habit, but all cases of actions\napparently violating the law of energy; it is that all these phenomena\ndepend upon aggregations of trillions of molecules in one and the same\ncondition and neighborhood; and it is by no means clear how they could\nhave all been brought and left in the same place and state by any\nconservative forces. But let the mechanical explanation be as perfect as\nit may, the state of things which it supposes presents evidence of a\nprimordial habit-taking tendency. For it shows us like things acting in\nlike ways because they are alike. Now, those who insist on the doctrine\nof necessity will for the most part insist that the physical world is\nentirely individual. Yet law involves an element of generality. Now to\nsay that generality is primordial, but generalization not, is like\nsaying that diversity is primordial but diversification not. It turns\nlogic upside down. At any rate, it is clear that nothing but a principle\nof habit, itself due to the growth by habit of an infinitesimal chance\ntendency toward habit-taking, is the only bridge that can span the chasm\nbetween the chance-medley of chaos and the cosmos of order and law.\n\nI shall not attempt a molecular explanation of the phenomena of\nreproduction, because that would require a subsidiary hypothesis, and\ncarry me away from my main object. Such phenomena, universally diffused\nthough they be, appear to depend upon special conditions; and we do not\nfind that all protoplasm has reproductive powers.\n\nBut what is to be said of the property of feeling? If consciousness\nbelongs to all protoplasm, by what mechanical constitution is this to be\naccounted for? The slime is nothing but a chemical compound. There is no\ninherent impossibility in its being formed synthetically in the\nlaboratory, out of its chemical elements; and if it were so made, it\nwould present all the characters of natural protoplasm. No doubt, then,\nit would feel. To hesitate to admit this would be puerile and\nultra-puerile. By what element of the molecular arrangement, then, would\nthat feeling be caused? This question cannot be evaded or pooh-poohed.\nProtoplasm certainly does feel; and unless we are to accept a weak\ndualism, the property must be shown to arise from some peculiarity of\nthe mechanical system. Yet the attempt to deduce it from the three laws\nof mechanics, applied to never so ingenious a mechanical contrivance,\nwould obviously be futile. It can never be explained, unless we admit\nthat physical events are but degraded or undeveloped forms of psychical\nevents. But once grant that the phenomena of matter are but the result\nof the sensibly complete sway of habits upon mind, and it only remains\nto explain why in the protoplasm these habits are to some slight extent\nbroken up, so that according to the law of mind, in that special clause\nof it sometimes called the principle of accommodation,[71] feeling\nbecomes intensified. Now the manner in which habits generally get broken\nup is this. Reactions usually terminate in the removal of a stimulus;\nfor the excitation continues as long as the stimulus is present.\nAccordingly, habits are general ways of behavior which are associated\nwith the removal of stimuli. But when the expected removal of the\nstimulus fails to occur, the excitation continues and increases, and\nnon-habitual reactions take place; and these tend to weaken the habit.\nIf, then, we suppose that matter never does obey its ideal laws with\nabsolute precision, but that there are almost insensible fortuitous\ndepartures from regularity, these will produce, in general, equally\nminute effects. But protoplasm is in an excessively unstable condition;\nand it is the characteristic of unstable equilibrium, that near that\npoint excessively minute causes may produce startlingly large effects.\nHere, then, the usual departures from regularity will be followed by\nothers that are very great; and the large fortuitous departures from law\nso produced, will tend still further to break up the laws, supposing\nthat these are of the nature of habits. Now, this breaking up of habit\nand renewed fortuitous spontaneity will, according to the law of mind,\nbe accompanied by an intensification of feeling. The nerve-protoplasm\nis, without doubt, in the most unstable condition of any kind of matter;\nand consequently, there the resulting feeling is the most manifest.\n\nThus we see that the idealist has no need to dread a mechanical theory\nof life. On the contrary, such a theory, fully developed, is bound to\ncall in a tychistic idealism as its indispensable adjunct. Wherever\nchance-spontaneity is found, there, in the same proportion, feeling\nexists. In fact, chance is but the outward aspect of that which within\nitself is feeling. I long ago showed that real existence, or thing-ness,\nconsists in regularities. So, that primeval chaos in which there was no\nregularity was mere nothing, from a physical aspect. Yet it was not a\nblank zero; for there was an intensity of consciousness there in\ncomparison with which all that we ever feel is but as the struggling of\na molecule or two to throw off a little of the force of law to an\nendless and innumerable diversity of chance utterly unlimited.\n\nBut after some atoms of the protoplasm have thus become partially\nemancipated from law, what happens next to them? To understand this, we\nhave to remember that no mental tendency is so easily strengthened by\nthe action of habit as is the tendency to take habits. Now, in the\nhigher kinds of protoplasm, especially, the atoms in question have not\nonly long belonged to one molecule or another of the particular mass of\nslime of which they are parts; but before that, they were constituents\nof food of a protoplasmic constitution. During all this time, they have\nbeen liable to lose habits and to recover them again; so that now, when\nthe stimulus is removed, and the foregone habits tend to reassert\nthemselves, they do so in the case of such atoms with great promptness.\nIndeed, the return is so prompt that there is nothing but the feeling to\nshow conclusively that the bonds of law have ever been relaxed.\n\nIn short, diversification is the vestige of chance-spontaneity; and\nwherever diversity is increasing, there chance must be operative. On the\nother hand, wherever uniformity is increasing, habit must be operative.\nBut wherever actions take place under an established uniformity, there\nso much feeling as there may be takes the mode of a sense of reaction.\nThat is the manner in which I am led to define the relation between the\nfundamental elements of consciousness and their physical equivalents.\n\nIt remains to consider the physical relations of general ideas. It may\nbe well here to reflect that if matter has no existence except as a\nspecialization of mind, it follows that whatever affects matter\naccording to regular laws is itself matter. But all mind is directly or\nindirectly connected with all matter, and acts in a more or less regular\nway; so that all mind more or less partakes of the nature of matter.\nHence, it would be a mistake to conceive of the psychical and the\nphysical aspects of matter as two aspects absolutely distinct. Viewing a\nthing from the outside, considering its relations of action and reaction\nwith other things, it appears as matter. Viewing it from the inside,\nlooking at its immediate character as feeling, it appears as\nconsciousness. These two views are combined when we remember that\nmechanical laws are nothing but acquired habits, like all the\nregularities of mind, including the tendency to take habits, itself; and\nthat this action of habit is nothing but generalization, and\ngeneralization is nothing but the spreading of feelings. But the\nquestion is, how do general ideas appear in the molecular theory of\nprotoplasm?\n\nThe consciousness of a habit involves a general idea. In each action of\nthat habit certain atoms get thrown out of their orbit, and replaced by\nothers. Upon all the different occasions it is different atoms that are\nthrown off, but they are analogous from a physical point of view, and\nthere is an inward sense of their being analogous. Every time one of the\nassociated feelings recurs, there is a more or less vague sense that\nthere are others, that it has a general character, and of about what\nthis general character is. We ought not, I think, to hold that in\nprotoplasm habit never acts in any other than the particular way\nsuggested above. On the contrary, if habit be a primary property of\nmind, it must be equally so of matter, as a kind of mind. We can hardly\nrefuse to admit that wherever chance motions have general characters,\nthere is a tendency for this generality to spread and to perfect itself.\nIn that case, a general idea is a certain modification of consciousness\nwhich accompanies any regularity or general relation between chance\nactions.\n\nThe consciousness of a general idea has a certain \u201cunity of the ego,\u201d in\nit, which is identical when it passes from one mind to another. It is,\ntherefore, quite analogous to a person; and, indeed, a person is only a\nparticular kind of general idea. Long age, in the _Journal of\nSpeculative Philosophy_ (Vol. II, p. 156), I pointed out that a person\nis nothing but a symbol involving a general idea; but my views were,\nthen, too nominalistic to enable me to see that every general idea has\nthe unified living feeling of a person.\n\nAll that is necessary, upon this theory, to the existence of a person is\nthat the feelings out of which he is constructed should be in close\nenough connection to influence one another. Here we can draw a\nconsequence which it may be possible to submit to experimental test.\nNamely, if this be the case, there should be something like personal\nconsciousness in bodies of men who are in intimate and intensely\nsympathetic communion. It is true that when the generalization of\nfeeling has been carried so far as to include all within a person, a\nstopping-place, in a certain sense, has been attained; and further\ngeneralization will have a less lively character. But we must not think\nit will cease. _Esprit de corps_, national sentiment, sympathy, are no\nmere metaphors. None of us can fully realize what the minds of\ncorporations are, any more than one of my brain-cells can know what the\nwhole brain is thinking. But the law of mind clearly points to the\nexistence of such personalities, and there are many ordinary\nobservations which, if they were critically examined and supplemented by\nspecial experiments, might, as first appearances promise, give evidence\nof the influence of such greater persons upon individuals. It is often\nremarked that on one day half a dozen people, strangers to one another,\nwill take it into their heads to do one and the same strange deed,\nwhether it be a physical experiment, a crime, or an act of virtue. When\nthe thirty thousand young people of the society for Christian Endeavor\nwere in New York, there seemed to me to be some mysterious diffusion of\nsweetness and light. If such a fact is capable of being made out\nanywhere, it should be in the church. The Christians have always been\nready to risk their lives for the sake of having prayers in common, of\ngetting together and praying simultaneously with great energy, and\nespecially for their common body, for \u201cthe whole state of Christ\u2019s\nchurch militant here in earth,\u201d as one of the missals has it. This\npractice they have been keeping up everywhere, weekly, for many\ncenturies. Surely, a personality ought to have developed in that church,\nin that \u201cbride of Christ,\u201d as they call it, or else there is a strange\nbreak in the action of mind, and I shall have to acknowledge my views\nare much mistaken. Would not the societies for psychical research be\nmore likely to break through the clouds, in seeking evidences of such\ncorporate personality, than in seeking evidences of telepathy, which,\nupon the same theory, should be a far weaker phenomenon?\n\nFootnote 63:\n\n  _The Monist_, October, 1892.\n\nFootnote 64:\n\n  I am rejoiced to find, since my last paper was printed, that a\n  philosopher as subtle and profound as Dr. Edmund Montgomery has long\n  been arguing for the same element in the universe. Other\n  world-renowned thinkers, as M. Renouvier and M. Delb\u0153uf, appear to\n  share this opinion.\n\nFootnote 65:\n\n  By a _vera causa_, in the logic of science, is meant a state of things\n  known to exist in some cases and supposed to exist in other cases,\n  because it would account for observed phenomena.\n\nFootnote 66:\n\n  Wiedemann, _Annalen_, 1887-1889.\n\nFootnote 67:\n\n  See Maxwell on Spherical Harmonics, in his _Electricity and\n  Magnetism_.\n\nFootnote 68:\n\n  The word _system_ has three peculiar meanings in mathematics. (_A._)\n  It means an orderly exposition of the truths of astronomy, and hence a\n  theory of the motions of the stars; as the Ptolemaic _system_, the\n  Copernican _system_. This is much like the sense in which we speak of\n  the Calvinistic _system_ of theology, the Kantian _system_ of\n  philosophy, etc. (_B._) It means the aggregate of the planets\n  considered as all moving in somewhat the same way, as the solar\n  _system_; and hence any aggregate of particles moving under mutual\n  forces. (_C._) It means a number of forces acting simultaneously upon\n  a number of particles.\n\nFootnote 69:\n\n  But, in fact, an inspection of these curves is sufficient to show that\n  they are of a higher degree than the third. For they have the line _V_\n  = O, or some line _V_ a constant for an asymptote, while for small\n  values of _P_, the values of _d_^2_p_/(_dV_)^2 are positive.\n\nFootnote 70:\n\n  Anticipated by Clausius as long ago as 1857; and by Williamson in\n  1851.\n\nFootnote 71:\n\n  \u201cPhysiologically, ... accommodation means the breaking up of a\n  habit.... Psychologically, it means reviving consciousness.\u201d Baldwin,\n  _Psychology_, Part III, ch. i., \u00a7 5.\n\n\n\n\n                        V. EVOLUTIONARY LOVE[72]\n                    AT FIRST BLUSH. COUNTER-GOSPELS\n\n\nPhilosophy, when just escaping from its golden pupa-skin, mythology,\nproclaimed the great evolutionary agency of the universe to be Love. Or,\nsince this pirate-lingo, English, is poor in such-like words, let us say\nEros, the exuberance-love. Afterwards, Empedocles set up passionate-love\nand hate as the two co-ordinate powers of the universe. In some\npassages, kindness is the word. But certainly, in any sense in which it\nhas an opposite, to be senior partner of that opposite, is the highest\nposition that love can attain. Nevertheless, the ontological gospeller,\nin whose days those views were familiar topics, made the One Supreme\nBeing, by whom all things have been made out of nothing, to be\ncherishing-love. What, then, can he say to hate? Never mind, at this\ntime, what the scribe of the apocalypse, if he were John, stung at\nlength by persecution into a rage unable to distinguish suggestions of\nevil from visions of heaven, and so become the Slanderer of God to men,\nmay have dreamed. The question is rather what the sane John thought, or\nought to have thought, in order to carry out his idea consistently. His\nstatement that God is love seems aimed at that saying of Ecclesiastes\nthat we cannot tell whether God bears us love or hatred. \u201cNay,\u201d says\nJohn, \u201cwe can tell, and very simply! We know and have trusted the love\nwhich God hath in us. God is love.\u201d There is no logic in this, unless it\nmeans that God loves all men. In the preceding paragraph, he had said,\n\u201cGod is light and in him is no darkness at all.\u201d We are to understand,\nthen, that as darkness is merely the defect of light, so hatred and evil\nare mere imperfect stages of \u1f00\u03b3\u1f00\u03c0\u03b7 and \u1f00\u03b3\u03b1\u03b8\u03cc\u03bd, love and loveliness. This\nconcords with that utterance reported in John\u2019s Gospel: \u201cGod sent not\nthe Son into the world to judge the world; but that the world should\nthrough him be saved. He that believeth on him is not judged: he that\nbelieveth not hath been judged already.... And this is the judgment,\nthat the light is come into the world, and that men loved darkness\nrather than the light.\u201d That is to say, God visits no punishment on\nthem; they punish themselves, by their natural affinity for the\ndefective. Thus, the love that God is, is not a love of which hatred is\nthe contrary; otherwise Satan would be a co-ordinate power; but it is a\nlove which embraces hatred as an imperfect stage of it, an Anteros\u2014yea,\neven needs hatred and hatefulness as its object. For self-love is no\nlove; so if God\u2019s self is love, that which he loves must be defect of\nlove; just as a luminary can light up only that which otherwise would be\ndark. Henry James, the Swedenborgian, says: \u201cIt is no doubt very\ntolerable finite or creaturely love to love one\u2019s own in another, to\nlove another for his conformity to one\u2019s self: but nothing can be in\nmore flagrant contrast with the creative Love, all whose tenderness _ex\nvi termini_ must be reserved only for what intrinsically is most\nbitterly hostile and negative to itself.\u201d This is from _Substance and\nShadow_: an _Essay on the Physics of Creation_. It is a pity he had not\nfilled his pages with things like this, as he was able easily to do,\ninstead of scolding at his reader and at people generally, until the\nphysics of creation was well-nigh forgot. I must deduct, however, from\nwhat I just wrote: obviously no genius could make his every sentence as\nsublime as one which discloses for the problem of evil its everlasting\nsolution.\n\nThe movement of love is circular, at one and the same impulse projecting\ncreations into independency and drawing them into harmony. This seems\ncomplicated when stated so; but it is fully summed up in the simple\nformula we call the Golden Rule. This does not, of course, say, Do\neverything possible to gratify the egoistic impulses of others, but it\nsays, Sacrifice your own perfection to the perfectionment of your\nneighbor. Nor must it for a moment be confounded with the Benthamite, or\nHelvetian, or Beccarian motto, Act for the greatest good of the greatest\nnumber. Love is not directed to abstractions but to persons; not to\npersons we do not know, nor to numbers of people, but to our own dear\nones, our family and neighbors. \u201cOur neighbor,\u201d we remember, is one whom\nwe live near, not locally perhaps, but in life and feeling.\n\nEverybody can see that the statement of St. John is the formula of an\nevolutionary philosophy, which teaches that growth comes only from love,\nfrom\u2014I will not say self-_sacrifice_, but from the ardent impulse to\nfulfil another\u2019s highest impulse. Suppose, for example, that I have an\nidea that interests me. It is my creation. It is my creature; for as\nshown in last July\u2019s _Monist_, it is a little person. I love it; and I\nwill sink myself in perfecting it. It is not by dealing out cold justice\nto the circle of my ideas that I can make them grow, but by cherishing\nand tending them as I would the flowers in my garden. The philosophy we\ndraw from John\u2019s gospel is that this is the way mind develops; and as\nfor the cosmos, only so far as it yet is mind, and so has life, is it\ncapable of further evolution. Love, recognizing germs of loveliness in\nthe hateful, gradually warms it into life, and makes it lovely. That is\nthe sort of evolution which every careful student of my essay _The Law\nof Mind_, must see that _synechism_ calls for.\n\nThe nineteenth century is now fast sinking into the grave, and we all\nbegin to review its doings and to think what character it is destined to\nbear as compared with other centuries in the minds of future historians.\nIt will be called, I guess, the Economical Century; for political\neconomy has more direct relations with all the branches of its activity\nthan has any other science. Well, political economy has its formula of\nredemption, too. It is this: Intelligence in the service of greed\nensures the justest prices, the fairest contracts, the most enlightened\nconduct of all the dealings between men, and leads to the _summum\nbonum_, food in plenty and perfect comfort. Food for whom? Why, for the\ngreedy master of intelligence. I do not mean to say that this is one of\nthe legitimate conclusions of political economy, the scientific\ncharacter of which I fully acknowledge. But the study of doctrines,\nthemselves true, will often temporarily encourage generalizations\nextremely false, as the study of physics has encouraged\nnecessitarianism. What I say, then, is that the great attention paid to\neconomical questions during our century has induced an exaggeration of\nthe beneficial effects of greed and of the unfortunate results of\nsentiment, until there has resulted a philosophy which comes unwittingly\nto this, that greed is the great agent in the elevation of the human\nrace and in the evolution of the universe.\n\nI open a handbook of political economy,\u2014the most typical and middling\none I have at hand,\u2014and there find some remarks of which I will here\nmake a brief analysis. I omit qualifications, sops thrown to Cerberus,\nphrases to placate Christian prejudice, trappings which serve to hide\nfrom author and reader alike the ugly nakedness of the greed-god. But I\nhave surveyed my position. The author enumerates \u201cthree motives to human\naction:\n\nThe love of self;\n\nThe love of a limited class having common interests and feelings with\none\u2019s self;\n\nThe love of mankind at large.\u201d\n\nRemark, at the outset, what obsequious title is bestowed on greed,\u2014\u201cthe\nlove of self.\u201d Love! The second motive _is_ love. In place of \u201ca limited\nclass\u201d put \u201ccertain persons,\u201d and you have a fair description. Taking\n\u201cclass\u201d in the old-fashioned sense, a weak kind of love is described. In\nthe sequel, there seems to be some haziness as to the delimitation of\nthis motive. By the love of mankind at large, the author does not mean\nthat deep, subconscious passion that is properly so called; but merely\npublic-spirit, perhaps little more than a fidget about pushing ideas.\nThe author proceeds to a comparative estimate of the worth of these\nmotives. Greed, says he, but using, of course, another word, \u201cis not so\ngreat an evil as is commonly supposed... Every man can promote his own\ninterests a great deal more effectively than he can promote any one\nelse\u2019s, or than any one else can promote his.\u201d Besides, as he remarks on\nanother page, the more miserly a man is, the more good he does. The\nsecond motive \u201cis the most dangerous one to which society is exposed.\u201d\nLove is all very pretty: \u201cno higher or purer source of human happiness\nexists.\u201d (Ahem!) But it is a \u201csource of enduring injury,\u201d and, in short,\nshould be overruled by something wiser. What is this wiser motive? We\nshall see.\n\nAs for public spirit, it is rendered nugatory by the \u201cdifficulties in\nthe way of its effective operation.\u201d For example, it might suggest\nputting checks upon the fecundity of the poor and the vicious; and \u201cno\nmeasure of repression would be too severe,\u201d in the case of criminals.\nThe hint is broad. But unfortunately, you cannot induce legislatures to\ntake such measures, owing to the pestiferous \u201ctender sentiments of man\ntowards man.\u201d It thus appears, that public-spirit, or Benthamism, is not\nstrong enough to be the effective tutor of love, (I am skipping to\nanother page), which must, therefore, be handed over to \u201cthe motives\nwhich animate men in the pursuit of wealth,\u201d in which alone we can\nconfide, and which \u201care in the highest degree beneficent.\u201d[73] Yes, in\nthe \u201chighest degree\u201d without exception are they beneficent to the being\nupon whom all their blessings are poured out, namely, the Self, whose\n\u201csole object,\u201d says the writer in accumulating wealth is his individual\n\u201csustenance and enjoyment.\u201d Plainly, the author holds the notion that\nsome other motive might be in a higher degree beneficent even for the\nman\u2019s self to be a paradox wanting in good sense. He seeks to gloze and\nmodify his doctrine; but he lets the perspicacious reader see what his\nanimating principle is; and when, holding the opinions I have repeated,\nhe at the same time acknowledges that society could not exist upon a\nbasis of intelligent greed alone, he simply pigeon-holes himself as one\nof the eclectics of inharmonious opinions. He wants his mammon flavored\nwith a _soup\u00e7on_ of god.\n\nThe economists accuse those to whom the enunciation of their atrocious\nvillainies communicates a thrill of horror of being _sentimentalists_.\nIt may be so: I willingly confess to having some tincture of\nsentimentalism in me, God be thanked! Ever since the French Revolution\nbrought this leaning of thought into ill-repute,\u2014and not altogether\nundeservedly, I must admit, true, beautiful, and good as that great\nmovement was\u2014it has been the tradition to picture sentimentalists as\npersons incapable of logical thought and unwilling to look facts in the\neyes. This tradition may be classed with the French tradition that an\nEnglishman says _godam_ at every second sentence, the English tradition\nthat an American talks about \u201cBritishers,\u201d and the American tradition\nthat a Frenchman carries forms of etiquette to an inconvenient extreme,\nin short with all those traditions which survive simply because the men\nwho use their eyes and ears are few and far between. Doubtless some\nexcuse there was for all those opinions in days gone by; and\nsentimentalism, when it was the fashionable amusement to spend one\u2019s\nevenings in a flood of tears over a woeful performance on a\ncandle-litten stage, sometimes made itself a little ridiculous. But what\nafter all is sentimentalism? It is an _ism_, a doctrine, namely, the\ndoctrine that great respect should be paid to the natural judgments of\nthe sensible heart. This is what sentimentalism precisely is; and I\nentreat the reader to consider whether to contemn it is not of all\nblasphemies the most degrading. Yet the nineteenth century has steadily\ncontemned it, because it brought about the Reign of Terror. That it did\nso is true. Still, the whole question is one of _how much_. The Reign of\nTerror was very bad; but now the Gradgrind banner has been this century\nlong flaunting in the face of heaven, with an insolence to provoke the\nvery skies to scowl and rumble. Soon a flash and quick peal will shake\neconomists quite out of their complacency, too late. The twentieth\ncentury, in its latter half, shall surely see the deluge-tempest burst\nupon the social order,\u2014to clear upon a world as deep in ruin as that\ngreed-philosophy has long plunged it into guilt. No post-thermidorian\nhigh jinks then!\n\nSo a miser is a beneficent power in a community, is he? With the same\nreason precisely, only in a much higher degree, you might pronounce the\nWall Street sharp to be a good angel, who takes money from heedless\npersons not likely to guard it properly, who wrecks feeble enterprises\nbetter stopped, and who administers wholesome lessons to unwary\nscientific men, by passing worthless checks upon them,\u2014as you did, the\nother day, to me, my millionaire Master in glomery, when you thought you\nsaw your way to using my process without paying for it, and of so\nbequeathing to your children something to boast of their father\nabout,\u2014and who by a thousand wiles puts money at the service of\nintelligent greed, in his own person. Bernard Mandeville, in his _Fable\nof the Bees_, maintains that private vices of all descriptions are\npublic benefits, and proves it, too, quite as cogently as the economist\nproves his point concerning the miser. He even argues, with no slight\nforce, that but for vice civilization would never have existed. In the\nsame spirit, it has been strongly maintained and is to-day widely\nbelieved that all acts of charity and benevolence, private and public,\ngo seriously to degrade the human race.\n\nThe _Origin of Species_ of Darwin merely extends politico-economical\nviews of progress to the entire realm of animal and vegetable life. The\nvast majority of our contemporary naturalists hold the opinion that the\ntrue cause of those exquisite and marvellous adaptations of nature for\nwhich, when I was a boy, men used to extol the divine wisdom is that\ncreatures are so crowded together that those of them that happen to have\nthe slightest advantage force those less pushing into situations\nunfavorable to multiplication or even kill them before they reach the\nage of reproduction. Among animals, the mere mechanical individualism is\nvastly re\u00ebnforced as a power making for good by the animal\u2019s ruthless\ngreed. As Darwin puts it on his title-page, it is the struggle for\nexistence; and he should have added for his motto: Every individual for\nhimself, and the Devil take the hindmost! Jesus, in his sermon on the\nMount, expressed a different opinion.\n\nHere, then, is the issue. The gospel of Christ says that progress comes\nfrom every individual merging his individuality in sympathy with his\nneighbors. On the other side, the conviction of the nineteenth century\nis that progress takes place by virtue of every individual\u2019s striving\nfor himself with all his might and trampling his neighbor under foot\nwhenever he gets a chance to do so. This may accurately be called the\nGospel of Greed.\n\nMuch is to be said on both sides. I have not concealed, I could not\nconceal, my own passionate predilection. Such a confession will probably\nshock my scientific brethren. Yet the strong feeling is in itself, I\nthink, an argument of some weight in favor of the agapastic theory of\nevolution,\u2014so far as it may be presumed to bespeak the normal judgment\nof the Sensible Heart. Certainly, if it were possible to believe in\nagapasm without believing it warmly, that fact would be an argument\nagainst the truth of the doctrine. At any rate, since the warmth of\nfeeling exists, it should on every account be candidly confessed;\nespecially since it creates a liability to onesidedness on my part\nagainst which it behooves my readers and me to be severally on our\nguard.\n\n\n                       SECOND THOUGHTS. IRENICA.\n\n\nLet us try to define the logical affinities of the different theories of\nevolution. Natural selection, as conceived by Darwin, is a mode of\nevolution in which the only positive agent of change in the whole\npassage from moner to man is fortuitous variation. To secure advance in\na definite direction chance has to be seconded by some action that shall\nhinder the propagation of some varieties or stimulate that of others. In\nnatural selection, strictly so called, it is the crowding out of the\nweak. In sexual selection, it is the attraction of beauty, mainly.\n\nThe _Origin of Species_ was published toward the end of the year 1859.\nThe preceding years since 1846 had been one of the most productive\nseasons,\u2014or if extended so as to cover the great book we are\nconsidering, _the_ most productive period of equal length in the entire\nhistory of science from its beginnings until now. The idea that chance\nbegets order, which is one of the corner-stones of modern physics\n(although Dr. Carus considers it \u201cthe weakest point in Mr. Peirce\u2019s\nsystem,\u201d) was at that time put into its clearest light. Quetelet had\nopened the discussion by his _Letters on the Application of\nProbabilities to the Moral and Political Sciences_, a work which deeply\nimpressed the best minds of that day, and to which Sir John Herschel had\ndrawn general attention in Great Britain. In 1857, the first volume of\nBuckle\u2019s _History of Civilisation_ had created a tremendous sensation,\nowing to the use he made of this same idea. Meantime, the \u201cstatistical\nmethod\u201d had, under that very name, been applied with brilliant success\nto molecular physics. Dr. John Herapath, an English chemist, had in 1847\noutlined the kinetical theory of gases in his _Mathematical Physics_;\nand the interest the theory excited had been refreshed in 1856 by\nnotable memoirs by Clausius and Kr\u00f6nig. In the very summer preceding\nDarwin\u2019s publication, Maxwell had read before the British Association\nthe first and most important of his researches on this subject. The\nconsequence was that the idea that fortuitous events may result in a\nphysical law, and further that this is the way in which those laws which\nappear to conflict with the principle of the conservation of energy are\nto be explained, had taken a strong hold upon the minds of all who were\nabreast of the leaders of thought. By such minds, it was inevitable that\nthe _Origin of Species_, whose teaching was simply the application of\nthe same principle to the explanation of another \u201cnon-conservative\u201d\naction, that of organic development, should be hailed and welcomed. The\nsublime discovery of the conservation of energy by Helmholtz in 1847,\nand that of the mechanical theory of heat by Clausius and by Rankine,\nindependently, in 1850, had decidedly overawed all those who might have\nbeen inclined to sneer at physical science. Thereafter a belated poet\nstill harping upon \u201cscience peddling with the names of things\u201d would\nfail of his effect. Mechanism was now known to be all, or very nearly\nso. All this time, utilitarianism,\u2014that improved substitute for the\nGospel,\u2014was in its fullest feather; and was a natural ally of an\nindividualistic theory. Dean Mansell\u2019s injudicious advocacy had led to\nmutiny among the bondsmen of Sir William Hamilton, and the nominalism of\nMill had profited accordingly; and although the real science that Darwin\nwas leading men to was sure some day to give a death-blow to the\nsham-science of Mill, yet there were several elements of the Darwinian\ntheory which were sure to charm the followers of Mill. Another thing:\nan\u00e6sthetics had been in use for thirteen years. Already, people\u2019s\nacquaintance with suffering had dropped off very much; and as a\nconsequence, that unlovely hardness by which our times are so contrasted\nwith those that immediately preceded them, had already set in, and\ninclined people to relish a ruthless theory. The reader would quite\nmistake the drift of what I am saying if he were to understand me as\nwishing to suggest that any of those things (except perhaps Malthus)\ninfluenced Darwin himself. What I mean is that his hypothesis, while\nwithout dispute one of the most ingenious and pretty ever devised, and\nwhile argued with a wealth of knowledge, a strength of logic, a charm of\nrhetoric, and above all with a certain magnetic genuineness that was\nalmost irresistible, did not appear, at first, at all near to being\nproved; and to a sober mind its case looks less hopeful now than it did\ntwenty years ago; but the extraordinarily favorable reception it met\nwith was plainly owing, in large measure, to its ideas being those\ntoward which the age was favorably disposed, especially, because of the\nencouragement it gave to the greed-philosophy.\n\nDiametrically opposed to evolution by chance, are those theories which\nattribute all progress to an inward necessary principle, or other form\nof necessity. Many naturalists have thought that if an egg is destined\nto go through a certain series of embryological transformations, from\nwhich it is perfectly certain not to deviate, and if in geological time\nalmost exactly the same forms appear successively, one replacing another\nin the same order, the strong presumption is that this latter succession\nwas as predeterminate and certain to take place as the former. So,\nN\u00e4geli, for instance, conceives that it somehow follows from the first\nlaw of motion and the peculiar, but unknown, molecular constitution of\nprotoplasm, that forms must complicate themselves more and more.\nKolliker makes one form generate another after a certain maturation has\nbeen accomplished. Weismann, too, though he calls himself a Darwinian,\nholds that nothing is due to chance, but that all forms are simple\nmechanical resultants of the heredity from two parents.[74] It is very\nnoticeable that all these different sectaries seek to import into their\nscience a mechanical necessity to which the facts that come under their\nobservation do not point. Those geologists who think that the variation\nof species is due to cataclysmic alterations of climate or of the\nchemical constitution of the air and water are also making mechanical\nnecessity chief factor of evolution.\n\nEvolution by sporting and evolution by mechanical necessity are\nconceptions warring against one another. A third method, which\nsupersedes their strife, lies enwrapped in the theory of Lamarck.\nAccording to his view, all that distinguishes the highest organic forms\nfrom the most rudimentary has been brought about by little hypertrophies\nor atrophies which have affected individuals early in their lives, and\nhave been transmitted to their offspring. Such a transmission of\nacquired characters is of the general nature of habit-taking, and this\nis the representative and derivative within the physiological domain of\nthe law of mind. Its action is essentially dissimilar to that of a\nphysical force; and that is the secret of the repugnance of such\nnecessitarians as Weismann to admitting its existence. The Lamarckians\nfurther suppose that although some of the modifications of form so\ntransmitted were originally due to mechanical causes, yet the chief\nfactors of their first production were the straining of endeavor and the\novergrowth superinduced by exercise, together with the opposite actions.\nNow, endeavor, since it is directed toward an end, is essentially\npsychical, even though it be sometimes unconscious; and the growth due\nto exercise, as I argued in my last paper, follows a law of a character\nquite contrary to that of mechanics.\n\nLamarckian evolution is thus evolution by the force of habit.\u2014That\nsentence slipped off my pen while one of those neighbors whose function\nin the social cosmos seems to be that of an Interrupter, was asking me a\nquestion. Of course, it is nonsense. Habit is mere inertia, a resting on\none\u2019s oars, not a propulsion. Now it is energetic projaculation (lucky\nthere is such a word, or this untried hand might have been put to\ninventing one) by which in the typical instances of Lamarckian evolution\nthe new elements of form are first created. Habit, however, forces them\nto take practical shapes, compatible with the structures they affect,\nand in the form of heredity and otherwise, gradually replaces the\nspontaneous energy that sustains them. Thus, habit plays a double part;\nit serves to establish the new features, and also to bring them into\nharmony with the general morphology and function of the animals and\nplants to which they belong. But if the reader will now kindly give\nhimself the trouble of turning back a page or two, he will see that this\naccount of Lamarckian evolution coincides with the general description\nof the action of love, to which, I suppose, he yielded his assent.\n\nRemembering that all matter is really mind, remembering, too, the\ncontinuity of mind, let us ask what aspect Lamarckian evolution takes on\nwithin the domain of consciousness. Direct endeavor can achieve almost\nnothing. It is as easy by taking thought to add a cubit to one\u2019s\nstature, as it is to produce an idea acceptable to any of the Muses by\nmerely straining for it, before it is ready to come. We haunt in vain\nthe sacred well and throne of Mnemosyne; the deeper workings of the\nspirit take place in their own slow way, without our connivance. Let but\ntheir bugle sound, and we may then make our effort, sure of an oblation\nfor the altar of whatsoever divinity its savor gratifies. Besides this\ninward process, there is the operation of the environment, which goes to\nbreak up habits destined to be broken up and so to render the mind\nlively. Everybody knows that the long continuance of a routine of habit\nmakes us lethargic, while a succession of surprises wonderfully\nbrightens the ideas. Where there is a motion, where history is a-making,\nthere is the focus of mental activity, and it has been said that the\narts and sciences reside within the temple of Janus, waking when that is\nopen, but slumbering when it is closed. Few psychologists have perceived\nhow fundamental a fact this is. A portion of mind abundantly commissured\nto other portions works almost mechanically. It sinks to a condition of\na railway junction. But a portion of mind almost isolated, a spiritual\npeninsula, or _cul-de-sac_, is like a railway terminus. Now mental\ncommissures are habits. Where they abound, originality is not needed and\nis not found; but where they are in defect, spontaneity is set free.\nThus, the first step in the Lamarckian evolution of mind is the putting\nof sundry thoughts into situations in which they are free to play. As to\ngrowth by exercise, I have already shown, in discussing _Man\u2019s Glassy\nEssence_, in last October\u2019s _Monist_, what its _modus operandi_ must be\nconceived to be, at least, until a second equally definite hypothesis\nshall have been offered. Namely, it consists of the flying asunder of\nmolecules, and the reparation of the parts by new matter. It is, thus, a\nsort of reproduction. It takes place only during exercise, because the\nactivity of protoplasm consists in the molecular disturbance which is\nits necessary condition. Growth by exercise takes place also in the\nmind. Indeed, that is what it is to _learn_. But the most perfect\nillustration is the development of a philosophical idea by being put\ninto practice. The conception which appeared, at first, as unitary,\nsplits up into special cases; and into each of these new thought must\nenter to make a practicable idea. This new thought, however, follows\npretty closely the model of the parent conception; and thus a\nhomogeneous development takes place. The parallel between this and the\ncourse of molecular occurrences is apparent. Patient attention will be\nable to trace all these elements in the transaction called learning.\n\nThree modes of evolution have thus been brought before us; evolution by\nfortuitous variation, evolution by mechanical necessity, and evolution\nby creative love. We may term them _tychastic_ evolution, or _tychasm_,\n_anancastic_ evolution, or _anancasm_, and _agapastic_ evolution, or\n_agapasm_. The doctrines which represent these as severally of principal\nimportance, we may term _tychasticism_, _anancasticism_, and\n_agapasticism_. On the other hand the mere propositions that absolute\nchance, mechanical necessity, and the law of love, are severally\noperative in the cosmos, may receive the names of _tychism_, _anancism_,\nand _agapism_.\n\nAll three modes of evolution are composed of the same general elements.\nAgapasm exhibits them the most clearly. The good result is here brought\nto pass, first, by the bestowal of spontaneous energy by the parent upon\nthe offspring, and, second, by the disposition of the latter to catch\nthe general idea of those about it and thus to subserve the general\npurpose. In order to express the relation that tychasm and anancasm bear\nto agapasm, let me borrow a word from geometry. An ellipse crossed by a\nstraight line is a sort of cubic curve; for a cubic is a curve which is\ncut thrice by a straight line; now a straight line might cut the ellipse\ntwice and its associated straight line a third time. Still the ellipse\nwith the straight line across it would not have the characteristics of a\ncubic. It would have, for instance, no contrary flexure, which no true\ncubic wants; and it would have two nodes, which no true cubic has. The\ngeometers say that it is a _degenerate_ cubic. Just so, tychasm and\nanancasm are degenerate forms of agapasm.\n\nMen who seek to reconcile the Darwinian idea with Christianity will\nremark that tychastic evolution, like the agapastic, depends upon a\nreproductive creation, the forms preserved being those that use the\nspontaneity conferred upon them in such wise as to be drawn into harmony\nwith their original, quite after the Christian scheme. Very good! This\nonly shows that just as love cannot have a contrary, but must embrace\nwhat is most opposed to it, as a degenerate case of it, so tychasm is a\nkind of agapasm. Only, in the tychastic evolution progress is solely\nowing to the distribution of the napkin-hidden talent of the rejected\nservant among those not rejected, just as ruined gamesters leave their\nmoney on the table to make those not yet ruined so much the richer. It\nmakes the felicity of the lambs just the damnation of the goats,\ntransposed to the other side of the equation. In genuine agapasm, on the\nother hand, advance takes place by virtue of a positive sympathy among\nthe created springing from continuity of mind. This is the idea which\ntychasticism knows not how to manage.\n\nThe anancasticist might here interpose, claiming that the mode of\nevolution for which he contends agrees with agapasm at the point at\nwhich tychasm departs from it. For it makes development go through\ncertain phases, having its inevitable ebbs and flows, yet tending on the\nwhole to a foreordained perfection. Bare existence by this its destiny\nbetrays an intrinsic affinity for the good. Herein, it must be admitted,\nanancasm shows itself to be in a broad acception a species of agapasm.\nSome forms of it might easily be mistaken for the genuine agapasm. The\nHegelian philosophy is such an anancasticism. With its revelatory\nreligion, with its synechism (however imperfectly set forth), with its\n\u201creflection,\u201d the whole idea of the theory is superb, almost sublime.\nYet, after all, living freedom is practically omitted from its method.\nThe whole movement is that of a vast engine, impelled by a _vis a\ntergo_, with a blind and mysterious fate of arriving at a lofty goal. I\nmean that such an engine it _would_ be, if it really worked; but in\npoint of fact, it is a Keely motor. Grant that it really acts as it\nprofesses to act, and there is nothing to do but accept the philosophy.\nBut never was there seen such an example of a long chain of\nreasoning,\u2014shall I say with a flaw in every link?\u2014no, with every link a\nhandful of sand, squeezed into shape in a dream. Or say, it is a\npasteboard model of a philosophy that in reality does not exist. If we\nuse the one precious thing it contains, the idea of it, introducing the\ntychism which the arbitrariness of its every step suggests, and make\nthat the support of a vital freedom which is the breath of the spirit of\nlove, we may be able to produce that genuine agapasticism, at which\nHegel was aiming.\n\n\n                     A THIRD ASPECT. DISCRIMINATION\n\n\nIn the very nature of things, the line of demarcation between the three\nmodes of evolution is not perfectly sharp. That does not prevent its\nbeing quite real; perhaps it is rather a mark of its reality. There is\nin the nature of things no sharp line of demarcation between the three\nfundamental colors, red, green, and violet. But for all that they are\nreally different. The main question is whether three radically different\nevolutionary elements have been operative; and the second question is\nwhat are the most striking characteristics of whatever elements have\nbeen operative.\n\nI propose to devote a few pages to a very slight examination of these\nquestions in their relation to the historical development of human\nthought. I first formulate for the reader\u2019s convenience the briefest\npossible definitions of the three conceivable modes of development of\nthought, distinguishing also two varieties of anancasm and three of\nagapasm. The tychastic development of thought, then, will consist in\nslight departures from habitual ideas in different directions\nindifferently, quite purposeless and quite unconstrained whether by\noutward circumstances or by force of logic, these new departures being\nfollowed by unforeseen results which tend to fix some of them as habits\nmore than others. The anancastic development of thought will consist of\nnew ideas adopted without foreseeing whither they tend, but having a\ncharacter determined by causes either external to the mind, such as\nchanged circumstances of life, or internal to the mind as logical\ndevelopments of ideas already accepted, such as generalizations. The\nagapastic development of thought is the adoption of certain mental\ntendencies, not altogether heedlessly, as in tychasm, nor quite blindly\nby the mere force of circumstances or of logic, as in anancasm, but by\nan immediate attraction for the idea itself, whose nature is divined\nbefore the mind possesses it, by the power of sympathy, that is, by\nvirtue of the continuity of mind; and this mental tendency may be of\nthree varieties, as follows: First, it may affect a whole people or\ncommunity in its collective personality, and be thence communicated to\nsuch individuals as are in powerfully sympathetic connection with the\ncollective people, although they may be intellectually incapable of\nattaining the idea by their private understandings or even perhaps of\nconsciously apprehending it. Second, it may affect a private person\ndirectly, yet so that he is only enabled to apprehend the idea, or to\nappreciate its attractiveness, by virtue of his sympathy with his\nneighbors, under the influence of a striking experience or development\nof thought. The conversion of St. Paul may be taken as an example of\nwhat is meant. Third, it may affect an individual, independently of his\nhuman affections, by virtue of an attraction it exercises upon his mind,\neven before he has comprehended it. This is the phenomenon which has\nbeen well called the _divination_ of genius; for it is due to the\ncontinuity between the man\u2019s mind and the Most High.\n\nLet us next consider by means of what tests we can discriminate between\nthese different categories of evolution. No absolute criterion is\npossible in the nature of things, since in the nature of things there is\nno sharp line of demarcation between the different classes.\nNevertheless, quantitative symptoms may be found by which a sagacious\nand sympathetic judge of human nature may be able to estimate the\napproximate proportions in which the different kinds of influence are\ncommingled.\n\nSo far as the historical evolution of human thought has been tychastic,\nit should have proceeded by insensible or minute steps; for such is the\nnature of chances when so multiplied as to show phenomena of regularity.\nFor example, assume that of the native-born white adult males of the\nUnited States in 1880, one-fourth part were below 5 feet 4 inches in\nstature and one-fourth part above 5 feet 8 inches. Then by the\nprinciples of probability, among the whole population, we should expect\n\n                             216 under 4 feet 6 inches,\n                              48   \u201c   4   \u201d  5   \u201c\n                               9   \u201d   4   \u201c  4   \u201d\n                     less than 2   \u201c   4   \u201d  3   \u201c\n\n                             216 above 6 feet 6 inches,\n                              48   \u201c   6   \u201d  7   \u201c\n                               9   \u201d   6   \u201c  8   \u201d\n                     less than 2   \u201c   6   \u201d  9   \u201c\n\nI set down these figures to show how insignificantly few are the cases\nin which anything very far out of the common run presents itself by\nchance. Though the stature of only every second man is included within\nthe four inches between 5 feet 4 inches and 5 feet 8 inches, yet if this\ninterval be extended by thrice four inches above and below, it will\nembrace all our 8 millions odd of native-born adult white males (of\n1880), except only 9 taller and 9 shorter.\n\nThe test of minute variation, if _not_ satisfied, absolutely negatives\ntychasm. If it is satisfied, we shall find that it negatives anancasm\nbut not agapasm. We want a positive test, satisfied by tychasm, only.\nNow wherever we find men\u2019s thought taking by imperceptible degrees a\nturn contrary to the purposes which animate them, in spite of their\nhighest impulses, there, we may safely conclude, there has been a\ntychastic action.\n\nStudents of the history of mind there be of an erudition to fill an\nimperfect scholar like me with envy edulcorated by joyous admiration,\nwho maintain that ideas when just started are and can be little more\nthan freaks, since they cannot yet have been critically examined, and\nfurther that everywhere and at all times progress has been so gradual\nthat it is difficult to make out distinctly what original step any given\nman has taken. It would follow that tychasm has been the sole method of\nintellectual development. I have to confess I cannot read history so; I\ncannot help thinking that while tychasm has sometimes been operative, at\nothers great steps covering nearly the same ground and made by different\nmen independently, have been mistaken for a succession of small steps,\nand further that students have been reluctant to admit a real entitative\n\u201cspirit\u201d of an age or of a people, under the mistaken and unscrutinized\nimpression that they should thus be opening the door to wild and\nunnatural hypotheses. I find, on the contrary, that, however it may be\nwith the education of individual minds, the historical development of\nthought has seldom been of a tychastic nature, and exclusively in\nbackward and barbarizing movements. I desire to speak with the extreme\nmodesty which befits a student of logic who is required to survey so\nvery wide a field of human thought that he can cover it only by a\nreconnaissance, to which only the greatest skill and most adroit methods\ncan impart any value at all; but, after all, I can only express my own\nopinions and not those of anybody else; and in my humble judgment, the\nlargest example of tychasm is afforded by the history of Christianity,\nfrom about its establishment by Constantine, to, say, the time of the\nIrish monasteries, an era or eon of about 500 years. Undoubtedly the\nexternal circumstance which more than all others at first inclined men\nto accept Christianity in its loveliness and tenderness, was the fearful\nextent to which society was broken up into units by the unmitigated\ngreed and hard-heartedness into which the Romans had seduced the world.\nAnd yet it was that very same fact, more than any other external\ncircumstance, that fostered that bitterness against the wicked world of\nwhich the primitive gospel of Mark contains not a single trace. At\nleast, I do not detect it in the remark about the blasphemy against the\nHoly Ghost, where nothing is said about vengeance, nor even in that\nspeech where the closing lines of Isaiah are quoted, about the worm and\nthe fire that feed upon the \u201ccarcasses of the men that have transgressed\nagainst me.\u201d But little by little the bitterness increases until in the\nlast book of the New Testament, its poor distracted author represents\nthat all the time Christ was talking about having come to save the\nworld, the secret design was to catch the entire human race, with the\nexception of a paltry 144,000, and souse them all in a brimstone lake,\nand as the smoke of their torment went up forever and ever, to turn and\nremark, \u201cThere is no curse any more.\u201d Would it be an insensible smirk or\na fiendish grin that should accompany such an utterance? I wish I could\nbelieve St. John did not write it; but it is his gospel which tells\nabout the \u201cresurrection unto condemnation,\u201d\u2014that is of men\u2019s being\nresuscitated just for the sake of torturing them;\u2014and, at any rate, the\nRevelation is a very ancient composition. One can understand that the\nearly Christians were like men trying with all their might to climb a\nsteep declivity of smooth wet clay; the deepest and truest element of\ntheir life, animating both heart and head, was universal love; but they\nwere continually, and against their wills, slipping into a party spirit,\nevery slip serving as a precedent, in a fashion but too familiar to\nevery man. This party feeling insensibily grew until by about A.D. 330\nthe luster of the pristine integrity that in St. Mark reflects the white\nspirit of light was so far tarnished that Eusebius, (the Jared Sparks of\nthat day), in the preface to his History, could announce his intention\nof exaggerating everything that tended to the glory of the church and of\nsuppressing whatever might disgrace it. His Latin contemporary\nLactantius is worse, still; and so the darkling went on increasing until\nbefore the end of the century the great library of Alexandria was\ndestroyed by Theophilus,[75] until Gregory the Great, two centuries\nlater, burnt the great library of Rome, proclaiming that \u201cIgnorance is\nthe mother of devotion,\u201d (which is true, just as oppression and\ninjustice is the mother of spirituality), until a sober description of\nthe state of the church would be a thing our not too nice newspapers\nwould treat as \u201cunfit for publication.\u201d All this movement is shown by\nthe application of the test given above to have been tychastic. Another\nvery much like it on a small scale, only a hundred times swifter, for\nthe study of which there are documents by the library-full, is to be\nfound in the history of the French Revolution.\n\nAnancastic evolution advances by successive strides with pauses between.\nThe reason is that in this process a habit of thought having been\noverthrown is supplanted by the next strongest. Now this next strongest\nis sure to be widely disparate from the first, and as often as not is\nits direct contrary. It reminds one of our old rule of making the second\ncandidate vice-president. This character, therefore, clearly\ndistinguishes anancasm from tychasm. The character which distinguishes\nit from agapasm is its purposelessness. But external and internal\nanancasm have to be examined separately. Development under the pressure\nof external circumstances, or cataclysmine evolution, is in most cases\nunmistakable enough. It has numberless degrees of intensity, from the\nbrute force, the plain war, which has more than once turned the current\nof the world\u2019s thought, down to the hard fact of evidence, or what has\nbeen taken for it, which has been known to convince men by hordes. The\nonly hesitation than can subsist in the presence of such a history is a\nquantitative one. Never are external influences the only ones which\naffect the mind, and therefore it must be a matter of judgment for which\nit would scarcely be worth while to attempt to set rules, whether a\ngiven movement is to be regarded as principally governed from without or\nnot. In the rise of medieval thought, I mean scholasticism and the\nsynchronistic art developments, undoubtedly the crusades and the\ndiscovery of the writings of Aristotle were powerful influences. The\ndevelopment of scholasticism from Roscellin to Albertus Magnus closely\nfollows the successive steps in the knowledge of Aristotle. Prantl\nthinks that that is the whole story, and few men have thumbed more books\nthan Carl Prantl. He has done good solid work, notwithstanding his\nslap-dash judgments. But we shall never make so much as a good beginning\nof comprehending scholasticism until the whole has been systematically\nexplored and digested by a company of students regularly organized and\nheld under rule for that purpose. But as for the period we are now\nspecially considering, that which synchronised the Romanesque\narchitecture, the literature is easily mastered. It does not quite\njustify Prantl\u2019s dicta as to the slavish dependence of these authors\nupon their authorities. Moreover, they kept a definite purpose steadily\nbefore their minds, throughout all their studies. I am, therefore,\nunable to offer this period of scholasticism as an example of pure\nexternal anancasm, which seems to be the fluorine of the intellectual\nelements. Perhaps the recent Japanese reception of western ideas is the\npurest instance of it in history. Yet in combination with other\nelements, nothing is commoner. If the development of ideas under the\ninfluence of the study of external facts be considered as external\nanancasm,\u2014it is on the border between the external and the internal\nforms,\u2014it is, of course, the principal thing in modern learning. But\nWhewell, whose masterly comprehension of the history of science critics\nhave been too ignorant properly to appreciate, clearly shows that it is\nfar from being the overwhelmingly preponderant influence, even there.\n\nInternal anancasm, or logical groping, which advances upon a predestined\nline without being able to foresee whither it is to be carried nor to\nsteer its course, this is the rule of development of philosophy. Hegel\nfirst made the world understand this; and he seeks to make logic not\nmerely the subjective guide and monitor of thought, which was all it had\nbeen ambitioning before, but to be the very main-spring of thinking, and\nnot merely of individual thinking but of discussion, of the history of\nthe development of thought, of all history, of all development. This\ninvolves a positive, clearly demonstrable error. Let the logic in\nquestion be of whatever kind it may, a logic of necessary inference or a\nlogic of probable inference (the theory might perhaps be shaped to fit\neither), in any case it supposes that logic is sufficient of itself to\ndetermine what conclusion follows from given premises; for unless it\nwill do so much, it will not suffice to explain why an individual train\nof reasoning should take just the course it does take, to say nothing of\nother kinds of development. It thus supposes that from given premises,\nonly one conclusion can logically be drawn, and that there is no scope\nat all for free choice. That from given premises only one conclusion can\nlogically be drawn, is one of the false notions which have come from\nlogicians\u2019 confining their attention to that Nantucket of thought, the\nlogic of non-relative terms. In the logic of relatives, it does not hold\ngood.\n\nOne remark occurs to me. If the evolution of history is in considerable\npart of the nature of internal anancasm, it resembles the development of\nindividual men; and just as 33 years is a rough but natural unit of time\nfor individuals, being the average age at which man has issue, so there\nshould be an approximate period at the end of which one great historical\nmovement ought to be likely to be supplanted by another. Let us see if\nwe can make out anything of the kind. Take the governmental development\nof Rome as being sufficiently long and set down the principal dates.\n\n                B.C.  753, Foundation of Rome.\n                B.C.  510, Expulsion of the Tarquins.\n                B.C.   27, Octavius assumes title Augustus.\n                A.D.  476, End of Western Empire.\n                A.D.  962, Holy Roman Empire.\n                A.D. 1453, Fall of Constantinople.\n\nThe last event was one of the most significant in history, especially\nfor Italy. The intervals are 243, 483, 502, 486, 491 years. All are\nrather curiously near equal, except the first which is half the others.\nSuccessive reigns of kings would not commonly be so near equal. Let us\nset down a few dates in the history of thought.\n\n    B.C.  585, Eclipse of Thales. Beginning of Greek philosophy.\n    A.D.   30, The crucifixion.\n    A.D.  529, Closing of Athenian schools. End of Greek philosophy.\n    A.D. 1125, (Approximate) Rise of the Universities of Bologna and\n       Paris.\n    A.D. 1543, Publication of the \u201cDe Revolutionibus\u201d of Copernicus.\n       Beginning of Modern Science.\n\nThe intervals are 615, 499, 596, 418, years. In the history of\nmetaphysics, we may take the following:\n\n                       B.C.  322, Death of Aristotle.\n                       A.D. 1274, Death of Aquinas.\n                       A.D. 1804, Death of Kant.\n\nThe intervals are 1595 and 530 years. The former is about thrice the\nlatter.\n\nFrom these figures, no conclusion can fairly be drawn. At the same time,\nthey suggest that perhaps there may be a rough natural era of about 500\nyears. Should there be any independent evidence of this, the intervals\nnoticed may gain some significance.\n\nThe agapastic development of thought should, if it exists, be\ndistinguished by its purposive character, this purpose being the\ndevelopment of an idea. We should have a direct agapic or sympathetic\ncomprehension and recognition of it, by virtue of the continuity of\nthought. I here take it for granted that such continuity of thought has\nbeen sufficiently proved by the arguments used in my paper on the \u201cLaw\nof Mind\u201d in _The Monist_ of last July. Even if those arguments are not\nquite convincing in themselves, yet if they are re\u00ebnforced by an\napparent agapasm in the history of thought, the two propositions will\nlend one another mutual aid. The reader will, I trust, be too well\ngrounded in logic to mistake such mutual support for a vicious circle in\nreasoning. If it could be shown directly that there is such an entity as\nthe \u201cspirit of an age\u201d or of a people, and that mere individual\nintelligence will not account for all the phenomena, this would be proof\nenough at once of agapasticism and of synechism. I must acknowledge that\nI am unable to produce a cogent demonstration of this; but I am, I\nbelieve, able to adduce such arguments as will serve to confirm those\nwhich have been drawn from other facts. I believe that all the greatest\nachievements of mind have been beyond the powers of unaided individuals;\nand I find, apart from the support this opinion receives from\nsynechistic considerations, and from the purposive character of many\ngreat movements, direct reason for so thinking in the sublimity of the\nideas and in their occurring simultaneously and independently to a\nnumber of individuals of no extraordinary general powers. The pointed\nGothic architecture in several of its developments appears to me to be\nof such a character. All attempts to imitate it by modern architects of\nthe greatest learning and genius appear flat and tame, and are felt by\ntheir authors to be so. Yet at the time the style was living, there was\nquite an abundance of men capable of producing works of this kind of\ngigantic sublimity and power. In more than one case, extant documents\nshow that the cathedral chapters, in the selection of architects,\ntreated high artistic genius as a secondary consideration, as if there\nwere no lack of persons able to supply that; and the results justify\ntheir confidence. Were individuals in general, then, in those ages\npossessed of such lofty natures and high intellect? Such an opinion\nwould break down under the first examination.\n\nHow many times have men now in middle life seen great discoveries made\nindependently and almost simultaneously! The first instance I remember\nwas the prediction of a planet exterior to Uranus by Leverrier and\nAdams. One hardly knows to whom the principle of the conservation of\nenergy ought to be attributed, although it may reasonably be considered\nas the greatest discovery science has ever made. The mechanical theory\nof heat was set forth by Rankine and by Clausius during the same month\nof February, 1850; and there are eminent men who attribute this great\nstep to Thomson.[76] The kinetical theory of gases, after being started\nby John Bernoulli and long buried in oblivion, was reinvented and\napplied to the explanation not merely of the laws of Boyle, Charles, and\nAvogadro, but also of diffusion and viscosity, by at least three modern\nphysicists separately. It is well known that the doctrine of natural\nselection was presented by Wallace and by Darwin at the same meeting of\nthe British Association; and Darwin in his \u201cHistorical Sketch\u201d prefixed\nto the later editions of his book shows that both were anticipated by\nobscure forerunners. The method of spectrum analysis was claimed for\nSwan as well as for Kirchhoff, and there were others who perhaps had\nstill better claims. The authorship of the Periodical Law of the\nChemical Elements is disputed between a Russian, a German, and an\nEnglishman; although there is no room for doubt that the principal merit\nbelongs to the first. These are nearly all the greatest discoveries of\nour times. It is the same with the inventions. It may not be surprising\nthat the telegraph should have been independently made by several\ninventors, because it was an easy corollary from scientific facts well\nmade out before. But it was not so with the telephone and other\ninventions. Ether, the first an\u00e6sthetic, was introduced independently by\nthree different New England physicians. Now ether had been a common\narticle for a century. It had been in one of the pharmacop\u0153ias three\ncenturies before. It is quite incredible that its an\u00e6sthetic property\nshould not have been known; it was known. It had probably passed from\nmouth to ear as a secret from the days of Basil Valentine; but for long\nit had been a secret of the Punchinello kind. In New England, for many\nyears, boys had used it for amusement. Why then had it not been put to\nits serious use? No reason can be given, except that the motive to do so\nwas not strong enough. The motives to doing so could only have been\ndesire for gain and philanthropy. About 1846, the date of the\nintroduction, philanthropy was undoubtedly in an unusually active\ncondition. That sensibility, or sentimentalism, which had been\nintroduced in the previous century, had undergone a ripening process, in\nconsequence of which, though now less intense than it had previously\nbeen, it was more likely to influence unreflecting people than it had\never been. All three of the ether-claimants had probably been influenced\nby the desire for gain; but nevertheless they were certainly not\ninsensible to the agapic influences.\n\nI doubt if any of the great discoveries ought, properly, to be\nconsidered as altogether individual achievements; and I think many will\nshare this doubt. Yet, if not, what an argument for the continuity of\nmind, and for agapasticism is here! I do not wish to be very strenuous.\nIf thinkers will only be persuaded to lay aside their prejudices and\napply themselves to studying the evidences of this doctrine, I shall be\nfully content to await the final decision.\n\nFootnote 72:\n\n  _The Monist_, January, 1893.\n\nFootnote 73:\n\n  How can a writer have any respect for science, as such, who is capable\n  of confounding with the scientific propositions of political economy,\n  which have nothing to say concerning what is \u201cbeneficent,\u201d such\n  brummagem generalisations as this?\n\nFootnote 74:\n\n  I am happy to find that Dr. Carus, too, ranks Weismann among the\n  opponents of Darwin, notwithstanding his flying that flag.\n\nFootnote 75:\n\n  See _Draper\u2019s History of Intellectual Development_, chap. x.\n\nFootnote 76:\n\n  Thomson, himself, in his article _Heat_ in the _Encyclopedia\n  Britannica_, never once mentions the name of Clausius.\n\n\n\n\n                         _Supplementary Essay_\n                        THE PRAGMATISM OF PEIRCE\n                                   BY\n                               JOHN DEWEY\n\n\nThe term pragmatism was introduced into literature in the opening\nsentences of Professor James\u2019s California Union address in 1898. The\nsentences run as follows: \u201cThe principle of pragmatism, as we may call\nit, may be expressed in a variety of ways, all of them very simple. In\nthe _Popular Science Monthly_ for January, 1878, Mr. Charles S. Peirce\nintroduces it as follows:\u201d etc. The readers who have turned to the\nvolume referred to have not, however, found the word there. From other\nsources we know that the name as well as the idea was furnished by Mr.\nPeirce. The latter has told us that both the word and the idea were\nsuggested to him by a reading of Kant, the idea by the _Critique of Pure\nReason_, the term by the \u201cCritique of Practical Reason.\u201d[77] The article\nin the _Monist_ gives such a good statement of both the idea and the\nreason for selecting the term that it may be quoted _in extenso_. Peirce\nsets out by saying that with men who work in laboratories, the habit of\nmind is molded by experimental work much more than they are themselves\naware. \u201cWhatever statement you may make to him, he [the experimentalist]\nwill either understand as meaning that if a given prescription for an\nexperiment ever can be and ever is carried out in act, an experience of\na given description will result, or else he will see no sense at all in\nwhat you say.\u201d Having himself the experimental mind and being interested\nin methods of thinking, \u201che framed the theory that a _conception_, that\nis, the rational purport of a word or other expression, lies exclusively\nin its bearing upon the conduct of life; so that, since obviously\nnothing that might not result from experiment can have any direct\nbearing upon conduct, if one can define accurately all the conceivable\nexperimental phenomena which the affirmation or denial of a concept\ncould imply, one will have therein a complete definition of the concept,\nand _there is absolutely nothing more in it_. For this doctrine, he\ninvented the name _pragmatism_.\u201d\n\nAfter saying that some of his friends wished him to call the doctrine\npracticism or practicalism, he says that he had learned philosophy from\nKant, and that to one \u201cwho still thought in Kantian terms most readily,\n_praktisch_ and _pragmatisch_ were as far apart as the two poles, the\nformer belonging to a region of thought where no mind of the\nexperimentalist type can ever make sure of solid ground under his feet,\nthe latter expressing relation to some definite human purpose. Now quite\nthe most striking feature of the new theory was its recognition of an\ninseparable connection between rational cognition and human\npurpose.\u201d[78]\n\nFrom this brief statement, it will be noted that Peirce confined the\nsignificance of the term to the determination of the meaning of terms,\nor better, propositions; the theory was not, of itself, a theory of the\ntest, or the truth, of propositions. Hence the title of his original\narticle: _How to Make Ideas Clear_. In his later writing, after the term\nhad been used as a theory of truth,\u2014he proposed the more limited\n\u201cpragmaticism\u201d to designate his original specific meaning.[79] But even\nwith respect to the meaning of propositions, there is a marked\ndifference between his pragmaticism and the pragmatism of, say, James.\nSome of the critics (especially continental) of the latter would have\nsaved themselves some futile beating of the air, if they had reacted to\nJames\u2019s statements instead of to their own associations with the word\n\u201cpragmatic.\u201d Thus James says in his California address: \u201cThe effective\nmeaning of any philosophic proposition can always be brought down to\nsome particular consequence, in our future practical experience, whether\nactive or passive; the point lying rather in the fact that the\nexperience must be _particular_, than in the fact that it must be\n_active_.\u201d (Italics mine.)\n\nNow the curious fact is that Peirce puts more emphasis upon practise (or\nconduct) and less upon the particular; in fact, he transfers the\nemphasis to the general. The following passage is worth quotation\nbecause of the definiteness with which it identifies meaning with both\nthe future and with the general. \u201cThe rational meaning of every\nproposition lies in the future. How so? The meaning of a proposition is\nitself a proposition. Indeed, it is no other than the very proposition\nof which it is the meaning: it is a translation of it. But of the\nmyriads of forms into which a proposition may be translated, which is\nthat one which is to be called its very meaning? It is, according to the\npragmaticist, that form in which the proposition becomes applicable to\nhuman conduct, not in these or those special circumstances nor when one\nentertains this or that special design, but that form which is most\napplicable to self-control under every situation and to every purpose.\u201d\nHence, \u201cit must be simply the general description of all the\nexperimental phenomena which the assertion of the proposition virtually\npredicts.\u201d Or, paraphrasing, pragmatism identifies meaning with\nformation of a habit, or way of acting having the greatest generality\npossible, or the widest range of application to particulars. Since\nhabits or ways of acting are just as real as particulars, it is\ncommitted to a belief in the reality of \u201cuniversals.\u201d Hence it is not a\ndoctrine of phenomenalism, for while the richness of phenomena lies in\ntheir sensuous quality, pragmatism does not intend to define these\n(leaving them, as it were, to speak for themselves), but \u201celiminates\ntheir sential element, and endeavors to define the rational purport, and\nthis it finds in the purposive bearing of the word or proposition in\nquestion.\u201d Moreover, not only are generals real, but they are physically\nefficient. The meanings \u201cthe air is stuffy\u201d and \u201cstuffy air is\nunwholesome\u201d may determine, for example, the opening of the window.\nAccordingly on the ethical side, \u201cthe pragmaticist does not make the\n_summum bonum_ to consist in action, but makes it to consist in that\nprocess of evolution whereby the existent comes more and more to embody\nthose generals...; in other words, becomes, through action an embodiment\nof rational purports or habits generalized as widely as possible.\u201d[80]\n\nThe passages quoted should be compared with what Peirce has to say in\nthe Baldwin Dictionary article. There he says that James\u2019s doctrine\nseems to commit us to the belief \u201cthat the end of man is action\u2014a\nstoical maxim which does not commend itself as forcibly to the present\nwriter at the age of sixty as it did at thirty. If it be admitted, on\nthe contrary, that action wants an end, and that the end must be\nsomething of a general description, then the spirit of the maxim itself\n... would direct us toward something different from practical facts,\nnamely, to general ideas.... The only ultimate good which the practical\nfacts to which the maxim directs attention can subserve is to further\nthe development of concrete reasonableness.... Almost everybody will now\nagree that the ultimate good lies in the evolutionary process in some\nway. If so, it is not in individual reactions in their segregation, but\nin something general or continuous. Synechism is founded on the notion\nthat the coalescence, the becoming continuous, the becoming governed by\nlaws, the becoming instinct with general ideas, are but phases of one\nand the same process of the growth of reasonableness. This is first\nshown to be true with mathematical exactitude in the field of logic, and\nis thence inferred to hold good metaphysically. It is not opposed to\npragmaticism ... but includes that procedure as a step.\u201d\n\nHere again we have the doctrine of pragmaticism as a doctrine that\nmeaning or rational purport resides in the setting up of habits or\ngeneralized methods, a doctrine passing over into the metaphysics of\nsynechism. It will be well now to recur explicitly to Peirce\u2019s earlier\ndoctrine which he seems to qualify\u2014although, as he notes, he upheld the\ndoctrine of the reality of generals even at the earlier period. Peirce\nsets out, in his article on the \u201cFixation of Belief,\u201d with the empirical\ndifference of doubt and belief expressed in the facts that belief\ndetermines a habit while doubt does not, and that belief is calm and\nsatisfactory while doubt is an uneasy and dissatisfied state from which\nwe struggle to emerge; to attain, that is, a state of belief, a struggle\nwhich may be called inquiry. The sole object of inquiry is the fixation\nof belief. The scientific method of fixation has, however, certain\nrivals: one is that of \u201ctenacity\u201d\u2014constant reiteration, dwelling upon\neverything conducive to the belief, avoidance of everything which might\nunsettle it\u2014the will to believe. The method breaks down in practice\nbecause of man\u2019s social nature; we have to take account of contrary\nbeliefs in others, so that the real problem is to fix the belief of the\ncommunity; for otherwise our own belief is precariously exposed to\nattack and doubt. Hence the resort to the method of authority. This\nmethod breaks down in time by the fact that authority can not fix all\nbeliefs in all their details, and because of the conflict which arises\nbetween organized traditions. There may then be recourse to what is\n\u201cagreeable to reason\u201d\u2014a method potent in formation of taste and in\nesthetic productions and in the history of philosophy,\u2014but a method\nwhich again fails to secure permanent agreements in society, and so\nleaves individual belief at the mercy of attack. Hence, finally,\nrecourse to science, whose fundamental hypothesis is this: \u201cThere are\nreal things, whose characters are entirely independent of our opinions\nabout them; those realities affect our senses according to regular laws,\nand ... by taking advantage of the laws of perception, we can ascertain\nby _reasoning_ how things really are, and any man if he have sufficient\nexperience and reason enough about it, will be led to the one true\nconclusion.\u201d[81]\n\nIt will be noted that the quotation employs the terms \u201creality\u201d and\n\u201ctruth,\u201d while it makes them a part of the statement of the _hypothesis_\nentertained in scientific procedure. Upon such a basis, what meanings\nattach to the terms \u201creality\u201d and \u201ctruth\u201d? Since they are general terms,\ntheir meanings must be determined on the basis of the effects, having\npractical bearings, which the object of our conception has. Now the\neffect which real things have is to cause beliefs; beliefs are then the\nconsequences which give the general term reality a \u201crational purport.\u201d\nAnd on the assumption of the scientific method, the _distinguishing_\ncharacter of the _real_ object must be that it tends to produce a single\nuniversally accepted belief. \u201cAll the followers of science are fully\npersuaded that the processes of investigation, if only pushed far\nenough, will give one certain solution to every question to which they\ncan be applied.\u201d \u201cThis activity of thought by which we are carried, not\nwhere we wish, but to a foreordained goal, is like the operation of\ndestiny.... This great law is embodied in the conception of truth and\nreality. The opinion which is fated to be ultimately agreed to by all\n_who investigate_, is what we mean by the truth, and the object\nrepresented in this opinion is the real.\u201d[82] In a subsequent essay (on\nthe \u201cProbability of Induction\u201d) Peirce expressly draws the conclusion\nwhich follows from this statement; viz., that this conception of truth\nand reality makes everything depend upon the character of the methods of\ninquiry and inference by which conclusions are reached. \u201cIn the case of\nsynthetic inferences we know only the degree of trustworthiness of our\nproceeding. As all knowledge comes from synthetic inference, we must\nalso infer that all human certainty consists merely in our knowing that\nthe processes by which our knowledge has been derived are such as must\ngenerally have led to true conclusions\u201d[83]\u2014true conclusions, once more,\nbeing those which command the agreement of competent inquiries.\n\nSumming up, we may say that Peirce\u2019s pragmaticism is a doctrine\nconcerning the meaning, conception, or rational purport of objects,\nnamely, that these consist in the \u201ceffects, which might conceivably have\npractical bearings, we conceive the object of our conception to have.\nThen, our conception of these effects is the whole of our conception of\nthe object.\u201d[84] \u201cOur idea of anything is our idea of its sensible\neffects,\u201d and if we have any doubt as to whether we really believe the\neffects to be sensible or no, we have only to ask ourselves whether or\nno we should act any differently in their presence. In short, our own\nresponses to sensory stimuli are the ultimate, or testing, ingredients\nin our conception of an object. In the literal sense of the word\npragmatist, therefore, Peirce is more of a pragmatist than James.\n\nHe is also less of a nominalist. That is to say, he emphasizes much less\nthe _particular_ sensible consequence, and much more the habit, the\ngeneric attitude of response, set up in consequence of experiences with\na thing. In the passage in the Dictionary already quoted he speaks as if\nin his later life he attached less importance to action, and more to\n\u201cconcrete reasonableness\u201d than in his earlier writing. It may well be\nthat the relative emphasis had shifted. But there is at most but a\ndifference of emphasis. For in his later doctrine, concrete rationality\nmeans a change in existence brought about _through_ action, and through\naction which embodies conceptions whose own specific existence consists\nin habitual attitudes of response. In his earlier writing, the emphasis\nupon habits, as something generic, is explicit. \u201cWhat a thing means is\nsimply what habits it involves.\u201d[85] More elaborately, \u201cInduction infers\na rule. Now the belief of a rule is a habit. That a habit is a rule,\nactive in us, is evident. That every belief is of the nature of a habit,\nin so far as it is of a general character, has been shown in the earlier\npapers of this series.\u201d[86]\n\nThe difference between Peirce and James which next strikes us is the\ngreater emphasis placed by the former upon the method of procedure. As\nthe quotations already made show, everything ultimately turned, for\nPeirce, upon the trustworthiness of the procedures of inquiry. Hence his\nhigh estimate of logic, as compared with James\u2014at least James in his\nlater days. Hence also his definite rejection of the appeal to the Will\nto Believe\u2014under the form of what he calls the method of tenacity.\nClosely associated with this is the fact that Peirce has a more explicit\ndependence upon the social factor than has James. The appeal in Peirce\nis essentially to the consensus of those who have investigated, using\nmethods which are capable of employment by all. It is the need for\nsocial agreement, and the fact that in its absence \u201cthe method of\ntenacity\u201d will be exposed to disintegration from without, which finally\nforces upon mankind the wider and wider utilization of the scientific\nmethod.\n\nFinally, both Peirce and James are realists. The reasonings of both\ndepend upon the assumption of real things which really have effects or\nconsequences. Of the two, Peirce makes clearer the fact that in\nphilosophy at least we are dealing with the _conception_ of reality,\nwith reality as a term having rational purport, and hence with something\nwhose meaning is itself to be determined in terms of consequences. That\n\u201creality\u201d means the object of those beliefs which have, after prolonged\nand co\u00f6perative inquiry, becomes stable, and \u201ctruth\u201d the quality of\nthese beliefs is a logical consequence of this position. Thus while \u201cwe\nmay define the real as that whose characters are independent of what\nanybody may think them to be ... it would be a great mistake to suppose\nthat this definition makes the idea of reality perfectly clear.\u201d[87] For\nit is only the outcome of persistent and conjoint inquiry which enables\nus to give intelligible meaning in the concrete to the expression\n\u201ccharacters independent of what anybody may think them to be.\u201d (This is\nthe pragmatic way out of the egocentric predicament.) And while my\npurpose is wholly expository I can not close without inquiring whether\nrecourse to Peirce would not have a most beneficial influence in\ncontemporary discussion. Do not a large part of our epistemological\ndifficulties arise from an attempt to define the \u201creal\u201d as something\ngiven prior to reflective inquiry instead of as that which reflective\ninquiry is forced to reach and to which when it is reached belief can\nstably cling?\n\nFootnote 77:\n\n  See article on \u201cPragmatism,\u201d in _Baldwin\u2019s Dictionary_, Vol. 2., p.\n  322, and the _Monist_, Vol. 15, p. 162.\n\nFootnote 78:\n\n  Kant discriminates the laws of morality, which are _a priori_, from\n  rules of skill, having to do with technique or art, and counsels of\n  prudence, having to do with welfare. The latter he calls pragmatic;\n  the _a priori_ laws practical. See _Metaphysics of Morals_, Abbott\u2019s\n  trans., pp. 33 and 34.\n\nFootnote 79:\n\n  See the article in the _Monist_ already mentioned, and another one in\n  the same volume, p. 481, \u201cThe Issues of Pragmaticism.\u201d\n\nFootnote 80:\n\n  It is probably fair to see here an empirical rendering of the Kantian\n  generality of moral action, while the distinction and connection of\n  \u201crational purport\u201d and \u201csensible particular\u201d have also obvious Kantian\n  associations.\n\nFootnote 81:\n\n  P. 26.\n\nFootnote 82:\n\n  P. 56-57.\n\nFootnote 83:\n\n  P. 105.\n\nFootnote 84:\n\n  P. 45.\n\nFootnote 85:\n\n  P. 43.\n\nFootnote 86:\n\n  P. 151.\n\nFootnote 87:\n\n  P. 53.\n\n\n\n\n              BIBLIOGRAPHY OF PEIRCE\u2019S PUBLISHED WRITINGS\n\n\nI. Writings of General Interest.[88]\n\n    _A._ Three papers in the _Journal of Speculative Philosophy_, Vol. 2\n    (1868).\n\n    1. \u201cQuestions Concerning Certain Faculties Claimed for Man,\u201d pp.\n    103-114.\n\n    2. \u201cSome Consequences of Four Incapacities,\u201d pp. 140-157.\n\n    3. \u201cGround of Validity of the Laws of Logic,\u201d pp. 193-208.\n\nThese three papers, somewhat loosely connected, deal mainly with the\nphilosophy of discursive thought. The first deals with our power of\nintuition, and holds that \u201cevery thought is a sign.\u201d The second, one of\nthe most remarkable of Peirce\u2019s writings, contains an acute criticism of\nthe Cartesian tradition and a noteworthy argument against the\ntraditional emphasis on \u201cimages\u201d in thinking. The third contains, _inter\nalia_, a refutation of Mill\u2019s indictment of the syllogism. The same\nvolume of the _Journal_ contains two unsigned communications on\nNominalism and on the Meaning of Determined.\n\n    _B._ Review of Fraser\u2019s \u201cBerkeley,\u201d in the _North American Review_,\n    Vol. 113 (1871), pp. 449-472.\n\nThis paper contains an important analysis on medieval realism, and of\nBerkeley\u2019s nominalism. (A Scotist realism continues to distinguish\nPeirce\u2019s work after this.)\n\n    _C._ \u201cIllustrations of the Logic of Science,\u201d in _Popular Science\n    Monthly_, Vols. 12-13 (1877-1878). Reprinted in Pt. I of this\n    volume. The first and second papers were also published in the\n    _Revue Philosophique_, Vols. 6-7 (1879).\n\n    _D._ Ten papers in the _Monist_, Vols. 1-3 (1891-1893), and 15-16\n    (1905-1906). The first five are reprinted in Pt. II of this volume.\n\nThe sixth paper, \u201cReply to the Necessitarians,\u201d Vol. 3, pp. 526-570, is\nan answer to the criticism of the foregoing by the editor of the\n_Monist_, Vol. 2, pp. 560ff.; cf. Vol. 3, pp. 68ff. and 571ff., and\nMcCrie, \u201cThe Issues of Synechism,\u201d Vol. 3, pp. 380ff.\n\n    7. \u201cWhat Pragmatism Is?\u201d Vol. 15, pp. 161-181.\n\n    8. \u201cThe Issues of Pragmaticism,\u201d Vol. 15, pp. 481-499.\n\n    9. \u201cMr. Peterson\u2019s Proposed Discussion,\u201d Vol. 16, pp. 147ff.\n\n    10. \u201cProlegomena to an Apology for Pragmaticism,\u201d Vol. 16, pp.\n    492-546.\n\nThe last four papers develop Peirce\u2019s thought by showing its agreement\nand disagreement with the pragmatism of James and Schiller. The last\npaper contains his Method of Existential Graphs.\n\n    _E._ \u201cThe Reality of God,\u201d in the _Hibbert Journal_, Vol. 7 (1908),\n    pp. 96-112. (This article contains brief indications of many of\n    Peirce\u2019s leading ideas.)\n\n    _F._ Six Papers in the _Open Court_, Vols. 6-7 (1893).\n\n    1. \u201cPythagorics\u201d (on the Pythagorean brotherhood), pp. 3375-3377.\n\n    2. \u201cDmesis\u201d (on charity towards criminals), pp. 3399-3402.\n\n    3. \u201cThe Critic of Arguments (I.), Exact Thinking,\u201d pp. 3391-3394.\n\n    4. \u201cThe Critic of Arguments (II.), The Reader is Introduced to\n    Relatives,\u201d pp. 3415-3419. (The last two contain a very clear\n    succinct account of the general character of Peirce\u2019s logic.)\n\n    5. \u201cWhat is Christian Faith?\u201d pp. 3743-3745.\n\n    6. \u201cThe Marriage of Religion and Science,\u201d pp. 3559-3560.\n\n    _G._ Articles in Baldwin\u2019s \u201cDictionary of Philosophy\u201d: Individual,\n    kind, matter and form, possibility, pragmatism, priority, reasoning,\n    sign, scientific method, sufficient reason, synechism, and\n    uniformity.\n\n    _H._ \u201cPearson\u2019s Grammar of Science,\u201d in _Popular Science Monthly_,\n    Vol. 58 (1901), pp. 296-306. (A critique of Pearson\u2019s conceptualism\n    and of his utilitarian view as to the aim of science.)\n\nII. Writings of Predominantly Logical Interest.\n\n    _A._ Five Papers on Logic, read before the American Academy of Arts\n    and Sciences. Published in the _Proceedings of the Academy_, Vol. 7\n    (1867).\n\n    1. \u201cOn an Improvement in Boole\u2019s Calculus of Logic,\u201d pp. 250-261.\n    (Suggests improvements in Boole\u2019s logic, especially in the\n    representation of particular propositions. The association of\n    probability with the notion of relative frequency became a leading\n    idea of Peirce\u2019s thought.)\n\n    2. \u201cOn the Natural Classification of Arguments,\u201d pp. 261-287. (A\n    suggestive distinction between the leading principle and the premise\n    of an argument. Contains also an interesting note (pp. 283-284)\n    denying the positivistic maxim that, \u201cno hypothesis is admissible\n    which is not capable of verification by direct observation.\u201d)\n\n    3. \u201cOn a New List of Categories,\u201d pp. 287-298. The categories are:\n    Being, Quality (Reference to a Ground), Relation (Reference to a\n    Correlate), Representation (Reference to an Interpretant),\n    Substance. \u201cLogic has for its subject-genus all symbols and not\n    merely concepts.\u201d Symbols include terms, propositions, and\n    arguments.\n\n    4. \u201cUpon the Logic of Mathematics,\u201d pp. 402-412. \u201cThere are certain\n    general propositions from which the truths of mathematics follow\n    syllogistically.\u201d\n\n    5. \u201cUpon Logical Comprehension and Extension,\u201d pp. 416-432.\n    (Interesting historical references to the use of these terms and an\n    attack on the supposed rule as to their inverse proportionality.)\n\n    _B._ \u201cDescription of a Notation for the Logic of Relations,\u201d in\n    _Memoires of the American Academy_, Vol. 9 (1870), pp. 317-378.\n    (Shows the relation of inclusion between classes to be more\n    fundamental than Boole\u2019s use of equality. Extends the Booleian\n    calculus to DeMorgan\u2019s logic of relative terms.)\n\n    _C._ \u201cOn the Algebra of Logic,\u201d _American Journal of Mathematics_,\n    Vol. 3 (1880), pp. 15-57. (Referred to by Schroeder as Peirce\u2019s\n    _Hauptwerk_ in \u201cVorlesungen \u00fcber die Algebra der Logik,\u201d Vol. 1., p.\n    107.)\n\n    _D._ \u201cOn the Logic of Number,\u201d _American Journal of Mathematics_,\n    Vol. 4 (1881), pp. 85-95.\n\n    _E._ \u201cBrief Description of the Algebra of Relatives,\u201d Reprinted from\n    ??, pp. 1-6.\n\n    _F._ \u201cOn the Algebra of Logic: A Contribution to the Philosophy of\n    Notation,\u201d _American Journal of Mathematics_, Vol. 7 (1884), pp.\n    180-202.\n\n    _G._ \u201cA Theory of Probable Inference\u201d and notes \u201cOn a Limited\n    Universe of Marks\u201d and on the \u201cLogic of Relatives\u201d in \u201cStudies in\n    Logic by members of the Johns Hopkins University,\u201d Boston, 1883, pp.\n    126-203.\n\n    _H._ \u201cThe Regenerated Logic,\u201d _Monist_, Vol. 7, pp. 19-40.\n\n    \u201cThe Logic of Relatives,\u201d _Monist_, Vol. 7, pp. 161-217. (An\n    elaborate development of his own logic of relatives, by way of\n    review of Schroeder\u2019s book.)\n\n    _I._ Miscellaneous Notes, etc.\n\n    1. Review of Venn\u2019s \u201cLogic of Chance,\u201d _North American Review_,\n    July, 1867.\n\n    2. \u201cOn the Application of Logical Analysis to Multiple Algebra,\u201d\n    _Proceedings of the American Academy_, Vol. 10 (1875), pp. 392-394.\n\n    3. \u201cNote on Grassman\u2019s \u2018Calculus of Extension,\u2019\u201d _Proceedings of the\n    American Academy_, Vol. 13 (1878), pp. 115-116.\n\n    4. \u201cNote on Conversion,\u201d _Mind_, Vol. 1, p. 424.\n\n    5. Notes and Additions to Benjamin Peirce\u2019s \u201cLinear Associative\n    Algebra,\u201d _American Journal of Mathematics_, Vol. 4 (1881), pp.\n    92ff., especially pp. 221-229.\n\n    6. \u201cLogical Machines,\u201d _American Journal of Psychology_, Vol. 1\n    (1888).\n\n    7. \u201cInfinitesimals,\u201d _Science_, Vol. 11 (1900), p. 430.\n\n    8. \u201cSome Amazing Mazes,\u201d _Monist_, Vol. 18 (April and July, 1908),\n    and Vol. 19 (Jan., 1909).\n\n    9. \u201cOn Non-Aristotelian Logic\u201d (Letter), _Monist_, Vol. 20.\n\n    _J._ A Syllabus of Certain Topics of Logic. 1903. Boston. Alfred\n    Mudge & Son (a four page brochure).\n\n    _K._ Articles in Baldwin\u2019s \u201cDictionary of Philosophy\u201d on: laws of\n    thought, leading principle, logic (exact and symbolic), modality,\n    negation, predicate and predication, probable inference, quality,\n    quantity, relatives, significant, simple, subject, syllogism,\n    theory, truth and falsity universal, universe, validity,\n    verification, whole and parts.\n\nIII. Researches in the Theory and Methods of Measurement.\n\n    _A._ General and Astronomic.\n\n    1. \u201cOn the Theory of Errors of Observation,\u201d _Report of the\n    Superintendent of the U. S. Coast Survey_ for 1870, pp. 220-224.\n\n    2. \u201cNote on the Theory of Economy of Research,\u201d _Report of the U. S.\n    Coast Survey_ for 1876, pp. 197-201. (This paper deals with the\n    relation between the utility and the cost of diminishing the\n    probable error.)\n\n    3. \u201cApparatus for Recording a Mean of Observed Times,\u201d _U. S. Coast\n    Survey_, 1877. Appendix No. 15 to _Report_ of 1875.\n\n    4. \u201cFerrero\u2019s Metodo dei Minimi Quadrati,\u201d _American Journal of\n    Mathematics_, Vol. 1 (1878), pp. 55-63.\n\n    5. \u201cPhotometric Researches,\u201d _Annals of the Astronomical Observatory\n    of Harvard College_, Vol. 9 (1878), pp. 1-181.\n\n    6. \u201cMethods and Results. Measurement of Gravity.\u201d Washington. 1879.\n\n    7. \u201cMethods and Results. A Catalogue of Stars for Observations of\n    Latitude.\u201d Washington. 1879.\n\n    8. \u201cOn the Ghosts in Rutherford\u2019s \u2018Diffraction Spectra,\u2019\u201d _American\n    Journal of Mathematics_, Vol. 2 (1879), pp. 330-347.\n\n    9. \u201cNote on a Comparison of a Wave-Length with a Meter,\u201d _American\n    Journal of Science_, Vol. 18 (1879), p. 51.\n\n    10. \u201cA Quincuncial Projection of the Sphere,\u201d _American Journal of\n    Mathematics_, Vol. 2 (1879), pp. 394, 396.\n\n    11. \u201cNumerical Measure of Success of Predictions,\u201d _Science_, Vol. 4\n    (1884), p. 453.\n\n    12. \u201cProceedings Assay Commission\u201d Washington, 1888. (Joint Reports\n    on Weighing.)\n\n    _B._ Geodetic Researches. The Pendulum.\n\n    1. \u201cMeasurement of Gravity at Initial Stations in America and\n    Europe,\u201d _Report of the U. S. Coast Survey_, 1876, pp. 202-237 and\n    410-416.\n\n    2. \u201cDe l\u2019influence de la flexibilit\u00e9 du tr\u00e9pied sur l\u2019oscillation du\n    pendule a r\u00e9version,\u201d Conf\u00e9rence Geodesique Internationale (1877)\n    Comptes Rendus, Berlin, 1878, pp. 171-187. (This paper was\n    introduced by Plantamour and was followed by the notes of Appolzer.)\n\n    3. \u201cOn the Influence of Internal Friction upon the Correction of the\n    Length of the Second\u2019s Pendulum,\u201d _Proceedings of the American\n    Academy_, Vol. 13 (1878), pp. 396-401.\n\n    4. \u201cOn a Method of Swinging Pendulums for the Determination of\n    Gravity proposed by M. Faye,\u201d _American Journal of Science_, Vol. 18\n    (1879), pp. 112-119.\n\n    5. \u201cResults of Pendulum Experiments,\u201d _American Journal of Science_,\n    Vol. 20 (1880).\n\n    6. \u201cFlexure of Pendulum Supports,\u201d _Report of the U. S. Coast\n    Survey_, 1881, pp. 359-441.\n\n    7. \u201cOn the Deduction of the Ellipticity of the Earth from the\n    Pendulum Experiment,\u201d _Report of the U. S. Coast Survey_, 1881, pp.\n    442-456.\n\n    8. \u201cDeterminations of Gravity at Stations in Pennsylvania,\u201d _Report\n    of U. S. Coast Survey_, 1883, Appendix 19 and pp. 473-486.\n\n    9. \u201cOn the Use of the Noddy,\u201d _Report of the U. S. Coast Survey_,\n    1884, pp. 475-482.\n\n    10. \u201cEffect of the Flexure of a Pendulum upon the Period of\n    Oscillation,\u201d _Report of the U. S. Coast Survey_, 1884, pp. 483-485.\n\n    11. \u201cOn the Influence of a Noddy, and of Unequal Temperature upon\n    the Periods of a Pendulum,\u201d _Report of the U. S. Coast and Geodetic\n    Survey_ for 1885, pp. 509-512.\n\n    _C._ Psychologic. \u201cOn Small Differences in Sensation\u201d (in\n    cooperation with J. Jastrow), _National Academy of Sciences_, Vol. 3\n    (1884), pp. 1-11.\n\nIV. Philologic.\n\n    \u201cShakespearian Pronunciation\u201d (in co\u00f6peration with J. B. Noyes),\n    _North American Review_, Vol. 98 (April, 1864), pp. 342-369.\n\nV. Contributions to the _Nation_.\n\n    Lazelle, Capt. H. M., One Law in Nature. _Nation_, Vol. 17, No. 419.\n\n    Newcomb, S., Popular Astronomy. Vol. 27, No. 683.\n\n    Read, C., Theory of Logic, 1878. Vol. 28, No. 718.\n\n    Rood, O. N., Modern Chromatics, 1879. Vol. 29, No. 746.\n\n    Note on the _American Journal of Mathematics_. Vol. 29, No. 756.\n\n    Jevons, W. S., Studies in Deductive Logic, 1880. Vol. 32, No. 822.\n\n    Ribot, Th., The Psychology of Attention, 1890. Vol. 50, No. 1303.\n\n    James, W., The Principles of Psychology, 1890. Vol. 53, Nos. 1357\n    and 1358.\n\n    Comte, A. (F. Harrison, editor), The New Calendar of Great Men,\n    1892. Vol. 54, No. 1386.\n\n    Lobatchewsky, N. (Translator: G. B. Halsted), Geometrical Researches\n    on the Theory of Parallels, 1891. Vol. 54, No. 1389.\n\n    Lombroso, C., The Man of Genius, 1891. Vol. 54, No. 1391.\n\n    Note on William James\u2019 abridgment of his Psychology, 1892. Vol. 54,\n    No. 1394.\n\n    McClelland, W. J., A Treatise on the Geometry of the Circle, 1891.\n    Vol. 54, No. 1395.\n\n    Buckley, Arabella B., Moral Teachings of Science, 1892. Vol. 54, No.\n    1405.\n\n    Hale, E. E., A New England Boyhood, 1893. Vol. 57, No. 1468.\n\n    Mach, E. (Translator: T. J. McCormack), The Science of Mechanics,\n    1893. Vol. 57, No. 1475.\n\n    Ritchie, D. G., Darwin and Hegel, 1893. Vol. 57, No. 1482.\n\n    Huxley, T. H., Method and Results, 1893. Vol. 58, No. 1489.\n\n    Scott, Sir Walter, Familiar Letters of Sir Walter Scott. Vol. 58,\n    No. 1493.\n\n    Gilbert, W. (Translator: P. F. Mottelay), Magnetic Bodies. Vol. 58,\n    No. 1494 and No. 1495.\n\n    Forsyth, A. R., Theory of Functions of a Complex Variable, 1893; and\n    Harkness, J., A Treatise on the Theory of Functions, 1893; and\n    Picard, E., Trait\u00e9 d\u2019analyse, 1893. Vol. 58, No. 1498.\n\n    A Short Sketch of Helmholtz, Sept. 13, 1894. Vol. 59, No. 1524.\n\n    Windelband, W. (Translator: J. H. Tufts), A History of Philosophy;\n    and Falkenberg, R. (Translator: A. C. Armstrong), History of Modern\n    Philosophy; and Bascom, J., An Historical Interpretation of\n    Philosophy; and Burt, B. C., A History of Modern Philosophy. Vol.\n    59, Nos. 1526 and 1527.\n\n    Spinoza (Translators: W. H. White and Amelia H. Stirling), Ethics,\n    1894. Vol. 59, No. 1532.\n\n    Watson, J., Comte, Mill, and Spencer, 1895. Vol. 60, No. 1554.\n\n    Jones, H., A Critical Account of the Philosophy of Lotze, 1895; and\n    Eberhard, V., Die Grundbegriffe der ebenen Geometrie, 1895; and\n    Klein, F. (Translator: A. Ziwet), Riemann and his Significance for\n    the Development of Modern Mathematics, 1895; and Davis, N. K.,\n    Elements of Inductive Logic, 1895. Vol. 61, No. 1566.\n\n    Benjamin, P., The Intellectual Rise in Electricity, 1895. Vol. 62,\n    No. 1592.\n\n    Baldwin, J. M., The Story of the Mind, 1898. Vol. 67, No. 1737.\n\n    Darwin, G. H., The Tides and Kindred Phenomena in the Solar System,\n    1898. Vol. 67, No. 1747.\n\n    Marshall, H. R., Instinct and Reason, 1898. Vol. 68, No. 1774.\n\n    Britten, F. J., Old Clocks and Watches and their Makers, 1899. Vol.\n    69, No. 1778.\n\n    Renouvier, Ch., et Prat, L. La Nouvelle Monadologie, 1899. Vol. 69,\n    No. 1779.\n\n    Mackintosh, R., From Comte to Benjamin Kidd, 1899; and Moore, J. H.,\n    Better-World Philosophy, 1899. Vol. 69, No. 1784.\n\n    Ford, P. L., The Many-sided Franklin, 1899. Vol. 69, No. 1793.\n\n    Avenel, G. d\u2019, Le M\u00e9canisme de la vie moderne, 1900. Vol. 70, No.\n    1805.\n\n    Reid, W., Memoirs and Correspondence of Lyon Playfair, 1899. Vol.\n    70, No. 1806.\n\n    Stevenson, F. S., Robert Grosseteste, 1899. Vol. 70, No. 1816.\n\n    Thilly, F., Introduction to Ethics, 1900. Vol. 70, No. 1825.\n\n    Wallace, A. R., Studies, Scientific and Social, 1900. Vol. 72, No.\n    1854.\n\n    Sime, J., William Herschel and His Work, 1900. Vol. 72, No. 1856.\n\n    Rand, B. (Editor), The Life, Unpublished Letters, and Philosophical\n    Regimen of Anthony, Earl of Shaftesbury, 1900; and Robertson, J. M.\n    (Editor), Characteristics of Men, _etc._, by Shaftesbury, 1900. Vol.\n    72, No. 1857.\n\n    Bacon, Rev. J. M., By Land and Sea, 1901. Vol. 72, No. 1865.\n\n    Jordan, W. L., Essays in Illustration of the Action of Astral\n    Gravitation in Natural Phenomena, 1900. Vol. 72, No. 1876.\n\n    Goblot, E., Le Vocabulaire Philosophique, 1901. Vol. 72, No. 1877.\n\n    Fraser, A. C. (Editor), The Works of George Berkeley, 1901. Vol. 73,\n    No. 1883.\n\n    Frazer, P., Bibliotics, 1901. Vol. 73, No. 1883.\n\n    Caldecott, A., The Philosophy of Religion in England and America,\n    1901. Vol. 73, No. 1885.\n\n    Review of four physical books. Vol. 73, No. 1887.\n\n    Maher, M., Psychology: Empirical and Rational, 1901. Vol. 73, No.\n    1892.\n\n    Mezes, S. E., Ethics, 1901. Vol. 73, No. 1895.\n\n    Report of the Meeting of the National Academy of Sciences,\n    Philadelphia, 1901. Vol. 73, No. 1899.\n\n    Crozier, J. B., History of Intellectual Developments on the Lines of\n    Modern Evolution. Vol. III., 1901, Vol. 74, No. 1908.\n\n    Richardson, E. C., Classification, Theoretical and Practical, 1901.\n    Vol. 74, No. 1913.\n\n    Vallery-Radot, R. (Translator: Mrs. R. L. Devonshire), The Life of\n    Pasteur. Vol. 74, No. 1914.\n\n    Giddings, F. H., Inductive Sociology, 1902. Vol. 74, No. 1918.\n\n    Report on the Meeting of the National Academy of Sciences,\n    Washington, D. C., 1902. Vol. 74, No. 1921.\n\n    Emerson, E. R., The Story of the Vine, 1902. Vol. 74, No. 1926.\n\n    Joachim, H. H., A Study of the Ethics of Spinoza, 1901. Vol. 75, No.\n    1932.\n\n    Review of four chemistry text-books, 1902. Vol. 75, No. 1934.\n\n    Royce, J., The World and the Individual, Vol. II., 1901. Vol. 75,\n    No. 1935. (For a review of Vol. I., probably by Peirce, see 1900,\n    Vol. 70, No. 1814.)\n\n    Thorpe, T. E., Essays in Historical Chemistry, 1902. Vol. 75, No.\n    1938.\n\n    Paulsen, F., Immanuel Kant: His Life and Doctrine, 1902. Vol. 75,\n    No. 1941.\n\n    Aikens, H. A., The Principles of Logic, 1902. Vol. 75, No. 1942.\n\n    Drude, P., The Theory of Optics, 1902. Vol. 75, No. 1944.\n\n    Valentine, E. S., Travels in Space, 1902; and Walker, F., Aerial\n    Navigation, 1902. Vol. 75, No. 1947.\n\n    Baillie, J. B., The Origin and Significance of Hegel\u2019s Logic, 1901.\n    Vol. 75, No. 1950.\n\n    Forsyth, A. R., Theory of Differential Equations, Vol. IV., 1902.\n    Vol. 75, No. 1952.\n\n    Ellwanger, G. W., The Pleasures of the Table, 1902. Vol. 75, No.\n    1955.\n\n    Earle, Alice M., Sundials and Roses of Yesterday, 1902. Vol. 75, No.\n    1956.\n\n    Smith, Rev. T., Euclid: His Life and System, 1902. Vol. 76, No.\n    1961.\n\n    Report on the Meeting of the National Academy of Sciences,\n    Washington, D. C., 1903. Vol. 76, No. 1974.\n\n    Hibben, J. G., Hegel\u2019s Logic, 1902. Vol. 76, No. 1977.\n\n    Mellor, J. W., Higher Mathematics for Students of Chemistry and\n    Physics, 1903. Vol. 76, No. 1977.\n\n    Sturt, H. C. (Editor), Personal Idealism, 1902. Vol. 76, No. 1979.\n\n    Baldwin, J. M., Dictionary of Philosophy and Psychology, Vol. II.,\n    1902. Vol. 76, No. 1980.\n\n    Note on Kant\u2019s Prolegomene edited in English by Dr. P. Carus, 1903.\n    Vol. 76, No. 1981.\n\n    Smith, N., Studies in the Cartesian Philosophy, 1902. Vol. 77, No.\n    1985.\n\n    Hinds, J. I. D., Inorganic Chemistry, 1902. Vol. 77, No. 1986.\n\n    Clerke, Agnes M., Problems in Astrophysics, 1903. Vol. 77, No. 1987.\n\n    Michelson, A. A., Light Waves and their Uses, 1903; and Fleming, J.\n    A., Waves and Ripples in Water, 1902. Vol. 77, No. 1989.\n\n    Note on Sir Norman Lockyer. Vol. 77, No. 1794.\n\n    Note on British and American Science, 1903. Vol. 77, No. 1996.\n\n    Welby, Lady Victoria, What is Meaning? 1903; and Russell, B., The\n    Principles of Mathematics, 1903. Vol. 77, No. 1998.\n\n    Note on the Practical Application of the Theory of Functions, 1903.\n    Vol. 77, No. 1999.\n\n    Fahie, J. J., Galileo. Vol. 78, No. 2015.\n\n    Halsey, F. A., The Metric Fallacy, and Dale, S. S., The Metric\n    Failure in the Textile Industry. Vol. 78, No. 2020.\n\n    Newcomb, S., The Reminiscences of an Astronomer, 1903. Vol. 78, No.\n    2021.\n\n    Boole, Mrs. M. E., Lectures on the Logic of Arithmetic, 1903; and\n    Bowden, J., Elements of the Theory of Integers, 1903. Vol. 78, No.\n    2024.\n\n    Report on the Meeting of the National Academy of Sciences,\n    Washington, D. C., 1904. Vol. 78, No. 2026.\n\n    L\u00e9vy-Bruhl, L. (Translator: Kathleen de Beaumont-Klein), The\n    Philosophy of Auguste Comte, 1903. Vol. 78, No. 2026.\n\n    Turner, W., History of Philosophy, 1903. Vol. 79, No. 2036.\n\n    Duff, R. A., Spinoza\u2019s Political and Ethical Philosophy. Vol. 79,\n    No. 2038.\n\n    Allbutt, T. C., Notes on the Composition of Scientific Papers, 1904.\n    Vol. 79, No. 2039.\n\n    Sylvester, J. J., The Collected Mathematical Papers of, Vol. I. Vol.\n    79, No. 2045.\n\n    Renouvier, Ch., Les Derniers Entretiens, 1904, and Dewey, J.,\n    Studies in Logical Theory, 1903. Vol. 79, No. 2046.\n\n    Royce, J., Outlines of Psychology. Vol. 79, No. 2048.\n\n    Straton, G. M., Experimental Psychology and its Bearing upon\n    Culture. Vol. 79, No. 2055.\n\n    Report on the Meeting of the National Academy of Sciences, New York,\n    1904. Vol. 79, No. 2057.\n\n    Boole, Mrs. M. E., The Preparation of the Child for Science, 1904.\n    Vol. 80, No. 2062.\n\n    Royce, J., Herbert Spencer, 1904. Vol. 80, No. 2065.\n\n    Strutt, R. J., The Becquerel Rays and the Properties of Radium,\n    1904. Vol. 80, No. 2066.\n\n    Schuster, A., An Introduction to the Theory of Optics, 1904. Vol.\n    80, No. 2071.\n\n    Findlay, A., The Phase Rule and its Application, 1904. Vol. 80, No.\n    2074.\n\n    Report on the Meeting of the National Academy of Sciences,\n    Washington, D. C., 1905. Vol. 80, No. 2078.\n\n    Flint, R., Philosophy as Scientia Scientiarum, 1904; and Peirce, C.\n    S., A Syllabus of Certain Topics of Logic, 1903. Vol. 80, No. 2079.\n\n    Arnold, R. B., Scientific Fact and Metaphysical Reality, 1904, also\n    a Note on Mendeleeff\u2019s Principles of Chemistry. Vol. 80, No. 2083.\n\n    Note on Ida Freund\u2019s The Study of Chemical Composition. Vol. 80, No.\n    2086.\n\n    Carnegie, A., James Watt, 1905. Vol. 80, No. 2087.\n\n    Ross, E. A., Foundations of Sociology, 1905, and Sociological\n    Papers, 1905, published by the Sociological Society. Vol. 81, No.\n    2089.\n\n    Wundt, W. (Translator: E. B. Titchener), Principles of Physiological\n    Psychology, 1904. Vol. 81, No. 2090.\n\n    Roscoe, H. E., A Treatise on Chemistry, Vol. I., 1905, and de\n    Fleury, M., Nos Enfants au Coll\u00e8ge, 1905. Vol. 81, No. 2097.\n\n    Varigny, H. de, La Nature et la Vie, 1905. Vol. 81, No. 2101.\n\n    Note on Mr. G. W. Hill\u2019s Moon Theory. Vol. 81, 2103.\n\n    Report on the Meeting of the National Academy of Sciences, New\n    Haven, 1905. Vol. 81, No. 2108.\n\n    Gosse, E., Sir Thomas Browne, 1905. Vol. 81, No. 2111.\n\n    Rutherford, E., Radio-Activity, 1905. Vol. 82, No. 2116.\n\n    Wallace, A. R., My Life, 1905. Vol. 82, No. 2121.\n\n    Haldane, Elizabeth S., Descartes. Vol. 82, No. 2125.\n\n    Report on the Meeting of the National Academy of Sciences,\n    Washington, D. C., 1906. Vol. 82, No. 2130.\n\n    Rogers, H. J. (Editor), Congress of Arts and Sciences, Universal\n    Exposition, St. Louis, 1904. Vol. 82, No. 2136.\n\n    Loeb, J., The Dynamics of Living Matter; and Mann, G., Chemistry of\n    the Proteids. Vol. 83, No. 2140.\n\n    Roscoe, H. E., The Life and Experiences of Sir Henry Enfield Roscoe.\n    Vol. 83, No. 2141.\n\n    Marshall, T., Aristotle\u2019s Theory of Conduct. Vol. 83, No. 2150.\n\n    Joseph, H. W. B., An Introduction to Logic. Vol. 83, No. 2156.\n\nOTHER ARTICLES AND REVIEWS\n\n    Old Stone Mill at Newport, _Science_, 4, 1884, 512.\n\n    Criticism on \u201cPhantasms of the Living,\u201d _Proc. Am. Soc. Psychical\n    Research_, Vol. 1, No. 3 (1887).\n\n    Napoleon Intime, _The Independent_, December 21 and December 28,\n    1893.\n\n    Decennial Celebration of Clark University, _Science_, 11 (1900), p.\n    620.\n\n    Century\u2019s Great Men of Science, _Smithsonian Institute Reports_,\n    1900.\n\n    Campanus _Science_, 13 (1901), p. 809.\n\n    French Academy of Science, N. Y. Evening _Post_, March 5, 1904.\n\nFootnote 88:\n\n  The following classification is arbitrary, as some of Peirce\u2019s most\n  significant reflections occur in papers under headings II. and III. It\n  may, however, be useful.\n\n\n\n\n \u25cf Transcriber\u2019s Notes:\n    \u25cb Text that was in italics is enclosed by underscores (_italics_).\n      Text that was in bold face is enclosed by equals signs (=bold=).\n    \u25cb Footnotes have been moved to follow the chapters in which they are\n      referenced.\n    \u25cb Numbers raised to a power are denoted by the caret sign: 2^5 is 2\n      raised to the 5th power. Powers may be enclosed in curly brackets,\n      so 2^{32} is 2 raised to the 32nd power.\n    \u25cb Subscripts are denoted by an underscore followed by the subscript\n      in curly brackets, so O_{2} means O followed by a subscript 2.","title":"Chance, Love, and Logic: Philosophical Essays","tradition":"philosophy-ethics","translated_text":null,"word_count":96720}