{"collection":"philosophy-ethics","full_text_available":true,"graph_url":"https://unchartedknowledge.5gfusion.net/v2/api/page/gutenberg_31796/graph","html_url":"https://unchartedknowledge.5gfusion.net/v2/page/gutenberg_31796","id":"gutenberg_31796","license":"Public Domain (US)","rights_basis":"gutenberg_metadata_copyright_false","source":"gutenberg","source_url":"https://www.gutenberg.org/ebooks/31796","summary":null,"tags":["Category: Philosophy & Ethics","Category: Teaching & Education","Logic","Philosophy"],"text":"Produced by Thierry Alberto, Lesley Halamek and the Online\nDistributed Proofreading Team at http://www.pgdp.net\n\n\n\n\n\nUNIVERSITY MANUALS\n\nEDITED BY PROFESSOR KNIGHT\n\n\nLOGIC\n\nINDUCTIVE AND DEDUCTIVE\n\n  PUBLISHED MAY, 1893\n  _Reprinted December, 1893_\n     \"      _November, 1894_\n     \"      _January, 1899_\n     \"      _August, 1904_\n     \"      _June, 1909_\n     \"      _September, 1912_\n     \"      _July, 1913_\n     \"      _January, 1915_\n\n\n\n\n  LOGIC\n\n  INDUCTIVE AND DEDUCTIVE\n\n\n  BY WILLIAM MINTO, M.A.\n  HON. LL.D. ST. ANDREWS\n  LATE PROFESSOR OF LOGIC IN THE UNIVERSITY OF ABERDEEN\n\n\n\n\n  LONDON\n  JOHN MURRAY, ALBEMARLE STREET, W.\n  1915\n\n\n\n\nPREFACE.\n\nIn this little treatise two things are attempted that at first might\nappear incompatible. One of them is to put the study of logical\nformulae on a historical basis. Strangely enough, the scientific\nevolution of logical forms, is a bit of history that still awaits the\nzeal and genius of some great scholar. I have neither ambition nor\nqualification for such a _magnum opus_, and my life is already more\nthan half spent; but the gap in evolutionary research is so obvious\nthat doubtless some younger man is now at work in the field unknown to\nme. All that I can hope to do is to act as a humble pioneer according\nto my imperfect lights. Even the little I have done represents work\nbegun more than twenty years ago, and continuously pursued for the\nlast twelve years during a considerable portion of my time.\n\nThe other aim, which might at first appear inconsistent with this,\nis to increase the power of Logic as a practical discipline. The main\npurpose of this practical science, or scientific art, is conceived to\nbe the organisation of reason against error, and error in its various\nkinds is made the basis of the division of the subject. To carry out\nthis practical aim along with the historical one is not hopeless,\nbecause throughout its long history Logic has been a practical\nscience; and, as I have tried to show at some length in introductory\nchapters, has concerned itself at different periods with the risks of\nerror peculiar to each.\n\nTo enumerate the various books, ancient and modern, to which I have\nbeen indebted, would be a vain parade. Where I have consciously\nadopted any distinctive recent contribution to the long line of\ntradition, I have made particular acknowledgment. My greatest\nobligation is to my old professor, Alexander Bain, to whom I owe my\nfirst interest in the subject, and more details than I can possibly\nseparate from the general body of my knowledge.\n\n  W. M.\n\n  ABERDEEN, _January, 1893_.\n\n\n\n\nSince these sentences were written, the author of this book has\ndied; and Professor Minto's _Logic_ is his last contribution to the\nliterature of his country. It embodies a large part of his teaching in\nthe philosophical class-room of his University, and doubtless reflects\nthe spirit of the whole of it.\n\nScottish Philosophy has lost in him one of its typical\nrepresentatives, and the University of the North one of its most\nstimulating teachers. There have been few more distinguished men than\nWilliam Minto in the professoriate of Aberdeen; and the memory of what\nhe was, of his wide and varied learning, his brilliant conversation,\nhis urbanity, and his rare power of sympathy with men with whose\nopinions he did not agree, will remain a possession to many who mourn\nhis loss.\n\nIt will be something if this little book keeps his memory alive, both\namongst the students who owed so much to him, and in the large circle\nof friends who used to feel the charm of his personality.\n\n  WILLIAM KNIGHT.\n\n\n\n\n_GENERAL PLAN OF THE SERIES._\n\n_This Series is primarily designed to aid the University Extension\nMovement throughout Great Britain and America, and to supply the need\nso widely felt by students, of Text-books for study and reference, in\nconnexion with the authorised Courses of Lectures._\n\n_The Manuals differ from those already in existence in that they are\nnot intended for School use, or for Examination purposes; and that\ntheir aim is to educate, rather than to inform. The statement of\ndetails is meant to illustrate the working of general laws, and the\ndevelopment of principles; while the historical evolution of the\nsubject dealt with is kept in view, along with its philosophical\nsignificance._\n\n_The remarkable success which has attended University Extension in\nBritain has been partly due to the combination of scientific treatment\nwith popularity, and to the union of simplicity with thoroughness.\nThis movement, however, can only reach those resident in the larger\ncentres of population, while all over the country there are thoughtful\npersons who desire the same kind of teaching. It is for them also that\nthis Series is designed. Its aim is to supply the general reader with\nthe same kind of teaching as is given in the Lectures, and to reflect\nthe spirit which has characterised the movement, viz., the combination\nof principles with facts, and of methods with results._\n\n_The Manuals are also intended to be contributions to the Literature\nof the Subjects with which they respectively deal, quite apart from\nUniversity Extension; and some of them will be found to meet a general\nrather than a special want._\n\n_They will be issued simultaneously in England and America. Volumes\ndealing with separate sections of Literature, Science, Philosophy,\nHistory, and Art have been assigned to representative literary men,\nto University Professors, or to Extension Lecturers connected with\nOxford, Cambridge, London, and the Universities of Scotland and\nIreland._\n\n_A list of the works in this Series will be found at the end of the\nvolume._\n\n\n\n\n  CONTENTS.\n\n  INTRODUCTION.\n\n  I.\n                                                                  PAGE\n\n  The Origin and Scope of Logic,                                    1\n\n  II.\n\n  Logic as a Preventive of Error or Fallacy--The Inner\n Sophist,                                                          17\n\n  III.\n\n  The Axioms of Dialectic and of Syllogism,                        29\n\n  BOOK I.\n\n  THE LOGIC OF CONSISTENCY--SYLLOGISM AND\n  DEFINITION.\n\n  PART I.\n\n  THE ELEMENTS OF PROPOSITIONS.\n\n  CHAPTER I.\n\n  General Names and Allied Distinctions,                           43\n\n  CHAPTER II.\n\n  The Syllogistic Analysis of Proposition, into Terms. (1)\n  The Bare Analytic Forms. (2) The Practice of Syllogistic\n  Analysis. (3) Some Technical Difficulties,                        62\n\n  PART II.\n\n  DEFINITION.\n\n  CHAPTER I.\n\n  (1) Imperfect Understanding of Words. (2) Verification of\n  the Meaning--Dialectic. (3) Fixation of the Meaning--Division\n  or Classification, Definition, Naming,                           82\n\n  CHAPTER II.\n\n  The Five Predicables--Verbal and Real Predication,              105\n\n  CHAPTER III.\n\n  Aristotle's Categories,                                         112\n\n  CHAPTER IV.\n\n  The Controversy about Universals--Difficulties concerning\n  the Relation of General Names to Thought and to Reality,        120\n\n  PART III.\n\n  THE INTERPRETATION OF PROPOSITIONS.\n\n  CHAPTER I.\n\n  Theories of Predication--Theories of Judgment,                  131\n\n  CHAPTER II.\n\n  The \"Opposition\" of Propositions--The Interpretation of\n  \"No,\"                                                           139\n\n  CHAPTER III.\n\n  The Implication of Propositions--Immediate Formal Inference\n  --Eduction,                                                     146\n\n  CHAPTER IV.\n\n  The Counter-Implication of Propositions,                        156\n\n  PART IV.\n\n  THE INTERDEPENDENCE OF PROPOSITIONS.\n\n  CHAPTER I.\n\n  The Syllogism,                                                  167\n\n  CHAPTER II.\n\n  The Figures and Moods of the Syllogism. (1) The First\n  Figure. (2) The Minor Figures and their Reduction to\n  the First. (3) Sorites,                                         173\n\n  CHAPTER III.\n\n  The Demonstration of the Syllogistic Moods--The Canons\n  of the Syllogism,                                               185\n\n  CHAPTER IV.\n\n  The Analysis of Arguments into Syllogistic Forms,               196\n\n  CHAPTER V.\n\n  Enthymemes,                                                     205\n\n  CHAPTER VI.\n\n  The Utility of the Syllogism,                                   209\n\n  CHAPTER VII.\n\n  Conditional Arguments--Hypothetical Syllogism, Disjunctive\n  Syllogism and Dilemma,                                          215\n\n  CHAPTER VIII.\n\n  Fallacies in Deductive Argument--_Petitio Principii_ and\n  _Ignoratio Elenchi_,                                            226\n\n  CHAPTER IX.\n\n  Formal or Aristotelian Induction--Inductive Argument--The\n  Inductive Syllogism,                                            235\n\n  BOOK II.\n\n  INDUCTIVE LOGIC, OR THE LOGIC OF SCIENCE.\n\n  Introduction,                                                   243\n\n  CHAPTER I.\n\n  The Data of Experience as Grounds of Inference or Rational\n  Belief,                                                         273\n\n  CHAPTER II.\n\n  Ascertainment of Simple Facts in their Order--Personal\n  Observation--Hearsay Evidence--Method of Testing\n  Traditional Evidence,                                           285\n\n  CHAPTER III.\n\n  Ascertainment of Facts of Causation. (1) _Post Hoc Ergo\n  Propter Hoc._ (2) Meaning of Cause--Methods of Observation\n  --Mill's Experimental Methods,                                  295\n\n  CHAPTER IV.\n\n  Method of Observation--Single Difference. (1) The Principle\n  of Single Difference. (2) Application of the Principle,         308\n\n  CHAPTER V.\n\n  Methods of Observation--Elimination--Single Agreement.\n  (1) The Principle of Elimination. (2) The Principle of\n  Single Agreement. (3) Mill's \"Joint Method of Agreement\n  and Difference,\"                                                318\n\n  CHAPTER VI.\n\n  Methods of Observation--Minor Methods. (1) Concomitant\n  Variations. (2) Single Residue,                                 329\n\n  CHAPTER VII.\n\n  The Method of Explanation. (1) The Four Stages of Orderly\n  Procedure. (2) Obstacles to Explanation--Plurality of Causes\n  and Intermixture of Effects. (3) The Proof of a Hypothesis,     334\n\n  CHAPTER VIII.\n\n  Supplementary Methods of Investigation. (1) The Maintenance\n  of Averages--Supplement to the Method of Difference.\n  (2) The Presumption from Extra-Casual Coincidence,              351\n\n  CHAPTER IX.\n\n  Probable Inference to Particulars--The Measurement of\n  Probability,                                                    362\n\n  CHAPTER X.\n\n  Inference from Analogy,                                         367\n\n\n\n\nINTRODUCTION.\n\n\nI.--THE ORIGIN AND SCOPE OF LOGIC.\n\nThe question has sometimes been asked, Where should we begin in Logic?\nParticularly within the present century has this difficulty been felt,\nwhen the study of Logic has been revived and made intricate by the\ndifferent purposes of its cultivators.\n\nWhere did the founder of Logic begin? Where did Aristotle begin? This\nseems to be the simplest way of settling where we should begin, for\nthe system shaped by Aristotle is still the trunk of the tree, though\nthere have been so many offshoots from the old stump and so many\nparasitic plants have wound themselves round it that Logic is now\nalmost as tangled a growth as the Yews of Borrowdale--\n\n  An intertwisted mass of fibres serpentine\n  Upcoiling and inveterately convolved.\n\nIt used to be said that Logic had remained for two thousand years\nprecisely as Aristotle left it. It was an example of a science or\nart perfected at one stroke by the genius of its first inventor.\nThe bewildered student must often wish that this were so: it is only\nsuperficially true. Much of Aristotle's nomenclature and his central\nformulae have been retained, but they have been very variously\nsupplemented and interpreted to very different purposes--often to no\npurpose at all.\n\nThe Cambridge mathematician's boast about his new theorem--\"The best\nof it all is that it can never by any possibility be made of the\nslightest use to anybody for anything\"--might be made with truth about\nmany of the later developments of Logic. We may say the same, indeed,\nabout the later developments of any subject that has been a playground\nfor generation after generation of acute intellects, happy in\ntheir own disinterested exercise. Educational subjects--subjects\nappropriated for the general schooling of young minds--are\nparticularly apt to be developed out of the lines of their original\nintention. So many influences conspire to pervert the original aim.\nThe convenience of the teacher, the convenience of the learner,\nthe love of novelty, the love of symmetry, the love of subtlety;\neasy-going indolence on the one hand and intellectual restlessness\non the other--all these motives act from within on traditional\nmatter without regard to any external purpose whatever. Thus in\nLogic difficulties have been glossed over and simplified for the dull\nunderstanding, while acute minds have revelled in variations and new\nand ingenious manipulations of the old formulae, and in multiplication\nand more exact and symmetrical definition of the old distinctions.\n\nTo trace the evolution of the forms and theories of Logic under these\nvarious influences during its periods of active development is a task\nmore easily conceived than executed, and one far above the ambition of\nan introductory treatise. But it is well that even he who writes for\nbeginners should recognise that the forms now commonly used have been\nevolved out of a simpler tradition. Without entering into the details\nof the process, it is possible to indicate its main stages, and thus\nfurnish a clue out of the modern labyrinthine confusion of purposes.\n\nHow did the Aristotelian Logic originate? Its central feature is the\nsyllogistic forms. In what circumstances did Aristotle invent these?\nFor what purpose? What use did he contemplate for them? In rightly\nunderstanding this, we shall understand the original scope or province\nof Logic, and thus be in a position to understand more clearly how it\nhas been modified, contracted, expanded, and supplemented.\n\nLogic has always made high claims as the _scientia scientiarum_,\nthe science of sciences. The builders of this Tower of Babel are\nthreatened in these latter days with confusion of tongues. We may\nescape this danger if we can recover the designs of the founder, and\nof the master-builders who succeeded him.\n\nAristotle's Logic has been so long before the world in abstract\nisolation that we can hardly believe that its form was in any way\ndetermined by local accident. A horror as of sacrilege is excited by\nthe bare suggestion that the author of this grand and venerable work,\none of the most august monuments of transcendent intellect, was in his\nday and generation only a pre-eminent tutor or schoolmaster, and\nthat his logical writings were designed for the accomplishment of his\npupils in a special art in which every intellectually ambitious young\nAthenian of the period aspired to excel. Yet such is the plain fact,\nbaldly stated. Aristotle's Logic in its primary aim was as practical\nas a treatise on Navigation, or \"Cavendish on Whist\". The latter is\nthe more exact of the two comparisons. It was in effect in its various\nparts a series of handbooks for a temporarily fashionable intellectual\ngame, a peculiar mode of disputation or dialectic,[1] the game of\nQuestion and Answer, the game so fully illustrated in the Dialogues of\nPlato, the game identified with the name of Socrates.\n\nWe may lay stress, if we like, on the intellectuality of the game, and\nthe high topics on which it was exercised. It was a game that could\nflourish only among a peculiarly intellectual people; a people less\nacute would find little sport in it. The Athenians still take a\nsingular delight in disputation. You cannot visit Athens without being\nstruck by it. You may still see groups formed round two protagonists\nin the cafes or the squares, or among the ruins of the Acropolis, in\na way to remind you of Socrates and his friends. They do not argue as\nGil Blas and his Hibernians did with heat and temper, ending in blows.\nThey argue for the pure love of arguing, the audience sitting\nor standing by to see fair play with the keenest enjoyment of\nintellectual thrust and parry. No other people could argue like the\nGreeks without coming to blows. It is one of their characteristics\nnow, and so it was in old times two thousand years ago. And about\na century before Aristotle reached manhood, they had invented this\npeculiarly difficult and trying species of disputative pastime, in\nwhich we find the genesis of Aristotle's logical treatises.\n\nTo get a proper idea of this debate by Question and Answer, which we\nmay call Socratic disputation after its most renowned master, one\nmust read some of the dialogues of Plato. I will indicate merely\nthe skeleton of the game, to show how happily it lent itself to\nAristotle's analysis of arguments and propositions.\n\nA thesis or proposition is put up for debate, _e.g._, that knowledge\nis nothing else than sensible perception,[2] that it is a greater\nevil to do wrong than to suffer wrong,[3] that the love of gain is not\nreprehensible.[4] There are two disputants, but they do not speak on\nthe question by turns, so many minutes being allowed to each as in\na modern encounter of wits. One of the two, who may be called the\nQuestioner, is limited to asking questions, the other, the Respondent,\nis limited to answering. Further, the Respondent can answer only \"Yes\"\nor \"No,\" with perhaps a little explanation: on his side the Questioner\nmust ask only questions that admit of the simple answer \"Yes\" or \"No\".\nThe Questioner's business is to extract from the Respondent admissions\ninvolving the opposite of what he has undertaken to maintain. The\nQuestioner tries in short to make him contradict himself. Only a very\nstupid Respondent would do this at once: the Questioner plies him\nwith general principles, analogies, plain cases; leads him on from\nadmission to admission, and then putting the admissions together\nconvicts him out of his own mouth of inconsistency.[5]\n\nNow mark precisely where Aristotle struck in with his invention of the\nSyllogism, the invention on which he prided himself as specially his\nown, and the forms of which have clung to Logic ever since, even\nin the usage of those who deride Aristotle's Moods and Figures as\nantiquated superstitions. Suppose yourself the Questioner, where did\nhe profess to help you with his mechanism? In effect, as the word\nSyllogism indicates, it was when you had obtained a number of\nadmissions, and wished to reason them together, to demonstrate how\nthey bore upon the thesis in dispute, how they hung together, how they\nnecessarily involved what you were contending for. And the essence of\nhis mechanism was the reduction of the admitted propositions to common\nterms, and to certain types or forms which are manifestly equivalent\nor inter-dependent. Aristotle advised his pupils also in the\ntactics of the game, but his grand invention was the form or type\nof admissions that you should strive to obtain, and the effective\nmanipulation of them when you had got them.\n\nAn example will show the nature of this help, and what it was worth.\nTo bring the thing nearer home, let us, instead of an example from\nPlato, whose topics often seem artificial to us now, take a thesis\nfrom last century, a paradox still arguable, Mandeville's famous--some\nwould say infamous--paradox that Private Vices are Public Benefits.\nUndertake to maintain this, and you will have no difficulty in getting\na respondent prepared to maintain the negative. The plain men, such as\nSocrates cross-questioned, would have declared at once that a vice is\na vice, and can never do any good to anybody. Your Respondent denies\nyour proposition simply: he upholds that private vices never are\npublic benefits, and defies you to extract from him any admission\ninconsistent with this. Your task then is to lure him somehow into\nadmitting that in some cases what is vicious in the individual may\nbe of service to the State. This is enough: you are not concerned to\nestablish that this holds of all private vices. A single instance\nto the contrary is enough to break down his universal negative. You\ncannot, of course, expect him to make the necessary admission in\ndirect terms: you must go round about. You know, perhaps, that he\nhas confidence in Bishop Butler as a moralist. You try him with the\nsaying: \"To aim at public and private good are so far from being\ninconsistent that they mutually promote each other\". Does he admit\nthis?\n\nPerhaps he wants some little explanation or exemplification to enable\nhim to grasp your meaning. This was within the rules of the game. You\nput cases to him, asking for his \"Yes\" or \"No\" to each. Suppose a man\ngoes into Parliament, not out of any zeal for the public good, but in\npure vainglory, or to serve his private ends, is it possible for him\nto render the State good service? Or suppose a milk-seller takes\ngreat pains to keep his milk pure, not because he cares for the public\nhealth, but because it pays, is this a benefit to the public?\n\nLet these questions be answered in the affirmative, putting you in\npossession of the admission that some actions undertaken for private\nends are of public advantage, what must you extract besides to make\ngood your position as against the Respondent? To see clearly at this\nstage what now is required, though you have to reach it circuitously,\nmasking your approach under difference of language, would clearly be\nan advantage. This was the advantage that Aristotle's method offered\nto supply. A disputant familiar with his analysis would foresee at\nonce that if he could get the Respondent to admit that all actions\nundertaken for private ends are vicious, the victory was his, while\nnothing short of this would serve.\n\nHere my reader may interject that he could have seen this without any\nhelp from Aristotle, and that anybody may see it without knowing\nthat what he has to do is, in Aristotelian language, to construct a\nsyllogism in Bokardo. I pass this over. I am not concerned at this\npoint to defend the utility of Aristotle's method. All that I want\nis to illustrate the kind of use that it was intended for. Perhaps if\nAristotle had not habituated men's minds to his analysis, we should\nnone of us have been able to discern coherence and detect incoherence\nas quickly and clearly as we do now.\n\nBut to return to our example. As Aristotle's pupil, you would have\nseen at the stage we are speaking of that the establishment of your\nthesis must turn upon the definition of virtue and vice. You must\nproceed, therefore, to cross-examine your Respondent about this. You\nare not allowed to ask him what he means by virtue, or what he means\nby vice. In accordance with the rules of the dialectic, it is your\nbusiness to propound definitions, and demand his Yes or No to them.\nYou ask him, say, whether he agrees with Shaftesbury's definition of a\nvirtuous action as an action undertaken purely for the good of others.\nIf he assents, it follows that an action undertaken with any suspicion\nof a self-interested motive cannot be numbered among the virtues.\nIf he agrees, further, that every action must be either vicious\nor virtuous, you have admissions sufficient to prove your original\nthesis. All that you have now to do to make your triumph manifest, is\nto display the admissions you have obtained in common terms.\n\n    Some actions done with a self-interested motive are public\n    benefits. All actions done with a self-interested motive are\n    private vices.\n\nFrom these premisses it follows irresistibly that\n\n    Some private vices are public benefits.\n\nThis illustration may serve to show the kind of disputation for which\nAristotle's logic was designed, and thus to make clear its primary\nuses and its limitations.\n\nTo realise its uses, and judge whether there is anything analogous\nto them in modern needs, conceive the chief things that it behoved\nQuestioner and Respondent in this game to know. All that a proposition\nnecessarily implies; all that two propositions put together imply; on\nwhat conditions and to what extent one admission is inconsistent with\nanother; when one admission necessarily involves another; when two\nnecessarily involve a third. And to these ends it was obviously\nnecessary to have an exact understanding of the terms used, so as to\navoid the snares of ambiguous language.\n\nThat a Syllogistic or Logic of Consistency should emerge out of\nYes-and-No Dialectic was natural. Things in this world come when they\nare wanted: inventions are made on the spur of necessity. It was above\nall necessary in this kind of debate to avoid contradicting yourself:\nto maintain your consistency. A clever interrogator spread out\nproposition after proposition before you and invited your assent,\nchoosing forms of words likely to catch your prejudices and lure\nyou into self-contradiction. An organon, instrument, or discipline\ncalculated to protect you as Respondent and guide you as Questioner\nby making clear what an admission led to, was urgently called for,\nand when the game had been in high fashion for more than a century\nAristotle's genius devised what was wanted, meeting at the same time,\nno doubt, collateral needs that had arisen from the application of\nDialectic to various kinds of subject-matter.\n\nThe thoroughness of Aristotle's system was doubtless due partly to\nthe searching character of the dialectic in which it had its birth.\nNo other mode of disputation makes such demands upon the disputant's\nintellectual agility and precision, or is so well adapted to lay bare\nthe skeleton of an argument.\n\nThe uses of Aristotle's logical treatises remained when the fashion\nthat had called them forth had passed.[6] Clear and consistent\nthinking, a mastery of the perplexities and ambiguities of language,\npower to detect identity of meaning under difference of expression, a\nready apprehension of all that a proposition implies, all that may\nbe educed or deduced from it--whatever helps to these ends must be of\nperpetual use. \"To purge the understanding of those errors which lie\nin the confusion and perplexities of an inconsequent thinking,\" is\na modern description of the main scope of Logic.[7] It is a good\ndescription of the branch of Logic that keeps closest to the\nAristotelian tradition.\n\nThe limitations as well as the uses of Aristotle's logic may be traced\nto the circumstances of its origin. Both parties to the disputation,\nQuestioner and Respondent alike, were mainly concerned with the\ninter-dependence of the propositions put forward. Once the Respondent\nhad given his assent to a question, he was bound in consistency to all\nthat it implied. He must take all the consequences of his admission.\nIt might be true or it might be false as a matter of fact: all the\nsame he was bound by it: its truth or falsehood was immaterial to his\nposition as a disputant. On the other hand, the Questioner could not\ngo beyond the admissions of the Respondent. It has often been alleged\nas a defect in the Syllogism that the conclusion does not go beyond\nthe premisses, and ingenious attempts have been made to show that\nit is really an advance upon the premisses. But having regard to the\nprimary use of the syllogism, this was no defect, but a necessary\ncharacter of the relation. The Questioner could not in fairness assume\nmore than had been granted by implication. His advance could only be\nan argumentative advance: if his conclusion contained a grain more\nthan was contained in the premisses, it was a sophistical trick, and\nthe Respondent could draw back and withhold his assent. He was bound\nin consistency to stand by his admissions; he was not bound to go a\nfraction of an inch beyond them.\n\nWe thus see how vain it is to look to the Aristotelian tradition\nfor an organon of truth or a criterion of falsehood. Directly and\nprimarily, at least, it was not so; the circumstances of its origin\ngave it a different bent. Indirectly and secondarily, no doubt, it\nserved this purpose, inasmuch as truth was the aim of all serious\nthinkers who sought to clear their minds and the minds of others by\nDialectic. But in actual debate truth was represented merely by the\ncommon-sense of the audience. A dialectician who gained a triumph\nby outraging this, however cleverly he might outwit his antagonist,\nsucceeded only in amusing his audience, and dialecticians of the\ngraver sort aimed at more serious uses and a more respectful homage,\nand did their best to discountenance merely eristic disputation.\nFurther, it would be a mistake to conclude because Aristotle's Logic,\nas an instrument of Dialectic, concerned itself with the syllogism\nof propositions rather than their truth, that it was merely an art of\nquibbling. On the contrary, it was essentially the art of preventing\nand exposing quibbling. It had its origin in quibbling, no doubt,\ninasmuch as what we should call verbal quibbling was of the essence\nof Yes-and-No Dialectic, and the main secret of its charm for an\nintellectual and disputatious people; but it came into being as a\nsafeguard against quibbling, not a serviceable adjunct.\n\n\nThe mediaeval developments of Logic retained and even exaggerated\nthe syllogistic character of the original treatises. Interrogative\ndialectic had disappeared in the Middle Ages whether as a diversion or\nas a discipline: but errors of inconsistency still remained the errors\nagainst which principally educated men needed a safeguard. Men had\nto keep their utterances in harmony with the dogmas of the Church. A\nclear hold of the exact implications of a proposition, whether singly\nor in combination with other propositions, was still an important\npractical need. The Inductive Syllogism was not required, and its\ntreatment dwindled to insignificance in mediaeval text-books, but the\nDeductive Syllogism and the formal apparatus for the definition of\nterms held the field.\n\nIt was when observation of Nature and its laws became a paramount\npursuit that the defects of Syllogistic Logic began to be felt. Errors\nagainst which this Logic offered no protection then called for a\nsafeguard--especially the errors to which men are liable in the\ninvestigation of cause and effect. \"Bring your thoughts into harmony\none with another,\" was the demand of Aristotle's age. \"Bring your\nthoughts into harmony with authority,\" was the demand of the Middle\nAges. \"Bring them into harmony with fact,\" was the requirement most\nkeenly felt in more recent times. It is in response to this demand\nthat what is commonly but not very happily known as Inductive Logic\nhas been formulated.\n\nIn obedience to custom, I shall follow the now ordinary division of\nLogic into Deductive and Inductive. The titles are misleading in many\nways, but they are fixed by a weight of usage which it would be vain\nto try to unsettle. Both come charging down the stream of time\neach with its cohort of doctrines behind it, borne forward with\nirresistible momentum.\n\nThe best way of preventing confusion now is to retain the established\ntitles, recognise that the doctrines behind each have a radically\ndifferent aim or end, and supply the interpretation of this end from\nhistory. What they have in common may be described as the prevention\nof error, the organisation of reason against error. I have shown\nthat owing to the bent impressed upon it by the circumstances of its\norigin, the errors chiefly safeguarded by the Aristotelian logic\nwere the errors of inconsistency. The other branch of Logic, commonly\ncalled Induction, was really a separate evolution, having its origin\nin a different practical need. The history of this I will trace\nseparately after we have seen our way through the Aristotelian\ntradition and its accretions. The Experimental Methods are no less\nmanifestly the germ, the evolutionary centre or starting-point, of\nthe new Logic than the Syllogism is of the old, and the main errors\nsafeguarded are errors of fact and inference from fact.\n\nAt this stage it will be enough to indicate briefly the broad\nrelations between Deductive Logic and Inductive Logic.\n\nInductive Logic, as we now understand it--the Logic of Observation and\nExplanation--was first formulated and articulated to a System of Logic\nby J. S. Mill. It was he that added this wing to the old building.\nBut the need of it was clearly expressed as early as the thirteenth\ncentury. Roger Bacon, the Franciscan friar (1214-1292), and not his\nmore illustrious namesake Francis, Lord Verulam, was the real founder\nof Inductive Logic. It is remarkable that the same century saw\nSyllogistic Logic advanced to its most complete development in the\nsystem of Petrus Hispanus, a Portuguese scholar who under the title of\nJohn XXI. filled the Papal Chair for eight months in 1276-7.\n\nA casual remark of Roger Bacon's in the course of his advocacy of\nExperimental Science in the _Opus Majus_ draws a clear line between\nthe two branches of Logic. \"There are,\" he says, \"two ways of knowing,\nby Argument and by Experience. Argument concludes a question, but\nit does not make us feel certain, unless the truth be also found in\nexperience.\"\n\nOn this basis the old Logic may be clearly distinguished from the new,\ntaking as the general aim of Logic the protection of the mind against\nthe errors to which it is liable in the acquisition of knowledge.\n\nAll knowledge, broadly speaking, comes either from Authority, _i.e._,\nby argument from accepted premisses, or from Experience. If it comes\nfrom Authority it comes through the medium of words: if it comes from\nExperience it comes through the senses. In taking in knowledge through\nwords we are liable to certain errors; and in taking in knowledge\nthrough the senses we are liable to certain errors. To protect against\nthe one is the main end of \"Deductive\" Logic: to protect against the\nother is the main end of \"Inductive\" Logic. As a matter of fact the\npith of treatises on Deduction and Induction is directed to those ends\nrespectively, the old meanings of Deduction and Induction as formal\nprocesses (to be explained afterwards) being virtually ignored.\n\nThere is thus no antagonism whatever between the two branches of\nLogic. They are directed to different ends. The one is supplementary\nto the other. The one cannot supersede the other.\n\nAristotelian Logic can never become superfluous as long as men are apt\nto be led astray by words. Its ultimate business is to safeguard in\nthe interpretation of the tradition of language. The mere syllogistic,\nthe bare forms of equivalent or consistent expression, have a very\nlimited utility, as we shall see. But by cogent sequence syllogism\nleads to proposition, and proposition to term, and term to a close\nstudy of the relations between words and thoughts and things.\n\n    [Footnote 1: We know for certain--and it is one of the\n    evidences of the importance attached to this trivial-looking\n    pastime--that two of the great teacher's logical treatises,\n    the Topics and the Sophistical Refutations, were written\n    especially for the guidance of Questioners and Respondents.\n    The one instructs the disputant how to qualify himself\n    methodically for discussion before an ordinary audience, when\n    the admissions extracted from the respondent are matters of\n    common belief, the questioner's skill being directed to make\n    it appear that the respondent's position is inconsistent\n    with these. The other is a systematic exposure of sophistical\n    tricks, mostly verbal quibbles, whereby a delusive appearance\n    of victory in debate may be obtained. But in the concluding\n    chapter of the _Elenchi_, where Aristotle claims not only\n    that his method is superior to the empirical methods of\n    rival teachers, but that it is entirely original, it is the\n    Syllogism upon which he lays stress as his peculiar and\n    chief invention. The Syllogism, the pure forms of which are\n    expounded in his Prior Analytics, is really the centre of\n    Aristotle's logical system, whether the propositions to\n    which it is applied are matters of scientific truth as in the\n    Posterior Analytics, or matters of common opinion as in\n    the Topics. The treatise on Interpretation, _i.e._, the\n    interpretation of the Respondent's \"Yes\" and \"No,\" is\n    preliminary to the Syllogism, the reasoning of the admissions\n    together. Even in the half-grammatical half-logical treatise\n    on the Categories, the author always keeps an eye on the\n    Syllogistic analysis.]\n\n    [Footnote 2: Theaetetus, 151 E.]\n\n    [Footnote 3: Gorgias, 473 D.]\n\n    [Footnote 4: Hipparchus, 225 A.]\n\n    [Footnote 5: In its leading and primary use, this was a mode\n    of debate, a duel of wits, in which two men engaged before\n    an audience. But the same form could be used, and was used,\n    notably by Socrates, not in an eristic spirit but as a means\n    of awakening people to the consequences of certain admissions\n    or first principles, and thus making vague knowledge explicit\n    and clear. The mind being detained on proposition after\n    proposition as assent was given to it, dialectic was a\n    valuable instrument of instruction and exposition. But\n    whatever the purpose of the exercise, controversial triumph,\n    or solid grounding in the first principles--\"the evolution\n    of in-dwelling conceptions\"--the central interest lay in the\n    syllogising or reasoning together of the separately assumed or\n    admitted propositions.]\n\n    [Footnote 6: Like every other fashion, Yes-and-No Dialectic\n    had its period, its rise and fall. The invention of it is\n    ascribed to Zeno the Eleatic, the answering and questioning\n    Zeno, who flourished about the middle of the fifth century\n    B.C. Socrates (469-399) was in his prime at the beginning of\n    the great Peloponnesian War when Pericles died in 429. In that\n    year Plato was born, and lived to 347, \"the olive groves of\n    Academe\" being established centre of his teaching from\n    about 386 onwards. Aristotle (384-322), who was the tutor of\n    Alexander the Great, established his school at the Lyceum\n    when Alexander became king in 336 and set out on his career\n    of conquest. That Yes-and-No Dialectic was then a prominent\n    exercise, his logical treatises everywhere bear witness. The\n    subsequent history of the game is obscure. It is probable that\n    Aristotle's thorough exposition of its legitimate arts and\n    illegitimate tricks helped to destroy its interest as an\n    amusement.]\n\n    [Footnote 7: Hamilton's _Lectures_, iii. p. 37.]\n\n\nII.--LOGIC AS A PREVENTIVE OF ERROR OR FALLACY.--THE INNER SOPHIST.\n\nWhy describe Logic as a system of defence against error? Why say that\nits main end and aim is the organisation of reason against confusion\nand falsehood? Why not rather say, as is now usual, that its end is\nthe attainment of truth? Does this not come to the same thing?\n\nSubstantially, the meaning is the same, but the latter expression\nis more misleading. To speak of Logic as a body of rules for the\ninvestigation of truth has misled people into supposing that Logic\nclaims to be an art of Discovery, that it claims to lay down rules\nby simply observing which investigators may infallibly arrive at new\ntruths. Now, this does not hold even of the Logic of Induction, still\nless of the older Logic, the precise relation of which to truth will\nbecome apparent as we proceed. It is only by keeping men from going\nastray and by disabusing them when they think they have reached their\ndestination that Logic helps men on the road to truth. Truth often\nlies hid in the centre of a maze, and logical rules only help the\nsearcher onwards by giving him warning when he is on the wrong track\nand must try another. It is the searcher's own impulse that carries\nhim forward: Logic does not so much beckon him on to the right path\nas beckon him back from the wrong. In laying down the conditions of\ncorrect interpretation, of valid argument, of trustworthy evidence,\nof satisfactory explanation, Logic shows the inquirer how to test and\npurge his conclusions, not how to reach them.\n\nTo discuss, as is sometimes done, whether Fallacies lie within the\nproper sphere of Logic, is to obscure the real connexion between\nFallacies and Logic. It is the existence of Fallacies that calls Logic\ninto existence; as a practical science Logic is needed as a protection\nagainst Fallacies. Such historically is its origin. We may, if we\nlike, lay down an arbitrary rule that a treatise on Logic should be\ncontent to expound the correct forms of interpretation and reasoning\nand should not concern itself with the wrong. If we take this view we\nare bound to pronounce Fallacies extra-logical. But to do so is\nsimply to cripple the usefulness of Logic as a practical science.\nThe manipulation of the bare logical forms, without reference to\nfallacious departures from them, is no better than a nursery exercise.\nEvery correct form in Logic is laid down as a safeguard against some\nerroneous form to which men are prone, whether in the interpretation\nof argument or the interpretation of experience, and the statement and\nillustration of the typical forms of wrong procedure should accompany\n_pari passu_ the exposition of the right procedure.\n\n\nIn accordance with this principle, I shall deal with special\nfallacies, special snares or pitfalls--misapprehension of words,\nmisinterpretation of propositions, misunderstanding of arguments,\nmisconstruction of facts, evidences, or signs--each in connexion\nwith its appropriate safeguard. This seems to me the most profitable\nmethod. But at this stage, it may be worth while, by way of\nemphasising the need for Logic as a science of rational belief, to\ntake a survey of the most general tendencies to irrational belief,\nthe chief kinds of illusion or bias that are rooted in the human\nconstitution. We shall then better appreciate the magnitude of the\ntask that Logic attempts in seeking to protect reason against its own\nfallibility and the pressure of the various forces that would usurp\nits place.\n\nIt is a common notion that we need Logic to protect us against the\narts of the Sophist, the dishonest juggler with words and specious\nfacts. But in truth the Inner Sophist, whose instruments are our own\ninborn propensities to error, is a much more dangerous enemy. For once\nthat we are the victims of designing Sophists, we are nine times the\nvictims of our own irrational impulses and prejudices. Men generally\ndeceive themselves before they deceive others.\n\nFrancis Bacon drew attention to these inner perverting influences,\nthese universal sources of erroneous belief, in his _De Augmentis_\nand again in his _Novum Organum_, under the designation of _Idola_\n([Greek: eidola]), deceptive appearances of truth, illusions. His\nclassification of _Idola--Idola Tribus_, illusions common to all men,\nillusions of the race; _Idola Specus_, personal illusions, illusions\npeculiar to the \"den\" in which each man lives; _Idola Fori_, illusions\nof conversation, vulgar prejudices embodied in words; _Idola Theatri_,\nillusions of illustrious doctrine, illusions imposed by the dazzling\nauthority of great names--is defective as a classification inasmuch as\nthe first class includes all the others, but like all his writings it\nis full of sagacious remarks and happy examples. Not for the sake of\nnovelty, but because it is well that matters so important should be\npresented from more than one point of view, I shall follow a division\nadapted from the more scientific, if less picturesque, arrangement\nof Professor Bain, in his chapter on the Fallacious Tendencies of the\nHuman Mind.[1]\n\nThe illusions to which we are all subject may best be classified\naccording to their origin in the depths of our nature. Let us try to\nrealise how illusory beliefs arise.\n\nWhat is a belief? One of the uses of Logic is to set us thinking about\nsuch simple terms. An exhaustive analysis and definition of belief is\none of the most difficult of psychological problems. We cannot enter\nupon that: let us be content with a few simple characters of belief.\n\nFirst, then, belief is a state of mind. Second, this state of mind is\noutward-pointing: it has a reference beyond itself, a reference to the\norder of things outside us. In believing, we hold that the world as it\nis, has been, or will be, corresponds to our conceptions of it.\nThird, belief is the guide of action: it is in accordance with what we\nbelieve that we direct our activities. If we want to know what a man\nreally believes, we look at his action. This at least is the clue to\nwhat he believes at the moment. \"I cannot,\" a great orator once said,\n\"read the minds of men.\" This was received with ironical cheers. \"No,\"\nhe retorted, \"but I can construe their acts.\" Promoters of companies\nare expected to invest their own money as a guarantee of good faith.\nIf a man says he believes the world is coming to an end in a year,\nand takes a lease of a house for fifteen years, we conclude that his\nbelief is not of the highest degree of strength.\n\nThe close connexion of belief with our activities, enables us to\nunderstand how illusions, false conceptions of reality, arise. The\nillusions of Feeling and the illusions of Custom are well understood,\nbut other sources of illusion, which may be designated Impatient\nImpulse and Happy Exercise, are less generally recognised. An example\nor two will show what is meant. We cannot understand the strength of\nthese perverting influences till we realise them in our own case. We\ndetect them quickly enough in others. Seeing that in common speech the\nword illusion implies a degree of error amounting almost to insanity,\nand the illusions we speak of are such as no man is ever quite free\nfrom, it is perhaps less startling to use the word _bias_.\n\n\n_The Bias of Impatient Impulse._\n\nAs a being formed for action, not only does healthy man take\na pleasure in action, physical and mental, for its own sake,\nirrespective of consequences, but he is so charged with energy that\nhe cannot be comfortable unless it finds a free vent. In proportion\nto the amount and excitability of his energy, restraint, obstruction,\ndelay is irksome, and soon becomes a positive and intolerable pain.\nAny bar or impediment that gives us pause is hateful even to think of:\nthe mere prospect annoys and worries.\n\nHence it arises that belief, a feeling of being prepared for action,\na conviction that the way is clear before us for the free exercise of\nour activities, is a very powerful and exhilarating feeling, as much\na necessity of happy existence as action itself. We see this when we\nconsider how depressing and uncomfortable a condition is the opposite\nstate to belief, namely, doubt, perplexity, hesitation, uncertainty as\nto our course. And realising this, we see how strong a bias we have in\nthis fact of our nature, this imperious inward necessity for action;\nhow it urges us to act without regard to consequences, and to jump at\nbeliefs without inquiry. For, unless inquiry itself is our business, a\nself-sufficient occupation, it means delay and obstruction.\n\nThis ultimate fact of our nature, this natural inbred constitutional\nimpatience, explains more than half of the wrong beliefs that we form\nand persist in. We must have a belief of some kind: we cannot be happy\ntill we get it, and we take up with the first that seems to show the\nway clear. It may be right or it may be wrong: it is not, of course,\nnecessarily always wrong: but that, so far as we are concerned, is a\nmatter of accident. The pressing need for a belief of some sort, upon\nwhich our energies may proceed in anticipation at least, will not\nallow us to stop and inquire. Any course that offers a relief from\ndoubt and hesitation, any conviction that lets the will go free, is\neagerly embraced.\n\nIt may be thought that this can apply only to beliefs concerning\nthe consequences of our own personal actions, affairs in which we\nindividually play a part. It is from them, no doubt, that our nature\ntakes this set: but the habit once formed is extended to all sorts\nof matters in which we have no personal interest. Tell an ordinary\nEnglishman, it has been wittily said, that it is a question whether\nthe planets are inhabited, and he feels bound at once to have a\nconfident opinion on the point. The strength of the conviction bears\nno proportion to the amount of reason spent in reaching it, unless it\nmay be said that as a general rule the less a belief is reasoned the\nmore confidently it is held.\n\n\"A grocer,\" writes Mr. Bagehot in an acute essay on \"The Emotion of\nConviction,\"[2] \"has a full creed as to foreign policy, a young lady a\ncomplete theory of the Sacraments, as to which neither has any doubt.\nA girl in a country parsonage will be sure that Paris never can be\ntaken, or that Bismarck is a wretch.\" An attitude of philosophic\ndoubt, of suspended judgment, is repugnant to the natural man. Belief\nis an independent joy to him.\n\nThis bias works in all men. While there is life, there is pressure\nfrom within on belief, tending to push reason aside. The force of\nthe pressure, of course, varies with individual temperament, age, and\nother circumstances. The young are more credulous than the old, as\nhaving greater energy: they are apt, as Bacon puts it, to be \"carried\naway by the sanguine element in their temperament\". Shakespeare's\nLaertes is a study of the impulsive temperament, boldly contrasted\nwith Hamlet, who has more discourse of reason. When Laertes hears that\nhis father has been killed, he hurries home, collects a body of armed\nsympathisers, bursts into the presence of the king, and threatens with\nhis vengeance--the wrong man. He never pauses to make inquiry: like\nHotspur he is \"a wasp-stung and impatient fool\"; he must wreak his\nrevenge on somebody, and at once. Hamlet's father also has been\nmurdered, but his reason must be satisfied before he proceeds to his\nrevenge, and when doubtful proof is offered, he waits for proof more\nrelative.\n\nBacon's _Idola Tribus_ and Dr. Bain's illustrations of incontinent\nenergy, are mostly examples of unreasoning intellectual activity,\nhurried generalisations, unsound and superficial analogies, rash\nhypotheses. Bacon quotes the case of the sceptic in the temple of\nPoseidon, who, when shown the offerings of those who had made vows\nin danger and been delivered, and asked whether he did not now\nacknowledge the power of the god, replied: \"But where are they who\nmade vows and yet perished?\" This man answered rightly, says Bacon.\nIn dreams, omens, retributions, and such like, we are apt to remember\nwhen they come true and to forget the cases when they fail. If we\nhave seen but one man of a nation, we are apt to conclude that all his\ncountrymen are like him; we cannot suspend our judgment till we have\nseen more. Confident belief, as Dr. Bain remarks, is the primitive\nattitude of the human mind: it is only by slow degrees that this is\ncorrected by experience. The old adage, \"Experience teaches fools,\"\nhas a meaning of its own, but in one sense it is the reverse of the\ntruth. The mark of a fool is that he is not taught by experience, and\nwe are all more or less intractable pupils, till our energies begin to\nfail.\n\n\n_The Bias of Happy Exercise._\n\nIf an occupation is pleasant in itself, if it fully satisfies our\ninner craving for action, we are liable to be blinded thereby to its\nconsequences. Happy exercise is the fool's Paradise. The fallacy lies\nnot in being content with what provides a field for the full activity\nof our powers: to be content in such a case may be the height of\nwisdom: but the fallacy lies in claiming for our occupation results,\nbenefits, utilities that do not really attend upon it. Thus we see\nsubjects of study, originally taken up for some purpose, practical,\nartistic, or religious, pursued into elaborate detail far beyond their\noriginal purpose, and the highest value, intellectual, spiritual,\nmoral, claimed for them by their votaries, when in truth they merely\nserve to consume so much vacant energy, and may be a sheer waste of\ntime that ought to be otherwise employed.\n\nBut as I am in danger of myself furnishing an illustration of this\nbias--it is nowhere more prevalent than in philosophy--I will pass to\nour next head.\n\n\n_The Bias of the Feelings._\n\nThis source of illusion is much more generally understood. The\nblinding and perverting influence of passion on reason has been a\nfavourite theme with moralists ever since man began to moralise, and\nis acknowledged in many a popular proverb. \"Love is blind;\" \"The wish\nis father to the thought;\" \"Some people's geese are all swans;\" and so\nforth.\n\nWe need not dwell upon the illustration of it. Fear and Sloth magnify\ndangers and difficulties; Affection can see no imperfection in its\nobject: in the eyes of Jealousy a rival is a wretch. From the nature\nof the case we are much more apt to see examples in others than in\nourselves. If the strength of this bias were properly understood by\neverybody, the mistake would not so often be committed of suspecting\nbad faith, conscious hypocrisy, when people are found practising\nthe grossest inconsistencies, and shutting their eyes apparently in\ndeliberate wilfulness to facts held under their very noses. Men are\ninclined to ascribe this human weakness to women. Reasoning from\nfeeling is said to be feminine logic. But it is a human weakness.\n\nTo take one very powerful feeling, the feeling of self-love or\nself-interest--this operates in much more subtle ways than most people\nimagine, in ways so subtle that the self-deceiver, however honest,\nwould fail to be conscious of the influence if it were pointed out to\nhim. When the slothful man saith, There is a lion in the path, we can\nall detect the bias to his belief, and so we can when the slothful\nstudent says that he will work hard to-morrow, or next week, or next\nmonth; or when the disappointed man shows an exaggerated sense of\nthe advantages of a successful rival or of his own disadvantages. But\nself-interest works to bias belief in much less palpable ways than\nthose. It is this bias that accounts for the difficulty that men of\nantagonistic interests have in seeing the arguments or believing\nin the honesty of their opponents. You shall find conferences\nheld between capitalists and workmen in which the two sides, both\nrepresented by men incapable of consciously dishonest action, fail\naltogether to see the force of each other's arguments, and are\nmutually astonished each at the other's blindness.\n\n\n_The Bias of Custom._\n\nThat custom, habits of thought and practice, affect belief, is also\ngenerally acknowledged, though the strength and wide reach of the bias\nis seldom realised. Very simple cases of unreasoning prejudice were\nadduced by Locke, who was the first to suggest a general explanation\nof them in the \"Association of Ideas\" (_Human Understanding_, bk. ii.\nch. xxxiii.). There is, for instance, the fear that overcomes many\npeople when alone in the dark. In vain reason tells them that there is\nno real danger; they have a certain tremor of apprehension that they\ncannot get rid of, because darkness is inseparably connected in\ntheir minds with images of horror. Similarly we contract unreasonable\ndislikes to places where painful things have happened to us. Equally\nunreasoning, if not unreasonable, is our attachment to customary\ndoctrines or practices, and our invincible antipathy to those who do\nnot observe them.\n\nWords are very common vehicles for the currency of this kind of\nprejudice, good or bad meanings being attached to them by custom. The\npower of words in this way is recognised in the proverb: \"Give a dog\na bad name, and then hang him\". These verbal prejudices are Bacon's\n_Idola Fori_, illusions of conversation. Each of us is brought up in a\ncertain sect or party, and accustomed to respect or dishonour\ncertain sectarian or party names, Whig, Tory, Radical, Socialist,\nEvolutionist, Broad, Low, or High Church. We may meet a man without\nknowing under what label he walks and be charmed with his company:\nmeet him again when his name is known, and all is changed.\n\nSuch errors are called Fallacies of Association to point to the\npsychological explanation. This is that by force of association\ncertain ideas are brought into the mind, and that once they are there,\nwe cannot help giving them objective reality. For example, a doctor\ncomes to examine a patient, and finds certain symptoms. He has lately\nseen or heard of many cases of influenza, we shall say; influenza is\nrunning in his head. The idea once suggested has all the advantage of\npossession.\n\nBut why is it that a man cannot get rid of an idea? Why does it force\nitself upon him as a belief? Association, custom, explains how it got\nthere, but not why it persists in staying.\n\nTo explain this we must call in our first fallacious principle, the\nImpatience of Doubt or Delay, the imperative inward need for a belief\nof some sort.\n\nAnd this leads to another remark, that though for convenience of\nexposition, we separate these various influences, they are not\nseparated in practice. They may and often do act all together, the\nInner Sophist concentrating his forces.\n\nFinally, it may be asked whether, seeing that illusions are the\noffspring of such highly respectable qualities as excess of energy,\nexcess of feeling, excess of docility, it is a good thing for man to\nbe disillusioned. The rose-colour that lies over the world for youth\nis projected from the abundant energy and feeling within: disillusion\ncomes with failing energies, when hope is \"unwilling to be fed\". Is\nit good then to be disillusioned? The foregoing exposition would\nbe egregiously wrong if the majority of mankind did not resent the\nintrusion of Reason and its organising lieutenant Logic. But really\nthere is no danger that this intrusion succeeds to the extent of\nparalysing action and destroying feeling, and uprooting custom.\nThe utmost that Logic can do is to modify the excess of these good\nqualities by setting forth the conditions of rational belief. The\nstudent who masters those conditions will soon see the practical\nwisdom of applying his knowledge only in cases where the grounds of\nrational belief are within his reach. To apply it to the consequences\nof every action would be to yield to that bias of incontinent activity\nwhich is, perhaps, our most fruitful source of error.\n\n    [Footnote 1: Bain's _Logic_, bk. vi. chap. iii. Bacon intended\n    his _Idola_ to bear the same relation to his _Novum Organum_\n    that Aristotle's Fallacies or Sophistical Tricks bore to the\n    old Organum. But in truth, as I have already indicated, what\n    Bacon classifies is our inbred tendencies to form _idola_ or\n    false images, and it is these same tendencies that make\n    us liable to the fallacies named by Aristotle. Some of\n    Aristotle's, as we shall see, are fallacies of Induction.]\n\n    [Footnote 2: Bagehot's _Literary Studies_, ii. 427.]\n\n\nIII.--THE AXIOMS OF DIALECTIC AND OF SYLLOGISM.\n\nThere are certain principles known as the Laws of Thought or the\nMaxims of Consistency. They are variously expressed, variously\ndemonstrated, and variously interpreted, but in one form or another\nthey are often said to be the foundation of all Logic. It is even said\nthat all the doctrines of Deductive or Syllogistic Logic may be educed\nfrom them. Let us take the most abstract expression of them, and see\nhow they originated. Three laws are commonly given, named respectively\nthe Law of Identity, the Law of Contradiction and the Law of Excluded\nMiddle.\n\n1. _The Law of Identity._ A is A. Socrates is Socrates. Guilt is\nguilt.\n\n2. _The Law of Contradiction._ A is not not-A. Socrates is not other\nthan Socrates. Guilt is not other than guilt. Or A is not at once _b_\nand not-_b_. Socrates is not at once good and not-good. Guilt is not\nat once punishable and not-punishable.\n\n3. _The Law of Excluded Middle._ Everything is either A or not-A;\nor, A is either _b_ or not-_b_. A given thing is either Socrates\nor not-Socrates, either guilty or not-guilty. It must be one or the\nother: no middle is possible.\n\nWhy lay down principles so obvious, in some interpretations, and so\nmanifestly sophistical in others? The bare forms of modern Logic have\nbeen reached by a process of attenuation from a passage in Aristotle's\n_Metaphysics_[1] (iii. 3, 4, 1005_b_ - 1008). He is there laying down\nthe first principle of demonstration, which he takes to be that \"it is\nimpossible that the same predicate can both belong, and not belong,\nto the same subject, at the same time, and in the same sense\".[2]\nThat Socrates knows grammar, and does not know grammar--these two\npropositions cannot both be true at the same time, and in the same\nsense. Two contraries cannot exist together in the same subject. The\ndouble answer Yes and No cannot be given to one and the same question\nunderstood in the same sense.\n\nBut why did Aristotle consider it necessary to lay down a principle\nso obvious? Simply because among the subtle dialecticians who\npreceded him the principle had been challenged. The Platonic dialogue\nEuthydemus shows the farcical lengths to which such quibbling was\ncarried. The two brothers vanquish all opponents, but it is by\nclaiming that the answer No does not preclude the answer Yes. \"Is not\nthe honourable honourable, and the base base?\" asks Socrates. \"That is\nas I please,\" replies Dionysodorus. Socrates concludes that there\nis no arguing with such men: they repudiate the first principles of\ndialectic.\n\nThere were, however, more respectable practitioners who canvassed on\nmore plausible grounds any form into which ultimate doctrines about\ncontraries and contradictions, truth and falsehood, could be put, and\ntherefore Aristotle considered it necessary to put forth and defend\nat elaborate length a statement of a first principle of demonstration.\n\"Contradictions cannot both be true of the same subject at the same\ntime and in the same sense.\" This is the original form of the Law of\nContradiction.\n\nThe words \"of the same subject,\" \"at the same time,\" and \"in the\nsame sense,\" are carefully chosen to guard against possible quibbles.\n\"_Socrates knows grammar._\" By Socrates we must mean the same\nindividual man. And even of the same man the assertion may be true at\none time and not at another. There was a time when Socrates did not\nknow grammar, though he knows it now. And the assertion may be true\nin one sense and not in another. It may be true that Socrates knows\ngrammar, yet not that he knows everything that is to be known about\ngrammar, or that he knows as much as Aristarchus.\n\nAristotle acknowledges that this first principle cannot itself be\ndemonstrated, that is, deduced from any other. If it is denied, you\ncan only reduce the denier to an absurdity. And in showing how to\nproceed in so doing, he says you must begin by coming to an agreement\nabout the words used, that they signify the same for one and the other\ndisputant.[3] No dialectic is possible without this understanding.\nThis first principle of Dialectic is the original of the Law of\nIdentity. While any question as to the truth or falsehood of a\nquestion is pending, from the beginning to the end of any logical\nprocess, the words must continue to be accepted in the same sense.\nWords must have an identical reference to things.\n\nIncidentally in discussing the Axiom of Contradiction ([Greek:\naxioma tes antiphaseos]),[4] Aristotle lays down what is now known\nas the Law of Excluded Middle. Of two contradictories one or other\nmust be true: we must either affirm or deny any one thing of any\nother: no mean or middle is possible.\n\n\nIn their origin, then, these so-called Laws of Thought were simply the\nfirst principles of Dialectic and Demonstration. Consecutive argument,\ncoherent ratiocination, is impossible unless they are taken for\ngranted.\n\nIf we divorce or abstract them from their original application, and\nconsider them merely as laws of thinking or of being, any abstract\nexpression, or illustration, or designation of them may easily be\npushed into antagonism with other plain truths or first principles\nequally rudimentary. Without entering into the perplexing and\nvoluminous discussion to which these laws have been subjected by\nlogicians within the last hundred years, a little casuistry is\nnecessary to enable the student to understand within what limits they\nhold good.\n\n_Socrates is Socrates._ The name Socrates is a name for something to\nwhich you and I refer when we use the name. Unless we have the same\nreference, we cannot hold any argument about the thing, or make any\ncommunication one to another about it.\n\nBut if we take _Socrates is Socrates_ to mean that, \"An object of\nthought or thing is identical with itself,\" \"An object of thought or\nthing cannot be other than itself,\" and call this a law of thought, we\nare met at once by a difficulty. Thought, properly speaking, does\nnot begin till we pass beyond the identity of an object with itself.\nThought begins only when we recognise the likeness between one object\nand others. To keep within the self-identity of the object is to\nsuspend thought. \"Socrates was a native of Attica,\" \"Socrates was\na wise man,\" \"Socrates was put to death as a troubler of the\ncommonweal\"--whenever we begin to think or say anything about\nSocrates, to ascribe any attributes to him, we pass out of his\nself-identity into his relations of likeness with other men, into what\nhe has in common with other men.\n\nHegelians express this plain truth with paradoxical point when they\nsay: \"Of any definite existence or thought, therefore, it may be said\nwith quite as much truth that it _is not_, as that it _is_, its own\nbare self\".[5] Or, \"A thing must other itself in order to be itself\".\nControversialists treat this as a subversion of the laws of Identity\nand Contradiction. But it is only Hegel's fun--his paradoxical way of\nputting the plain truth that any object has more in common with other\nobjects than it has peculiar to itself. Till we enter into those\naspects of agreement with other objects, we cannot truly be said to\nthink at all. If we say merely that a thing is itself, we may as well\nsay nothing about it. To lay down this is not to subvert the Law of\nIdentity, but to keep it from being pushed to the extreme of appearing\nto deny the Law of Likeness, which is the foundation of all the\ncharacters, attributes, or qualities of things in our thoughts.\n\nThat self-same objects are like other self-same objects, is an\nassumption distinct from the Law of Identity, and any interpretation\nof it that excludes this assumption is to be repudiated. But does not\nthe law of Identity as well as the law of the likeness of mutually\nexclusive identities presuppose that there are objects self-same,\nlike others, and different from others? Certainly: this is one of the\npresuppositions of Logic.[6] We assume that the world of which we talk\nand reason is separated into such objects in our thoughts. We assume\nthat such words as _Socrates_ represent individual objects with a\nself-same being or substance; that such words as _wisdom_, _humour_,\n_ugliness_, _running_, _sitting_, _here_, _there_, represent\nattributes, qualities, characters or predicates of individuals; that\nsuch words as _man_ represent groups or classes of individuals.\n\nSome logicians in expressing the Law of Identity have their eye\nspecially upon the objects signified by general names or abstract\nnames, _man_, _education_.[7] \"A concept is identical with the sum\nof its characters,\" or, \"Classes are identical with the sum of\nthe individuals composing them\". The assumptions thus expressed in\ntechnical language which will hereafter be explained are undoubtedly\nassumptions that Logic makes: but since they are statements of the\ninternal constitution of some of the identities that words represent,\nto call them the Law of Identity is to depart confusingly from\ntraditional usage.[8]\n\nThat throughout any logical process a word must signify the same\nobject, is one proposition: that the object signified by a general\nname is identical with the sum of the individuals to each of whom it\nis applicable, or with the sum of the characters that they bear in\ncommon, is another proposition. Logic assumes both: Aristotle assumed\nboth: but it is the first that is historically the original of all\nexpressions of the Law of Identity in modern text-books.\n\nYet another expression of a Law of Identity which is really distinct\nfrom and an addition to Aristotle's original. _Socrates was an\nAthenian, a philosopher, an ugly man, an acute dialectician, etc._\nLet it be granted that the word Socrates bears the same signification\nthroughout all these and any number more of predicates, we may still\nask: \"But what is it that Socrates signifies?\" The title Law of\nIdentity is sometimes given[9] to a theory on this point. _Socrates is\nSocrates._ \"An individual is the identity running through the totality\nof its attributes.\" Is this not, it may be asked, to confuse thought\nand being, to resolve Socrates into a string of words? No: real\nexistence is one of the admissible predicates of Socrates: one of\nthe attributes under which we conceive him. But whether we accept\nor reject this \"Law of Identity,\" it is an addition to Aristotle's\ndialectical \"law of identity\"; it is a theory of the metaphysical\nnature of the identity signified by a Singular name. And the same may\nbe said of yet another theory of Identity, that, \"An individual is\nidentical with the totality of its predicates,\" or (another way\nof putting the same theory), \"An individual is a conflux of\ngeneralities\".\n\n\nTo turn next to the Laws of Contradiction and Excluded Middle. These\nalso may be subjected to Casuistry, making clearer what they assert by\nshowing what they do not deny.\n\nThey do not deny that things change, and that successive states of the\nsame thing may pass into one another by imperceptible degrees. A thing\nmay be neither here nor there: it may be on the passage from here to\nthere: and, while it is in motion, we may say, with equal truth, that\nit is neither here nor there, or that it is both here and there. Youth\npasses gradually into age, day into night: a given man or a given\nmoment may be on the borderland between the two.\n\nLogic does not deny the existence of indeterminate margins: it merely\nlays down that for purposes of clear communication and coherent\nreasoning the line must be drawn somewhere between _b_, and not-_b_.\n\nA difference, however, must be recognised between logical negation\nand the negations of common thought and common speech. The latter are\ndefinite to a degree with which the mere Logic of Consistency does\nnot concern itself. To realise this is to understand more clearly the\nlimitations of Formal Logic.\n\nIn common speech, to deny a quality of anything is by implication to\nattribute to it some other quality of the same kind. Let any man tell\nme that \"the streets of such and such a town are not paved with wood,\"\nI at once conclude that they are paved with some other material. It\nis the legitimate effect of his negative proposition to convey this\nimpression to my mind. If, proceeding on this, I go on to ask: \"Then\nthey are paved with granite or asphalt, or this or that?\" and he turns\nround and says: \"I did not say they were paved at all,\" I should be\njustified in accusing him of a quibble. In ordinary speech, to deny\none kind of pavement is to assert pavement of some kind. Similarly, to\ndeny that So-and-so is not in the Twenty-first Regiment, is to\nimply that he is in another regiment, that he is in the army in some\nregiment. To retort upon this inference: \"He is not in the army at\nall,\" is a quibble: as much so as it would be to retort: \"There is no\nsuch person in existence\".\n\nNow Logic does not take account of this implication, and nothing has\ncontributed more to bring upon it the reproach of quibbling. In Logic,\nto deny a quality is simply to declare a repugnance between it and the\nsubject; negation is mere sublation, taking away, and implies nothing\nmore. Not-_b_ is entirely indefinite: it may cover anything except\n_b_.\n\nIs Logic then really useless, or even misleading, inasmuch as it\nignores the definite implication of negatives in ordinary thought\nand speech? In ignoring this implication, does Logic oppose this\nimplication as erroneous? Does Logic shelter the quibbler who\ntrades upon it? By no means: to jump to this conclusion were a\nmisunderstanding. The fact only is that nothing beyond the logical\nLaw of Contradiction needs to be assumed for any of the processes\nof Formal Logic. Aristotle required to assume nothing more for his\nsyllogistic formulae, and Logic has not yet included in its scope any\nprocess that requires any further assumption. \"If not-_b_ represent\neverything except _b_, everything outside _b_, then that A is _b_, and\nthat A is not-_b_, cannot both be true, and one or other of them must\nbe true.\"\n\nWhether the scope of Logic ought to be extended is another question.\nIt seems to me that the scope of Logic may legitimately be extended so\nas to take account both of the positive implication of negatives and\nthe negative implication of positives. I therefore deal with this\nsubject in a separate chapter following on the ordinary doctrines of\nImmediate Inference, where I try to explain the simple Law of Thought\ninvolved. When I say that the extension is legitimate, I mean that it\nmay be made without departing from the traditional view of Logic as\na practical science, conversant with the nature of thought and its\nexpression only in so far as it can provide practical guidance against\nerroneous interpretations and inferences. The extension that I propose\nis in effect an attempt to bring within the fold of Practical Logic\nsome of the results of the dialectic of Hegel and his followers,\nsuch as Mr. Bradley and Mr. Bosanquet, Professor Caird and Professor\nWallace.[10]\n\nThe logical processes formulated by Aristotle are merely stages in the\nmovement of thought towards attaining definite conceptions of reality.\nTo treat their conclusions as positions in which thought may dwell and\nrest, is an error, against which Logic itself as a practical science\nmay fairly be called upon to guard. It may even be conceded that the\nAristotelian processes are artificial stages, courses that thought\ndoes not take naturally, but into which it has to be forced for a\npurpose. To concede this is not to concede that the Aristotelian logic\nis useless, as long as we have reason on our side in holding that\nthought is benefited and strengthened against certain errors by\npassing through those artificial stages.\n\n    [Footnote 1: The first statement of the Law of Identity in the\n    form _Ens est ens_ is ascribed by Hamilton (_Lectures_, iii.\n    91) to Antonius Andreas, a fourteenth century commentator\n    on the _Metaphysics_. But Andreas is merely expounding what\n    Aristotle sets forth in iii. 4, 1006 _a, b_. _Ens est ens_\n    does not mean in Andreas what A is A means in Hamilton.]\n\n    [Footnote 2: Greek: to gar auto hama huparchein te kai me\n    huparchein adynaton to auto kai kata to auto, . . . ahute de\n    pason esti bebaiotate ton archon. iii. 3, 1005_b_, 19-23.]\n\n    [Footnote 3: Hamilton credits Andreas with maintaining,\n    \"against Aristotle,\" that \"the principle of Identity, and not\n    the principle of Contradiction, is the one absolutely first\".\n    Which comes first, is a scholastic question on which ingenuity\n    may be exercised. But in fact Aristotle put the principle\n    of Identity first in the above plain sense, and Andreas only\n    expounded more formally what Aristotle had said.]\n\n    [Footnote 4: [Greek: Metaxu antiphaseos endechetai einai outhen,\n    all' ananke e phanai e apophanai en kath henos hotioun.]\n    _Metaph._ iii. 7, 1011_b_, 23-4.]\n\n    [Footnote 5: Prof. Caird's _Hegel_, p. 138.]\n\n    [Footnote 6: See Venn, _Empirical Logic_, 1-8.]\n\n    [Footnote 7: _E.g._, Hamilton, lect. v.; Veitch's _Institutes\n    of Logic_, chaps, xii., xiii.]\n\n    [Footnote 8: The confusion probably arises in this way. First,\n    these \"laws\" are formulated as laws of thought that Logic\n    assumes. Second, a notion arises that these laws are the\n    only postulates of Logic: that all logical doctrines can be\n    \"evolved\" from them. Third, when it is felt that more than the\n    identical reference of words or the identity of a thing\n    with itself must be assumed in Logic, the Law of Identity is\n    extended to cover this further assumption.]\n\n    [Footnote 9: _E.g._, Bosanquet's _Logic_, ii. 207.]\n\n    [Footnote 10: Bradley, _Principles of Logic_; Bosanquet,\n    _Logic or The Morphology of Knowledge_; Caird, _Hegel_ (in\n    Blackwood's Philosophical Classics); Wallace, _The Logic of\n    Hegel_.]\n\n\n\n\nBOOK I.\n\nTHE LOGIC OF CONSISTENCY. SYLLOGISM AND DEFINITION.\n\n\nPART I.\n\nTHE ELEMENTS OF PROPOSITIONS.\n\n\n\n\nCHAPTER I.\n\nGENERAL NAMES AND ALLIED DISTINCTIONS.\n\nTo discipline us against the errors we are liable to in receiving\nknowledge through the medium of words--such is one of the objects of\nLogic, the main object of what may be called the Logic of Consistency.\n\nStrictly speaking, we may receive knowledge about things through signs\nor single words, as a nod, a wink, a cry, a call, a command. But an\nassertory sentence, proposition, or predication, is the unit with\nwhich Logic concerns itself--a sentence in which a subject is\nnamed and something is said or predicated about it. Let a man once\nunderstand the errors incident to this regular mode of communication,\nand he may safely be left to protect himself against the errors\nincident to more rudimentary modes.\n\nA proposition, whether long or short, is a unit, but it is an\nanalysable unit. And the key to syllogistic analysis is the General\nName. Every proposition, every sentence in which we convey knowledge\nto another, contains a general name or its equivalent. That is to say,\nevery proposition may be resolved into a form in which the predicate\nis a general name. A knowledge of the function of this element of\nspeech is the basis of all logical discipline. Therefore, though we\nmust always remember that the proposition is the real unit of speech,\nand the general name only an analytic element, we take the general\nname and its allied distinctions in thought and reality first.\n\nHow propositions are analysed for syllogistic purposes will be shown\nby-and-by, but we must first explain various technical terms that\nlogicians have devised to define the features of this cardinal\nelement. The technical terms CLASS, CONCEPT, NOTION, ATTRIBUTE,\nEXTENSION or DENOTATION, INTENSION or CONNOTATION, GENUS, SPECIES,\nDIFFERENTIA, SINGULAR NAME, COLLECTIVE NAME, ABSTRACT NAME, all centre\nround it.\n\nA general name is a name applicable to a number of different things on\nthe ground of some likeness among them, as _man_, _ratepayer_, _man of\ncourage_, _man who fought at Waterloo_.\n\nFrom the examples it will be seen that a general name logically is\nnot necessarily a single word. Any word or combination of words that\nserves a certain function is technically a general name. The different\nways of making in common speech the equivalent of a general name\nlogically are for the grammarian to consider.\n\nIn the definition of a general name attention is called to two\ndistinct considerations, the individual objects to each of which\nthe name is applicable, and the points of resemblance among them, in\nvirtue of which they have a common name. For those distinctions there\nare technical terms.\n\nCLASS is the technical term for the objects, different yet agreeing,\nto each of which a general name may be applied.\n\nThe points of resemblance are called the common ATTRIBUTES of the\nclass.\n\nA class may be constituted on one attribute or on several.\n_Ratepayer_, _woman ratepayer_, _unmarried woman ratepayer_;\n_soldier_, _British soldier_, _British soldier on foreign service_.\nBut every individual to which the general name can be applied must\npossess the common attribute or attributes.\n\nThese common attributes are also called the NOTION of the class,\ninasmuch as it is these that the mind notes or should note when the\ngeneral name is applied. CONCEPT is a synonym perhaps in more common\nuse than notion; the rationale of this term (derived from _con_ and\n_capere_, to take or grasp together) being that it is by means of\nthe points of resemblance that the individuals are grasped or held\ntogether by the mind. These common points are the one in the many, the\nsame amidst the different, the identity signified by the common name.\nThe name of an attribute as thought of by itself without reference to\nany individual or class possessing it, is called an ABSTRACT name. By\ncontradistinction, the name of an individual or a class is CONCRETE.\n\nTechnical terms are wanted also to express the relation of the\nindividuals and the attributes to the general name. The individuals\njointly are spoken of as the DENOTATION, or EXTENSION or SCOPE of\nthe name; the common attributes as its CONNOTATION, INTENSION,\nCOMPREHENSION, or GROUND. The whole denotation, etc., is the class;\nthe whole connotation, etc., is the concept.[1] The limits of a\n\"class\" in Logic are fixed by the common attributes. Any individual\nobject that possesses these is a member. The statement of them is the\nDEFINITION.\n\nTo predicate a general name of any object, as, \"This is a cat,\" \"This\nis a very sad affair,\" is to refer that object to a class, which is\nequivalent to saying that it has certain features of resemblance with\nother objects, that it reminds us of them by its likeness to them.\nThus to say that the predicate of every proposition is a general name,\nexpressed or implied, is the same as to say that every predication may\nbe taken as a reference to a class.\n\nOrdinarily our notion or concept of the common features signified by\ngeneral names is vague and hazy. The business of Logic is to make them\nclear. It is to this end that the individual objects of the class are\nsummoned before the mind. In ordinary thinking there is no definite\narray or muster of objects: when we think of \"dog\" or \"cat,\"\n\"accident,\" \"book,\" \"beggar,\" \"ratepayer,\" we do not stop to call\nbefore the mind a host of representatives of the class, nor do we take\nprecise account of their common attributes. The concept of \"house\" is\nwhat all houses have in common. To make this explicit would be no\neasy matter, and yet we are constantly referring objects to the\nclass \"house\". We shall see presently that if we wish to make the\nconnotation or concept clear we must run over the denotation or class,\nthat is to say, the objects to which the general name is applied in\ncommon usage. Try, for example, to conceive clearly what is meant\nby house, tree, dog, walking-stick. You think of individual objects,\nso-called, and of what they have in common.\n\nA class may be constituted on one property or on many. There are\nseveral points common to all houses, enclosing walls, a roof, a means\nof exit and entrance. For the full concept of the natural kinds,\n_men_, _dogs_, _mice_, etc., we should have to go to the natural\nhistorian.\n\nDEGREES OF GENERALITY. One class is said to be of higher generality\nthan another when it includes that other and more. Thus animal\nincludes man, dog, horse, etc.; man includes Aryan, Semite, etc.;\nAryan includes Hindoo, Teuton, Celt, etc.\n\nThe technical names for higher and lower classes are GENUS and\nSPECIES. These terms are not fixed as in Natural History to certain\ngrades, but are purely relative one to another, and movable up and\ndown a scale of generality. A class may be a species relatively to one\nclass, which is above it, and a genus relatively to one below it. Thus\nAryan is a species of the genus man, Teuton a species of the genus\nAryan.\n\nIn the graded divisions of Natural History genus and species are fixed\nnames for certain grades. Thus: Vertebrates form a \"division\"; the\nnext subdivision, _e.g._, Mammals, Birds, Reptiles, etc., is called a\n\"class\"; the next, _e.g_., Rodents, Carnivora, Ruminants, an \"order\";\nthe next, _e.g._, Rats, Squirrels, Beavers, a \"genus\"; the next,\n_e.g._, Brown rats, Mice, a \"species\".\n\n                Vertebrates (division).\n                      |\n             Mammals, Birds, Reptiles, etc. (class).\n                |\n         Rodents, Ruminants, Carnivors, etc. (order).\n            |\n     Rats, Squirrels, Beavers, etc. (genus).\n       |\n  Brown rats, Mice, etc. (species).\n\nIf we subdivide a large class into smaller classes, and, again,\nsubdivide these subdivisions, we come at last to single objects.\n\n              Men\n               |\n             ------------\n          Europeans, Asiatics, etc.\n              |\n          -------------\n      Englishmen, Frenchmen, etc.\n           |\n      ---------------------\n  John Doe, Richard Roe, etc.\n\nA table of higher and lower classes arranged in order has been known\nfrom of old as a _tree_ of division or classification. The following\nis Porphyry's \"tree\":--\n\n            Being\n           /     \\\n  Corporeal       Incorporeal\n           \\     /\n            (Body)\n           /     \\\n    Animate       Inanimate\n           \\     /\n         (Living Being)\n           /     \\\n   Sensible       Insensible\n           \\     /\n           (Animal)\n           /     \\\n   Rational       Irrational\n           \\     /\n            (Man)\n              |\n  ---------------------------------------\n  Socrates, Plato, and other individuals.\n\nThe single objects are called INDIVIDUALS, because the division cannot\nbe carried farther. The highest class is technically the SUMMUM GENUS,\nor _Genus generalissimum_; the next highest class to any species is\nthe PROXIMUM GENUS; the lowest group before you descend to individuals\nis the INFIMA SPECIES, or _Species specialissima_.\n\nThe attribute or attributes whereby a species is distinguished\nfrom other species of the same genus, is called its DIFFERENTIA or\nDIFFERENTIAE. The various species of houses are differentiated by their\nseveral uses, dwelling-house, town-house, ware-house, public-house.\nPoetry is a species of Fine Art, its differentia being the use of\nmetrical language as its instrument.\n\nA lower class, indicated by the name of its higher class qualified by\nadjectives or adjective phrases expressing its differential property\nor properties, is said to be described PER GENUS ET DIFFERENTIAM.\nExamples: \"Black-bird,\" \"note-book,\" \"clever man,\" \"man of Kent,\"\n\"eminent British painter of marine subjects\". By giving a combination\nof attributes common to him with nobody else, we may narrow down the\napplication of a name to an individual: \"The Commander-in-Chief of the\nBritish forces at the battle of Waterloo\".\n\nOther attributes of classes as divided and defined, have received\ntechnical names.\n\nAn attribute common to all the individuals of a class, found in that\nclass only, and following from the essential or defining attributes,\nthough not included among them, is called a PROPRIUM.\n\nAn attribute that belongs to some, but not to all, or that belongs to\nall, but is not a necessary consequence of the essential attributes,\nis called an ACCIDENT.\n\nThe clearest examples of Propria are found in mathematical figures.\nThus, the defining property of an equilateral triangle is the equality\nof the sides: the equality of the angles is a proprium. That the\nthree angles of a triangle are together equal to two right angles is\na proprium, true of all triangles, and deducible from the essential\nproperties of a triangle.\n\nOutside Mathematics, it is not easy to find _propria_ that satisfy\nthe three conditions of the definition. It is a useful exercise of\nthe wits to try for such. Educability--an example of the proprium\nin mediaeval text-books--is common to men, and results from man's\nessential constitution; but it is not peculiar; other animals are\neducable. That man cooks his food is probably a genuine proprium.\n\nThat horses run wild in Thibet: that gold is found in California: that\nclergymen wear white ties, are examples of Accidents. Learning is an\naccident in man, though educability is a proprium.\n\nWhat is known technically as an INSEPARABLE ACCIDENT, such as the\nblack colour of the crow or the Ethiopian, is not easy to distinguish\nfrom the Proprium. It is distinguished only by the third character,\ndeducibility from the essence.[2]\n\nAccidents that are both common and peculiar are often useful for\ndistinguishing members of a class. Distinctive dresses or badges, such\nas the gown of a student, the hood of a D.D., are accidents, but mark\nthe class of the individual wearer. So with the colours of flowers.\n\n_Genus_, _Species_, _Differentia_, _Proprium_, and _Accidens_ have\nbeen known since the time of Porphyry as the FIVE PREDICABLES. They\nare really only terms used in dividing and defining. We shall return\nto them and endeavour to show that they have no significance except\nwith reference to fixed schemes, scientific or popular, of Division or\nClassification.\n\nGiven such a fixed scheme, very nice questions may be raised as to\nwhether a particular attribute is a defining attribute, or a proprium,\nor an accident, or an inseparable accident. Such questions afford\ngreat scope for the exercise of the analytic intellect.\n\n\nWe shall deal more particularly with degrees of generality when\nwe come to Definition. This much has been necessary to explain an\nunimportant but much discussed point in Logic, what is known as the\ninverse variation of Connotation and Denotation.\n\nConnotation and Denotation are often said to vary inversely in\nquantity. The larger the connotation the smaller the denotation, and\n_vice versa_. With certain qualifications the statement is correct\nenough, but it is a rough compendious way of expressing the facts and\nit needs qualification.\n\nThe main fact to be expressed is that the more general a name is, the\nthinner is its meaning. The wider the scope, the shallower the ground.\nAs you rise in the scale of generality, your classes are wider but the\nnumber of common attributes is less. Inversely, the name of a species\nhas a smaller denotation than the name of its genus, but a richer\nconnotation. _Fruit-tree_ applies to fewer objects than _tree_,\nbut the objects denoted have more in common: so with _apple_ and\n_fruit-tree_, _Ribston Pippin_ and _apple_.\n\nAgain, as a rule, if you increase the connotation you contract the\narea within which the name is applicable. Take any group of things\nhaving certain attributes in common, say, _men of ability_: add\n_courage_, _beauty_, _height of six feet_, _chest measurement of 40\ninches_, and with each addition fewer individuals are to be found\npossessing all the common attributes.\n\nThis is obvious enough, and yet the expression inverse variation is\nopen to objection. For the denotation may be increased in a sense\nwithout affecting the connotation. The birth of an animal may be said\nto increase the denotation: every year thousands of new houses are\nbuilt: there are swarms of flies in a hot summer and few in a cold.\nBut all the time the connotation of _animal_, _house_, or _fly_\nremains the same: the word does not change its meaning.\n\nIt is obviously wrong to say that they vary in inverse proportion.\nDouble or treble the number of attributes, and you do not necessarily\nreduce the denotation by one-half or one-third.\n\nIt is, in short, the meaning or connotation that is the main thing.\nThis determines the application of a word. As a rule if you increase\nmeaning, you restrict scope. Let your idea, notion, or concept of\n_culture_ be a knowledge of Mathematics, Latin and Greek: your _men of\nculture_ will be more numerous than if you require from each of them\nthese qualifications _plus_ a modern language, an acquaintance with\nthe Fine Arts, urbanity of manners, etc.\n\nIt is just possible to increase the connotation without decreasing the\ndenotation, to thicken or deepen the concept without diminishing\nthe class. This is possible only when two properties are exactly\nco-extensive, as equilaterality and equiangularity in triangles.\n\nSINGULAR and PROPER NAMES. A Proper or Singular name is a name used to\ndesignate an individual. Its function, as distinguished from that of\nthe general name, is to be used purely for the purpose of distinctive\nreference.\n\nA man is not called Tom or Dick because he is like in certain respects\nto other Toms or other Dicks. The Toms or the Dicks do not form a\nlogical class. The names are given purely for purposes of distinction,\nto single out an individual subject. The Arabic equivalent for a\nProper name, _alam_, \"a mark,\" \"a sign-post,\" is a recognition of\nthis.\n\nIn the expressions \"a Napoleon,\" \"a Hotspur,\" \"a Harry,\" the names\nare not singular names logically, but general names logically, used to\nsignify the possession of certain attributes.\n\nA man may be nicknamed on a ground, but if the name sticks and is\noften used, the original meaning is forgotten. If it suggests\nthe individual in any one of his qualities, any point in which he\nresembles other individuals, it is no longer a Proper or Singular name\nlogically, that is, in logical function. That function is fulfilled\nwhen it has called to mind the individual intended.\n\nTo ask, as is sometimes done, whether Proper names are connotative or\ndenotative, is merely a confusion of language. The distinction between\nconnotation and denotation, extension and intension, applies only to\ngeneral names. Unless a name is general, it has neither extension nor\nintension:[3] a Proper or Singular name is essentially the opposite of\na general name and has neither the one nor the other.\n\nA nice distinction may be drawn between Proper and Singular names,\nthough they are strict synonyms for the same logical function. It is\nnot essential to the discharge of that function that the name should\nbe strictly appropriated to one object. There are many Toms and many\nDicks. It is enough that the word indicates the individual without\nconfusion in the particular circumstances.\n\nThis function may be discharged by words and combinations of words\nthat are not Proper in the grammatical sense. \"This man,\" \"the cover\nof this book,\" \"the Prime Minister of England,\" \"the seer of Chelsea,\"\nmay be Singular names as much as Honolulu or Lord Tennyson.\n\nIn common speech Singular names are often manufactured _ad hoc_\nby taking a general name and narrowing it down by successive\nqualifications till it applies only to one individual, as \"The leading\nsubject of the Sovereign of England at the present time\". If it so\nhappens that an individual has some attribute or combination peculiar\nto himself, he may be suggested by the mention of that attribute\nor combination:--\"the inventor of the steam-engine,\" \"the author of\nHudibras\".\n\nHave such names a connotation? The student may exercise his wits\non the question. It is a nice one, an excellent subject of debate.\nBriefly, if we keep rigid hold of the meaning of connotation, this\nSingular name has none. The combination is a singular name only\nwhen it is the subject of a predication or an attribution, as in\nthe sentences, \"The position of the leading subject of etc., is a\ndifficult one,\" or \"The leading subject of etc., wears an eyeglass\".\nIn such a sentence as \"So-and-so is the leading subject of etc.,\" the\ncombined name has a connotation, but then it is a general and not a\nsingular name.\n\nCOLLECTIVE NAMES, as distinguished from General Names. A collective\nname is a name for a number of similar units taken as a whole--a name\nfor a totality of similar units, as army, regiment, mob, mankind,\npatrimony, personal estate.\n\nA group or collection designated by a collective name is so far like\na class that the individual objects have something in common: they\nare not heterogeneous but homogeneous. A mob is a collection of human\nbeings; a regiment of soldiers; a library of books.\n\nThe distinction lies in this, that whatever is said of a collective\nname is said about the collection as a whole, and does not apply to\neach individual; whatever is said of a general name applies to each\nindividual. Further, the collective name can be predicated only of\nthe whole group, as a whole; the general name is predicable of each,\ndistributively. \"Mankind has been in existence for thousands of\nyears;\" \"The mob passed through the streets.\" In such expressions as\n\"An honest man's the noblest work of God,\" the subject is functionally\na collective name.\n\nA collective name may be used as a general name when it is extended on\nthe ground of what is common to all such totalities as it designates.\n\"An excited mob is dangerous;\" \"An army without discipline is\nuseless.\" The collective name is then \"connotative\" of the common\ncharacters of the collection.\n\nMATERIAL OR SUBSTANTIAL NAMES. The question has been raised whether\nnames of material, gold, water, snow, coal, are general or collective\nsingular. In the case of pieces or bits of a material, it is true that\nany predicate made concerning the material, such as \"Sugar is sweet,\"\nor \"Water quenches thirst,\" applies to any and every portion. But\nthe separate portions are not individuals in the whole signified by\na material name as individuals are in a class. Further, the name of\nmaterial cannot be predicated of a portion as a class name can be of\nan individual. We cannot say, \"This is a sugar\". When we say, \"This is\na piece of sugar,\" sugar is a collective name for the whole material.\nThere are probably words on the borderland between general names and\ncollective names. In such expressions as \"This is a _coal_,\" \"The\nbonnie _water_ o' Urie,\" the material name is used as a general\nname. The real distinction is between the distributive use and the\ncollective use of a name; as a matter of grammatical usage, the same\nword may be used either way, but logically in any actual proposition\nit must be either one or the other.\n\nABSTRACT NAMES are names for the common attributes or concepts on\nwhich classes are constituted. A concrete name is a name directly\napplicable to an individual in all his attributes, that is, as he\nexists in the concrete. It may be written on a ticket and pinned to\nhim. When we have occasion to speak of the point or points in which a\nnumber of individuals resemble one another, we use what is called an\nabstract name. \"Generous man,\" \"clever man,\" \"timid man,\" are concrete\nnames; \"generosity,\" \"cleverness,\" \"timidity,\" are abstract names.\n\nIt is disputed whether abstract names are connotative. The question\nis a confused one: it is like asking whether the name of a town is\nmunicipal. An abstract name is the name of a connotation as a separate\nobject of thought or reference, conceived or spoken of in abstraction\nfrom individual accidents. Strictly speaking it is notative rather\nthan _con_notative: it cannot be said to have a connotation because\nit is itself the symbol of what is called the connotation of a general\nname.[4]\n\nThe distinction between abstract names and concrete names is\nvirtually a grammatical distinction, that is, a distinction in mode\nof predication. We may use concrete names or abstract names at our\npleasure to express the same meaning. To say that \"John is a timid\nman\" is the same thing as saying that \"Timidity is one of the\nproperties or characteristics or attributes of John\". \"Pride and\ncruelty generally go together;\" \"Proud men are generally cruel men.\"\n\nGeneral names are predicable of individuals because they possess\ncertain attributes: to predicate the possession of those attributes is\nthe same thing as to predicate the general name.\n\nAbstract forms of predication are employed in common speech quite as\nfrequently as concrete, and are, as we shall see, a great source of\nambiguity and confusion.\n\n    [Footnote 1: It has been somewhat too hastily assumed on the\n    authority of Mansel (Note to Aldrich, pp. 16, 17) that Mill\n    inverted the scholastic tradition in his use of the word\n    _Connotative_. Mansel puts his statement doubtfully, and\n    admits that there was some licence in the use of the word\n    Connotative, but holds that in Scholastic Logic an adjective\n    was said to \"signify _primarily_ the attribute, and to\n    _connote_ or _signify secondarily_ ([Greek: prossemainein])\n    the subject of inhesion\". The truth is that Mansel's view was\n    a theory of usage not a statement of actual usage, and he had\n    good reason for putting it doubtfully.\n\n    As a matter of fact, the history of the distinction follows\n    the simple type of increasing precision and complexity, and\n    Mill was in strict accord with standard tradition. By the\n    Nominalist commentators on the _Summulae_ of Petrus Hispanus\n    certain names, adjectives grammatically, are called\n    _Connotativa_ as opposed to _Absoluta_, simply because they\n    have a double function. White is connotative as signifying\n    both a subject, such as Socrates, of whom \"whiteness\" is an\n    attribute, and an attribute \"whiteness\": the names \"Socrates\"\n    and \"whiteness\" are Absolute, as having but a single\n    signification. Occam himself speaks of the subject as the\n    primary signification, and the attribute as the secondary,\n    because the answer to \"What is white?\" is \"Something informed\n    with whiteness,\" and the subject is in the nominative case\n    while the attribute is in an oblique case (_Logic_, part I.\n    chap. x.). Later on we find that Tataretus (_Expositio in\n    Summulas_, A.D. 1501), while mentioning (Tract. Sept. _De\n    Appellationibus_) that it is a matter of dispute among\n    Doctores whether a connotative name _connotat_ the subject or\n    the attribute, is perfectly explicit in his own definition,\n    \"Terminus connotativus est qui praeter illud pro quo supponit\n    connotat aliquid adjacere vel non adjacere rei pro qua\n    supponit\" (Tract. Sept. _De Suppositionibus_). And this\n    remained the standard usage as long as the distinction\n    remained in logical text-books. We find it very clearly\n    expressed by Clichtoveus, a Nominalist, quoted as an authority\n    by Guthutius in his _Gymnasium Speculativum_, Paris, 1607 (_De\n    Terminorum Cognitione_, pp. 78-9). \"Terminus absolutus est,\n    qui solum illud pro quo in propositione supponit, significat.\n    Connotativus autem, qui ultra idipsum, aliud importat.\" Thus\n    _man_ and _animal_ are absolute terms, which simply stand\n    for (supponunt pro) the things they signify. _White_ is a\n    connotative name, because \"it stands for (supponit pro) a\n    subject in which it is an accident: and beyond this, still\n    signifies an accident, which is in that subject, and is\n    expressed by an abstract name\". Only Clichtoveus drops the\n    verb _connotat_, perhaps as a disputable term, and says simply\n    _ultra importat_.\n\n    So in the Port Royal Logic (1662), from which possibly Mill\n    took the distinction: \"Les noms qui signifient les choses\n    comme modifiees, marquant premierement et directement la\n    chose, quoique plus confusement, et indirectement le mode,\n    quoique plus distinctement, sont appeles _adjectifs_ ou\n    _connotatifs_; comme rond, dur, juste, prudent\" (part i. chap\n    ii.).\n\n    What Mill did was not to invert Scholastic usage but to revive\n    the distinction, and extend the word connotative to general\n    names on the ground that they also imported the possession\n    of attributes. The word has been as fruitful of meticulous\n    discussion as it was in the Renaissance of Logic, though\n    the ground has changed. The point of Mill's innovation was,\n    premising that general names are not absolute but are applied\n    in virtue of a meaning, to put emphasis on this meaning as\n    the cardinal consideration. What he called the connotation had\n    dropped out of sight as not being required in the Syllogistic\n    Forms. This was as it were the point at which he put in his\n    horn to toss the prevalent conception of Logic as Syllogistic.\n\n    The real drift of Mill's innovation has been obscured by\n    the fact that it was introduced among the preliminaries\n    of Syllogism, whereas its real usefulness and significance\n    belongs not to Syllogism in the strict sense but to\n    Definition. He added to the confusion by trying to devise\n    forms of Syllogism based on connotation, and by discussing\n    the Axiom of the Syllogism from this point of view. For\n    syllogistic purposes, as we shall see, Aristotle's forms are\n    perfect, and his conception of the proposition in extension\n    the only correct conception. Whether the centre of gravity in\n    Consistency Logic should not be shifted back from Syllogism to\n    Definition, the latter being the true centre of consistency,\n    is another question. The tendency of Mill's polemic was to\n    make this change. And possibly the secret of the support it\n    has recently received from Mr. Bradley and Mr. Bosanquet is\n    that they, following Hegel, are moving in the same direction.\n\n    In effect, Mill's doctrine of Connotation helped to fix\n    a conception of the general name first dimly suggested by\n    Aristotle when he recognised that names of genera and species\n    signify Quality, in showing what sort a thing is. Occam\n    carried this a step farther towards clear light by including\n    among Connotative Terms such general names as \"monk,\" name of\n    classes that at once suggest a definite attribute. The third\n    step was made by Mill in extending the term Connotation to\n    such words as \"man,\" \"horse,\" the _Infimae Species_ of the\n    Schoolmen, the Species of modern science.\n\n    Whether connotation was the best term to use for this purpose,\n    rather than extension, may be questioned: but at least it was\n    in the line of tradition through Occam.]\n\n    [Footnote 2: The history of the definition of the _Proprium_\n    is an example of the tendency of distinctions to become more\n    minute and at the same time more purposeless. Aristotle's\n    [Greek: idion] was an attribute, such as the laugh of the man\n    or the bark of the dog, common to all of a class and peculiar\n    to the class (_quod convenit omni soli et semper_) yet not\n    comprised in the definition of the class. Porphyry recognised\n    three varieties of [Greek: idia] besides this, four in all,\n    as follows:--(1) an attribute peculiar to a species but not\n    possessed by all, as knowledge of medicine or geometry; (2)\n    possessed by a whole species but not peculiar to it, as being\n    a biped in man; (3) peculiar to a species, and possessed\n    by all at a certain time, as turning grey in old age; (4)\n    Aristotle's \"proprium,\" peculiar and possessed by all, as\n    risibility. The idea of the Proprium as deducible from or\n    consequent on the essence would seem to have originated in\n    the desire to find something common to all Poryphyry's four\n    varieties.]\n\n    [Footnote 3: It is a plausible contention that in the case\n    of the Singular name the extension is at a minimum and the\n    intension at a maximum, the extension being one individual,\n    and the intension the totality of his attributes. But this is\n    an inexact and confused use of words. A name does not _extend_\n    beyond the individual except when it is used to signify one\n    or more of his prominent qualities, that is, is used with the\n    function of a general name. The _ex_tension of a Singular name\n    is zero: it has no extension. On the other hand, it suggests,\n    in its function as a Singular name, no properties or\n    qualities; it suggests only a subject; _i.e._, it has no\n    intension. The ambiguity of the term Denotation helps the\n    confusion in the case of Singular names. \"Denote\" in common\n    speech means to indicate, to distinguish. But when in Logic\n    we say that a general name denotes individuals, we have no\n    thought of indicating or distinguishing: we mean only that\n    it is applicable to any one, without respect of individuals,\n    either in predication or epithetic description.]\n\n    [Footnote 4: Strictly speaking, as I have tried to indicate\n    all along, the words Connotation and Denotation, or Extension\n    and Intension, apply only to general names. Outside general\n    names, they have no significance. An adjective with its noun\n    is a general name, of which the adjective gives part of the\n    Connotation. If we apply the word connotation to signify\n    merely the suggestion of an attribute in whatever grammatical\n    connexion, then an abstract name is undoubtedly as much\n    connotative as an adjective. The word _Sweetness_ has the same\n    meaning as _Sweet_: it indicates or signifies, conveys to the\n    mind of the reader the same attribute: the only difference is\n    that it does not at the same time indicate a subject in which\n    the attribute is found, as _sweet apple_. The meaning is not\n    _con_noted.]\n\n\n\n\nCHAPTER II.\n\nTHE SYLLOGISTIC ANALYSIS OF PROPOSITIONS INTO TERMS.\n\n\nI.--THE BARE ANALYTIC FORMS.\n\nThe word \"term\" is loosely used as a mere synonym for a name: strictly\nspeaking, a term ([Greek: horos], a boundary) is one of the parts of\na proposition as analysed into Subject and Predicate. In Logic, a term\nis a technical word in an analysis made for a special purpose, that\npurpose being to test the mutual consistency of propositions.\n\nFor this purpose, the propositions of common speech may be viewed as\nconsisting of two TERMS, a linkword called the copula (positive or\nnegative) expressing a relation between them, and certain symbols of\nquantity used to express that relation more precisely.\n\nLet us indicate the Subject term by S, and the Predicate term by P.\n\nAll propositions may be analysed into one or other of four forms:--\n\n  All S is P,\n  No S is P,\n  Some S is P,\n  Some S is not P.\n\nAll S is P is called the UNIVERSAL AFFIRMATIVE, and is indicated by\nthe symbol A (the first vowel of Affirmo).\n\nNo S is P is called the UNIVERSAL NEGATIVE, symbol E (the first vowel\nof Nego).\n\nSome S is P is called the PARTICULAR AFFIRMATIVE, symbol I (the second\nvowel of _aff_Irmo).\n\nSome S is not P is called the PARTICULAR NEGATIVE, symbol O (the\nsecond vowel of _neg_O).\n\nThe distinction between Universal and Particular is called a\ndistinction in QUANTITY; between Affirmative and Negative, a\ndistinction in QUALITY. A and E, I and O, are of the same quantity,\nbut of different quality: A and I, E and O, same in quality, different\nin quantity.\n\nIn this symbolism, no provision is made for expressing degrees of\nparticular quantity. _Some_ stands for any number short of all: it may\nbe one, few, most, or all but one. The debates in which Aristotle's\npupils were interested turned mainly on the proof or disproof of\ngeneral propositions; if only a proposition could be shown to be not\nuniversal, it did not matter how far or how little short it came. In\nthe Logic of Probability, the degree becomes of importance.\n\nDistinguish, in this Analysis, to avoid subsequent confusion, between\nthe Subject and the Subject Term, the Predicate and the Predicate\nTerm. The Subject is the Subject Term quantified: in A and E,[1] \"All\nS\"; in I and O, \"Some S\". The Predicate is the Predicate Term with the\nCopula, positive or negative: in A and I, \"is P\"; in E and O, \"is not\nP\".\n\nIt is important also, in the interest of exactness, to note that S and\nP, with one exception, represent general names. They are symbols\nfor classes. P is so always: S also except when the Subject is an\nindividual object. In the machinery of the Syllogism, predications\nabout a Singular term are treated as Universal Affirmatives. \"Socrates\nis a wise man\" is of the form All S is P.\n\nS and P being general names, the signification of the symbol \"is\" is\nnot the same as the \"is\" of common speech, whether the substantive\nverb or the verb of incomplete predication. In the syllogistic form,\n\"is\" means _is contained in_, \"is not,\" _is not contained in_.\n\nThe relations between the terms in the four forms are represented by\nsimple diagrams known as Euler's circles.\n\n[Illustration:\n\n  1  concentric circles of P and S - S in centre        A\n  2  S and P in the same circle                         A\n  3  S and P each in a circle, overlapping circle.      I & O\n  4  S in one circle and P in another circle.           E\n  5  concentric circles of S and P - P in centre        I?\n]\n\n\nDiagram 5 is a purely artificial form, having no representative in\ncommon speech. In the affirmations of common speech, P is always a\nterm of greater extent than S.\n\nNo. 2 represents the special case where S and P are coextensive, as in\nAll equiangular triangles are equilateral.\n\nS and P being general names, they are said to be DISTRIBUTED when the\nproposition applies to them in their whole extent, that is, when the\nassertion covers every individual in the class.\n\nIn E, the Universal Negative, both terms are distributed: \"No S is P\"\nwholly excludes the two classes one from the other, imports that not\none individual of either is in the other.\n\nIn A, S is distributed, but not P. S is wholly in P, but nothing is\nsaid about the extent of P beyond S.\n\nIn O, S is undistributed, P is distributed. A part of S is declared to\nbe wholly excluded from P.\n\nIn I, neither S nor P is distributed.\n\nIt will be seen that the Predicate term of a Negative proposition is\nalways distributed, of an Affirmative, always undistributed.\n\nA little indistinctness in the signification of P crept into mediaeval\ntext-books, and has tended to confuse modern disputation about the\nimport of Predication. Unless P is a class name, the ordinary doctrine\nof distribution is nonsense; and Euler's diagrams are meaningless. Yet\nmany writers who adopt both follow mediaeval usage in treating P as the\nequivalent of an adjective, and consequently \"is\" as identical with\nthe verb of incomplete predication in common speech.\n\n\nIt should be recognised that these syllogistic forms are purely\nartificial, invented for a purpose, namely, the simplification of\nsyllogising. Aristotle indicated the precise usage on which his\nsyllogism is based (_Prior Analytics_, i. 1 and 4). His form[2] for\nAll S is P, is S is wholly in P; for No S is P, S is wholly not in P.\nHis copula is not \"is,\" but \"is in,\" and it is a pity that this usage\nwas not kept. \"All S is in P\" would have saved much confusion. But,\ndoubtless for the sake of simplicity, the besetting sin of tutorial\nhandbooks, All S is P crept in instead, illustrated by such examples\nas \"All men are mortal\".\n\nThus the \"is\" of the syllogistic form became confused with the \"is\"\nof common speech, and the syllogistic view of predication as\nbeing equivalent to inclusion in, or exclusion from a class, was\nmisunderstood. The true Aristotelian doctrine is not that predication\nconsists in referring subjects to classes, but only that for certain\nlogical purposes it may be so regarded. The syllogistic forms are\nartificial forms. They were not originally intended to represent the\nactual processes of thought expressed in common speech. To argue\nthat when I say \"All crows are black,\" I do not form a class of\nblack things, and contemplate crows within it as one circle is within\nanother, is to contradict no intelligent logical doctrine.\n\nThe root of the confusion lies in quoting sentences from common speech\nas examples of the logical forms, forgetting that those forms are\npurely artificial. \"Omnis homo est mortalis,\" \"All men are mortal,\" is\nnot an example formally of All S is P. P is a symbol for a substantive\nword or combination of words, and mortal is an adjective. Strictly\nspeaking, there is no formal equivalent in common speech, that is,\nin the forms of ordinary use--no strict grammatical formal\nequivalent--for the syllogistic propositional symbols. We can make\nan equivalent, but it is not a form that men would use in ordinary\nintercourse. \"All man is in mortal being\" would be a strict\nequivalent, but it is not English grammar.\n\nInstead of disputing confusedly whether All S is P should be\ninterpreted in extension or in comprehension, it would be better to\nrecognise the original and traditional use of the symbols S and P\nas class names, and employ other symbols for the expression in\ncomprehension or connotation. Thus, let _s_ and _p_ stand for the\nconnotation. Then the equivalent for All S is P would be All S has\n_p_, or _p_ always accompanies _s_, or _p_ belongs to all S.\n\nIt may be said that if predication is treated in this way, Logic is\nsimplified to the extent of childishness. And indeed, the manipulation\nof the bare forms with the help of diagrams and mnemonics is a very\nhumble exercise. The real discipline of Syllogistic Logic lies in the\nreduction of common speech to these forms.\n\nThis exercise is valuable because it promotes clear ideas about the\nuse of general names in predication, their ground in thought and\nreality, and the liabilities to error that lurk in this fundamental\ninstrument of speech.\n\n    [Footnote 1: For perfect symmetry, the form of E should be\n    All S is not P. \"No S is P\" is adopted for E to avoid conflict\n    with a form of common speech, in which All S is not P conveys\n    the meaning of the Particular Negative. \"All advices are not\n    safe\" does not mean that safeness is denied of all advices,\n    but that safeness cannot be affirmed of all, _i.e._, Not all\n    advices are safe, _i.e._, some are not.]\n\n    [Footnote 2: His most precise form, I should say, for in \"P is\n    predicated of every S\" he virtually follows common speech.]\n\n\nII.--THE PRACTICE OF SYLLOGISTIC ANALYSIS.\n\nThe basis of the analysis is the use of general names in predication.\nTo say that in predication a subject is referred to a class, is only\nanother way of saying that in every categorical sentence the predicate\nis a general name express or implied: that it is by means of general\nnames that we convey our thoughts about things to others.\n\n\"Milton is a great poet.\" \"Quoth Hudibras, _I smell a rat_.\" _Great\npoet_ is a general name: it means certain qualities, and applies to\nanybody possessing them. _Quoth_ implies a general name, a name for\npersons _speaking_, connoting or meaning a certain act and applicable\nto anybody in the performance of it. _Quoth_ expresses also past time:\nthus it implies another general name, a name for persons _in past\ntime_, connoting a quality which differentiates a species in the genus\npersons speaking, and making the predicate term \"persons speaking in\npast time\". Thus the proposition _Quoth Hudibras_, analysed into the\nsyllogistic form S is in P, becomes S (Hudibras) is in P (persons\nspeaking in past time). The Predicate term P is a class constituted on\nthose properties. _Smell a rat_ also implies a general name, meaning\nan act or state predicable of many individuals.\n\nEven if we add the grammatical object of _Quoth_ to the analysis, the\nPredicate term is still a general name. Hudibras is only one of the\npersons speaking in past time who have spoken of themselves as being\nin a certain mood of suspicion.[1]\n\nThe learner may well ask what is the use of twisting plain speech into\nthese uncouth forms. The use is certainly not obvious. The analysis\nmay be directly useful, as Aristotle claimed for it, when we wish\nto ascertain exactly whether one proposition contradicts another, or\nforms with another or others a valid link in an argument. This is\nto admit that it is only in perplexing cases that the analysis is of\ndirect use. The indirect use is to familiarise us with what the\nforms of common speech imply, and thus strengthen the intellect for\ninterpreting the condensed and elliptical expression in which common\nspeech abounds.\n\nThere are certain technical names applied to the components of\nmany-worded general names, CATEGOREMATIC and SYNCATEGOREMATIC, SUBJECT\nand ATTRIBUTIVE. The distinctions are really grammatical rather than\nlogical, and of little practical value.\n\nA word that can stand by itself as a term is said to be Categorematic.\n_Man_, _poet_, or any other common noun.\n\nA word that can only form part of a term is Syncategorematic. Under\nthis definition come all adjectives and adverbs.\n\nThe student's ingenuity may be exercised in applying the\ndistinction to the various parts of speech. A verb may be said to be\n_Hypercategorematic_, implying, as it does, not only a term, but also\na copula.\n\nA nice point is whether the Adjective is categorematic or\nsyncategorematic. The question depends on the definition of \"term\"\nin Logic. In common speech an adjective may stand by itself as a\npredicate, and so might be said to be Categorematic. \"This heart is\nmerry.\" But if a term is a class, or the name of a class, it is not\nCategorematic in the above definition. It can only help to specify a\nclass when attached to the name of a higher genus.\n\nMr. Fowler's words SUBJECT and ATTRIBUTIVE express practically the\nsame distinction, except that Attributive is of narrower extent than\nsyncategorematic. An Attributive is a word that connotes an attribute\nor property, as _hot_, _valorous_, and is always grammatically an\nadjective.\n\nThe EXPRESSION OF QUANTITY, that is, of Universality or\nnon-universality, is all-important in syllogistic formulae. In them\nuniversality is expressed by _All_ or _None_. In ordinary speech\nuniversality is expressed in various forms, concrete and abstract,\nplain and figurative, without the use of \"all\" or \"none\".\n\n  Uneasy lies the head that wears a crown.\n  He can't be wrong whose life is in the right.\n  What cat's averse to fish?\n  Can the leopard change his spots?\n  The longest road has an end.\n  Suspicion ever haunts the guilty mind.\n  Irresolution is always a sign of weakness.\n  Treason never prospers.\n\nA proposition in which the quantity is not expressed is called by\nAristotle INDEFINITE ([Greek: adioristos]). For \"indefinite\"[2]\nHamilton suggests PREINDESIGNATE, undesignated, that is, before being\nreceived from common speech for the syllogistic mill. A proposition is\nPREDESIGNATE when the quantity is definitely indicated. All the above\npropositions are \"Predesignate\" universals, and reducible to the form\nAll S is P, or No S is P.\n\nThe following propositions are no less definitely particular,\nreducible to the form I or O. In them as in the preceding quantity\nis formally expressed, though the forms used are not the artificial\nsyllogistic forms:--\n\n  Afflictions are often salutary.\n  Not every advice is a safe one.\n  All that glitters is not gold.\n  Rivers generally[3] run into the sea.\n\nOften, however, it is really uncertain from the form of common speech\nwhether it is intended to express a universal or a particular. The\nquantity is not formally expressed. This is especially the case\nwith proverbs and loose floating sayings of a general tendency. For\nexample:--\n\n  Haste makes waste.\n  Knowledge is power.\n  Light come, light go.\n  Left-handed men are awkward antagonists.\n  Veteran soldiers are the steadiest in fight.\n\nSuch sayings are in actual speech for the most part delivered as\nuniversals.[4] It is a useful exercise of the Socratic kind to decide\nwhether they are really so. This can only be determined by a survey of\nfacts. The best method of conducting such a survey is probably (1)\nto pick out the concrete subject, \"hasty actions,\" \"men possessed of\nknowledge,\" \"things lightly acquired\"; (2) to fix the attribute or\nattributes predicated; (3) to run over the individuals of the subject\nclass and settle whether the attribute is as a matter of fact meant to\nbe predicated of each and every one.\n\nThis is the operation of INDUCTION. If one individual can be found of\nwhom the attribute is not meant to be predicated, the proposition is\nnot intended as Universal.\n\nMark the difference between settling what is intended and settling\nwhat is true. The conditions of truth and the errors incident to the\nattempt to determine it, are the business of the Logic of Rational\nBelief, commonly entitled Inductive Logic. The kind of \"induction\"\nhere contemplated has for its aim merely to determine the quantity of\na proposition in common acceptation, which can be done by considering\nin what cases the proposition would generally be alleged. This\ncorresponds nearly as we shall see to Aristotelian Induction, the\nacceptance of a universal statement when no instance to the contrary\nis alleged.\n\nIt is to be observed that for this operation we do not practically use\nthe syllogistic form All S is P. We do not raise the question Is All\nS, P? That is, we do not constitute in thought a class P: the class in\nour minds is S, and what we ask is whether an attribute predicated of\nthis class is truly predicated of every individual of it.\n\nSuppose we indicate by _p_ the attribute, knot of attributes, or\nconcept on which the class P is constituted, then All S is P is\nequivalent to \"All S has _p_\": and Has All S _p_? is the form of a\nquestion that we have in our minds when we make an inductive survey on\nthe above method. I point this out to emphasise the fact that there is\nno prerogative in the form All S is P except for syllogistic purposes.\n\nThis inductive survey may be made a useful COLLATERAL DISCIPLINE. The\nbare forms of Syllogistic are a useless item of knowledge unless they\nare applied to concrete thought. And determining the quantity of a\ncommon aphorism or saw, the limits within which it is meant to hold\ngood, is a valuable discipline in exactness of understanding. In\ntrying to penetrate to the inner intention of a loose general maxim,\nwe discover that what it is really intended to assert is a general\nconnexion of attributes, and a survey of concrete cases leads to\na more exact apprehension of those attributes. Thus in considering\nwhether _Knowledge is power_ is meant to be asserted of all knowledge,\nwe encounter along with such examples as the sailor's knowledge that\nwetting a rope shortens it, which enabled some masons to raise a stone\nto its desired position, or the knowledge of French roads possessed by\nthe German invaders,--along with such examples as these we encounter\ncases where a knowledge of difficulties without a knowledge of the\nmeans of overcoming them is paralysing to action. Samuel Daniel\nsays:--\n\n  Where timid knowledge stands considering\n  Audacious ignorance has done the deed.\n\nStudying numerous cases where \"Knowledge is power\" is alleged or\ndenied, we find that what is meant is that a knowledge of the right\nmeans of doing anything is power--in short, that the predicate is not\nmade of all knowledge, but only of a species of knowledge.\n\nTake, again, _Custom blunts sensibility_. Putting this in the\nconcrete, and inquiring what predicate is made about \"men accustomed\nto anything\" (S), we have no difficulty in finding examples where such\nmen are said to become indifferent to it. We find such illustrations\nas Lovelace's famous \"Paradox\":--\n\n  Through foul we follow fair\n    For had the world one face\n  And earth been bright as air\n    We had known neither place.\n  Indians smell not their nest\n  The Swiss and Finn taste best\n    The spices of the East.\n\nSo men accustomed to riches are not acutely sensible of their\nadvantages: dwellers in noisy streets cease to be distracted by the\ndin: the watchmaker ceases to hear the multitudinous ticking in his\nshop: the neighbours of chemical works are not annoyed by the smells\nlike the casual passenger. But we find also that wine-tasters\nacquire by practice an unusual delicacy of sense; that the eyes once\naccustomed to a dim light begin to distinguish objects that were at\nfirst indistinguishable; and so on. What meanings of \"custom\" and of\n\"sensibility\" will reconcile these apparently conflicting examples?\nWhat are the exact attributes signified by the names? We should\nprobably find that by sensibility is meant emotional sensibility as\ndistinguished from intellectual discrimination, and that by custom is\nmeant familiarity with impressions whose variations are not attended\nto, or subjection to one unvarying impression.\n\nTo verify the meaning of abstract proverbs in this way is to travel\nover the road by which the Greek dialecticians were led to feel the\nimportance of definition. Of this more will be said presently. If\nit is contended that such excursions are beyond the bounds of Formal\nLogic, the answer is that the exercise is a useful one and that it\nstarts naturally and conveniently from the formulae of Logic. It is the\npractice and discipline that historically preceded the Aristotelian\nLogic, and in the absence of which the Aristotelian formulae would have\na narrowing and cramping effect.\n\nCAN ALL PROPOSITIONS BE REDUCED TO THE SYLLOGISTIC FORM? Probably: but\nthis is a purely scientific inquiry, collateral to Practical Logic.\nThe concern of Practical Logic is chiefly with forms of proposition\nthat favour inaccuracy or inexactness of thought. When there is no\nroom for ambiguity or other error, there is no virtue in artificial\nsyllogistic form. The attempt so to reduce any and every proposition\nmay lead, however, to the study of what Mr. Bosanquet happily calls\nthe \"Morphology\" of Judgment, Judgment being the technical name for\nthe mental act that accompanies the utterance of a proposition. Even\nin such sentences as \"How hot it is!\" or \"It rains,\" the rudiment of\nsubject and predicate may be detected. When a man says \"How hot it\nis,\" he conveys the meaning, though there is no definitely formed\nsubject in his mind, that the outer world at the moment of his\nspeaking has a certain quality or attribute. So with \"It rains\". The\nstudy of such examples in their context, however, reveals the fact\nthat the same form of Common speech may cover different subjects and\npredicates in different connexions. Thus in the argument:--\n\n  \"Whatever is, is best.\n    It rains!\"--\n\nthe Subject is _Rain_ and the Predicate _is now_, \"is at the present\ntime,\" \"is in the class of present events\".\n\n    [Footnote 1: Remember that when we speak of a general name,\n    we do not necessarily mean a single word. A general name,\n    logically viewed, is simply the name of a _genus_, kind, or\n    class: and whether this is single-worded or many-worded\n    is, strictly speaking, a grammatical question. \"Man,\"\n    \"man-of-ability,\" \"man-of-ability-and-courage,\"\n    \"man-of-ability-and-courage-and-gigantic-stature,\"\n    \"man-who-fought-at-Marathon\"--these are all general names\n    in their logical function. No matter how the constitutive\n    properties of the class are indicated, by one word or in\n    combination, that word or combination is a general name. In\n    actual speech we can seldom indicate by a single word the\n    meaning predicated.]\n\n    [Footnote 2: The objection taken to the word \"indefinite,\"\n    that the quantity of particular propositions is indefinite,\n    _some_ meaning any quantity less than all, is an example of\n    the misplaced and frivolous subtlety that has done so much\n    to disorder the tradition of Logic. By \"indefinite\" is\n    simply meant not definitely expressed as either Universal\n    or Particular, Total or Partial. The same objection might be\n    taken to any word used to express the distinction: the degree\n    of quantity in Some S is not \"designate\" any more than it is\n    \"definite\" or \"dioristic\".]\n\n    [Footnote 3: _Generally._ In this word we have an instance of\n    the frequent conflict between the words of common speech and\n    logical terminology. How it arises shall be explained in next\n    chapter. A General proposition is a synonym for a Universal\n    proposition (if the forms A and E are so termed): but\n    \"generally\" in common speech means \"for the most part,\" and is\n    represented by the symbol of particular quantity, _Some_.]\n\n    [Footnote 4: With some logicians it is a mechanical rule in\n    reducing to syllogistic form to treat as I or O all sentences\n    in which there is no formal expression of quantity. This is to\n    err on the safe side, but common speakers are not so guarded,\n    and it is to be presumed rather that they have a universal\n    application in their minds when they do not expressly\n    qualify.]\n\n\nIII.--SOME TECHNICAL DIFFICULTIES.\n\n_The formula for_ EXCLUSIVE PROPOSITIONS. \"None but the brave deserve\nthe fair\": \"No admittance except on business\": \"Only Protestants can\nsit on the throne of England\".\n\nThese propositions exemplify different ways in common speech of naming\na subject _exclusively_, the predication being made of all outside a\ncertain term. \"None that are not brave, etc.;\" \"none that are not on\nbusiness, etc.;\" \"none that are not Protestants, etc.\". No not-S is\nP. It is only about all outside the given term that the universal\nassertion is made: we say nothing universally about the individuals\nwithin the term: we do not say that all Protestants are eligible, nor\nthat all persons on business are admitted, nor that every one of the\nbrave deserves the fair. All that we say is that the possession of the\nattribute named is an indispensable condition: a person may possess\nthe attribute, and yet on other grounds may not be entitled to the\npredicate.\n\nThe justification for taking special note of this form in Logic is\nthat we are apt by inadvertence to make an inclusive inference from\nit. Let it be said that None but those who work hard can reasonably\nexpect to pass, and we are apt to take this as meaning that all who\nwork hard may reasonably expect to pass. But what is denied of every\nNot-S is not necessarily affirmed of every S.\n\n_The expression of_ TENSE or TIME _in the Syllogistic Forms_. Seeing\nthat the Copula in S is P or S is in P does not express time, but only\na certain relation between S and P, the question arises Where are we\nto put time in the analytic formula? \"Wheat is dear;\" \"All had fled;\"\ntime is expressed in these propositions, and our formula should\nrender the whole content of what is given. Are we to include it in\nthe Predicate term or in the Subject term? If it must not be left out\naltogether, and we cannot put it with the copula, we have a choice\nbetween the two terms.\n\nIt is a purely scholastic question. The common technical treatment is\nto view the tense as part of the predicate. \"All had fled,\" All S is\nP, _i.e._, the whole subject is included in a class constituted on the\nattributes of flight at a given time. It may be that the Predicate is\nsolely a predicate of time. \"The Board met yesterday at noon.\" S is P,\n_i.e._, the meeting of the Board is one of the events characterised by\nhaving happened at a certain time, agreeing with other events in that\nrespect.\n\nBut in some cases the time is more properly regarded as part of the\nsubject. _E.g._, \"Wheat is dear\". S does not here stand for wheat\ncollectively, but for the wheat now in the market, the wheat of the\npresent time: it is concerning this that the attribute of dearness is\npredicated; it is this that is in the class of dear things.\n\n_The expression of_ MODALITY _in the Syllogistic Forms_. Propositions\nin which the predicate is qualified by an expression of necessity,\ncontingency, possibility or impossibility [_i.e._, in English by\n_must_, _may_, _can_, or _cannot_], were called in Mediaeval Logic\n_Modal_ Propositions. \"Two and two _must_ make four.\" \"Grubs _may_\nbecome butterflies.\" \"Z _can_ paint.\" \"Y _cannot_ fly.\"\n\nThere are two recognised ways of reducing such propositions to the\nform S is P. One is to distinguish between the _Dictum_ and the\n_Mode_, the proposition and the qualification of its certainty, and\nto treat the _Dictum_ as the Subject and the _Mode_ as the Predicate.\nThus: \"That two and two make four is necessary\"; \"That Y can fly is\nimpossible\".\n\nThe other way is to treat the Mode as part of the predicate.\nThe propriety of this is not obvious in the case of Necessary\npropositions, but it is unobjectionable in the case of the other three\nmodes. Thus: \"Grubs are things that have the potentiality of becoming\nbutterflies\"; \"Z has the faculty of painting\"; \"Y has not the faculty\nof flying\".\n\nThe chief risk of error is in determining the quantity of the subject\nabout which the Contingent or Possible predicate is made. When it is\nsaid that \"Victories may be gained by accident,\" is the predicate made\nconcerning All victories or Some only? Here we are apt to confuse the\nmeaning of the contingent assertion with the matter of fact on which\nin common belief it rests. It is true only that some victories have\nbeen gained by accident, and it is on this ground that we assert in\nthe absence of certain knowledge concerning any victory that it\nmay have been so gained. The latter is the effect of the contingent\nassertion: it is made about any victory in the absence of certain\nknowledge, that is to say, formally about all.\n\nThe history of Modals in Logic is a good illustration of intricate\nconfusion arising from disregard of a clear traditional definition.\nThe treatment of them by Aristotle was simple, and had direct\nreference to tricks of disputation practised in his time. He specified\nfour \"modes,\" the four that descended to mediaeval logic, and he\nconcerned himself chiefly with the import of contradicting these\nmodals. What is the true contradictory of such propositions as, \"It\nis possible to be\" ([Greek: dynaton einai]), \"It admits of being\"\n([Greek: endechetai einai]), \"It must be\" ([Greek: anankaion einai]),\n\"It is impossible to be\" ([Greek: adynaton einai])? What is implied in\nsaying \"No\" to such propositions put interrogatively? \"Is it possible\nfor Socrates to fly?\" \"No.\" Does this mean that it is not possible for\nSocrates to fly, or that it is possible for Socrates not to fly?\n\nA disputant who had trapped a respondent into admitting that it is\npossible for Socrates not to fly, might have pushed the concession\nfarther in some such way as this: \"Is it possible for Socrates not to\nwalk?\" \"Certainly.\" \"Is it possible for him to walk?\" \"Yes.\" \"When you\nsay that it is possible for a man to do anything do you not believe\nthat it is possible for him to do it?\" \"Yes.\" \"But you have admitted\nthat it is possible for Socrates not to fly?\"\n\nIt was in view of such perplexities as these that Aristotle set forth\nthe true contradictories of his four Modals. We may laugh at such\nquibbles now and wonder that a grave logician should have thought them\nworth guarding against. But historically this is the origin of the\nModals of Formal Logic, and to divert the names of them to signify\nother distinctions than those between modes of qualifying the\ncertainty of a statement is to introduce confusion.\n\nThus we find \"Alexander was a great general,\" given as an example of\na Contingent Modal, on the ground that though as a matter of fact\nAlexander was so he might have been otherwise. It was not _necessary_\nthat Alexander should be a great general: therefore the proposition\nis _contingent_. Now the distinction between Necessary truth and\nContingent truth may be important philosophically: but it is merely\nconfusing to call the character of propositions as one or the other by\nthe name of Modality. The original Modality is a mode of expression:\nto apply the name to this character is to shift its meaning.\n\nA more simple and obviously unwarrantable departure from tradition\nis to extend the name Modality to any grammatical qualification of\na single verb in common speech. On this understanding \"Alexander\nconquered Darius\" is given by Hamilton as a _Pure_ proposition, and\n\"Alexander conquered Darius honourably\" as a _Modal_. This is a merely\ngrammatical distinction, a distinction in the mode of composing the\npredicate term in common speech. In logical tradition Modality is a\nmode of qualifying the certainty of an affirmation. \"The conquest\nof Darius by Alexander was honourable,\" or \"Alexander in conquering\nDarius was an honourable conqueror,\" is the syllogistic form of the\nproposition: it is simply assertory, not qualified in any \"mode\".\n\nThere is a similar misunderstanding in Mr. Shedden's treatment of\n\"generally\" as constituting a Modal in such sentences, as \"Rivers\n_generally_ flow into the sea\". He argues that as _generally_ is not\npart either of the Subject term or of the Predicate term, it must\nbelong to the Copula, and is therefore a _modal_ qualification of the\nwhole assertion. He overlooked the fact that the word \"generally\" is\nan expression of Quantity: it determines the quantity of the Subject\nterm.\n\nFinally it is sometimes held (_e.g._, by Mr. Venn) that the question\nof Modality belongs properly to Scientific or Inductive Logic, and is\nout of place in Formal Logic. This is so far accurate that it is\nfor Inductive Logic to expound the conditions of various degrees of\ncertainty. The consideration of Modality is pertinent to Formal Logic\nonly in so far as concerns special perplexities in the expression of\nit. The treatment of it by Logicians has been rendered intricate by\ntorturing the old tradition to suit different conceptions of the end\nand aim of Logic.\n\n\n\n\nPART II.\n\nDEFINITION.\n\n\n\n\nCHAPTER I.\n\nIMPERFECT UNDERSTANDING OF WORDS AND THE REMEDIES\nTHEREFOR.--DIALECTIC.--DEFINITION.\n\nWe cannot inquire far into the meaning of proverbs or traditional\nsayings without discovering that the common understanding of general\nand abstract names is loose and uncertain. Common speech is a\nquicksand.\n\nConsider how we acquire our vocabulary, how we pick up the words that\nwe use from our neighbours and from books, and why this is so soon\nbecomes apparent. Theoretically we know the full meaning of a name\nwhen we know all the attributes that it connotes, and we are not\njustified in extending it except to objects that possess all the\nattributes. This is the logical ideal, but between the _ought to be_\nof Logic and the _is_ of practical life, there is a vast difference.\nHow seldom do we conceive words in their full meaning! And who is to\ninstruct us in the full meaning? It is not as in the exact sciences,\nwhere we start with a knowledge of the full meaning. In Geometry, for\nexample, we learn the definitions of the words used, _point_, _line_,\n_parallel_, etc., before we proceed to use them. But in common speech,\nwe learn words first in their application to individual cases. Nobody\never defined _good_ to us, or _fair_, or _kind_, or _highly educated_.\nWe hear the words applied to individual objects: we utter them in the\nsame connexion: we extend them to other objects that strike us as like\nwithout knowing the precise points of likeness that the convention\nof common speech includes. The more exact meaning we learn by\ngradual induction from individual cases. _Ugly_, _beautiful_, _good_,\n_bad_--we learn the words first as applicable to things and persons:\ngradually there arises a more or less definite sense of what the\nobjects so designated have in common. The individual's extension of\nthe name proceeds upon what in the objects has most impressed him\nwhen he caught the word: this may differ in different individuals; the\nusage of neighbours corrects individual eccentricities. The child\nin arms shouts _Da_ at the passing stranger who reminds him of his\nfather: for him at first it is a general name applicable to every man:\nby degrees he learns that for him it is a singular name.\n\nThe mode in which words are learnt and extended may be studied most\nsimply in the nursery. A child, say, has learnt to say _mambro_ when\nit sees its nurse. The nurse works a hand-turned sewing machine,\nand sings to it as she works. In the street the child sees an\norgan-grinder singing as he turns his handle: it calls _mambro_:\nthe nurse catches the meaning and the child is overjoyed. The\norgan-grinder has a monkey: the child has an india-rubber monkey toy:\nit calls this also _mambro_. The name is extended to a monkey in\na picture-book. It has a toy musical box with a handle: this also\nbecomes _mambro_, the word being extended along another line of\nresemblance. A stroller with a French fiddle comes within the\ndenotation of the word: a towel-rail is also called _mambro_ from some\nfancied resemblance to the fiddle. A very swarthy hunch-back _mambro_\nfrightens the child: this leads to the transference of the word to a\nterrific coalman with a bag of coals on his back. In a short time\nthe word has become a name for a great variety of objects that have\nnothing whatever common to all of them, though each is strikingly like\nin some point to a predecessor in the series. When the application\nbecomes too heterogeneous, the word ceases to be of use as a sign and\nis gradually abandoned, the most impressive meaning being the last\nto go. In a child's vocabulary where the word _mambro_ had a run of\nnearly two years, its last use was as an adjective signifying ugly or\nhorrible.\n\nThe history of such a word in a child's language is a type of what\ngoes on in the language of men. In the larger history we see similar\nextensions under similar motives, checked and controlled in the same\nway by surrounding usage.\n\nIt is obvious that to avoid error and confusion, the meaning or\nconnotation of names, the concepts, should somehow be fixed: names\ncannot otherwise have an identical reference in human intercourse. We\nmay call this ideal fixed concept the LOGICAL CONCEPT: or we may call\nit the SCIENTIFIC CONCEPT, inasmuch as one of the main objects of the\nsciences is to attain such ideals in different departments of study.\nBut in actual speech we have also the PERSONAL CONCEPT, which varies\nmore or less with the individual user, and the POPULAR or VERNACULAR\nCONCEPT, which, though roughly fixed, varies from social sect to\nsocial sect and from generation to generation.\n\nThe variations in Popular Concepts may be traced in linguistic\nhistory. Words change with things and with the aspects of things,\nas these change in public interest and importance. As long as the\nattributes that govern the application of words are simple, sensible\nattributes, little confusion need arise: the variations are matters of\ncurious research for the philologist, but are logically insignificant.\nMurray's Dictionary, or such books as Trench's _English Past and\nPresent_, supply endless examples, as many, indeed as there are\nwords in the language. _Clerk_ has almost as many connotations as\nour typical _mambro_: clerk in holy orders, church clerk, town clerk,\nclerk of assize, grocer's clerk. In Early English, the word meant \"man\nin a religious order, cleric, clergyman\"; ability to read, write, and\nkeep accounts being a prominent attribute of the class, the word was\nextended on this simple ground till it has ceased altogether to cover\nits original field except as a formal designation. But no confusion is\ncaused by the variation, because the property connoted is simple.[1]\nSo with any common noun: street, carriage, ship, house, merchant,\nlawyer, professor. We might be puzzled to give an exact definition of\nsuch words, to say precisely what they connote in common usage; but\nthe risk of error in the use of them is small.\n\nWhen we come to words of which the logical concept is a complex\nrelation, an obscure or intangible attribute, the defects of the\npopular conception and its tendencies to change and confusion, are\nof the greatest practical importance. Take such words as _Monarchy_,\n_tyranny_, _civil freedom_, _freedom of contract_, _landlord_,\n_gentleman_, _prig_, _culture_, _education_, _temperance_,\n_generosity_. Not merely should we find it difficult to give an\nanalytic definition of such words: we might be unable to do so, and\nyet flatter ourselves that we had a clear understanding of their\nmeaning. But let two men begin to discuss any proposition in which any\nsuch word is involved, and it will often be found that they take the\nword in different senses. If the relation expressed is complex, they\nhave different sides or lines of it in their minds; if the meaning\nis an obscure quality, they are guided in their application of it by\ndifferent outward signs.\n\nMonarchy, in its original meaning, is applied to a form of government\nin which the will of one man is supreme, to make laws or break them,\nto appoint or dismiss officers of state and justice, to determine\npeace or war, without control of statute or custom. But supreme power\nis never thus uncontrolled in reality; and the word has been extended\nto cover governments in which the power of the titular head is\ncontrolled in many different modes and degrees. The existence of a\nhead, with the title of King or Emperor, is the simplest and most\nsalient fact: and wherever this exists, the popular concept of a\nmonarchy is realised. The President of the United States has more real\npower than the Sovereign of Great Britain; but the one government\nis called a Republic and the other a Monarchy. People discuss the\nadvantages and disadvantages of monarchy without first deciding\nwhether they take the word in its etymological sense of unlimited\npower, or its popular sense of titular kingship, or its logical sense\nof power definitely limited in certain ways. And often in debate,\nmonarchy is really a singular term for the government of Great\nBritain.\n\n_Culture_, _religious_, _generous_, are names for inward states or\nqualities: with most individuals some simple outward sign directs\nthe application of the word--it may be manner, or bearing, or routine\nobservances, or even nothing more significant than the cut of the\nclothes or of the hair. Small things undoubtedly are significant, and\nwe must judge by small things when we have nothing else to go by: but\ninstead of trying to get definite conceptions for our moral epithets,\nand suspending judgment till we know that the use of the epithet is\njustified, the trifling superficial sign becomes for us practically\nthe whole meaning of the word. We feel that we must have a judgment of\nsome sort at once: only simple signs are suited to our impatience.\n\nIt was with reference to this state of things that Hegel formulated\nhis paradox that the true abstract thinker is the plain man who laughs\nat philosophy as what he calls abstract and unpractical. He holds\ndecided opinions for or against this or the other abstraction,\n_freedom_, _tyranny_, _revolution_, _reform_, _socialism_, but what\nthese words mean and within what limits the things signified are\ndesirable or undesirable, he is in too great a hurry to pause and\nconsider.\n\nThe disadvantages of this kind of \"abstract\" thinking are obvious.\nThe accumulated wisdom of mankind is stored in language. Until we have\ncleared our conceptions, and penetrated to the full meaning of words,\nthat wisdom is a sealed book to us. Wise maxims are interpreted by\nus hastily in accordance with our own narrow conceptions. All the\nvocables of a language may be more or less familiar to us, and yet we\nmay not have learnt it as an instrument of thought. Outside the very\nlimited range of names for what we see and use in the daily routine of\nlife, food and clothes and the common occupations of men, words\nhave little meaning for us, and are the vehicles merely of thin\npreconceptions and raw prejudices.\n\n\nThe remedy for \"abstract\" thinking is more thinking, and in pursuing\nthis two aims may be specified for the sake of clearness, though they\nare closely allied, and progress towards both may often be made by\none and the same operation. (1) We want to reach a clear and full\nconception of the meaning of names as used now or at a given time.\nLet us call this the _Verification of the Meaning_. (2) We want to fix\nsuch conceptions, and if necessary readjust their boundaries. This is\nthe province of _Definition_, which cannot be effectually performed\nwithout _Scientific Classification_ or _Division_.\n\n\nI.--VERIFICATION OF THE MEANING--DIALECTIC.\n\nThis can only be done by assembling the objects to which the words are\napplied, and considering what they have in common. To ascertain the\nactual connotation we must run over the actual denotation. And since\nin such an operation two or more minds are better than one, discussion\nor dialectic is both more fruitful and more stimulating than solitary\nreflection or reading.\n\nThe first to practise this process on a memorable scale, and with\na distinct method and purpose, was Socrates. To insist upon the\nnecessity of clear conceptions, and to assist by his dialectic\nprocedure in forming them, was his contribution to philosophy.\n\nHis plan was to take a common name, profess ignorance of its meaning,\nand ask his interlocutor whether he would apply it in such and such\nan instance, producing one after another. According to Xenophon's\n_Memorabilia_ he habitually chose the commonest names, _good_,\n_unjust_, _fitting_, and so forth, and tried to set men thinking\nabout them, and helped them by his questions to form an intelligent\nconception of the meaning.\n\nFor example, what is the meaning of injustice? Would you say that\nthe man who cheats or deceives is unjust? Suppose a man deceives his\nenemies, is there any injustice in that? Can the definition be that\na man who deceives his friends is unjust? But there are cases where\nfriends are deceived for their own good: are these cases of injustice?\nA general may inspirit his soldiers by a falsehood. A man may cajole\na weapon out of his friend's hand when he sees him about to commit\nsuicide. A father may deceive his son into taking medicine. Would you\ncall these men unjust? By some such process of interrogation we\nare brought to the definition that a man is unjust who deceives his\nfriends to their hurt.\n\nObserve that in much of his dialectic the aim of Socrates was merely\nto bring out the meaning lying vague and latent, as it were, in\nthe common mind. His object was simply what we have called the\nverification of the meaning. And a dialectic that confines itself to\nthe consideration of what is ordinarily meant as distinct from what\nought to be meant may often serve a useful purpose. Disputes about\nwords are not always as idle as is sometimes supposed. Mr. H. Sidgwick\ntruly remarks (_a propos_ of the terms of Political Economy) that\nthere is often more profit in seeking a definition than in finding it.\nConceptions are not merely cleared but deepened by the process. Mr.\nSidgwick's remarks are so happy that I must take leave to quote them:\nthey apply not merely to the verification of ordinary meaning but also\nto the study of special uses by authorities, and the reasons for those\nspecial uses.\n\n    \"The truth is--as most readers of Plato know, only it is a\n    truth difficult to retain and apply--that what we gain by\n    discussing a definition is often but slightly represented in\n    the superior fitness of the formula that we ultimately adopt;\n    it consists chiefly in the greater clearness and fulness in\n    which the characteristics of the matter to which the formula\n    refers have been brought before the mind in the process of\n    seeking for it. While we are apparently aiming at definitions\n    of terms, our attention should be really fixed on distinctions\n    and relations of fact. These latter are what we are concerned\n    to know, contemplate, and as far as possible arrange and\n    systematise; and in subjects where we cannot present them to\n    the mind in ordinary fulness by the exercise of the organs of\n    sense, there is no way of surveying them so convenient as\n    that of reflecting on our use of common terms.... In comparing\n    different definitions our aim should be far less to decide\n    which we ought to adopt, than to apprehend and duly consider\n    the grounds on which each has commended itself to reflective\n    minds. We shall generally find that each writer has noted some\n    relation, some resemblance or difference, which others have\n    overlooked; and we shall gain in completeness, and often\n    in precision, of view by following him in his observations,\n    whether or not we follow him in his conclusions.\"[2]\n\nMr. Sidgwick's own discussions of _Wealth_, _Value_, and _Money_ are\nmodels. A clue is often found to the meaning in examining startlingly\ndiscrepant statements connected with the same leading word. Thus\nwe find some authorities declaring that \"style\" cannot be taught or\nlearnt, while others declare that it can. But on trying to ascertain\nwhat they mean by \"style,\" we find that those who say it cannot be\ntaught mean either a certain marked individual character or manner of\nwriting--as in Buffon's saying, _Le style c'est l'homme meme_--or a\ncertain felicity and dignity of expression, while those who say style\ncan be taught mean lucid method in the structure of sentences or in\nthe arrangement of a discourse. Again in discussions on the rank of\npoets, we find different conceptions of what constitutes greatness in\npoetry lying at the root of the inclusion of this or the other poet\namong great poets. We find one poet excluded from the first rank of\ngreatness because his poetry was not serious; another because his\npoetry was not widely popular; another because he wrote comparatively\nlittle; another because he wrote only songs or odes and never\nattempted drama or epic. These various opinions point to different\nconceptions of what constitutes greatness in poets, different\nconnotations of \"great poet\". Comparing different opinions concerning\n\"education\" we may be led to ask whether it means more than\ninstruction in the details of certain subjects, whether it does not\nalso import the formation of a disposition to learn or an interest in\nlearning or instruction in a certain method of learning.\n\n\nHistorically, dialectic turning on the use of words preceded the\nattempt to formulate principles of Definition, and attempts at precise\ndefinition led to Division and Classification, that is to systematic\narrangement of the objects to be defined. Attempt to define any such\nword as \"education,\" and you gradually become sensible of the needs in\nrespect of method that forced themselves upon mankind in the history\nof thought. You soon become aware that you cannot define it by itself\nalone; that you are beset by a swarm of more or less synonymous words,\n_instruction_, _discipline_, _culture_, _training_, and so on; that\nthese various words represent distinctions and relations among things\nmore or less allied; and that, if each must be fixed to a definite\nmeaning, this must be done with reference to one another and to the\nwhole department of things that they cover.\n\nThe first memorable attempts at scientific arrangement were\nAristotle's treatises on Ethics and Politics, which had been the\nsubjects of active dialectic for at least a century before. That\nthese the most difficult of all departments to subject to scientific\ntreatment should have been the first chosen was due simply to their\npreponderating interest: \"The proper study of mankind is man\". The\nsystems of what are known as the Natural Sciences are of modern\norigin: the first, that of Botany, dates from Cesalpinus in the\nsixteenth century. But the principles on which Aristotle proceeded in\ndividing and defining, principles which have gradually themselves been\nmore precisely formulated, are principles applicable to all systematic\narrangements for purposes of orderly study. I give them in the precise\nformulae which they have gradually assumed in the tradition of Logic.\nThe principles of Division are often given in Formal Logic, and the\nprinciples of Classification in Inductive Logic, but there is no\nvalid reason for the separation. The classification of objects in the\nNatural Sciences, of animals, plants, and stones, with a view to\nthe thorough study of them in form, structure, and function, is\nmore complex than classifications for more limited purposes, and the\ntendency is to restrict the word classification to these elaborate\nsystems. But really they are only a series of divisions and\nsubdivisions, and the same principles apply to each of the subordinate\ndivisions as well as to the division of the whole department of study.\n\n\nII.--PRINCIPLES OF DIVISION OR CLASSIFICATION AND DEFINITION.\n\nConfusion in the boundaries of names arises from confused ideas\nregarding the resemblances and differences of things. As a protective\nagainst this confusion, things must be clearly distinguished in their\npoints of likeness and difference, and this leads to their arrangement\nin systems, that is, to division and classification. A name is not\nsecure against variation until it has a distinct place in such a\nsystem as a symbol for clearly distinguished attributes. Nor must we\nforget, further, that systems have their day, that the best system\nattainable is only temporary, and may have to be recast to correspond\nwith changes of things and of man's way of looking at them.\n\nThe leading principles of DIVISION may be stated as follows:--\n\n    I. Every division is made on the ground of differences in\n    some attribute common to all the members of the whole to be\n    divided.\n\nThis is merely a way of stating what a logical division is. It is\na division of a generic whole or _genus_, an indefinite number of\nobjects thought of together as possessing some common character or\nattribute. All have this attribute, which is technically called the\n_fundamentum divisionis_, or generic attribute. But the whole is\ndivisible into smaller groups (_species_), each of which possesses the\ncommon character with a difference (_differentia_). Thus, mankind may\nbe divided into White men, Black men, Yellow men, on ground of the\ndifferences in the colour of their skins: all have skins of some\ncolour: this is the _fundamentum divisionis_: but each subdivision or\nspecies has a different colour: this is the _differentia_. Rectilineal\nfigures are divided into triangles, quadrangles, pentagons, etc., on\nthe ground of differences in the number of angles.\n\nUnless there is a _fund. div._, _i.e._, unless the differences are\ndifferences in a common character, the division is not a logical\ndivision. To divide men into Europeans, opticians, tailors, blondes,\nbrunettes, and dyspeptics is not to make a logical division. This is\nseen more clearly in connexion with the second condition of a perfect\ndivision.\n\n    II. In a perfect division, the subdivisions or species are\n    mutually exclusive.\n\nEvery object possessing the common character should be in one or other\nof the groups, and none should be in more than one.\n\nConfusion between classes, or overlapping, may arise from two\ncauses. It may be due (1) to faulty division, to want of unity in\nthe _fundamentum divisionis_; (2) to the indistinct character of the\nobjects to be defined.\n\n(1) Unless the division is based upon a single ground, unless each\nspecies is based upon some mode of the generic character, confusion is\nalmost certain to arise. Suppose the field to be divided, the objects\nto be classified, are three-sided rectilineal plane figures, each\ngroup must be based upon some modification of the three sides. Divide\nthem into equilateral, isosceles, and scalene according as the three\nsides are all of equal length, or two of equal length, or each of\ndifferent length, and you have a perfect division. Similarly you can\ndivide them perfectly according to the character of the angles into\nacute-angled, right-angled and obtuse-angled. But if you do not keep\nto a single basis, as in dividing them into equilateral, isosceles,\nscalene, and right-angled, you have a cross-division. The same\ntriangle might be both right-angled and isosceles.\n\n(2) Overlapping, however, may be unavoidable in practice owing to\nthe nature of the objects. There may be objects in which the dividing\ncharacters are not distinctly marked, objects that possess the\ndifferentiae of more than one group in a greater or less degree. Things\nare not always marked off from one another by hard and fast lines.\nThey shade into one another by imperceptible gradations. A clear\nseparation of them may be impossible. In that case you must allow a\ncertain indeterminate margin between your classes, and sometimes it\nmay be necessary to put an object into more than one class.\n\nTo insist that there is no essential difference unless a clear\ndemarcation can be made is a fallacy. A sophistical trick called the\n_Sorites_ or Heap from the classical example of it was based upon this\ndifficulty of drawing sharp lines of definition. Assuming that it is\npossible to say how many stones constitute a heap, you begin by asking\nwhether three stones form a heap. If your respondent says No, you\nask whether four stones form a heap, then five, and so on and he is\npuzzled to say when the addition of a single stone makes that a heap\nwhich was not a heap before. Or you may begin by asking whether twenty\nstones form a heap, then nineteen, then eighteen, and so on, the\ndifficulty being to say when what was a heap ceases to be so.\n\nWhere the objects classified are mixed states or affections, the\nproducts of interacting factors, or differently interlaced or\ninterfused growths from common roots, as in the case of virtues, or\nemotions, or literary qualities, sharp demarcations are impossible.\nTo distinguish between wit and humour, or humour and pathos, or pathos\nand sublimity is difficult because the same composition may partake\nof more than one character. The specific characters cannot be made\nrigidly exclusive one of another.\n\nEven in the natural sciences, where the individuals are concrete\nobjects of perception, it may be difficult to decide in which of\ntwo opposed groups an object should be included. Sydney Smith has\ncommemorated the perplexities of Naturalists over the newly\ndiscovered animals and plants of Botany Bay, in especial with the\n_Ornithorynchus_,--\"a quadruped as big as a large cat, with the\neyes, colour, and skin of a mole, and the bill and web-feet of a\nduck--puzzling Dr. Shaw, and rendering the latter half of his life\nmiserable, from his utter inability to determine whether it was a bird\nor a beast\".\n\n    III. The classes in any scheme of division should be of\n    co-ordinate rank.\n\nThe classes may be mutually exclusive, and yet the division imperfect,\nowing to their not being of equal rank. Thus in the ordinary division\nof the Parts of Speech, parts, that is, of a sentence, Prepositions\nand Conjunctions are not co-ordinate in respect of function, which is\nthe basis of the division, with Nouns, Adjectives, Verbs, and Adverbs.\nThe preposition is a part of a phrase which serves the same function\nas an adjective, _e.g._, _royal_ army, army _of the king_; it is thus\nfunctionally part of a part, or a particle. So with the conjunction:\nit also is a part of a part, _i.e._, part of a clause serving the\nfunction of adjective or adverb.\n\n    IV. The basis of division (_fundamentum divisionis_) should be\n    an attribute admitting of important differences.\n\nThe importance of the attribute chosen as basis may vary with the\npurpose of the division. An attribute that is of no importance in one\ndivision, may be important enough to be the basis of another division.\nThus in a division of houses according to their architectural\nattributes, the number of windows or the rent is of little importance;\nbut if houses are taxed or rated according to the number of windows\nor the rent, these attributes become important enough to be a basis\nof division for purposes of taxation or rating. They then admit of\nimportant differences.\n\nThat the importance is relative to the purpose of the division should\nbe borne in mind because there is a tendency to regard attributes that\nare of importance in any familiar or pre-eminent division as if they\nhad an absolute importance. In short, disregard of this relativity is\na fallacy to be guarded against.\n\nIn the sciences, the purpose being the attainment and preservation\nof knowledge, the objects of study are divided so as to serve that\npurpose. Groups must be formed so as to bring together the objects\nthat have most in common. The question, Who are to be placed together?\nin any arrangement for purposes of study, receives the same answer\nfor individuals and for classes that have to be grouped into higher\nclasses, namely, Those that have most in common. This is what Dr. Bain\nhappily calls \"the golden rule\" of scientific classification: \"Of the\nvarious groupings of resembling things, preference is given to such as\nhave the greatest number of attributes in common\". I slightly\nmodify Dr. Bain's statement: he says \"the most numerous and the most\nimportant attributes in common\". But for scientific purposes number of\nattributes constitutes importance, as is well recognised by Dr. Fowler\nwhen he says that the test of importance in an attribute proposed as a\nbasis of classification is the number of other attributes of which it\nis an index or invariable accompaniment. Thus in Zoology the\nsquirrel, the rat, and the beaver are classed together as Rodents, the\ndifference between their teeth and the teeth of other Mammalia being\nthe basis of division, because the difference in teeth is accompanied\nby differences in many other properties. So the hedge-hog, the\nshrew-mouse, and the mole, though very unlike in outward appearance\nand habits, are classed together as Insectivora, the difference in\nwhat they feed on being accompanied by a number of other differences.\n\n\n_The Principles of_ DEFINITION. The word \"definition\" as used in Logic\nshows the usual tendency of words to wander from a strict meaning and\nbecome ambiguous. Throughout most of its uses it retains this much of\na common signification, the fixing or determining of the boundaries\nof a class[3] by making clear its constituent attributes. Now in this\nmaking clear two processes may be distinguished, a material process\nand a verbal process. We have (1) the clearing up of the common\nattributes by a careful examination of the objects included in the\nclass: and we have (2) the statement of these common attributes in\nlanguage. The rules of definition given by Dr. Bain, who devotes a\nseparate Book in his Logic to the subject of Definition, concern the\nfirst of these processes: the rules more commonly given concern mainly\nthe second.\n\nOne eminent merit in Dr. Bain's treatment is that it recognises the\nclose connexion between Definition and Classification. His cardinal\nrules are reduced to two.\n\n    I. _Assemble for comparison representative individuals of the\n    class._\n\n    II. _Assemble for comparison representative individuals of the\n    contrasted class or classes._\n\nSeeing that the contrasted classes are contrasted on some basis of\ndivision, this is in effect to recognise that you cannot clearly\ndefine any class except in a scheme of classification. You must have\na wide _genus_ with its _fundamentum divisionis_, and, within this,\n_species_ distinguished by their several _differentiae_.\n\nNext, as to the verbal process, rules are commonly laid down mostly\nof a trifling and obvious character. That \"a definition should state\nneither more nor less than the common attributes of the class,\" or\nthan the attributes signified by the class-name, is sometimes given\nas a rule of definition. This is really an explanation of what a\ndefinition is, a definition of a definition. And as far as mere\nstatement goes it is not strictly accurate, for when the attributes\nof a genus are known it is not necessary to give all the attributes of\nthe species, which include the generic attributes as well, but it is\nsufficient to give the generic name and the differentia. Thus\nPoetry may be defined as \"a Fine Art having metrical language as its\ninstrument\". This is technically known as definition _per genus\net differentiam_. This mode of statement is a recognition of the\nconnexion between Definition and Division.\n\nThe rule that \"a definition should not be a synonymous repetition of\nthe name of the class to be defined,\" is too obvious to require formal\nstatement. To describe a Viceroy as a man who exercises viceregal\nfunctions, may have point as an epigram in the case of a _faineant_\nviceroy, but it is not a definition.\n\nSo with the rule that \"a definition should not be couched in ambiguous\nunfamiliar, or figurative language\". To call the camel \"the ship of\nthe desert\" is a suggestive and luminous description of a property,\nbut it is not a definition. So with the noble description of Faith as\n\"the substance of things hoped for, the evidence of things not seen\".\nBut if one wonders why so obvious a \"rule\" should be laid down, the\nanswer is that it has its historical origin in the caprices of\ntwo classes of offenders, mystical philosophers and pompous\nlexicographers.[4]\n\nThat \"the definition should be simply convertible with the term for\nthe class defined,\" so that we may say, for example, either: \"Wine is\nthe juice of the grape,\" or, \"The juice of the grape is wine,\" is an\nobvious corollary from the nature of definition, but should hardly be\ndignified with the name of a \"rule\".\n\n\n_The Principles of_ NAMING. Rules have been formulated for the choice\nof names in scientific definition and classification, but it may be\ndoubted whether such choice can be reduced to precise rule. It is\nenough to draw attention to certain considerations obvious enough on\nreflection.\n\nWe may take for granted that there should be distinct names for every\ndefining attribute (a _Terminology_) and for every group or class (a\n_Nomenclature_). What about the selection of the names? Suppose an\ninvestigator is struck with likenesses and differences that seem to\nhim important enough to be the basis of a new division, how should he\nbe guided in his choice of names for the new groups that he proposes?\nShould he coin new names, or should he take old names and try to fit\nthem with new definitions?\n\nThe balance of advantages is probably in favour of Dr. Whewell's\ndictum that \"in framing scientific terms, the appropriation of old\nwords is preferable to the invention of new ones\". Only care must be\ntaken to keep as close as possible to the current meaning of the\nold word, and not to run counter to strong associations. This is\nan obvious precept with a view to avoiding confusion. Suppose, for\nexample, that in dividing Governments you take the distribution of\npolitical power as your basis of division and come to the conclusion\nthat the most important differences are whether this power is vested\nin a few or in the majority of the community. You want names to\nfix this broad division. You decide instead of coining the new word\n_Pollarchy_ to express the opposite of _Oligarchy_ to use the old\nwords _Republic_ and _Oligarchy_. You would find, as Sir George\nCornewall Lewis found, that however carefully you defined the word\nRepublic, a division under which the British Government had to be\nranked among Republics would not be generally understood and accepted.\nUsing the word in the sense explained above, Mr. Bagehot maintained\nthat the constitution of Great Britain was more Republican than that\nof the United States, but his meaning was not taken except by a few.\n\nThe difficulty in choosing between new words and old words to express\nnew meanings is hardly felt in the exact sciences. It is at least at\na minimum. The innovator may encounter violent prejudice, but, arguing\nwith experts, he can at least make sure of being understood, if his\nnew division is based upon real and important differences. But in\nother subjects the difficulty of transmitting truth or of expressing\nit in language suited for precise transmission, is almost greater than\nthe difficulty of arriving at truth. Between new names and old\nnames redefined, the possessor of fresh knowledge, assuming it to be\nperfectly verified, is in a quandary. The objects with which he deals\nare already named in accordance with loose divisions resting on strong\nprejudices. The names in current use are absolutely incapable of\nconveying his meaning. He must redefine them if he is to use them. But\nin that case he runs the risk of being misunderstood from people being\ntoo impatient to master his redefinition. His right to redefine may\neven be challenged without any reference to the facts to be expressed:\nhe may simply be accused of circulating false linguistic coin, of\ndebasing the verbal currency. The other alternative open to him is\nto coin new words. In that case he runs the risk of not being read at\nall. His contribution to verified knowledge is passed by as pedantic\nand unintelligible. There is no simple rule of safety: between Scylla\nand Charybdis the mariner must steer as best he may. Practically the\nadvantage lies with old words redefined, because thereby discussion is\nprovoked and discussion clears the air.\n\nWhether it is best to attempt a formal definition or to use words in a\nprivate, peculiar, or esoteric sense, and leave this to be gathered by\nthe reader from the general tenor of your utterances, is a question of\npolicy outside the limits of Logic. It is for the logician to expound\nthe method of Definition and the conditions of its application: how\nfar there are subjects that do not admit of its application profitably\nmust be decided on other grounds. But it is probably true that no\nman who declines to be bound by a formal definition of his terms is\ncapable of carrying them in a clear unambiguous sense through a heated\ncontroversy.\n\n    [Footnote 1: Except, perhaps, in new offices to which the\n    name is extended, such as _Clerk_ of School Board. The name,\n    bearing its most simple and common meaning, may cause popular\n    misapprehension of the nature of the duties. Any uncertainty\n    in meaning may be dangerous in practice: elections have been\n    affected by the ambiguity of this word.]\n\n    [Footnote 2: Sidgwick's _Political Economy_, pp. 52-3. Ed.\n    1883.]\n\n    [Footnote 3: Some logicians, however, speak of defining a\n    thing, and illustrate this as if by a thing they meant a\n    concrete individual, the realistic treatment of Universals\n    lending itself to such expressions. But though the authority\n    of Aristotle might be claimed for this, it is better to\n    confine the name in strictness to the main process of defining\n    a class. Since, however, the method is the same whether it is\n    an individual or a class that we want to make distinct, there\n    is no harm in the extension of the word definition to both\n    varieties. See Davidson's _Logic of Definition_, chap. ii.]\n\n    [Footnote 4: See Davidson's _Logic of Definition_, chap. iii.]\n\n\n\n\nCHAPTER II.\n\nTHE FIVE PREDICABLES.--VERBAL AND REAL PREDICATION.\n\nWe give a separate chapter to this topic out of respect for the space\nthat it occupies in the history of Logic. But except as an exercise in\nsubtle distinction for its own sake, all that falls to be said about\nthe Predicables might be given as a simple appendix to the chapter on\nDefinition.\n\nPrimarily, the Five Predicables or Heads of Predicables--Genus,\nSpecies, Differentia, Proprium, and Accidens--are not predicables at\nall, but merely a list or enumeration of terms used in dividing and\ndefining on the basis of attributes. They have no meaning except in\nconnexion with a fixed scheme of division. Given such a scheme, and\nwe can distinguish in it the whole to be divided (the _genus_), the\nsubordinate divisions (the _species_), the attribute or combination of\nattributes on which each species is constituted (the _differentia_),\nand other attributes, which belong to some or all of the individuals\nbut are not reckoned for purposes of division and definition\n(_Propria_ and _Accidentia_). The list is not itself a logical\ndivision: it is heterogeneous, not homogeneous; the two first are\nnames of classes, the three last of attributes. But corresponding to\nit we might make a homogeneous division of attributes, as follows:--\n\n                   Attributes\n            ___________|____________\n            |                      |\n         Defining             Non-defining\n       _____|______           ____|__________\n       |          |           |             |\n    Generic    Specific    Proprium      Accidens\n             (Differentia)\n\nThe origin of the title Predicables as applied to these five terms is\ncurious, and may be worth noting as an instance of the difficulty of\nkeeping names precise, and of the confusion arising from forgetting\nthe purpose of a name. Porphyry in his [Greek: eisagoge] or\nIntroduction explains the five words ([Greek: phonai]) simply as terms\nthat it is useful for various purposes to know, expressly mentioning\ndefinition and division. But he casually remarks that Singular names,\n\"This man,\" \"Socrates,\" can be predicated only of one individual,\nwhereas _Genera_, _Species_, _Differentiae_, etc., are predicables\nof many. That is to say he describes them as Predicables simply by\ncontradistinction from Singular names. A name, however, was wanted for\nthe five terms taken all together, and since they are not a logical\ndivision, but merely a list of terms used in dividing and defining,\nthere was no apt general designation for them such as would occur\nspontaneously. Thus it became the custom to refer to them as\nthe Predicables, a means of reference to them collectively being\ndesiderated, while the meaning of this descriptive title was\nforgotten.\n\nTo call the five divisional elements or _Divisoria_ Predicables is to\npresent them as a division of Predicate Terms on the basis of their\nrelation to the Subject Term: to suggest that every Predicate Term\nmust be either a Genus or a Species, or a Differentia, or a Proprium,\nor an Accidens of the Subject Term. They are sometimes criticised\nas such, and it is rightly pointed out that the Predicate is never a\nspecies of or with reference to the Subject. But, in truth, the five\nso-called Predicables were never meant as a division of predicates\nin relation to the subject: it is only the title that makes this\nmisleading suggestion.\n\nTo complete the confusion it so happens that Aristotle used three of\nthe Five terms in what was virtually a division of Predicates inasmuch\nas it was a division of Problems or Questions. In expounding the\nmethods of Dialectic in the Topica he divided Problems into four\nclasses according to the relation of the Predicate to the Subject. The\nPredicate must either be simply convertible with the subject or not.\nIf simply convertible, the two must be coextensive, and the\nPredicate must be either a Proprium or the Definition. If not simply\nconvertible, the Predicate must either be part of the Definition or\nnot. If part of the Definition it must be either a Generic Property\nor a Differentia (both of which in this connexion Aristotle includes\nunder Genus): if not part of the Definition, it is an Accident.\nAristotle thus arrives at a fourfold division of Problems or\nPredicates:--[Greek: genos] (_Genus_, including _Differentia_,\n[Greek: diaphora]); [Greek: horos] (Definition); [Greek: to idion]\n(_Proprium_); and [Greek: to symbebekos] (_Accidens_). The object of\nit was to provide a basis for his systematic exposition; each of the\nfour kinds admitted of differences in dialectic method. For us it is\na matter of simple curiosity and ingenuity. It serves as a monument\nof how much Greek dialectic turned on Definition, and it corresponds\nexactly to the division of attributes into Defining and Non-defining\ngiven above. It is sometimes said that Aristotle showed a more\nscientific mind than Porphyry in making the Predicables four instead\nof five. This is true if Porphyry's list had been meant as a division\nof attributes: but it was not so meant.\n\n\nThe distinction between VERBAL or ANALYTIC and REAL or SYNTHETIC\nPredication corresponds to the distinction between Defining and\nNon-defining attributes, and also has no significance except with\nreference to some scheme of Division, scientific and precise or loose\nand popular.\n\nWhen a proposition predicates of a subject something contained in the\nfull notion, concept, or definition of the subject term, it is called\nVerbal, Analytic, or Explicative: _verbal_, inasmuch as it merely\nexplains the meaning of a name; _explicative_ for the same reason;\n_analytic_, inasmuch as it unties the bundle of attributes held\ntogether in the concept and pays out one, or all one by one.\n\nWhen the attributes of the Predicate are not contained in the concept\nof the Subject, the proposition is called _Real_, _Synthetic_, or\n_Ampliative_, for parallel reasons.\n\nThus: \"A triangle is a three-sided rectilinear figure\" is Verbal or\nAnalytic; \"Triangles have three angles together equal to two right\nangles,\" or \"Triangles are studied in schools,\" is Real or Synthetic.\n\nAccording to this distinction, predications of the whole Definition\nor of a Generic attribute or of a Specific attribute are Verbal;\npredications of Accident are Real. A nice point is whether Propria are\nVerbal or Real. They can hardly be classed with Verbal, inasmuch as\none may know the full meaning of the name without knowing them: but\nit might be argued that they are Analytic, inasmuch as they are\nimplicitly contained in the defining attributes as being deducible\nfrom them.\n\nObserve, however, that the whole distinction is really valid only\nin relation to some fixed or accepted scheme of classification or\ndivision. Otherwise, what is Verbal or Analytic to one man may be\nReal or Synthetic to another. It might even be argued that every\nproposition is Analytic to the man who utters it and Synthetic to the\nman who receives it. We must make some analysis of a whole of thought\nbefore paying it out in words: and in the process of apprehending the\nmeaning of what we hear or read we must add the other members of the\nsentence on to the subject. Whether or not this is super-subtle, it\nclearly holds good that what is Verbal (in the sense defined) to the\nlearned man of science may be Real to the learner. That the horse has\nsix incisors in each jaw or that the domestic dog has a curly tail,\nis a Verbal Proposition to the Natural Historian, a mere exposition\nof defining marks; but the plain man has a notion of horse or dog into\nwhich this defining attribute does not enter, and to him accordingly\nthe proposition is Real.\n\nBut what of propositions that the plain man would at once recognise as\nVerbal? Charles Lamb, for example, remarks that the statement that \"a\ngood name shows the estimation in which a man is held in the world\" is\na verbal proposition. Where is the fixed scheme of division there?\nThe answer is that by a fixed scheme of division we do not necessarily\nmean a scheme that is rigidly, definitely and precisely fixed. To make\nsuch schemes is the business of Science. But the ordinary vocabulary\nof common intercourse as a matter of fact proceeds upon schemes\nof division, though the names used in common speech are not always\nscientifically accurate, not always the best that could be devised for\nthe easy acquisition and sure transmission of thorough knowledge. The\nplain man's vocabulary, though often twisted aside by such causes\nas we have specified, is roughly moulded on the most marked\ndistinguishing attributes of things. This was practically recognised\nby Aristotle when he made one of his modes of definition consist in\nsomething like what we have called verifying the meaning of a name,\nascertaining the attributes that it signifies in common speech or in\nthe speech of sensible men. This is to ascertain the essence, [Greek:\nousia], or _Substantia_, of things, the most salient attributes that\nstrike the common eye either at once or after the closer inspection\nthat comes of long companionship, and form the basis of the ordinary\nvocabulary. \"Properly speaking,\" Mansel says,[1] \"All Definition is an\ninquiry into _Attributes_. Our complex notions of Substances can only\nbe resolved into various Attributes, with the addition of an unknown\n_substratum_: a something to which we are compelled to regard\nthese attributes as belonging. _Man_, for example, is analysed\ninto Animality, Rationality, and the something which exhibits these\nphenomena. Pursue the analysis and the result is the same. We have a\nsomething corporeal, animated, sensible, rational. An unknown constant\nmust always be added to complete the integration.\" This \"unknown\nconstant\" was what Locke called the _Real_ Essence, as distinguished\nfrom the _Nominal_ Essence, or complex of attributes. It is upon this\nnominal essence, upon divisions of things according to attributes,\nthat common speech rests, and if it involves many cross-divisions,\nthis is because the divisions have been made for limited and\nconflicting purposes.\n\n    [Footnote 1: Aldrich's Compendium, Appendix, Note C. The\n    reader may be referred to Mansel's Notes A and C for valuable\n    historical notices of the Predicables and Definition.]\n\n\n\n\nCHAPTER III.\n\nARISTOTLE'S CATEGORIES.\n\nIn deference to tradition a place must be found in every logical\ntreatise for Aristotle's Categories. No writing of the same length\nhas exercised a tithe of its influence on human thought. It governed\nscholastic thought and expression for many centuries, being from its\nshortness and consequent easiness of transcription one of the\nfew books in every educated man's library. It still regulates the\nsubdivisions of Parts of Speech in our grammars. Its universality of\nacceptance is shown in the fact that the words _category_ ([Greek:\nkategoria]) and _predicament_, its Latin translation, have passed into\ncommon speech.\n\nThe Categories have been much criticised and often condemned as a\ndivision, but, strange to say, few have inquired what they originally\nprofessed to be a division of, or what was the original author's\nbasis of division. Whether the basis is itself important, is another\nquestion: but to call the division imperfect, without reference to the\nauthor's intention, is merely confusing, and serves only to illustrate\nthe fact that the same objects may be differently divided on different\nprinciples of division. Ramus was right in saying that the Categories\nhad no logical significance, inasmuch as they could not be made a\nbasis for departments of logical method; and Kant and Mill in saying\nthat they had no philosophical significance, inasmuch as they are\nfounded upon no theory of Knowing and Being: but this is to condemn\nthem for not being what they were never intended to be.\n\nThe sentence in which Aristotle states the objects to be divided, and\nhis division of them is so brief and bold that bearing in mind the\nsubsequent history of the Categories, one first comes upon it with a\ncertain surprise. He says simply:--\n\n\"Of things expressed without syntax (_i.e._, single words), each\nsignifies either substance, or quantity, or quality, or relation,\nor place, or time, or disposition (_i.e._, attitude or internal\narrangement), or appurtenance, or action (doing), or suffering (being\ndone to).\"[1]\n\nThe objects, then, that Aristotle proposed to classify were single\nwords (the _themata simplicia_ of the Schoolmen). He explains that by\n\"out of syntax\" ([Greek: aneu symplokes]) he means without reference\nto truth or falsehood: there can be no declaration of truth or\nfalsehood without a sentence, a combination, or syntax: \"man runs\" is\neither true or false, \"man\" by itself, \"runs\" by itself, is neither.\nHis division, therefore, was a division of single words according to\ntheir differences of signification, and without reference to the truth\nor falsehood of their predication.[2]\n\nSignification was thus the basis of division. But according to what\ndifferences? The Categories themselves are so abstract that this\nquestion might be discussed on their bare titles interminably. But\noften when abstract terms are doubtful, an author's intention may be\ngathered from his examples. And when Aristotle's examples are ranged\nin a table, certain principles of subdivision leap to the eyes.\nThus:--\n\n  Substance           Man                   } COMMON    { Substance\n  ([Greek: ousia])    ([Greek: anthropos])  }  NOUN     {\n  (_Substantia_)\n  --------------------------------------------------------------\n  Quantity            Five-feet-five        }           {\n  ([Greek: poson])    ([Greek: tripechu])   }           {\n  (_Quantitas_)                             }           {\n  Quality             Scholarly             }           { Permanent\n  ([Greek: poion])    ([Greek: grammatikon])} ADJECTIVE  { Attribute\n  (_Qualitas_)                              }           {\n  Relation            Bigger                }           {\n  ([Greek: pros ti])  ([Greek: meizon])     }           {\n  (_Relatio_)                               }           {\n  --------------------------------------------------------------\n  Place               In-the-Lyceum         }           {\n  ([Greek: pou])      ([Greek: en Lykeio])  }           {\n  (_Ubi_)                                   } ADVERB    { Temporary\n  Time                Yesterday             }           { Attribute\n  ([Greek: pote])     ([Greek: chthes])     }           {\n  (_Quando_)                                }           {\n  --------------------------------------------------------------\n  Disposition         Reclines              }           {\n  ([Greek: keisthai]) ([Greek: anakeitai])  }           {\n  (_Positio_)                               }           {\n  Appurtenance        Has-shoes-on          }           {\n  ([Greek: echein])   ([Greek: hypodedetai])}           {\n  (_Habitus_)                               } VERB      {\n  Action              Cuts                  }           { Temporary\n  ([Greek: poiein])   ([Greek: temnei])     }           { Attribute\n  (_Actio_)                                 }           {\n  Passion             Is cut                }           {\n  ([Greek: paschein]) ([Greek: temnetai])   }           {\n  (_Passio_)                                }           {\n\nIn looking at the examples, our first impression is that Aristotle has\nfallen into a confusion. He professes to classify words out of syntax,\nyet he gives words with the marks of syntax on them. Thus his division\nis accidentally grammatical, a division of parts of speech, parts of\na sentence, into Nouns, Adjectives, Adverbs, and Verbs. And his\nsubdivisions of these parts are still followed in our grammars. But\nreally it is not the grammatical function that he attends to, but\nthe signification: and looking further at the examples, we see what\ndifferences of signification he had in his mind. It is differences\nrelative to a concrete individual, differences in the words applied to\nhim according as they signify the substance of him or his attributes,\npermanent or temporary.\n\nTake any concrete thing, Socrates, this book, this table. It must\nbe some kind of a thing, a man, a book. It must have some size\nor quantity, six feet high, three inches broad. It must have some\nquality, white, learned, hard. It must have relations with other\nthings, half this, double that, the son of a father. It must be\nsomewhere, at some time, in some attitude, with some \"havings,\"\nappendages, appurtenances, or belongings, doing something, or having\nsomething done to it. Can you conceive any name (simple or composite)\napplicable to any object of perception, whose signification does not\nfall into one or other of these classes? If you cannot, the categories\nare justified as an exhaustive division of significations. They are\na complete list of the most general resemblances among individual\nthings, in other words, of the _summa genera_, the _genera\ngeneralissima_ of predicates concerning this, that or the other\nconcrete individual. No individual thing is _sui generis_: everything\nis like other things: the categories are the most general likenesses.\n\nThe categories are exhaustive, but do they fulfil another requisite of\na good division--are they mutually exclusive? Aristotle himself\nraised this question, and some of his answers to difficulties are\ninstructive. Particularly his discussion of the distinction between\nSecond Substances or Essences and Qualities. Here he approximates to\nthe modern doctrine of the distinction between Substance and Attribute\nas set forth in our quotation from Mansel at p. 110. Aristotle's\nSecond Essences ([Greek: deuterai ousiai]) are common nouns or general\nnames, Species and Genera, _man_, _horse_, _animal_, as distinguished\nfrom Singular names, _this man_, _this horse_, which he calls First\nSubstances ([Greek: protai ousiai]), essences _par excellence_, to\nwhich real existence in the highest sense is attributed. Common nouns\nare put in the First Category because they are predicated in answer to\nthe question, What is this? But he raises the difficulty whether they\nmay not rather be regarded as being in the Third Category, that of\nQuality ([Greek: to poion]). When we say, \"This is a man,\" do we not\ndeclare what sort of a thing he is? do we not declare his Quality? If\nAristotle had gone farther along this line, he would have arrived\nat the modern point of view that a man is a man in virtue of his\npossessing certain attributes, that general names are applied in\nvirtue of their connotation. This would have been to make the line\nof distinction between the First Category and the Third pass between\nFirst Essence and Second, ranking the Second Essences with Qualities.\nBut Aristotle did not get out of the difficulty in this way. He solved\nit by falling back on the differences in common speech. \"Man\" does not\nsignify the quality simply, as \"whiteness\" does. \"Whiteness\" signifies\nnothing but the quality. That is to say, there is no separate name in\ncommon speech for the common attributes of man. His further obscure\nremark that general names \"define quality round essence\" [Greek: peri\nousian], inasmuch as they signify what sort a certain essence is, and\nthat genera make this definition more widely than species, bore fruit\nin the mediaeval discussions between Realists and Nominalists by which\nthe signification of general names was cleared up.\n\nAnother difficulty about the mutual exclusiveness of the Categories\nwas started by Aristotle in connexion with the Fourth Category,\nRelation ([Greek: pros ti] _Ad aliquid_, _To something_). Mill remarks\nthat \"that could not be a very comprehensive view of the nature of\nRelation which would exclude action, passivity, and local situation\nfrom that Category,\" and many commentators, from Simplicius down to\nHamilton, have remarked that all the last six Categories might be\nincluded under Relation. This is so far correct that the word Relation\nis one of the vaguest and most extensive of words; but the criticism\nignores the strictness with which Aristotle confined himself in\nhis Categories to the forms of common speech. It is clear from\nhis examples that in his Fourth Category he was thinking only of\n\"relation\" as definitely expressed in common speech. In his meaning,\nany word is a relative which is joined with another in a sentence by\nmeans of a preposition or a case-inflection. Thus \"disposition\" is a\nrelative: it is the disposition _of_ something. This kind of relation\nis perfect when the related terms reciprocate grammatically; thus\n\"master,\" \"servant,\" since we can say either \"the master of the\nservant,\" or \"the servant of the master\". In mediaeval logic the term\n_Relata_ was confined to these perfect cases, but the Category had\na wider scope with Aristotle. And he expressly raised the question\nwhether a word might not have as much right to be put in another\nCategory as in this. Indeed, he went further than his critics in his\nsuggestions of what Relation might be made to include. Thus: \"big\"\nsignifies Quality; yet a thing is big with reference to something\nelse, and is so far a Relative. Knowledge must be knowledge of\nsomething, and is a relative: why then should we put \"knowing\"\n(_i.e._, learned) in the Category of Quality. \"Hope\" is a relative,\nas being the hope _of_ a man and the hope of something. Yet we say,\n\"I have hope,\" and there hope would be in the category of Having,\nAppurtenance. For the solution of all such difficulties, Aristotle\nfalls back upon the forms of common speech, and decides the place of\nwords in his categories according to them. This was hardly consistent\nwith his proposal to deal with separate words out of syntax, if by\nthis was meant anything more than dealing with them without reference\nto truth or falsehood. He did not and could not succeed in dealing\nwith separate words otherwise than as parts of sentences, owing their\nsignification to their position as parts of a transient plexus of\nthought. In so far as words have their being in common speech, and\nit is their being in this sense that Aristotle considers in the\nCategories, it is a transient being. What being they represent besides\nis, in the words of Porphyry, a very deep affair, and one that needs\nother and greater investigation.\n\n    [Footnote 1: [Greek: ton kata medemian symploken legomenon\n    hekaston etoi ousian semainei, e poson, e poion, e pros ti,\n    e pou, e pote, e keisthai, e echein, e poiein, e paschein.]\n    (Categ. ii. 5.)]\n\n    [Footnote 2: To describe the Categories as a grammatical\n    division, as Mansel does in his instructive Appendix C to\n    Aldrich, is a little misleading without a qualification.\n    They are non-logical inasmuch as they have no bearing on any\n    logical purpose. But they are grammatical only in so far as\n    they are concerned with words. They are not grammatical in\n    the sense of being concerned with the function of words\n    in predication. The unit of grammar in this sense is the\n    sentence, a combination of words in syntax; and it is\n    expressly with words out of syntax that Aristotle deals, with\n    single words not in relation to the other parts of a sentence,\n    but in relation to the things signified. In any strict\n    definition of the provinces of Grammar and Logic, the\n    Categories are neither grammatical nor logical: the\n    grammarians have appropriated them for the subdivision of\n    certain parts of the sentence, but with no more right than the\n    logicians. They really form a treatise by themselves, which\n    is in the main ontological, a discussion of substances and\n    attributes as underlying the forms of common speech. In saying\n    this I use the word substance in the modern sense: but it\n    must be remembered that Aristotle's [Greek: ousia], translated\n    substantia, covered the word as well as the thing signified,\n    and that his Categories are primarily classes of words. The\n    union between names and things would seem to have been closer\n    in the Greek mind than we can now realise. To get at it we\n    must note that every separate word [Greek: to legomenon]\n    is conceived as having a being or thing [Greek: to on]\n    corresponding to it, so that beings or things [Greek: ta\n    onta] are coextensive with single words: a being or thing is\n    whatever receives a separate name. This is clear and simple\n    enough, but perplexity begins when we try to distinguish\n    between this nameable being and concrete being, which last is\n    Aristotle's category of [Greek: ousia], the being signified by\n    a Proper or a Common as distinguished from an Abstract Noun.\n    As we shall see, it is relatively to the highest sense of this\n    last kind of being, namely, the being signified by a Proper\n    name, that he considers the other kinds of being.]\n\n\n\n\nCHAPTER IV.\n\nTHE CONTROVERSY ABOUT UNIVERSALS.--DIFFICULTIES CONCERNING THE\nRELATION OF GENERAL NAMES TO THOUGHT AND TO REALITY.\n\nIn the opening sentences of his Isagoge, before giving his simple\nexplanation of the Five Predicables, Porphyry mentions certain\nquestions concerning Genera and Species, which he passes over as being\ntoo difficult for the beginner. \"Concerning genera and species,\"\nhe says, \"the question whether they subsist (_i.e._, have real\nsubstance), or whether they lie in the mere thoughts only, or whether,\ngranting them to subsist, they are corporeal or incorporeal, or\nwhether they subsist apart, or in sensible things and cohering round\nthem--this I shall pass over, such a question being a very deep affair\nand one that needs other and greater investigation.\"\n\nThis passage, written about the end of the third century, A.D., is a\nkind of isthmus between Greek Philosophy and Mediaeval: it summarises\nquestions which had been turned over on every side and most\nintricately discussed by Plato and Aristotle and their successors,\nand the bald summary became a starting-point for equally intricate\ndiscussions among the Schoolmen, among whom every conceivable variety\nof doctrine found champions. The dispute became known as the dispute\nabout Universals, and three ultra-typical forms of doctrine\nwere developed, known respectively as Realism, Nominalism, and\nConceptualism. Undoubtedly the dispute, with all its waste of\ningenuity, had a clearing effect, and we may fairly try now what\nPorphyry shrank from, to gather some simple results for the better\nunderstanding of general names and their relations to thoughts and to\nthings. The rival schools had each some aspect of the general name in\nview, which their exaggeration served to render more distinct.\n\nWhat does a general name signify? For logical purposes it is\nsufficient to answer--the points of resemblance as grasped in\nthe mind, fixed by a name applicable to each of the resembling\nindividuals. This is the signification of the general name\n_logically_, its connotation or concept, the identical element of\nobjective reference in all uses of a general name.\n\nBut other questions may be asked that cannot be so simply answered.\nWhat is this concept in thought? What is there in our minds\ncorresponding to the general name when we utter it? How is its\nsignification conceived? What is the signification _psychologically_?\n\nWe may ask, further, What is there in nature that the general name\nsignifies? What is its relation to reality? What corresponds to it in\nthe real world? Has the unity that it represents among individuals\nno existence except in the mind? Calling this unity, this one in\nthe many, the Universal (_Universale_, [Greek: to pan]), what is the\nUniversal _ontologically_?\n\nIt was this ontological question that was so hotly and bewilderingly\ndebated among the Schoolmen. Before giving the ultra-typical answers\nto it, it may be well to note how this question was mixed up with\nstill other questions of Theology and Cosmogony. Recognising that\nthere is a unity signified by the general name, we may go on to\ninquire into the ground of the unity. Why are things essentially like\none another? How is the unity maintained? How is it continued? Where\ndoes the common pattern come from? The question of the nature of\nthe Universal thus links itself with metaphysical theories of the\nconstruction of the world, or even with the Darwinian theory of the\norigin of species.\n\nPassing by these remoter questions, we may give the answers of\nthe three extreme schools to the ontological question, What is a\nUniversal?\n\nThe answer of the Ultra-Realists, broadly put, was that a Universal is\na substance having an independent existence in nature.\n\nOf the Ultra-Nominalists, that the Universal is a name and nothing\nelse, _vox et praeterea nihil_; that this name is the only unity among\nthe individuals of a species, all that they have in common.\n\nOf the Ultra-Conceptualists, that the individuals have more in common\nthan the name, that they have the name plus the meaning,\n_vox_ + _significatio_, but that the Universals, the genera and\nspecies, exist only in the mind.\n\nNow these extreme doctrines, as literally interpreted by opponents,\nare so easily refuted and so manifestly untenable, that it may be\ndoubted whether they were ever held by any thinker, and therefore I\ncall them Ultra-Realism, Ultra-Nominalism, and Ultra-Conceptualism.\nThey are mere exaggerations or caricatures, set up by opponents\nbecause they can be easily knocked down.\n\nTo the Ultra-Realists, it is sufficient to say that if there existed\nanywhere a substance having all the common attributes of a species\nand only these, having none of the attributes peculiar to any of the\nindividuals of that species, corresponding to the general name as an\nindividual corresponds to a Proper or Singular name, it would not be\nthe Universal, the unity pervading the individuals, but only another\nindividual.\n\nTo the Ultra-Nominalists, it is sufficient to say that the individuals\nmust have more in common than the name, because the name is not\napplied arbitrarily, but on some ground. The individuals must have in\ncommon that on account of which they receive the common name: to call\nthem by the same name is not to make them of the same species.\n\nTo the Ultra-Conceptualists, it is sufficient to say that when we\nemploy a general name, as when we say \"Socrates is a man,\" we do\nnot refer to any passing thought or state of mind, but to certain\nattributes independent of what is passing in our minds. We cannot make\na thing of this or that species by merely thinking of it as such.\n\nThe ultra-forms of these doctrines are thus easily shown to\nbe inadequate, yet each of the three, Realism, Nominalism, and\nConceptualism, represents a phase of the whole truth.\n\nThus, take Realism. Although it is not true that there is anything\nin reality corresponding to the general name such as there is\ncorresponding to the singular name, the general name merely signifying\nattributes of what the singular name signifies, it does not follow, as\nthe opponents of Ultra-Realism hastily assume, that there is nothing\nin the real world corresponding to the general name. Three senses may\nbe particularised in which Realism is justified.\n\n(1) The points of resemblance from which the concept is formed are as\nreal as the individuals themselves. It is true in a sense that it\nis our thought that gives unity to the individuals of a class, that\ngathers the many into one, and so far the Conceptualists are right.\nStill we should not gather them into one if they did not resemble one\nanother: that is the reason why we think of them together: and the\nrespects in which they resemble one another are as much independent of\nus and our thinking as the individuals themselves, as much beyond the\npower of our thought to change. We must go behind the activity of the\nmind in unifying to the reason for the unification: and the ground of\nunity is found in what really exists. We do not confer the unity:\nwe do not make all men or all dogs alike: we find them so. The curly\ntails in a thousand domestic dogs, which serve to distinguish them\nfrom wolves and foxes, are as real as the thousand individual domestic\ndogs. In this sense the Aristotelian doctrine, _Universalia in re_,\nexpresses a plain truth.\n\n(2) The Platonic doctrine, formulated by the Schoolmen as _Universalia\nante rem_, has also a plain validity. Individuals come and go, but\nthe type, the Universal, is more abiding. Men are born and die: man\nremains throughout. The snows of last year have vanished, but snow is\nstill a reality to be faced. Wisdom does not perish with the wise\nmen of any generation. In this plain sense, at least, it is true that\nUniversals exist before Individuals, have a greater permanence, or, if\nwe like to say so, a higher, as it is a more enduring, reality.\n\n(3) Further, the \"idea,\" concept, or universal, though it cannot be\nseparated from the individual, and whether or not we ascribe to it\nthe separate suprasensual existence of the archetypal forms of Plato's\npoetical fancy, is a very potent factor in the real world. Ideals of\nconduct, of manners, of art, of policy, have a traditional life: they\ndo not pass away with the individuals in whom they have existed,\nin whom they are temporarily materialised: they survive as potent\ninfluences from age to age. The \"idea\" of Chaucer's Man of Law,\nwho always \"seemed busier than he was,\" is still with us. Mediaeval\nconceptions of chivalry still govern conduct. The Universal enters\ninto the Individual, takes possession of him, makes of him its\ntemporary manifestation.\n\nNevertheless, the Nominalists are right in insisting on the importance\nof names. What we call the real world is a common object of perception\nand knowledge to you and me: we cannot arrive at a knowledge of it\nwithout some means of communication with one another: our means of\ncommunication is language. It may be doubted whether even thinking\ncould go far without symbols with the help of which conceptions may\nbe made definite. A concept cannot be explained without reference to\na symbol. There is even a sense in which the Ultra-Nominalist doctrine\nthat the individuals in a class have nothing in common but the name\nis tenable. Denotability by the same name is the only respect in which\nthose individuals are absolutely identical: in this sense the name\nalone is common to them, though it is applied in virtue of their\nresemblance to one another.\n\nFinally, the Conceptualists are right in insisting on the mind's\nactivity in connexion with general names. Genera and species are not\nmere arbitrary subjective collections: the union is determined by the\ncharacters of the things collected. Still it is with the concept in\neach man's mind that the name is connected: it is by the activity of\nthought in recognising likenesses and forming concepts that we are\nable to master the diversity of our impressions, to introduce unity\ninto the manifold of sense, to reduce our various recollections to\norder and coherence.\n\nSo much for the Ontological question. Now for the PSYCHOLOGICAL. What\nis in the mind when we employ a general name? What is the Universal\npsychologically? How is it conceived?\n\nWhat breeds confusion in these subtle inquiries is the want of fixed\nunambiguous names for the things to be distinguished. It is only by\nmeans of such names that we can hold on to the distinctions, and\nkeep from puzzling ourselves. Now there are three things to be\ndistinguished in this inquiry, which we may call the Concept, the\nConception, and the Conceptual or Generic Image. Let us call them by\nthese names, and proceed to explain them.\n\nBy the Concept, I understand the meaning of the general name, what the\ngeneral name signifies: by the Conception, the mental act or state\nof him who conceives this meaning. The concept of \"triangle,\" _i.e._,\nwhat you and I mean by the word, is not my act of mind or your act of\nmind when we think or speak of a triangle. The Conception, which is\nthis act, is an event or incident in our mental history, a psychical\nact or state, a distinct occurrence, a particular fact in time as much\nas the battle of Waterloo. The concept is the objective reference of\nthe name, which is the same, or at least is understood to be the\nsame, every time we use it. I make a figure on paper with ink or on a\nblackboard with chalk, and recognise or conceive it as a triangle: you\nalso conceive it as such: we do the same to-morrow: we did the same\nyesterday: each act of conception is a different event, but the\nconcept is the same throughout.\n\nNow the psychological question about the Universal is, What is this\nconception? We cannot define it positively further than by saying that\nit consists in realising the meaning of a general name: the act being\nunique, we can only make it intelligible by producing an example of\nit. But we may define it negatively by distinguishing it from the\nconceptual image. Whenever we conceive anything, \"man,\" \"horse,\" there\nis generally present to our minds an image of a man or horse, with\naccidents of size, colour, position or other categories. But this\nconceptual image is not the concept, and the mental act of forming it\nis not conception.\n\nThis distinction between mental picturing or imaging and the\nconception of common attributes is variously expressed. The\ncorrelative terms _Intuitive_ and _Symbolical_ Thinking,\n_Presentative_ and _Representative_ Knowledge have been employed.[1]\nBut whatever terms we use, the distinction itself is vital, and the\nwant of it leads to confusion.\n\nThus the fact that we cannot form a conceptual image composed\nsolely of common attributes has been used to support the argument of\nUltra-Nominalism, that the individuals classed under a common name\nhave nothing in common but the name. What the word \"dog\" signifies,\n_i.e._, the \"concept\" of dog, is neither big nor little, neither black\nnor tan, neither here nor there, neither Newfoundland, nor Retriever,\nnor Terrier, nor Greyhound, nor Pug, nor Bulldog. The concept consists\nonly of the attributes common to all dogs apart from any that are\npeculiar to any variety or any individual. Now we cannot form any such\nconceptual image. Our conceptual image is always of some definite\nsize and shape. Therefore, it is argued, we cannot conceive what a dog\nmeans, and dogs have nothing in common but the name. This, however,\ndoes not follow. The concept is not the conceptual image, and\nforming the image is not conception. We may even, as in the case of\na chiliagon, or thousand-sided figure, conceive the meaning without\nbeing able to form any definite image.\n\nHow then, do we ordinarily proceed in conceiving, if we cannot picture\nthe common attributes alone and apart from particulars? We attend, or\nstrive to attend, only to those aspects of an image which it has in\ncommon with the individual things denoted. And if we want to make our\nconception definite, we pass in review an indefinite number of the\nindividuals, case after case.\n\nA minor psychological question concerns the nature of the conceptual\nimage. Is it a copy of some particular impression, or a confused blur\nor blend of many? Possibly neither: possibly it is something like\none of Mr. Galton's composite photographs, photographs produced by\nexposing the same surface to the impressions of a number of different\nphotographs in succession. If the individuals are nearly alike,\nthe result is an image that is not an exact copy of any one of the\ncomponents and yet is perfectly distinct. Possibly the image that\ncomes into our mind's eye when we hear such a word as \"horse\" or \"man\"\nis of this character, the result of the impressions of a number of\nsimilar things, but not identical with any one. As, however, different\npersons have different conceptual images of the same concept, so we\nmay have different conceptual images at different times. It is only\nthe concept that remains the same.\n\nBut how, it may be asked, can the concept remain the same? If the\nuniversal or concept psychologically is an intellectual act, repeated\nevery time we conceive, what guarantee have we for the permanence\nof the concept? Does this theory not do away with all possibility of\ndefining and fixing concepts?\n\nThis brings us back to the doctrine already laid down about the truth\nof Realism. The theory of the concept is not exhausted when it is\nviewed only psychologically, as a psychic act. If we would understand\nit fully, we must consider the act in its relations to the real\nexperience of ourselves and others. To fix this act, we give it a\nseparate name, calling it the conception: and then we must go behind\nthe activity of the mind to the objects on which it is exercised.\nThe element of fixity is found in them. And here also the truth of\nNominalism comes in. By means of words we enter into communication\nwith other minds. It is thus that we discover what is real, and what\nis merely personal to ourselves.\n\n    [Footnote 1: The only objection to these terms is that they\n    have slipped from their moorings in philosophical usage. Thus\n    instead of Leibnitz's use of Intuitive and Symbolical, which\n    corresponds to the above distinction between Imaging and\n    Conception, Mr. Jevons employs the terms to express a\n    distinction among conceptions proper. We can understand what\n    a chiliagon means, but we cannot form an image of it in our\n    minds, except in a very confused and imperfect way; whereas we\n    can form a distinct image of a triangle. Mr. Jevons would call\n    the conception of the triangle _Intuitive_, of the chiliagon\n    _Symbolical_.\n\n    Again, while Mansel uses the words Presentative and\n    Representative to express our distinction, a more common\n    usage is to call actual Perception Presentative Knowledge, and\n    ideation or recollection in idea Representative.]\n\n\n\n\nPART III.\n\nTHE INTERPRETATION OF PROPOSITIONS.--OPPOSITION AND IMMEDIATE\nINFERENCE.\n\n\n\n\nCHAPTER I.\n\nTHEORIES OF PREDICATION.--THEORIES OF JUDGMENT.\n\nWe may now return to the Syllogistic Forms, and the consideration of\nthe compatibility or incompatibility, implication, and interdependence\nof propositions.\n\nIt was to make this consideration clear and simple that what we have\ncalled the Syllogistic Form of propositions was devised. When are\npropositions incompatible? When do they imply one another? When do\ntwo imply a third? We have seen in the Introduction how such questions\nwere forced upon Aristotle by the disputative habits of his time.\nIt was to facilitate the answer that he analysed propositions into\nSubject and Predicate, and viewed the Predicate as a reference to a\nclass: in other words, analysed the Predicate further into a Copula\nand a Class Term.\n\nBut before showing how he exhibited the interconnexion of propositions\non this plan, we may turn aside to consider various so-called Theories\nof Predication or of Judgment. Strictly speaking, they are not\naltogether relevant to Logic, that is to say, as a practical science:\nthey are partly logical, partly psychological theories: some of\nthem have no bearing whatever on practice, but are matters of pure\nscientific curiosity: but historically they are connected with the\nlogical treatment of propositions as having been developed out of\nthis.\n\nThe least confusing way of presenting these theories is to state\nthem and examine them both logically and psychologically. The logical\nquestion is, Has the view any advantage for logical purposes? Does it\nhelp to prevent error, to clear up confusion? Does it lead to firmer\nconceptions of the truth? The psychological question is, Is this a\ncorrect theory of how men actually think when they make propositions?\nIt is a question of _what is_ in the one case, and of _what ought to\nbe for a certain purpose_ in the other.\n\nWhether we speak of Proposition or of Judgment does not materially\naffect our answer. A Judgment is the mental act accompanying a\nProposition, or that may be expressed in a proposition and cannot be\nexpressed otherwise: we can give no other intelligible definition or\ndescription of a judgment. So a proposition can only be defined as the\nexpression of a judgment: unless there is a judgment underneath them,\na form of words is not a proposition.\n\nLet us take, then, the different theories in turn. We shall find that\nthey are not really antagonistic, but only different: that each is\nsubstantially right from its own point of view: and that they seem to\ncontradict one another only when the point of view is misunderstood.\n\nI. _That the Predicate term may be regarded as a class in or\nfrom which the Subject is included or excluded._ Known as the\nClass-Inclusion, Class-Reference, or Denotative view.\n\nThis way of analysing propositions is possible, as we have seen,\nbecause every statement implies a general name, and the extension\nor denotation of a general name is a class defined by the common\nattribute or attributes. It is useful for syllogistic purposes:\ncertain relations among propositions can be most simply exhibited in\nthis way.\n\nBut if this is called a Theory of Predication or Judgment, and taken\npsychologically as a theory of what is in men's minds whenever they\nutter a significant Sentence, it is manifestly wrong. When discussed\nas such, it is very properly rejected. When a man says \"P struck Q,\"\nhe has not necessarily a class of \"strikers of Q\" definitely in his\nmind. What he has in his mind is the logical equivalent of this,\nbut it is not this directly. Similarly, Mr. Bradley would be quite\njustified in speaking of Two Terms and a Copula as a superstition, if\nit were meant that these analytic elements are present to the mind of\nan ordinary speaker.\n\nII. _That every Proposition may be regarded as affirming or denying\nan attribute of a subject._ Known sometimes as the Connotative or\nthe Denotative-Connotative view. This also follows from the implicit\npresence of a general name in every sentence. But it should not be\ntaken as meaning that the man who says: \"Tom came here yesterday,\"\nor \"James generally sits there,\" has a clearly analysed Subject and\nAttribute in his mind. Otherwise it is as far wrong as the other view.\n\nIII. _That every proposition may be regarded as an equation between\ntwo terms._ Known as the Equational View.\n\nThis is obviously not true for common speech or ordinary thought.\nBut it is a possible way of regarding the analytic components of\na proposition, legitimate enough if it serves any purpose. It is a\nmodification of the Class-Reference analysis, obtained by what is\nknown as Quantification of the Predicate. In \"All S is in P,\" P\nis undistributed, and has no symbol of Quantity. But since the\nproposition imports that All S is a part of P, _i.e._, Some P, we may,\nif we choose, prefix the symbol of Quantity, and then the proposition\nmay be read \"All S = Some P\". And so with the other forms.\n\nIs there any advantage in this? Yes: it enables us to subject the\nformulae to algebraic manipulation. But any logical advantage--any\nhelp to thinking? None whatever. The elaborate syllogistic systems of\nBoole, De Morgan, and Jevons are not of the slightest use in helping\nmen to reason correctly. The value ascribed to them is merely an\nillustration of the Bias of Happy Exercise. They are beautifully\ningenious, but they leave every recorded instance of learned\nScholastic trifling miles behind.\n\nIV. _That every proposition is the expression of a comparison between\nconcepts._ Sometimes called the Conceptualist View.\n\n\"To judge,\" Hamilton says, \"is to recognise the relation of congruence\nor confliction in which two concepts, two individual things, or a\nconcept and an individual compared together stand to each other.\"\n\nThis way of regarding propositions is permissible or not according to\nour interpretation of the words \"congruence\" and \"confliction,\" and\nthe word \"concept\". If by concept we mean a conceived attribute of\na thing, and if by saying that two concepts are congruent or\nconflicting, we mean that they may or may not cohere in the same\nthing, and by saying that a concept is congruent or conflicting with\nan individual that it may or may not belong to that individual, then\nthe theory is a corollary from Aristotle's analysis. Seeing that we\nmust pass through that analysis to reach it, it is obviously not\na theory of ordinary thought, but of the thought of a logician\nperforming that analysis.\n\nThe precise point of Hamilton's theory was that the logician does not\nconcern himself with the question whether two concepts are or are\nnot as a matter of fact found in the same subject, but only with the\nquestion whether they are of such a character that they may be found,\nor cannot be found, in the same subject. In so far as his theory\nis sound, it is an abstruse and technical way of saying that we may\nconsider the consistency of propositions without considering whether\nor not they are true, and that consistency is the peculiar business of\nsyllogistic logic.\n\nV. _That the ultimate subject of every judgment is reality._\n\nThis is the form in which Mr. Bradley and Mr. Bosanquet deny the\nUltra-Conceptualist position. The same view is expressed by Mill when\nhe says that \"propositions are concerned with things and not with our\nideas of them\".\n\nThe least consideration shows that there is justice in the view thus\nenounced. Take a number of propositions:--\n\n          The streets are wet.\n          George has blue eyes.\n          The Earth goes round the Sun.\n          Two and two make four.\n\nObviously, in any of these propositions, there is a reference beyond\nthe conceptions in the speaker's mind, viewed merely as incidents\nin his mental history. They express beliefs about things and the\nrelations among things _in rerum natura_: when any one understands\nthem and gives his assent to them, he never stops to think of the\nspeaker's state of mind, but of what the words represent. When states\nof mind are spoken of, as when we say that our ideas are confused, or\nthat a man's conception of duty influences his conduct, those states\nof mind are viewed as objective facts in the world of realities. Even\nwhen we speak of things that have in a sense no reality, as when we\nsay that a centaur is a combination of man and horse, or that centaurs\nwere fabled to live in the vales of Thessaly, it is not the passing\nstate of mind expressed by the speaker as such that we attend to or\nthink of; we pass at once to the objective reference of the words.\n\nPsychologically, then, the theory is sound: what is its logical\nvalue? It is sometimes put forward as if it were inconsistent with\nthe Class-reference theory or the theory that judgment consists in\na comparison of concepts. Historically the origin of its formal\nstatement is its supposed opposition to those theories. But really\nit is only a misconception of them that it contradicts. It is\ninconsistent with the Class-reference view only if by a class we\nunderstand an arbitrary subjective collection, not a collection of\nthings on the ground of common attributes. And it is inconsistent with\nthe Conceptualist theory only if by a concept we understand not the\nobjective reference of a general name, but what we have distinguished\nas a conception or a conceptual image. The theory that the ultimate\nsubject is reality is assumed in both the other theories, rightly\nunderstood. If every proposition is the utterance of a judgment, and\nevery proposition implies a general name, and every general name has\na meaning or connotation, and every such meaning is an attribute of\nthings and not a mental state, it is implied that the ultimate subject\nof every proposition is reality. But we may consider whether or not\npropositions are consistent without considering whether or not they\nare true, and it is only their mutual consistency that is considered\nin the syllogistic formulae. Thus, while it is perfectly correct to say\nthat every proposition expresses either truth or falsehood, or that\nthe characteristic quality of a judgment is to be true or false, it\nis none the less correct to say that we may temporarily suspend\nconsideration of truth or falsehood, and that this is done in what is\ncommonly known as Formal Logic.\n\nVI. _That every proposition may be regarded as expressing relations\nbetween phenomena._\n\nBain follows Mill in treating this as the final import of Predication.\nBut he indicates more accurately the logical value of this view in\nspeaking of it as important for laying out the divisions of Inductive\nLogic. They differ slightly in their lists of Universal Predicates\nbased upon Import in this sense--Mill's being Resemblance,\nCoexistence, Simple Sequence, and Causal Sequence, and Bain's being\nCoexistence, Succession, and Equality or Inequality. But both lay\nstress upon Coexistence and Succession, and we shall find that the\ndistinctions between Simple Sequence and Causal Sequence, and between\nRepeated and Occasional Coexistence, are all-important in the Logic of\nInvestigation. But for syllogistic purposes the distinctions have no\nrelevance.\n\n\n\n\nCHAPTER II.\n\nTHE \"OPPOSITION\" OF PROPOSITIONS.--THE INTERPRETATION OF \"NO\".\n\nPropositions are technically said to be \"opposed\" when, having the\nsame terms in Subject and Predicate, they differ in Quantity, or in\nQuality, or in both.[1]\n\nThe practical question from which the technical doctrine has been\ndeveloped was how to determine the significance of contradiction.\nWhat is meant by giving the answer \"No\" to a proposition put\ninterrogatively? What is the interpretation of \"No\"? What is the\nrespondent committed to thereby?\n\n\"Have all ratepayers a vote?\" If you answer \"No,\" you are bound to\nadmit that some ratepayers have not. O is the CONTRADICTORY of A. If A\nis false, O must be true. So if you deny O, you are bound to admit A:\none or other must be true: either Some ratepayers have not a vote or\nAll have.\n\nIs it the case that no man can live without sleep? Deny this, and you\ncommit yourself to maintaining that Some man, one at least, can live\nwithout sleep. I is the Contradictory of E; and _vice versa_.\n\nContradictory opposition is distinguished from CONTRARY, the\nopposition of one Universal to another, of A to E and E to A. There is\na natural tendency to meet a strong assertion with the very reverse.\nLet it be maintained that women are essentially faithless or that \"the\npoor in a lump is bad,\" and disputants are apt to meet this extreme\nwith another, that constancy is to be found only in women or true\nvirtue only among the poor. Both extremes, both A and E, may be false:\nthe truth may lie between: Some are, Some not.\n\nLogically, the denial of A or E implies only the admission of O or I.\nYou are not committed to the full contrary. But the implication of the\nContradictory is absolute; there is no half-way house where the\ntruth may reside. Hence the name of EXCLUDED MIDDLE is applied to the\nprinciple that \"Of two Contradictories one or other must be true: they\ncannot both be false\".\n\nWhile both CONTRARIES may be false, they cannot both be true.\n\nIt is sometimes said that in the case of Singular propositions, the\nContradictory and the Contrary coincide. A more correct doctrine is\nthat in the case of Singular propositions, the distinction is not\nneeded and does not apply. Put the question \"Is Socrates wise?\" or\n\"Is this paper white?\" and the answer \"No\" admits of only one\ninterpretation, provided the terms remain the same. Socrates may\nbecome foolish, or this paper may hereafter be coloured differently,\nbut in either case the subject term is not the same about which the\nquestion was asked. Contrary opposition belongs only to general terms\ntaken universally as subjects. Concerning individual subjects an\nattribute must be either affirmed or denied simply: there is no middle\ncourse. Such a proposition as \"Socrates is sometimes not wise,\" is\nnot a true Singular proposition, though it has a Singular term as\ngrammatical subject. Logically, it is a Particular proposition, of\nwhich the subject-term is the actions or judgments of Socrates.[2]\n\nOpposition, in the ordinary sense, is the opposition of incompatible\npropositions, and it was with this only that Aristotle concerned\nhimself. But from an early period in the history of Logic, the word\nwas extended to cover mere differences in Quantity and Quality\namong the four forms A E I O, which differences have been named\nand exhibited symmetrically in a diagram known as: The Square of\nOpposition.\n\n  A______Contraries______E\n  |\\                    /|\n  | \\                  s |\n  |  C                e  |\n  |   o              i   |\n  |    n            r    |\n  |     t          o     |\n  S      r        t      S\n  u       a      c       u\n  b        \\    i        b\n  a         \\  d         a\n  l          \\/          l\n  t          /\\          t\n  e         /  d         e\n  r        /    i        r\n  n       a      c       n\n  s      r        t      s\n  |     t          o     |\n  |    n            r    |\n  |   o              i   |\n  |  C                e  |\n  | /                  s |\n  |/                    \\|\n  I____Sub-contraries____O\n\nThe four forms being placed at the four corners of the Square, and\nthe sides and diagonals representing relations between them thus\nseparated, a very pretty and symmetrical doctrine is the result.\n\n_Contradictories_, A and O, E and I, differ both in Quantity and in\nQuality.\n\n_Contraries_, A and E, differ in Quality but not in Quantity, and are\nboth Universal.\n\n_Sub-contraries_, I and O, differ in Quality but not in Quantity, and\nare both Particular.\n\n_Subalterns_, A and I, E and O, differ in Quantity but not in Quality.\n\nAgain, in respect of concurrent truth and falsehood there is a certain\nsymmetry.\n\nContradictories cannot both be true, nor can they both be false.\n\nContraries may both be false, but cannot both be true.\n\nSub-contraries may both be true, but cannot both be false.\n\nSubalterns may both be false and both true. If the Universal is true,\nits subalternate Particular is true: but the truth of the Particular\ndoes not similarly imply the truth of its Subalternating Universal.\n\nThis last is another way of saying that the truth of the Contrary\ninvolves the truth of the Contradictory, but the truth of the\nContradictory does not imply the truth of the Contrary.\n\nThere, however, the symmetry ends. The sides and the diagonals of the\nSquare do not symmetrically represent degrees of incompatibility, or\nopposition in the ordinary sense.\n\nThere is no incompatibility between two Sub-contraries or a Subaltern\nand its Subalternant. Both may be true at the same time. Indeed, as\nAristotle remarked of I and O, the truth of the one commonly implies\nthe truth of the other: to say that some of the crew were drowned,\nimplies that some were not, and _vice versa_. Subaltern and\nSubalternant also are compatible, and something more. If a man has\nadmitted A or E, he cannot refuse to admit I or O, the Particular of\nthe same Quality. If All poets are irritable, it cannot be denied\nthat some are so; if None is, that Some are not. The admission of the\nContrary includes the admission of the Contradictory.\n\nConsideration of Subalterns, however, brings to light a nice ambiguity\nin Some. It is only when I is regarded as the Contradictory of E,\nthat it can properly be said to be Subalternate to A. In that case the\nmeaning of Some is \"not none,\" _i.e._, \"Some at least\". But when Some\nis taken as the sign of Particular quantity simply, _i.e._, as meaning\n\"not all,\" or \"some at most,\" I is not Subalternate to A, but opposed\nto it in the sense that the truth of the one is incompatible with the\ntruth of the other.\n\nAgain, in the diagram Contrary opposition is represented by a side and\nContradictory by the diagonal; that is to say, the stronger form of\nopposition by the shorter line. The Contrary is more than a denial: it\nis a counter-assertion of the very reverse, [Greek: to enantion].\n\"Are good administrators always good speakers?\" \"On the contrary, they\nnever are.\" This is a much stronger opposition, in the ordinary sense,\nthan a modest contradictory, which is warranted by the existence of\na single exception. If the diagram were to represent incompatibility\naccurately, the Contrary ought to have a longer line than the\nContradictory, and this it seems to have had in the diagram that\nAristotle had in mind (_De Interpret._, c. 10).\n\nIt is only when Opposition is taken to mean merely difference in\nQuantity and Quality that there can be said to be greater opposition\nbetween Contradictories than between Contraries. Contradictories\ndiffer both in Quantity and in Quality: Contraries, in Quality only.\n\nThere is another sense in which the Particular Contradictory may be\nsaid to be a stronger opposite than the Contrary. It is a stronger\nposition to take up argumentatively. It is easier to defend than a\nContrary. But this is because it offers a narrower and more limited\nopposition.\n\nWe deal with what is called Immediate Inference in the next chapter.\nPending an exact definition of the process, it is obvious that two\nimmediate inferences are open under the above doctrines, (1) Granted\nthe truth of any proposition, you may immediately infer the falsehood\nof its Contradictory. (2) Granted the truth of any Contrary, you may\nimmediately infer the truth of its Subaltern.[3]\n\n    [Footnote 1: This is the traditional definition of Opposition\n    from an early period, though the tradition does not start from\n    Aristotle. With him opposition ([Greek: antikeisthai]) meant,\n    as it still means in ordinary speech, incompatibility. The\n    technical meaning of Opposition is based on the diagram (given\n    afterwards in the text) known as the Square of Opposition, and\n    probably originated in a confused apprehension of the reason\n    why it received that name. It was called the Square of\n    Opposition, because it was intended to illustrate the doctrine\n    of Opposition in Aristotle's sense and the ordinary sense of\n    repugnance or incompatibility. What the Square brings out is\n    this. If the four forms A E I O are arranged symmetrically\n    according as they differ in quantity, or quality, or both, it\n    is seen that these differences do not correspond symmetrically\n    to compatibility and incompatibility: that propositions may\n    differ in quantity or in quality without being incompatible,\n    and that they may differ in both (as Contradictories) and be\n    less violently incompatible than when they differ in one only\n    (as Contraries). The original purpose of the diagram was to\n    bring this out, as is done in every exposition of it. Hence\n    it was called the Square of Opposition. But as a descriptive\n    title this is a misnomer: it should have been the Square of\n    Differences in Quantity or Quality. This misnomer has been\n    perpetuated by appropriating Opposition as a common name for\n    difference in Quantity or Quality when the terms are the same\n    and in the same order, and distinguishing it in this sense\n    from Repugnance or Incompatibility (Tataretus in Summulas,\n    _De Oppositionibus_ [1501], Keynes, _The Opposition of\n    Propositions_ [1887]). Seeing that there never is occasion to\n    speak of Opposition in the limited sense except in connexion\n    with the Square, there is no real risk of confusion. A common\n    name is certainly wanted in that connexion, if only to say\n    that Opposition (in the limited or diagrammatic sense) does\n    not mean incompatibility.]\n\n    [Footnote 2: Cp. Keynes, pt. ii. ch. ii. s. 57. Aristotle laid\n    down the distinction between Contrary and Contradictory to\n    meet another quibble in contradiction, based on taking\n    the Universal as a whole and indivisible subject like an\n    Individual, of which a given predicate must be either affirmed\n    or denied.]\n\n    [Footnote 3: I have said that there is little risk of\n    confusion in using the word Opposition in its technical or\n    limited sense. There is, however, a little. When it is\n    said that these Inferences are based on Opposition, or\n    that Opposition is a mode of Immediate Inference, there is\n    confusion of ideas unless it is pointed out that when this is\n    said, it is Opposition in the ordinary sense that is meant.\n    The inferences are really based on the rules of Contrary and\n    Contradictory Opposition; Contraries cannot both be true, and\n    of Contradictories one or other must be.]\n\n\n\n\nCHAPTER III.\n\nTHE IMPLICATION OF PROPOSITIONS.--IMMEDIATE FORMAL INFERENCE.\n--EDUCATION.\n\nThe meaning of Inference generally is a subject of dispute, and\nto avoid entering upon debatable ground at this stage, instead of\nattempting to define Inference generally, I will confine myself\nto defining what is called Formal Inference, about which there is\ncomparatively little difference of opinion.\n\nFORMAL INFERENCE then is the apprehension of what is implied in a\ncertain datum or admission: the derivation of one proposition,\ncalled the CONCLUSION, from one or more given, admitted, or assumed\npropositions, called the PREMISS or PREMISSES.\n\nWhen the conclusion is drawn from one proposition, the inference is\nsaid to be IMMEDIATE; when more than one proposition is necessary to\nthe conclusion, the inference is said to be MEDIATE.\n\nGiven the proposition, \"All poets are irritable,\" we can immediately\ninfer that \"Nobody that is not irritable is a poet\"; and the one\nadmission implies the other. But we cannot infer immediately that \"all\npoets make bad husbands\". Before we can do this we must have a second\nproposition conceded, that \"All irritable persons make bad husbands\".\nThe inference in the second case is called Mediate.[1]\n\nThe modes and conditions of valid Mediate Inference constitute\nSyllogism, which is in effect the reasoning together of separate\nadmissions. With this we shall deal presently. Meantime of Immediate\nInference.\n\nTo state all the implications of a certain form of proposition, to\nmake explicit all that it implies, is the same thing with showing\nwhat immediate inferences from it are legitimate. Formal inference, in\nshort, is the eduction of all that a proposition implies.\n\nMost of the modes of Immediate Inference formulated by logicians are\npreliminary to the Syllogistic process, and have no other practical\napplication. The most important of them technically is the process\nknown as Conversion, but others have been judged worthy of attention.\n\n\nAEQUIPOLLENT OR EQUIVALENT FORMS--OBVERSION.\n\nAEquipollence or Equivalence ([Greek: Isodynamia]) is defined as the\nperfect agreement in sense of two propositions that differ somehow in\nexpression.[2]\n\nThe history of AEquipollence in logical treatises illustrates two\ntendencies. There is a tendency on the one hand to narrow a theme\ndown to definite and manageable forms. But when a useful exercise is\ndiscarded from one place it has a tendency to break out in another\nunder another name. A third tendency may also be said to be specially\nwell illustrated--the tendency to change the traditional application\nof logical terms.\n\nIn accordance with the above definition of AEquipollence or\nEquivalence, which corresponds with ordinary acceptation, the term\nwould apply to all cases of \"identical meaning under difference of\nexpression\". Most examples of the reduction of ordinary speech into\nsyllogistic form would be examples of aequipollence; all, in fact,\nwould be so were it not that ordinary speech loses somewhat in the\nprocess, owing to the indefiniteness of the syllogistic symbol for\nparticular quality, Some. And in truth all such transmutations\nof expression are as much entitled to the dignity of being called\nImmediate Inferences as most of the processes so entitled.\n\nDr. Bain uses the word with an approach to this width of application\nin discussing all that is now most commonly called Immediate Inference\nunder the title of Equivalent Forms. The chief objection to this usage\nis that the Converse _per accidens_ is not strictly equivalent. A\ndebater may want for his argument less than the strict equivalent, and\ncontent himself with educing this much from his opponent's admission.\n(Whether Dr. Bain is right in treating the Minor and Conclusion of\na Hypothetical Syllogism as being equivalent to the Major, is not so\nmuch a question of naming.)\n\nBut in the history of the subject, the traditional usage has been\nto confine AEquipollence to cases of equivalence between positive and\nnegative forms of expression. \"Not all are,\" is equivalent to \"Some\nare not\": \"Not none is,\" to \"Some are\". In Pre-Aldrichian text-books,\nAEquipollence corresponds mainly to what it is now customary to call\n(_e.g._, Fowler, pt. iii. c. ii., Keynes, pt. ii. c. vii.) Immediate\nInference based on Opposition. The denial of any proposition involves\nthe admission of its contradictory. Thus, if the negative particle\n\"Not\" is placed before the sign of Quantity, All or Some, in\na proposition, the resulting proposition is equivalent to the\nContradictory of the original. Not all S is P = Some S is not P.\nNot any S is P = No S is P. The mediaeval logicians tabulated these\nequivalents, and also the forms resulting from placing the negative\nparticle after, or both before and after, the sign of Quantity. Under\nthe title of AEquipollence, in fact, they considered the interpretation\nof the negative particle generally. If the negative is placed after\nthe universal sign, it results in the Contrary: if both before and\nafter, in the Subaltern. The statement of these equivalents is a\npuzzling exercise which no doubt accounts for the prominence given it\nby Aristotle and the Schoolmen. The latter helped the student with the\nfollowing Mnemonic line: _Prae Contradic., post Contrar., prae postque\nSubaltern._[3]\n\nTo AEquipollence belonged also the manipulation of the forms known\nafter the _Summulae_ as _Exponibiles_, notably _Exclusive_ and\n_Exceptive propositions_, such as None but barristers are eligible,\nThe virtuous alone are happy. The introduction of a negative particle\ninto these already negative forms makes a very trying problem in\ninterpretation. The aequipollence of the Exponibiles was dropped from\ntext-books long before Aldrich, and it is the custom to laugh at them\nas extreme examples of frivolous scholastic subtlety: but most modern\ntext-books deal with part of the doctrine of the _Exponibiles_ in\ncasual exercises.\n\nCuriously enough, a form left unnamed by the scholastic logicians\nbecause too simple and useless, has the name AEquipollent appropriated\nto it, and to it alone, by Ueberweg, and has been adopted under\nvarious names into all recent treatises.\n\nBain calls it the FORMAL OBVERSE,[4] and the title of OBVERSION (which\nhas the advantage of rhyming with CONVERSION) has been adopted by\nKeynes, Miss Johnson, and others.\n\nFowler (following Karslake) calls it PERMUTATION. The title is not a\nhappy one, having neither rhyme nor reason in its favour, but it is\nalso extensively used.\n\nThis immediate inference is a very simple affair to have been honoured\nwith such a choice of terminology. \"This road is long: therefore, it\nis not short,\" is an easy inference: the second proposition is the\nObverse, or Permutation, or AEquipollent, or (in Jevons's title) the\nImmediate Inference by Privative Conception, of the first.\n\nThe inference, such as it is, depends on the Law of Excluded Middle.\nEither a term P, or its contradictory, not-P, must be true of any\ngiven subject, S: hence to affirm P of all or some S, is equivalent\nto denying not-P of the same: and, similarly, to deny P, is to affirm\nnot-P. Hence the rule of Obversion;--Substitute for the predicate term\nits Contrapositive,[5] and change the Quality of the proposition.\n\n       All S is P = No S is not-P.\n        No S is P = All S is not-P.\n      Some S is P = Some S is not not-P.\n  Some S is not P = Some S is not-P.\n\n\nCONVERSION.\n\nThe process takes its name from the interchange of the terms. The\nPredicate-term becomes the Subject-term, and the Subject-term the\nPredicate-term.\n\nWhen propositions are analysed into relations of inclusion or\nexclusion between terms, the assertion of any such relation between\none term and another, implies a Converse relation between the second\nterm and the first. The statement of this implied assertion is\ntechnically known as the CONVERSE of the original proposition, which\nmay be called the _Convertend_.\n\nThree modes of Conversion are commonly recognised:--(_a_) SIMPLE\nCONVERSION; (_b_) CONVERSION _per accidens_ or by limitation; (_c_)\nCONVERSION BY CONTRAPOSITION.\n\n(_a_) E and I can be simply converted, only the terms being\ninterchanged, and Quantity and Quality remaining the same.\n\nIf S is wholly excluded from P, P must be wholly excluded from S. If\nSome S is contained in P, then Some P must be contained in S.\n\n(_b_) A cannot be simply converted. To know that All S is contained in\nP, gives you no information about that portion of P which is outside\nS. It only enables you to assert that Some P is S; that portion of P,\nnamely, which coincides with S.\n\nO cannot be converted either simply or _per accidens_. Some S is not P\ndoes not enable you to make any converse assertion about P. All P\nmay be S, or No P may be S, or Some P may be not S. All the three\nfollowing diagrams are compatible with Some S being excluded from P.\n\n[Illustration:\n\n  Concentric circles of S and P - P in centre\n\n  S in one circle and P in another circle.\n\n  S and P each in a circle, overlapping circle.\n]\n\n(_c_) Another mode of Conversion, known by mediaeval logicians\nfollowing Boethius as _Conversio per contra positionem terminorum_, is\nuseful in some syllogistic manipulations. This Converse is obtained\nby substituting for the predicate term its Contrapositive or\nContradictory, not-P, making the consequent change of Quality, and\nsimply converting. Thus All S is P is converted into the equivalent No\nnot-P is S.[6]\n\nSome have called it \"Conversion by Negation,\" but \"negation\"\nis manifestly too wide and common a word to be thus arbitrarily\nrestricted to the process of substituting for one term its opposite.\n\nOthers (and this has some mediaeval usage in its favour, though not the\nmost intelligent) would call the form All not-P is not-S (the Obverse\nor Permutation of No not-P is S), the Converse by Contraposition. This\nis to conform to an imaginary rule that in Conversion the Converse\nmust be of the same Quality with the Convertend. But the essence of\nConversion is the interchange of Subject and Predicate: the Quality is\nnot in the definition except by a bungle: it is an accident. No\nnot-P is S, and Some not-P is S are the forms used in Syllogism,\nand therefore specially named. Unless a form had a use, it was left\nunnamed, like the Subalternate forms of Syllogism: Nomen habent\nnullum: nec, si bene colligis, usum.\n\n\nTABLE OF CONTRAPOSITIVE CONVERSES.\n\n                             Con. Con.\n  All S is P                 No not-P is S\n  No S is P                  Some not-P is S\n  Some S is not P            Some not-P is S\n  Some S is P                None.\n\nWhen not-P is substituted for P, Some S is P becomes Some S is not\nnot-P, and this form is inconvertible.\n\n\nOTHER FORMS OF IMMEDIATE INFERENCE.\n\nI have already spoken of the Immediate Inferences based on the rules\nof Contradictory and Contrary Opposition (see p. 145 - Part III, Ch.\nII).\n\nAnother process was observed by Thomson, and named _Immediate\nInference by Added Determinants_. If it is granted that \"A negro is\na fellow-creature,\" it follows that \"A negro in suffering is a\nfellow-creature in suffering\". But that this does not follow for every\nattribute[7] is manifest if you take another case:--\"A tortoise is\nan animal: therefore, a fast tortoise is a fast animal\". The form,\nindeed, holds in cases not worth specifying: and is a mere handle for\nquibbling. It could not be erected into a general rule unless it\nwere true that whatever distinguishes a species within a class, will\nequally distinguish it in every class in which the first is included.\n\nMODAL CONSEQUENCE has also been named among the forms of Immediate\nInference. By this is meant the inference of the lower degrees of\ncertainty from the higher. Thus _must be_ is said to imply _may be_;\nand _None can be_ to imply _None is_.\n\nDr. Bain includes also _Material Obversion_, the analogue of _Formal\nObversion_ applied to a Subject. Thus Peace is beneficial to commerce,\nimplies that War is injurious to commerce. Dr. Bain calls this\nMaterial Obversion because it cannot be practised safely without\nreference to the matter of the proposition. We shall recur to the\nsubject in another chapter.\n\n    [Footnote 1: I purposely chose disputable propositions to\n    emphasise the fact that Formal Logic has no concern with the\n    truth, but only with the interdependence of its propositions.]\n\n    [Footnote 2: Mark Duncan, _Inst. Log._, ii. 5, 1612.]\n\n    [Footnote 3: There can be no doubt that in their doctrine of\n    AEquipollents, the Schoolmen were trying to make plain a real\n    difficulty in interpretation, the interpretation of the force\n    of negatives. Their results would have been more obviously\n    useful if they had seen their way to generalising them.\n    Perhaps too they wasted their strength in applying it to the\n    artificial syllogistic forms, which men do not ordinarily\n    encounter except in the manipulation of syllogisms. Their\n    results might have been generalised as follows:--\n\n    (1) A \"not\" placed before the sign of Quantity contradicts\n    the whole proposition. Not \"All S is P,\" not \"No S is P,\"\n    not \"Some S is P,\" not \"Some S is not P,\" are equivalent\n    respectively to contradictories of the propositions thus\n    negatived.\n\n    (2) A \"not\" placed after the sign of Quantity affects the\n    copula, and amounts to inverting its Quality, thus denying\n    the predicate term of the same quantity of the subject term of\n    which it was originally affirmed, and _vice versa_.\n\n           All S is \"not\" P = No S is P.\n            No S is \"not\" P = All S is P.\n          Some S is \"not\" P = Some S is not P.\n      Some S is \"not\" not P = Some S is P.\n\n    (3) If a \"not\" is placed before as well as after, the\n    resulting forms are obviously equivalent (under Rule 1) to the\n    assertion of the contradictories of the forms on the right (in\n    the illustration of Rule 2).\n\n    Not | All S is \"not\" P      = No S is P       | = Some S is P.\n    Not | No S is \"not\" P       = All S is P      | = Some S is not P.\n    Not | Some S is \"not\" P     = Some S is not P | = All S is P.\n    Not | Some S is \"not\" not P = Some S is P     | = No S is P.\n    ]\n\n\n    [Footnote 4: _Formal_ to distinguish it from what he called\n    the _Material Obverse_, about which more presently.]\n\n    [Footnote 5: The mediaeval word for the opposite of a term, the\n    word Contradictory being confined to the propositional form.]\n\n    [Footnote 6: It is to be regretted that a practice has\n    recently crept in of calling this form, for shortness, the\n    Contrapositive simply. By long-established usage, dating from\n    Boethius, the word Contrapositive is a technical name for a\n    terminal form, not-A, and it is still wanted for this use.\n    There is no reason why the propositional form should not be\n    called the Converse by Contraposition, or the Contrapositive\n    Converse, in accordance with traditional usage.]\n\n    [Footnote 7: _Cf._ Stock, part iii. c. vii.; Bain,\n    _Deduction_, p. 109.]\n\n\n\n\nCHAPTER IV.\n\nTHE COUNTER-IMPLICATION OF PROPOSITIONS.\n\nIn discussing the Axioms of Dialectic, I indicated that the\npropositions of common speech have a certain negative implication,\nthough this does not depend upon any of the so-called Laws of Thought,\nIdentity, Contradiction, and Excluded Middle. Since, however, the\ncounter-implicate is an important guide in the interpretation of\npropositions, it is desirable to recognise it among the modes of\nImmediate Inference.\n\nI propose, then, first, to show that people do ordinarily infer at\nonce to a counter-sense; second, to explain briefly the Law of Thought\non which such an inference is justified; and, third, how this law\nmay be applied in the interpretation of propositions, with a view to\nmaking subject and predicate more definite.\n\nEvery affirmation about anything is an implicit negation about\nsomething else. Every say is a gainsay. That people ordinarily\nact upon this as a rule of interpretation a little observation is\nsufficient to show: and we find also that those who object to having\ntheir utterances interpreted by this rule often shelter themselves\nunder the name of Logic.\n\nSuppose, for example, that a friend remarks, when the conversation\nturns on children, that John is a good boy, the natural inference is\nthat the speaker has in his mind another child who is not a good boy.\nSuch an inference would at once be drawn by any actual hearer, and the\nspeaker would protest in vain that he said nothing about anybody but\nJohn. Suppose there are two candidates for a school appointment, A\nand B, and that stress is laid upon the fact that A is an excellent\nteacher. A's advocate would at once be understood to mean that B was\nnot equally excellent as a teacher.\n\nThe fairness of such inferences is generally recognised. A reviewer,\nfor example, of one of Mrs. Oliphant's historical works, after\npointing out some small errors, went on to say that to confine himself\nto censure of small points, was to acknowledge by implication that\nthere were no important points to find fault with.\n\nYet such negative implications are often repudiated as illogical.\nIt would be more accurate to call them extra-logical. They are not\ncondemned by any logical doctrine: they are simply ignored. They are\nextra-logical only because they are not legitimated by the Laws of\nIdentity, Contradiction, and Excluded Middle: and the reason why\nLogic confines itself to those laws is that they are sufficient for\nSyllogism and its subsidiary processes.\n\nBut, though extra-logical, to infer a counter-implicate is not\nunreasonable: indeed, if Definition, clear vision of things in their\nexact relations, is our goal rather than Syllogism, a knowledge of\nthe counter-implicate is of the utmost consequence. Such an implicate\nthere must always be under an all-pervading Law of Thought which has\nnot yet been named, but which may be called tentatively the law of\nHomogeneous Counter-relativity. The title, one hopes, is sufficiently\ntechnical-looking: though cumbrous, it is descriptive. The law itself\nis simple, and may be thus stated and explained.\n\n\n_The Law of Homogeneous Counter-relativity._\n\n    Every positive in thought has a contrapositive, and the\n    positive and contrapositive are of the same kind.\n\nThe first clause of our law corresponds with Dr. Bain's law of\nDiscrimination or Relativity: it is, indeed, an expansion and\ncompletion of that law. Nothing is known absolutely or in isolation;\nthe various items of our knowledge are inter-relative; everything is\nknown by distinction from other things. Light is known as the opposite\nof darkness, poverty of riches, freedom of slavery, in of out; each\nshade of colour by contrast to other shades. What Dr. Bain lays stress\nupon is the element of difference in this inter-relativity. He bases\nthis law of our knowledge on the fundamental law of our sensibility\nthat change of impression is necessary to consciousness. A long\ncontinuance of any unvaried impression results in insensibility to it.\nWe have seen instances of this in illustrating the maxim that\ncustom blunts sensibility (p. 74). Poets have been beforehand with\nphilosophers in formulating this principle. It is expressed with the\ngreatest precision by Barbour in his poem of \"The Bruce,\" where he\ninsists that men who have never known slavery do not know what freedom\nis.\n\n  Thus contrar thingis evermare\n  Discoverings of t' other are.\n\nSince, then, everything that comes within our consciousness comes as\na change or transition from something else, it results that our\nknowledge is counter-relative. It is in the clash or conflict of\nimpressions that knowledge emerges: every item of knowledge has its\nilluminating foil, by which it is revealed, over against which it is\ndefined. Every positive in thought has its contrapositive.\n\nSo much for the element of difference. But this is not the whole of\nthe inter-relativity. The Hegelians rightly lay stress on the common\nlikeness that connects the opposed items of knowledge.\n\n    \"Thought is not only _distinction_; it is, at the same time,\n    _relation_.[1] If it marks off one thing from another, it, at\n    the same time, connects one thing with another. Nor can either\n    of these functions of thought be separated from the other: as\n    Aristotle himself said, the knowledge of opposites is one. A\n    thing which has nothing to distinguish it is unthinkable, but\n    equally unthinkable is a thing which is so separated from all\n    other things as to have no community with them. If then the\n    law of contradiction be taken as asserting the self-identity\n    of things or thoughts in a sense that excludes their\n    community--in other words, if it be not taken as limited by\n    another law which asserts the _relativity_ of the things or\n    thoughts distinguished--it involves a false abstraction....\n    If, then, the world, as an intelligible world, is a world of\n    distinction, differentiation, individuality, it is equally\n    true that in it as an intelligible world there are no absolute\n    separations or oppositions, no antagonisms which cannot be\n    reconciled.\"[2]\n\nIn the penultimate sentence of this quotation Dr. Caird\n_differentiates_ his theory against a Logical counter-theory of\nthe Law of Identity, and in the last sentence against an Ethical\ncounter-theory: but the point here is that he insists on the relation\nof likeness among opposites. Every impression felt is felt as a change\nor transition from something else: but it is a variation of the same\nimpression--the something else, the contrapositive, is not entirely\ndifferent. Change itself is felt as the opposite of sameness,\ndifference of likeness, and likeness of difference. We do not\ndifferentiate our impression against the whole world, as it were,\nbut against something nearly akin to it--upon some common ground. The\npositive and the contrapositive are of the same kind.\n\nLet us surprise ourselves in the act of thinking and we shall find\nthat our thoughts obey this law. We take note, say, of the colour\nof the book before us: we differentiate it against some other colour\nactually before us in our field of vision or imagined in our minds.\nLet us think of the blackboard as black: the blackness is defined\nagainst the whiteness of the figures chalked or chalkable upon it, or\nagainst the colour of the adjacent wall. Let us think of a man as a\nsoldier; the opposite in our minds is not the colour of his hair,\nor his height, or his birthplace, or his nationality, but some other\nprofession--soldier, sailor, tinker, tailor. It is always by means of\nsome contrapositive that we make the object of our thoughts definite;\nit is not necessarily always the same opposite, but against\nwhatever opposite it is, they are always homogeneous. One colour is\ncontradistinguished from another colour, one shade from another shade:\ncolour may be contradistinguished from shape, but it is within the\ncommon genus of sensible qualities.\n\nA curious confirmation of this law of our thinking has been pointed\nout by Mr. Carl Abel.[3] In Egyptian hieroglyphics, the oldest\nextant language, we find, he says, a large number of symbols with\ntwo meanings, the one the exact opposite of the other. Thus the\nsame symbol represents _strong_ and _weak_; _above_--_below_;\n_with_--_without_; _for_--_against_. This is what the Hegelians mean\nby the reconciliation of antagonisms in higher unities. They do not\nmean that black is white, but only that black and white have something\nin common--they are both colours.\n\nI have said that this law of Homogeneous Counter-relativity has not\nbeen recognised by logicians. This, however, is only to say that it\nhas not been explicitly formulated and named, as not being required\nfor Syllogism; a law so all-pervading could not escape recognition,\ntacit or express. And accordingly we find that it is practically\nassumed in Definition: it is really the basis of definition _per\ngenus et differentiam_. When we wish to have a definite conception\nof anything, to apprehend what it is, we place it in some genus and\ndistinguish it from species of the same. In fact our law might be\ncalled the Law of Specification: in obeying the logical law of what\nwe ought to do with a view to clear thinking, we are only doing with\nexactness and conscious method what we all do and cannot help doing\nwith more or less definiteness in our ordinary thinking.\n\nIt is thus seen that logicians conform to this law when they are\nnot occupied with the narrow considerations proper to Syllogism. And\nanother unconscious recognition of it may be found in most logical\ntext-books. Theoretically the not-A of the Law of Contradiction--(A is\nnot not-A)--is an infinite term. It stands for everything but A. This\nis all that needs to be assumed for Conversion and Syllogism. But take\nthe examples given of the Formal Obverse or Permutation, \"All men are\nfallible\". Most authorities would give as the Formal Obverse of this,\n\"No men are infallible\". But, strictly speaking, \"infallible\" is\nof more limited and definite signification than not-fallible.\nNot-fallible, other than fallible, is brown, black, chair, table,\nand every other nameable thing except fallible. Thus in Obversion and\nConversion by Contraposition, the homogeneity of the negative term is\ntacitly assumed; it is assumed that A and not-A are of the same kind.\n\n\nNow to apply this Law of our Thought to the interpretation of\npropositions. Whenever a proposition is uttered we are entitled to\ninfer at once (or _immediately_) that the speaker has in his mind\nsome counter-proposition, in which what is overtly asserted of the\nostensible subject is covertly denied of another subject. And we must\nknow what this counter-proposition, the counter-implicate is, before\nwe can fully and clearly understand his meaning. But inasmuch as\nany positive may have more than one contrapositive, we cannot tell\nimmediately or without some knowledge of the circumstances or context,\nwhat the precise counter-implicate is. The peculiar fallacy incident\nto this mode of interpretation is, knowing that there must be some\ncounter-implicate, to jump rashly or unwarily to the conclusion that\nit is some definite one.\n\nDr. Bain applies the term Material Obverse to the form, Not-S is not\nP, as distinguished from the form S is not not-P, which he calls\nthe Formal Obverse, on the ground that we can infer the\nPredicate-contrapositive at once from the form, whereas we cannot tell\nthe Subject-contrapositive without an examination of the matter.\nBut in truth we cannot tell either Predicate-contrapositive or\nSubject-contrapositive as it is in the mind of the speaker from\nthe bare utterance. We can only tell that if he has in his mind a\nproposition definitely analysed into subject and predicate, he must\nhave contrapositives in his mind of both, and that they must be\nhomogeneous. Let a man say, \"This book is a quarto\". For all that we\nknow he may mean that it is not a folio or that it is not an\noctavo: we only know for certain, under the law of Homogeneous\nCounter-relativity, that he means some definite other size. Under\nthe same law, we know that he has a homogeneous contrapositive of the\nsubject, a subject that admits of the same predicate, some other book\nin short. What the particular book is we do not know.\n\nIt would however be a waste of ingenuity to dwell upon the\nmanipulation of formulae founded on this law. The practical concern is\nto know that for the interpretation of a proposition, a knowledge of\nthe counter-implicate, a knowledge of what it is meant to deny, is\nessential.\n\nThe manipulation of formulae, indeed, has its own special snare. We are\napt to look for the counterparts of them in the grammatical forms of\ncommon speech. Thus, it might seem to be a fair application of our law\nto infer from the sentence, \"Wheat is dear,\" that the speaker had in\nhis mind that Oats or Sugar or Shirting or some other commodity is\ncheap. But this would be a rash conclusion. The speaker may mean this,\nbut he _may_ also mean that wheat is dear now as compared with some\nother time: that is, the Positive subject in his mind may be \"Wheat as\nnow,\" and the Contrapositive \"Wheat as then\". So a man may say, \"All\nmen are mortal,\" meaning that the angels never taste death, \"angels\"\nbeing the contrapositive of his subject \"men\". Or he may mean merely\nthat mortality is a sad thing, his positive subject being men as\nthey are, and his contrapositive men as he desires them to be. Or his\nemphasis may be upon the _all_, and he may mean only to deny that some\none man in his mind (Mr. Gladstone, for example) is immortal. It would\nbe misleading, therefore, to prescribe propositions as exercises in\nMaterial Obversion, if we give that name to the explicit expression\nof the Contrapositive Subject: it is only from the context that we can\ntell what this is. The man who wishes to be clearly understood gives\nus this information, as when the epigrammatist said: \"We are all\nfallible--even the youngest of us\".\n\nBut the chief practical value of the law is as a guide in studying the\ndevelopment of opinions. Every doctrine ever put forward has been\nput forward in opposition to a previous doctrine on the same subject.\nUntil we know what the opposed doctrine is, we cannot be certain of\nthe meaning. We cannot gather it with precision from a mere study of\nthe grammatical or even (in the narrow sense of the word) the logical\ncontent of the words used. This is because the framers of doctrines\nhave not always been careful to put them in a clear form of subject\nand predicate, while their impugners have not moulded their denial\nexactly on the language of the original. No doubt it would have been\nmore conducive to clearness if they had done so. But they have not,\nand we must take them as they are. Thus we have seen that the Hegelian\ndoctrine of Relativity is directed against certain other doctrines\nin Logic and in Ethics; that Ultra-Nominalism is a contradiction of\na certain form of Ultra-Realism; and that various theories of\nPredication each has a backward look at some predecessor.\n\nI quote from Mr. A.B. Walkley a very happy application of this\nprinciple of interpretation:--\n\n    \"It has always been a matter for speculation why so sagacious\n    an observer as Diderot should have formulated the wild paradox\n    that the greatest actor is he who feels his part the least.\n    Mr. Archer's bibliographical research has solved this riddle.\n    Diderot's paradox was a protest against a still wilder one. It\n    seems that a previous eighteenth century writer on the\n    stage, a certain Saint-Albine, had advanced the fantastic\n    propositions that none but a magnanimous man can act\n    magnanimity, that only lovers can do justice to a love scene,\n    and kindred assertions that read like variations on the\n    familiar 'Who drives fat oxen must himself be fat'. Diderot\n    saw the absurdity of this; he saw also the essentially\n    artificial nature of the French tragedy and comedy of his own\n    day; and he hastily took up the position which Mr. Archer has\n    now shown to be untenable.\"\n\nThis instance illustrates another principle that has to be borne in\nmind in the interpretation of doctrines from their historical context\nof counter-implication. This is the tendency that men have to\nput doctrines in too universal a form, and to oppose universal to\nuniversal, that is, to deny with the flat contrary, the very reverse,\nwhen the more humble contradictory is all that the truth admits of. If\na name is wanted for this tendency, it might be called the tendency to\nOver-Contradiction. Between \"All are\" and \"None are,\" the sober\ntruth often is that \"Some are\" and \"Some are not,\" and the process of\nevolution has often consisted in the substitution of these sober forms\nfor their more violent predecessors.\n\n    [Footnote 1: It is significant of the unsuitableness of\n    the vague unqualified word Relativity to express a logical\n    distinction that Dr. Bain calls his law the Law of Relativity\n    simply, having regard to the relation of difference, _i.e._,\n    to Counter-Relativity, while Dr. Caird applies the name\n    Relativity simply to the relation of likeness, _i.e._, to\n    Co-relativity. It is with a view to taking both forms\n    of relation into account that I name our law the Law of\n    Homogeneous Counter-relativity. The Protagorean Law of\n    Relativity has regard to yet another relation, the relation of\n    knowledge to the knowing mind: these other logical laws are\n    of relations among the various items of knowledge. Aristotle's\n    category of Relation is a fourth kind of relation not to be\n    confused with the others. \"Father--son,\" \"uncle--nephew,\"\n    \"slave--master,\" are _relata_ in Aristotle's sense: \"father,\"\n    \"uncle\" are homogeneous counter-relatives, varieties of\n    kinship; so \"slave,\" \"freeman\" are counter-relatives in social\n    status.]\n\n    [Footnote 2: Dr. Caird's _Hegel_, p. 134.]\n\n    [Footnote 3: See article on Counter-Sense, _Contemporary\n    Review_, April, 1884.]\n\n\n\n\nPART IV.\n\nTHE INTERDEPENDENCE OF PROPOSITIONS.--MEDIATE INFERENCE.\n--SYLLOGISM.\n\n\n\n\nCHAPTER I.\n\nTHE SYLLOGISM.\n\nWe have already defined mediate inference as the derivation of a\nconclusion from more than one proposition. The type or form of a\nmediate inference fully expressed consists of three propositions so\nrelated that one of them is involved or implied in the other two.\n\n          Distraction is exhausting.\n          Modern life is full of distraction\n    [.'.] Modern life is exhausting.\n\nWe say nothing of the truth of these propositions. I purposely choose\nquestionable ones. But do they hang together? If you admit the first\ntwo, are you bound in consistency to admit the third? Is the truth of\nthe conclusion a necessary consequence of the truth of the premisses?\nIf so, it is a valid mediate inference from them.\n\nWhen one of the two premisses is more general than the conclusion, the\nargument is said to be Deductive. You lead down from the more general\nto the less general. The general proposition is called the Major\nPremiss, or Grounding Proposition, or Sumption: the other premiss the\nMinor, or Applying Proposition, or Subsumption.\n\n          Undue haste makes waste.\n          This is a case of undue hasting.\n    [.'.] It is a case of undue wasting.\n\nWe may, and constantly do, apply principles and draw conclusions\nin this way without making any formal analysis of the propositions.\nIndeed we reason mediately and deductively whenever we make any\napplication of previous knowledge, although the process is not\nexpressed in propositions at all and is performed so rapidly that we\nare not conscious of the steps.\n\nFor example, I enter a room, see a book, open it and begin to read. I\nwant to make a note of something: I look round, see a paper case,\nopen it, take a sheet of paper and a pen, dip the pen in the ink\nand proceed to write. In the course of all this, I act upon certain\ninferences which might be drawn out in the form of Syllogisms. First,\nin virtue of previous knowledge I recognise what lies before me as a\nbook. The process by which I reach the conclusion, though it passes in\na flash, might be analysed and expressed in propositions.\n\n        Whatever presents certain outward appearances,\n          contains readable print.\n        This presents such appearances.\n    [.'.]It contains readable print.\nSo with the paper case, and the pen, and the ink. I infer from\npeculiar appearances that what I see contains paper, that the liquid\nwill make a black mark on the white sheet, and so forth.\n\nWe are constantly in daily life subsuming particulars under known\nuniversals in this way. \"Whatever has certain visible properties, has\ncertain other properties: this has the visible ones: therefore, it has\nthe others\" is a form of reasoning constantly latent in our minds.\n\nThe Syllogism may be regarded as the explicit expression of this type\nof deductive reasoning; that is, as the analysis and formal expression\nof this every-day process of applying known universals to particular\ncases. Thus viewed it is simply the analysis of a mental process, as a\npsychological fact; the analysis of the procedure of all men when they\nreason from signs; the analysis of the kind of assumptions they make\nwhen they apply knowledge to particular cases. The assumptions may be\nwarranted, or they may not: but as a matter of fact the individual who\nmakes the confident inference has such assumptions and subsumptions\nlatent in his mind.\n\nBut practically viewed, that is _logically_ viewed, if you regard\nLogic as a practical science, the Syllogism is a contrivance to\nassist the correct performance of reasoning together or syllogising in\ndifficult cases. It applies not to mental processes but to results of\nsuch expressed in words, that is, to propositions. Where the Syllogism\ncomes in as a useful form is when certain propositions are delivered\nto you _ab extra_ as containing a certain conclusion; and the\nconnexion is not apparent. These propositions are analysed and thrown\ninto a form in which it is at once apparent whether the alleged\nconnexion exists. This form is the Syllogism: it is, in effect, an\nanalysis of given arguments.\n\nIt was as a practical engine or organon that it was invented by\nAristotle, an organon for the syllogising of admissions in Dialectic.\nThe germ of the invention was the analysis of propositions into terms.\nThe syllogism was conceived by Aristotle as a reasoning together\nof terms. His prime discovery was that whenever two propositions\nnecessarily contain or imply a conclusion, they have a common term,\nthat is, only three terms between them: that the other two terms which\ndiffer in each are the terms of the conclusion; and that the relation\nasserted in the conclusion between its two terms is a necessary\nconsequence of their relations with the third term as declared in the\npremisses.\n\nSuch was Aristotle's conception of the Syllogism and such it has\nremained in Logic. It is still, strictly speaking, a syllogism of\nterms: of propositions only secondarily and after they have been\nanalysed. The conclusion is conceived analytically as a relation\nbetween two terms. In how many ways may this relation be established\nthrough a third term? The various moods and figures of the Syllogism\ngive the answer to that question.\n\nThe use of the very abstract word \"relation\" makes the problem appear\nmuch more difficult than it really is. The great charm of Aristotle's\nSyllogism is its simplicity. The assertion of the conclusion is\nreduced to its simplest possible kind, a relation of inclusion or\nexclusion, contained or not contained. To show that the one term is\nor is not contained in the other we have only to find a third which\ncontains the one and is contained or not contained in the other.\n\nThe practical difficulties, of course, consist in the reduction of\nthe conclusions and arguments of common speech to definite terms thus\nsimply related. Once they are so reduced, their independence or the\nopposite is obvious. Therein lies the virtue of the Syllogism.\n\nBefore proceeding to show in how many ways two terms may be Syllogised\nthrough a third, we must have technical names for the elements.\n\nThe third term is called the MIDDLE (M) ([Greek: to meson]): the other\ntwo the Extremes ([Greek: akra]).\n\nThe EXTREMES are the Subject (S) and the Predicate (P) of the\nconclusion.\n\nIn an affirmative proposition (the normal form) S is contained in P:\nhence P is called the MAJOR[1] term ([Greek: to meixon]), and S the\nMINOR ([Greek: to elatton]), being respectively larger and smaller in\nextension. All difficulty about the names disappears if we remember\nthat in bestowing them we start from the conclusion. That was the\nproblem ([Greek: problema]) or thesis in dialectic, the question in\ndispute.\n\nThe two Premisses, or propositions giving the relations between the\ntwo Extremes and the Middle, are named on an equally simple ground.\n\nOne of them gives the relation between the Minor Term, S, and the\nMiddle, M. S, All or Some, is or is not in M. This is called the Minor\nPremiss.\n\nThe other gives the relation between the Major Term and the Middle. M,\nAll or Some, is or is not in P. This is called the Major Premiss.[2]\n\n    [Footnote 1: Aristotle calls the Major the First ([Greek:\n    to proton]) and the Minor the last ([Greek: to eschaton]),\n    probably because that was their order in the conclusion when\n    stated in his most usual form, \"P is predicated of S,\" or \"P\n    belongs to S\".]\n\n    [Footnote 2: When we speak of the Minor or the Major simply,\n    the reference is to the terms. To avoid a confusion into\n    which beginners are apt to stumble, and at the same time to\n    emphasise the origin of the names, the Premisses might be\n    spoken of at first as the Minor's Premiss and the Major's\n    Premiss. It was only in the Middle Ages when the origin of\n    the Syllogism had been forgotten, that the idea arose that the\n    terms were called Major and Minor because they occurred in the\n    Major and the Minor Premiss respectively.]\n\n\n\n\nCHAPTER II.\n\nFIGURES AND MOODS OF THE SYLLOGISM.\n\n\nI.--The First Figure.\n\nThe forms (technically called MOODS, _i.e._, modes) of the First\nFigure are founded on the simplest relations with the Middle that will\nyield or that necessarily involve the disputed relation between the\nExtremes.\n\nThe simplest type is stated by Aristotle as follows: \"When three terms\nare so related that the last (the Minor) is wholly in the Middle, and\nthe Middle wholly either in or not in the first (the Major) there must\nbe a perfect syllogism of the Extremes\".[1]\n\nWhen the Minor is partly in the Middle, the Syllogism holds equally\ngood. Thus there are four possible ways in which two terms ([Greek:\noroi], plane enclosures) may be connected or disconnected through a\nthird. They are usually represented by circles as being the neatest\nof figures, but any enclosing outline answers the purpose, and the\nrougher and more irregular it is the more truly will it represent the\nextension of a word.\n\n  Conclusion A.\n  All M is in P.\n  All S is in M.\n  All S is in P.\n\n  [Illustration: concentric circles of P, M and S - S in centre]\n\n  Conclusion E.\n  No M is in P.\n  All S is in M.\n  No S is in P.\n\n  [Illustration: Concentric circles of M and S,\n  S in centre and separate circle of P]\n\n  Conclusion I.\n  All M is in P.\n  Some S is in M.\n  Some S is in P.\n\n  [Illustration: Concentric circles of P and M,\n  M in centre, both overlapped by circle of S]\n\n  Conclusion O.\n  No M is in P.\n  Some S is in M.\n  Some S is not in P.\n\n  [Illustration: Circles of M and P touching,\n  each overlapped by circle of S]\n\nThese four forms constitute what are known as the moods of the First\nFigure of the Syllogism. Seeing that all propositions may be reduced\nto one or other of the four forms, A, E, I, or O, we have in these\npremisses abstract types of every possible valid argument from\ngeneral principles. It is all the same whatever be the matter of the\nproposition. Whether the subject of debate is mathematical, physical,\nsocial or political, once premisses in these forms are conceded, the\nconclusion follows irresistibly, _ex vi formae, ex necessitate formae_.\nIf an argument can be analysed into these forms, and you admit\nits propositions, you are bound in consistency to admit the\nconclusion--unless you are prepared to deny that if one thing is in\nanother and that other in a third, the first is in the third, or if\none thing is in another and that other wholly outside a third, the\nfirst is also outside the third.\n\nThis is called the AXIOM OF SYLLOGISM. The most common form of it in\nLogic is that known as the _Dictum_, or _Regula de Omni et Nullo:_\n\"Whatever is predicated of All or None of a term, is predicated of\nwhatever is contained in that term\". It has been expressed with many\nlittle variations, and there has been a good deal of discussion as to\nthe best way of expressing it, the relativity of the word best being\noften left out of sight. _Best_ for what purpose? Practically that\nform is the best which best commands general assent, and for this\npurpose there is little to choose between various ways of expressing\nit. To make it easy and obvious it is perhaps best to have two\nseparate forms, one for affirmative conclusions and one for negative.\nThus: \"Whatever is affirmed of all M, is affirmed of whatever is\ncontained in M: and whatever is denied of all M, is denied of whatever\nis contained in M\". The only advantage of including the two forms in\none expression, is compendious neatness. \"A part of a part is a part\nof the whole,\" is a neat form, it being understood that an individual\nor a species is part of a genus. \"What is said of a whole, is said\nof every one of its parts,\" is really a sufficient statement of the\nprinciple: the whole being the Middle Term, and the Minor being a\npart of it, the Major is predicable of the Minor affirmatively or\nnegatively if it is predicable similarly of the Middle.\n\nThis Axiom, as the name imports, is indemonstrable. As Aristotle\npointed out in the case of the Axiom of Contradiction, it can be\nvindicated, if challenged, only by reducing the challenger to a\npractical absurdity. You can no more deny it than you can deny that\nif a leaf is in a book and the book is in your pocket, the leaf is in\nyour pocket. If you say that you have a sovereign in your purse and\nyour purse is in your pocket, and yet that the sovereign is not in\nyour pocket: will you give me what is in your pocket for the value of\nthe purse?\n\n\nII.--THE MINOR FIGURES OF THE SYLLOGISM, AND THEIR REDUCTION TO THE\nFIRST.\n\nThe word Figure ([Greek: schema]) applies to the form or figure of\nthe premisses, that is, the order of the terms in the statement of the\npremisses, when the Major Premiss is put first, and the Minor second.\n\nIn the First Figure the order is\n\n  M  P\n  S  M\n\nBut there are three other possible orders or figures, namely:--\n\n  Fig. ii.      Fig. iii.      Fig. iv.\n    PM            MP             PM\n    SM            MS             MS.\n\nIt results from the doctrines of Conversion that valid arguments may\nbe stated in these forms, inasmuch as a proposition in one order of\nterms may be equivalent to a proposition in another. Thus No M is in P\nis convertible with No P is in M: consequently the argument\n\n  No P is in M\n  All S is in M,\n\nin the Second Figure is as much valid as when it is stated in the\nFirst--\n\n  No M is in P\n  All S is in M.\n\nSimilarly, since All M is in S is convertible into Some S is in M, the\nfollowing arguments are equally valid:--\n\n     Fig. iii.             Fig. i.\n  All M is in P         All M is in P\n                   =\n  All M is in S         Some S is in M.\n\nUsing both the above Converses in place of their Convertends, we\nhave--\n\n     Fig. iv.             Fig. i.\n  No P is in M          No M is in P\n                  =\n  All M is in S         Some S is in M.\n\nIt can be demonstrated (we shall see presently how) that altogether\nthere are possible four valid forms or moods of the Second Figure, six\nof the Third, and five of the Fourth. An ingenious Mnemonic of\nthese various moods and their reduction to the First Figure by the\ntransposition of terms and premisses has come down from the thirteenth\ncentury. The first line names the moods of the First, Normal, or\nStandard Figure.\n\n  BA_rb_A_r_A, CE_l_A_r_E_nt_, DA_r_II, FE_r_IO_que_ prioris;\n  CE_s_A_r_E, CA_m_E_str_E_s_, FE_st_I_n_O, BA_r_O_k_O, secundae;\n  Tertia DA_r_A_pt_I, DI_s_A_m_I_s_, DA_t_I_s_I, FE_l_A_pt_O_n_,\n  BO_k_A_rd_O, FE_r_I_s_O_que_, habet; quarta insuper addit,\n  B_r_A_m_A_nt_IP, CA_m_E_n_E_s_, DI_m_A_r_I_s_, FE_s_A_p_O,\n          F_r_E_s_I_s_O_n_.\n\nThe vowels in the names of the Moods indicate the propositions of the\nSyllogism in the four forms, A E I O. To write out any Mood at length\nyou have only to remember the Figure, and transcribe the propositions\nin the order of Major Premiss, Minor Premiss, and Conclusion. Thus,\nthe Second Figure being\n\n  PM\n  SM\n\nFE_st_I_n_O is written--\n\n  No P is in M.\n  Some S is in M.\n  Some S is not in P.\n\nThe Fourth Figure being\n\n  PM\n  MS\n\nDI_m_A_r_I_s_ is\n\n  Some P is in M.\n  All M is in S.\n  Some S is in P.\n\nThe initial letter in a Minor Mood indicates that Mood of the First to\nwhich it may be reduced. Thus Festino is reduced to Ferio, and Dimaris\nto Darii. In the cases of Baroko and Bokardo, B indicates that you\nmay employ Barbara to bring any impugner to confusion, as shall be\nafterwards explained.\n\nThe letters _s_, _m_, and _p_ are also significant. Placed after a\nvowel, _s_ indicates that the proposition has to be simply converted.\nThus, FE_st_I_n_O:--\n\n  No P is in M.\n  Some S is in M.\n  Some S is not in P.\n\nSimply convert the Major Premiss, and you get FE_r_IO, of the First.\n\n  No M is in P.\n  Some S is in M.\n  Some S is not in P.\n\n_m_ (_muta_, or _move_) indicates that the premisses have to be\ntransposed. Thus, in CA_m_E_str_E_s_, you have to transpose the\npremisses, as well as simply convert the Minor Premiss before reaching\nthe figure of CE_l_A_r_E_nt_.\n\n  All P is in M       No M is in S\n                  =\n  No S is in M        All P is in M.\n\nFrom this it follows in CE_l_A_r_E_nt_ that No P is in S, and this\nsimply converted yields No S is in P.\n\nA simple transposition of the premisses in DI_m_A_r_I_s_ of the Fourth\n\n  Some P is in M\n  All M is in S\n\nyields the premisses of DA_r_II\n\n  All M is in S\n  Some P is in M,\n\nbut the conclusion Some P is in S has to be simply converted.\n\nPlaced after a vowel, _p_ indicates that the proposition has to be\nconverted _per accidens_. Thus in FE_l_A_pt_O_n_ of the Third (MP, MS)\n\n  No M is in P\n  All M is in S\n  Some S is not in P\n\nyou have to substitute for All M is in S its converse by limitation to\nget the premisses of FE_r_IO.\n\nTwo of the Minor Moods, Baroko of the Second Figure, and Bokardo\nof the Third, cannot be reduced to the First Figure by the ordinary\nprocesses of Conversion and Transposition. It is for dealing with\nthese intractable moods that Contraposition is required. Thus in\nBA_r_O_k_O of the Second (PM, SM)\n\n  All P is in M.\n  Some S is not in M.\n\nSubstitute for the Major Premiss its Converse by Contraposition, and\nfor the Minor its Formal Obverse or Permutation, and you have FE_r_IO\nof the First, with not-M as the Middle.\n\n  No not-M is in P.\n  Some S is in not-M,\n  Some S is not in P.\n\nThe processes might be indicated by the Mnemonic FA_cs_O_c_O, with\n_c_ indicating the contraposition of the predicate term or Formal\nObversion.\n\nThe reduction of BO_k_A_rd_O,\n\n  Some M is not in P\n  All M is in S\n  Some S is not in P,\n\nis somewhat more intricate. It may be indicated by DO_cs_A_m_O_sc_.\nYou substitute for the Major Premiss its Converse by Contraposition,\ntranspose the Premisses and you have DA_r_II.\n\n  All M is in S.\n  Some not-P is in M.\n  Some not-P is in S.\n\nConvert now the conclusion by Contraposition, and you have Some S is\nnot in P.\n\nThe author of the Mnemonic apparently did not recognise\nContraposition, though it was admitted by Boethius; and, it being\nimpossible without this to demonstrate the validity of Baroko and\nBokardo by showing them to be equivalent with valid moods of the First\nFigure, he provided for their demonstration by the special process\nknown as _Reductio ad absurdum_. B indicates that Barbara is the\nmedium.\n\nThe rationale of the process is this. It is an imaginary opponent that\nyou reduce to an absurdity or self-contradiction. You show that it\nis impossible with consistency to admit the premisses and at the same\ntime deny the conclusion. For, let this be done; let it be admitted as\nin BA_r_O_k_O that,\n\n  All P is in M\n  Some S is not in M,\n\nbut denied that Some S is not in P. The denial of a proposition\nimplies the admission of its Contradictory. If it is not true that\nSome S is not in P, it must be true that All S is in P. Take this\nalong with the admission that All P is in M, and you have a syllogism\nin BA_rb_A_r_A,\n\n  All P is in M\n  All S is in P,\n\nyielding the conclusion All S is in M. If then the original conclusion\nis denied, it follows that All S is in M. But this contradicts the\nMinor Premiss, which has been admitted to be true. It is thus shown\nthat an opponent cannot admit the premisses and deny the conclusion\nwithout contradicting himself.\n\nThe same process may be applied to Bokardo.\n\n  Some M is not in P.\n  All M is in S.\n  Some S is not in P.\n\nDeny the conclusion, and you must admit that All S is in P. Syllogised\nin Barbara with All M is in S, this yields the conclusion that All M\nis in P, the contradictory of the Major Premiss.\n\nThe beginner may be reminded that the argument _ad absurdum_ is not\nnecessarily confined to Baroko and Bokardo. It is applied to them\nsimply because they are not reducible by the ordinary processes to the\nFirst Figure. It might be applied with equal effect to other Moods,\nDI_m_A_r_I_s_, _e.g._, of the Third.\n\n  Some M is in P.\n  All M is in S.\n  Some S is in P.\n\nLet Some S is in P be denied, and No S is in P must be admitted. But\nif No S is in P and All M is in S, it follows (in Celarent) that No M\nis in P, which an opponent cannot hold consistently with his admission\nthat Some M is in P.\n\nThe beginner sometimes asks: What is the use of reducing the Minor\nFigures to the First? The reason is that it is only when the relations\nbetween the terms are stated in the First Figure that it is at once\napparent whether or not the argument is valid under the Axiom or\n_Dictum de Omni_. It is then undeniably evident that if the Dictum\nholds the argument holds. And if the Moods of the First Figure hold,\ntheir equivalents in the other Figures must hold too.\n\nAristotle recognised only two of the Minor Figures, the Second and\nThird, and thus had in all only fourteen valid moods.\n\nThe recognition of the Fourth Figure is attributed by Averroes to\nGalen. Averroes himself rejects it on the ground that no arguments\nexpressed naturally, that is, in accordance with common usage, fall\ninto that form. This is a sufficient reason for not spending time upon\nit, if Logic is conceived as a science that has a bearing upon the\nactual practice of discussion or discursive thought. And this was\nprobably the reason why Aristotle passed it over.\n\nIf however the Syllogism of Terms is to be completed as an abstract\ndoctrine, the Fourth Figure must be noticed as one of the forms of\npremisses that contain the required relation between the extremes.\nThere is a valid syllogism between the extremes when the relations\nof the three terms are as stated in certain premisses of the Fourth\nFigure.\n\n\nIII.--THE SORITES.\n\nA chain of Syllogisms is called a Sorites. Thus:--\n\n      All A is in B.\n      All B is in C.\n      All C is in D.\n          :\n          :\n          :\n          :\n      All X is in Z.\n  [.'.] All A is in Z.\n\nA Minor Premiss can thus be carried through a series of Universal\nPropositions each serving in turn as a Major to yield a conclusion\nwhich can be syllogised with the next. Obviously a Sorites may contain\none particular premiss, provided it is the first; and one universal\nnegative premiss, provided it is the last. A particular or a negative\nat any other point in the chain is an insuperable bar.\n\n    [Footnote 1: [Greek: Hotan oun horoi treis autos echosi pros\n    allelous oste ton eschaton en holo einai to meso, kai ton meson\n    en holo to kroto e einai e me einai, ananke ton\n    akron einai syllogismon teleion.] (Anal. Prior., i. 4.)]\n\n\n\n\nCHAPTER III.\n\nTHE DEMONSTRATION OF THE SYLLOGISTIC MOODS.--THE CANONS OF THE\nSYLLOGISM.\n\nHow do we know that the nineteen moods are the only possible forms of\nvalid syllogism?\n\nAristotle treated this as being self-evident upon trial and simple\ninspection of all possible forms in each of his three Figures.\n\nGranted the parity between predication and position in or out of\na limited enclosure (term, [Greek: horos]), it is a matter of the\nsimplest possible reasoning. You have three such terms or enclosures,\nS, P and M; and you are given the relative positions of two of them to\nthe third as a clue to their relative positions to one another. Is\nS in or out of P, and is it wholly in or wholly out or partly in or\npartly out? You know how each of them lies toward the third: when can\nyou tell from this how S lies towards P?\n\nWe have seen that when M is wholly in or out of P, and S wholly or\npartly in M, S is wholly or partly in or out of P.\n\nTry any other given positions in the First Figure, and you find that\nyou cannot tell from them how S lies relatively to P. Unless the Major\nPremiss is Universal, that is, unless M lies wholly in or out of\nP, you can draw no conclusion, whatever the Minor Premiss may give.\nGiven, _e.g._, All S is in M, it may be that All S is in P, or that No\nS is in P, or that Some S is in P, or that Some S is not in P.\n\n[Illustration:\n\n  Circles of M and P, overlapping,\n  with 3 instances of a circle of S:\n    1. S in M, but not in P;\n    2. S in the overlap of M and P;\n    3. S in M, some S in P.\n]\n\nAgain, unless the Minor Premiss is affirmative, no matter what the\nMajor Premiss may be, you can draw no conclusion. For if the Minor\nPremiss is negative, all that you know is that All S or Some S lies\nsomewhere outside M; and however M may be situated relatively to P,\nthat knowledge cannot help towards knowing how S lies relatively to P.\nAll S may be P, or none of it, or part of it. Given all M is in P; the\nAll S (or Some S) which we know to be outside of M may lie anywhere in\nP or out of it.\n\n[Illustration:\n\n  Concentric circles of P and M, M in center,\n  with 5 instances of circle of S:\n  1. S wholly outside P and M;\n  2. S partly overlapping both P and M, and partly outside both;\n  3. S overlapping P, but outside M;\n  4. S wholly within P, but wholly outside M;\n  5. S touching circle of P, but outside both circles.\n]\n\nSimilarly, in the Second Figure, trial and simple inspection of all\npossible conditions shows that there can be no conclusion unless the\nMajor Premiss is universal, and one of the premisses negative.\n\nAnother and more common way of eliminating the invalid forms,\nelaborated in the Middle Ages, is to formulate principles applicable\nirrespective of Figure, and to rule out of each Figure the moods that\ndo not conform to them. These regulative principles are known as The\nCanons of the Syllogism.\n\n_Canon I._ In every syllogism there should be three, and not more than\nthree, terms, and the terms must be used throughout in the same sense.\n\nIt sometimes happens, owing to the ambiguity of words, that there seem\nto be three terms when there are really four. An instance of this is\nseen in the sophism:--\n\n      He who is most hungry eats most.\n      He who eats least is most hungry.\n  [.'.] He who eats least eats most.\n\nThis Canon, however, though it points to a real danger of error in the\napplication of the syllogism to actual propositions, is superfluous\nin the consideration of purely formal implication, it being a primary\nassumption that terms are univocal, and remain constant through any\nprocess of inference.\n\nUnder this Canon, Mark Duncan says (_Inst. Log._, iv. 3, 2), is\ncomprehended another commonly expressed in this form: There should be\nnothing in the conclusion that was not in the premisses: inasmuch as\nif there were anything in the conclusion that was in neither of the\npremisses, there would be four terms in the syllogism.\n\nThe rule that in every syllogism there must be three, and only three,\npropositions, sometimes given as a separate Canon, is only a corollary\nfrom Canon I.\n\n_Canon II._ The Middle Term must be distributed once at least in the\nPremisses.\n\nThe Middle Term must either be wholly in, or wholly out of, one or\nother of the Extremes before it can be the means of establishing a\nconnexion between them. If you know only that it is partly in both,\nyou cannot know from that how they lie relatively to one another: and\nsimilarly if you know only that it is partly outside both.\n\nThe Canon of Distributed Middle is a sort of counter-relative\nsupplement to the _Dictum de Omni_. Whatever is predicable of a whole\ndistributively is predicable of all its several parts. If in neither\npremiss there is a predication about the whole, there is no case for\nthe application of the axiom.\n\n_Canon III._ No term should be distributed in the conclusion that was\nnot distributed in the premisses.\n\nIf an assertion is not made about the whole of a term in the\npremisses, it cannot be made about the whole of that term in the\nconclusion without going beyond what has been given.\n\nThe breach of this rule in the case of the Major term is technically\nknown as the Illicit Process of the Major: in the case of the Minor\nterm, Illicit Process of the Minor.\n\nGreat use is made of this canon in cutting off invalid moods. It\nmust be remembered that the Predicate term is \"distributed\" or taken\nuniversally in O (Some S is not in P) as well as in E (No S is in P);\nand that P is never distributed in affirmative propositions.\n\n_Canon IV._ No conclusion can be drawn from two negative premisses.\n\nTwo negative premisses are really tantamount to a declaration that\nthere is no connexion whatever between the Major and Minor (as\nquantified in the premisses) and the term common to both premisses; in\nshort, that this is not a Middle term--that the condition of a valid\nSyllogism does not exist.\n\nThere is an apparent exception to this when the real Middle in an\nargument is a contrapositive term, not-M. Thus:--\n\n        Nobody who is not thirsty is suffering from fever.\n        This person is not thirsty.\n  [.'.] He is not suffering from fever.\n\nBut in such cases it is really the absence of a quality or rather\nthe presence of an opposite quality on which we reason; and the Minor\nPremiss is really Affirmative of the form S is in not-M.\n\n_Canon V._ If one premiss is negative, the conclusion must be\nnegative.\n\nIf one premiss is negative, one of the Extremes must be excluded in\nwhole or in part from the Middle term. The other must therefore (under\nCanon IV.) declare some coincidence between the Middle term and the\nother extreme; and the conclusion can only affirm exclusion in whole\nor in part from the area of this coincidence.\n\n_Canon VI._ No conclusion can be drawn from two particular premisses.\n\nThis is evident upon a comparison of terms in all possible positions,\nbut it can be more easily demonstrated with the help of the preceding\ncanons. The premisses cannot both be particular and yield a conclusion\nwithout breaking one or other of those canons.\n\nSuppose both are affirmative, II, the Middle is not distributed in\neither premiss.\n\nSuppose one affirmative and the other negative, IO, or OI. Then,\nwhatever the Figure may be, that is, whatever the order of the terms,\nonly one term can be distributed, namely, the predicate of O. This\n(Canon II.) must be the Middle. But in that case there must be Illicit\nProcess of the Major (Canon III.), for one of the premisses being\nnegative, the conclusion is negative (Canon V.), and P its predicate\nis distributed. Briefly, in a negative mood, both Major and Middle\nmust be distributed, and if both premisses are particular this cannot\nbe.\n\n_Canon VII._ If one Premiss is particular the conclusion is\nparticular.\n\nThis canon is sometimes combined with what we have given as Canon V.,\nin a single rule: \"The conclusion follows the weaker premiss\".\n\nIt can most compendiously be demonstrated with the help of the\npreceding canons.\n\nSuppose both premisses affirmative, then, if one is particular, only\none term can be distributed in the premisses, namely, the subject\nof the Universal affirmative premiss. By Canon II., this must be the\nMiddle, and the Minor, being undistributed in the Premisses, cannot\nbe distributed in the conclusion. That is, the conclusion cannot be\nUniversal--must be particular.\n\nSuppose one Premiss negative, the other affirmative. One premiss being\nnegative, the conclusion must be negative, and P must be distributed\nin the conclusion. Before, then, the conclusion can be universal, all\nthree terms, S, M, and P, must, by Canons II. and III., be distributed\nin the premisses. But whatever the Figure of the premisses, only two\nterms can be distributed. For if one of the Premisses be O, the other\nmust be A, and if one of them is E, the other must be I. Hence the\nconclusion must be particular, otherwise there will be illicit process\nof the Minor, or of the Major, or of the Middle.\n\nThe argument may be more briefly put as follows:\n\nIn an affirmative mood, with one premiss particular, only one term can\nbe distributed in the premisses, and this cannot be the Minor without\nleaving the Middle undistributed. In a negative mood, with one premiss\nparticular, only two terms can be distributed, and the Minor cannot\nbe one of them without leaving either the Middle or the Major\nundistributed.\n\n\nArmed with these canons, we can quickly determine, given any\ncombination of three propositions in one of the Figures, whether it is\nor is not a valid Syllogism.\n\nObserve that though these canons hold for all the Figures, the Figure\nmust be known, in all combinations containing A or O, before we can\nsettle a question of validity by Canons II. and III., because\nthe distribution of terms in A and O depends on their order in\npredication.\n\nTake AEE. In Fig. I.--\n\n  All M is in P\n  No S is in M\n  No S is in P--\n\nthe conclusion is invalid as involving an illicit process of the\nMajor. P is distributed in the conclusion and not in the premisses.\n\nIn Fig. II. AEE--\n\n  All P is in M\n  No S is in M\n  No S is in P--\n\nthe conclusion is valid (Camestres).\n\nIn Fig. III. AEE--\n\n  All M is in P\n  No M is in S\n  No S is in P--\n\nthe conclusion is invalid, there being illicit process of the Major.\n\nIn Fig. IV. AEE is valid (Camenes).\n\nTake EIO. A little reflection shows that this combination is valid in\nall the Figures if in any, the distribution of the terms in both cases\nnot being affected by their order in predication. Both E and I are\nsimply convertible. That the combination is valid is quickly seen\nif we remember that in negative moods both Major and Middle must be\ndistributed, and that this is done by E.\n\nEIE is invalid, because you cannot have a universal conclusion with\none premiss particular.\n\nAII is valid in Fig. I. or Fig. III., and invalid in Figs. II. and\nIV., because M is the subject of A in I. and III. and predicate in II.\nand IV.\n\nOAO is valid only in Fig. III., because only in that Figure would this\ncombination of premisses distribute both M and P.\n\nSimple exercises of this kind may be multiplied till all possible\ncombinations are exhausted, and it is seen that only the recognised\nmoods stand the test.\n\n\nIf a more systematic way of demonstrating the valid moods is desired,\nthe simplest method is to deduce from the Canons special rules for\neach Figure. Aristotle arrived at these special rules by simple\ninspection, but it is easier to deduce them.\n\n\nI. In the First Figure, the Major Premiss must be Universal, and the\nMinor Premiss affirmative.\n\nTo make this evident by the Canons, we bear in mind the Scheme or\nFigure--\n\n  M in P\n  S in M--\n\nand try the alternatives of Affirmative Moods and Negative Moods.\nObviously in an affirmative mood the Middle is undistributed unless\nthe Major Premiss is Universal. In a negative mood, (1) If the Major\nPremiss is O, the Minor must be affirmative, and M is undistributed;\n(2) if the Major Premiss is I, M may be distributed by a negative\nMinor Premiss, but in that case there would be an illicit process of\nthe Major--P being distributed in the conclusion (Canon V.) and not in\nthe Premisses. Thus the Major Premiss can neither be O nor I, and must\ntherefore be either A or E, _i.e._, must be Universal.\n\nThat the Minor must be affirmative is evident, for if it were\nnegative, the conclusion must be negative (Canon V.) and the Major\nPremiss must be affirmative (Canon IV.), and this would involve\nillicit process of the Major, P being distributed in the conclusion\nand not in the Premisses.\n\nThese two special rules leave only four possible valid forms in the\nFirst Figure. There are sixteen possible combinations of premisses,\neach of the four types of proposition being combinable with itself and\nwith each of the others.\n\n  AA    EA    IA    OA\n  AE    EE    IE    OE\n  AI    EI    II    OI\n  AO    EO    IO    OO\n\nSpecial Rule I. wipes out the columns on the right with the particular\nmajor premisses; and AE, EE, AO, and EO are rejected by Special Rule\nII., leaving BA_rb_A_r_A, CE_l_A_r_E_nt_, DA_r_II and FE_r_IO.\n\n\nII. In the Second Figure, only Negative Moods are possible, and the\nMajor Premiss must be universal.\n\nOnly Negative moods are possible, for unless one premiss is negative,\nM being the predicate term in both--\n\n  P in M\n  S in M--\n\nis undistributed.\n\nOnly negative moods being possible, there will be illicit process of\nthe Major unless the Major Premiss is universal, P being its subject\nterm.\n\nThese special rules reject AA and AI, and the two columns on the\nright.\n\nTo get rid of EE and EO, we must call in the general Canon IV.;\nwhich leaves us with EA, AE, EI, and AO--CE_s_A_r_E, CA_m_E_str_E_s_,\nFE_st_I_n_O BA_r_O_k_O.\n\n\nIII. In the Third Figure, the Minor Premiss must be affirmative.\n\nOtherwise, the conclusion would be negative, and the Major Premiss\naffirmative, and there would be illicit process of the Major, P being\nthe predicate term in the Major Premiss.\n\n  M in P\n  M in S.\n\nThis cuts off AE, EE, IE, OE, AO, EO, IO, OO,--the second and fourth\nrows in the above list.\n\nII and OI are inadmissible by Canon VI.; which leaves AA, IA, AI,\nEA, OA, EI--DA_r_A_pt_I, DI_s_A_m_I_s_, DA_t_I_s_I, FE_l_A_pt_O_n_,\nBO_k_A_rd_O, FE_r_I_s_O--three affirmative moods and three negative.\n\n\nIV. The Fourth Figure is fenced by three special rules. (1) In\nnegative moods, the Major Premiss is universal. (2) If the Minor\nis negative, both premisses are universal. (3) If the Major is\naffirmative, the Minor is universal.\n\n(1) Otherwise, the Figure being\n\n  P in M\n  M in S,\n\nthere would be illicit process of the Major.\n\n(2) The Major must be universal by special rule (1), and if the Minor\nwere not also universal, the Middle would be undisturbed.\n\n(3) Otherwise M would be undistributed.\n\nRule (1) cuts off the right-hand column, OA, OE, OI, and OO; also IE\nand IO.\n\nRule (2) cuts off AO, EO.\n\nRule (3) cuts off AI, II.\n\nEE goes by general Canon IV.; and we are left with AA, AE, IA, EA,\nEI--B_r_A_m_A_nt_I_p_, CA_m_E_n_E_s_, DI_m_A_r_I_s_, FE_s_A_p_O,\nF_r_E_s_I_s_O_n_.\n\n\n\n\nCHAPTER IV.\n\nTHE ANALYSIS OF ARGUMENTS INTO SYLLOGISTIC FORMS.\n\nTurning given arguments into syllogistic form is apt to seem as\ntrivial and useless as it is easy and mechanical. In most cases the\nnecessity of the conclusion is as apparent in the plain speech form as\nin the artificial logical form. The justification of such exercises\nis that they give familiarity with the instrument, serving at the same\ntime as simple exercises in ratiocination: what further uses may be\nmade of the instrument once it is mastered, we shall consider as we\nproceed.\n\n\nI.--FIRST FIGURE.\n\nGiven the following argument to be put into Syllogistic form: \"No war\nis long popular: for every war increases taxation; and the popularity\nof anything that touches the pocket is short-lived\".\n\nThe simplest method is to begin with the conclusion--\"No war is long\npopular\"--No S is P--then to examine the argument to see whether it\nyields premisses of the necessary form. Keeping the form in mind,\nCelarent of Fig. I.--\n\n  No M is P\n  All S is M\n  No S is P--\nwe see at once that \"Every war increases taxation\" is of the form All\nS is M. Does the other sentence yield the Major Premiss No M is P,\nwhen M represents the increasing of taxation, _i.e._, a class bounded\nby that attribute? We see that the last sentence of the argument is\nequivalent to saying that \"Nothing that increases taxation is long\npopular\"; and this with the Minor yields the conclusion in Celarent.\n\n  Nothing that increases taxation is long popular.\n  Every war increases taxation.\n  No war is long popular.\n\nObserve, now, what in effect we have done in thus reducing the\nargument to the First Figure. In effect, a general principle being\nalleged as justifying a certain conclusion, we have put that principle\ninto such a form that it has the same predicate with the conclusion.\nAll that we have then to do in order to inspect the validity of the\nargument is to see whether the subject of the conclusion is contained\nin the subject of the general principle. Is war one of the things that\nincrease taxation? Is it one of that class? If so, then it cannot long\nbe popular, long popularity being an attribute that cannot be affirmed\nof any of that class.\n\nReducing to the first figure, then, amounts simply to making the\npredication of the proposition alleged as ground uniform with the\nconclusion based upon it. The minor premiss or applying proposition\namounts to saying that the subject of the conclusion is contained in\nthe subject of the general principle. Is the subject of the conclusion\ncontained in the subject of the general principle when the two have\nidentical predicates? If so, the argument falls at once under the\n_Dictum de Omni et Nullo_.\n\n\nTwo things may be noted concerning an argument thus simplified.\n\n1. It is not necessary, in order to bring an argument under the\n_dictum de omni_, to reduce the predicate to the form of an extensive\nterm. In whatever form, abstract or concrete, the predication is made\nof the middle term, it is applicable in the same form to that which is\ncontained in the middle term.\n\n2. The quantity of the Minor Term does not require special attention,\ninasmuch as the argument does not turn upon it. In whatever quantity\nit is contained in the Middle, in that quantity is the predicate of\nthe Middle predicable of it.\n\nThese two points being borne in mind, the attention may be\nconcentrated on the Middle Term and its relations with the extremes.\n\nThat the predicate may be left unanalysed without affecting the\nsimplicity of the argument or in any way obscuring the exhibition\nof its turning-point, has an important bearing on the reduction of\nModals. The modality may be treated as part of the predicate without\nin any way obscuring what it is the design of the syllogism to make\nclear. We have only to bear in mind that however the predicate may be\nqualified in the premisses, the same qualification must be transferred\nto the conclusion. Otherwise we should have the fallacy of Four Terms,\n_quaternio terminorum_.\n\nTo raise the question: What is the proper form for a Modal of\nPossibility, A or I? is to clear up in an important respect our\nconceptions of the Universal proposition, \"Victories may be gained\nby accident\". Should this be expressed as A or I? Is the predicate\napplicable to All victories or only to Some? Obviously the meaning is\nthat of any victory it may be true that it was gained by accident, and\nif we treat the \"mode\" as part of the predicate term \"things that may\nbe gained by accident,\" the form of the proposition is All S is in P.\n\nBut, it may be asked, does not the proposition that victories may be\ngained by accident rest, as a matter of fact, on the belief that some\nvictories have been gained in this way? And is not, therefore, the\nproper form of proposition Some S is P?\n\nThis, however, is a misunderstanding. What we are concerned with is\nthe formal analysis of propositions as given. And Some victories have\nbeen gained by accident is not the formal analysis of Victories may be\ngained by accident. The two propositions do not give the same meaning\nin different forms: the meaning as well as the form is different.\nThe one is a statement of a matter of fact: the other of an inference\nfounded on it. The full significance of the Modal proper may be stated\nthus: In view of the fact that some victories have been gained by\naccident, we are entitled to say of any victory, in the absence of\ncertain knowledge, that it may be one of them.\n\nA general proposition, in short, is a proposition about a genus, taken\nuniversally.\n\n\nII.--SECOND FIGURE.\n\nFor testing arguments from general principles, the First Figure is the\nsimplest and best form of analysis.\n\nBut there is one common class of arguments that fall naturally,\nas ordinarily expressed, into the Second Figure, namely, negative\nconclusions from the absence of distinctive signs or symptoms, or\nnecessary conditions.\n\nThirst, for example, is one of the symptoms of fever: if a patient is\nnot thirsty, you can conclude at once that his illness is not fever,\nand the argument, fully expressed, is in the Second Figure.\n\n        All fever-stricken patients are thirsty.\n        This patient is not thirsty.\n  [.'.] He is not fever-stricken.\n\nArguments of this type are extremely common.\n\nArmed with the general principle that ill-doers are ill-dreaders,\nwe argue from a man's being unsuspicious that he is not guilty.\nThe negative diagnosis of the physician, as when he argues from the\nabsence of sore throat or the absence of a white speck in the throat\nthat the case before him is not one of scarlatina or diphtheria,\nfollows this type: and from its utility in making such arguments\nexplicit, the Second Figure may be called the Figure of Negative\nDiagnosis.\n\nIt is to be observed, however, that the character of the argument is\nbest disclosed when the Major Premiss is expressed by its Converse by\nContraposition. It is really from the absence of a symptom that the\nphysician concludes; as, for example: \"No patient that has not a sore\nthroat is suffering from scarlatina\". And the argument thus expressed\nis in the First Figure. Thus the reduction of Baroko to the First\nFigure by contraposition of the Middle is vindicated as a really\nuseful process. The real Middle is a contrapositive term, and the form\ncorresponds more closely to the reasoning when the argument is put in\nthe First Figure.\n\nThe truth is that if the positive term or sign or necessary condition\nis prominent as the basis of the argument, there is considerable risk\nof fallacy. Sore throat being one of the symptoms of scarlatina, the\nphysician is apt on finding this symptom present to jump to a positive\nconclusion. This is equivalent technically to drawing a positive\nconclusion from premisses of the Second Figure.\n\n  All scarlatina patients have sore throat.\n  This patient has sore throat.\n\nA positive conclusion is technically known as a Non-Sequitur (Doesn't\nfollow). So with arguments from the presence of a necessary condition\nwhich is only one of many. Given that it is impossible to pass without\nworking at the subject, or that it is impossible to be a good marksman\nwithout having a steady hand, we are apt to argue that given also the\npresence of this condition, a conclusion is implicated. But really the\npremisses given are only two affirmatives of the Second Figure.\n\n    \"It is impossible to pass without working at the subject.\"\n\nThis, put into the form No not-M is P, is to say that \"None who\nhave not worked can pass\". This is equivalent, as the converse by\ncontraposition, with--\n\n    All capable of passing have worked at the subject.\n\nBut though Q has worked at the subject, it does not follow that he is\ncapable of passing. Technically the middle is undistributed. On the\nother hand, if he has not worked at the subject, it follows that he\nis not capable of passing. We can draw a conclusion at once from the\nabsence of the necessary condition, though none can be drawn from its\npresence alone.\n\n\nTHIRD FIGURE.\n\nArguments are sometimes advanced in the form of the Third Figure. For\ninstance: Killing is not always murder: for tyrannicide is not murder,\nand yet it is undoubtedly killing. Or again: Unpleasant things\nare sometimes salutary: for afflictions are sometimes so, and no\naffliction can be called pleasant.\n\nThese arguments, when analysed into terms, are, respectively, Felapton\nand Disamis.\n\n  No tyrannicide is murder;\n  All tyrannicide is killing;\n  Some killing is not murder.\n\n  Some afflictions are salutary things;\n  All afflictions are unpleasant things;\n  Some unpleasant things are salutary things.\n\nThe syllogistic form cannot in such cases pretend to be a\nsimplification of the argument. The argument would be equally\nunmistakable if advanced in this form: Some S is not P, for example,\nM. Some killing is not murder, _e.g.,_ tyrannicide. Some unpleasant\nthings are salutary, _e.g.,_ some afflictions.\n\nThere is really no \"deduction\" in the third figure, no leading down\nfrom general to particular. The middle term is only an example of the\nminor. It is the syllogism of Contradictory Examples.\n\nIn actual debate examples are produced to disprove a universal\nassertion, affirmative or negative. Suppose it is maintained that\nevery wise man has a keen sense of humour. You doubt this: you\nproduce an instance of the opposite, say Milton. The force of your\ncontradictory instance is not increased by exhibiting the argument in\nsyllogistic form: the point is not made clearer.\n\nThe Third Figure was perhaps of some use in Yes and No Dialectic.\nWhen you had to get everything essential to your conclusion definitely\nadmitted, it was useful to know that the production of an example to\nrefute a generality involved the admission of two propositions. You\nmust extract from your opponent both that Milton was a wise man, and\nthat Milton had not a keen sense of humour, before you could drive him\nfrom the position that all wise men possess that quality.\n\n\n_Examples for Analysis._\n\nScarlet flowers have no fragrance: this flower has no fragrance: does\nit follow that this flower is of a scarlet colour?\n\nInterest in the subject is an indispensable condition of learning\neasily; Z is interested in the subject: he is bound, therefore, to\nlearn easily.\n\nIt is impossible to be a good shot without having a steady hand: John\nhas a steady hand: he is capable, therefore, of becoming a good shot.\n\nSome victories have been won by accident; for example, Maiwand.\n\nIntemperance is more disgraceful than cowardice, because people have\nmore opportunities of acquiring control of their bodily appetites.\n\n\"Some men are not fools, yet all men are fallible.\" What follows?\n\n\"Some men allow that their memory is not good: every man believes in\nhis own judgment.\" What is the conclusion, and in what Figure and Mood\nmay the argument be expressed?\n\n\"An honest man's the noblest work of God: Z is an honest man\":\ntherefore, he is--what?\n\nExamine the logical connexion between the following \"exclamation\"\nand \"answer\": \"But I hear some one exclaiming that wickedness is not\neasily concealed. To which I answer, Nothing great is easy.\"\n\n\"If the attention is actively aroused, sleep becomes impossible: hence\nthe sleeplessness of anxiety, for anxiety is a strained attention upon\nan impending disaster.\"\n\n\"To follow truth can never be a subject of regret: free inquiry does\nlead a man to regret the days of his childish faith; therefore it is\nnot following truth.\"--_J. H. Newman._\n\nHe would not take the crown: Therefore 'tis certain he was not\nambitious.\n\nAs he was valiant, I honour him; as he was ambitious, I slew him.\n\nThe Utopians learned the language of the Greeks with more readiness\nbecause they were originally of the same race with them.\n\nNothing which is cruel can be expedient, for cruelty is most revolting\nto the nature of man.\n\n\"The fifth century saw the foundation of the Frank dominion in Gaul,\nand the first establishment of the German races in Britain. The former\nwas effected in a single long reign, by the energy of one great ruling\ntribe, which had already modified its traditional usages, and now, by\nthe adoption of the language and religion of the conquered, prepared\nthe way for a permanent amalgamation with them.\" In the second of the\nabove sentences a general proposition is assumed. Show in syllogistic\nform how the last proposition in the sentence depends upon it.\n\n\"I do not mean to contend that active benevolence may not hinder a\nman's advancement in the world: for advancement greatly depends upon\na reputation for excellence in some one thing of which the world\nperceives that it has present need: and an obvious attention to other\nthings, though perhaps not incompatible with the excellence itself,\nmay easily prevent a person from obtaining a reputation for it.\" Pick\nout the propositions here given as interdependent. Examine whether the\nprinciple alleged is sufficiently general to necessitate a conclusion.\nIn what form would it be so?\n\n\n\n\nCHAPTER V.\n\nENTHYMEMES.\n\nThere is a certain variety in the use of the word Enthymeme among\nlogicians. In the narrowest sense, it is a valid formal syllogism,\nwith one premiss suppressed. In the widest sense it is simply an\nargument, valid or invalid, formal in expression or informal, with\nonly one premiss put forward or hinted at, the other being held in the\nmind ([Greek: en thymo]). This last is the Aristotelian sense.\n\nIt is only among formal logicians of the straitest sect that the\nnarrowest sense prevails. Hamilton divides Enthymemes into three\nclasses according as it is the Major Premiss, the Minor Premiss, or\nthe Conclusion that is suppressed. Thus, a full syllogism being:--\n\n        All liars are cowards:\n        Caius is a liar:\n  [.'.] Caius is a coward:--\n\nthis may be enthymematically expressed in three ways.\n\nI. Enthymeme of the First Order (_Major understood_).\n\n    Caius is a coward; for Caius is a liar.\n\nII. Enthymeme of the Second Order (_Minor understood_).\n\n    Caius is a coward; for all liars are cowards.\n\nIII. Enthymeme of the Third Order (_Conclusion understood_).\n\n    All liars are cowards, and Caius is a liar.\n\nThe Third Order is a contribution of Hamilton's own. It is\nsuperfluous, inasmuch as the conclusion is never suppressed except as\na rhetorical figure of speech. Hamilton confines the word Enthymeme\nto valid arguments, in pursuance of his view that Pure Logic has no\nconcern with invalid arguments.\n\nAristotle used Enthymeme in the wider sense of an elliptically\nexpressed argument. There has been some doubt as to the meaning of his\ndefinition, but that disappears on consideration of his examples.\nHe defines an Enthymeme (Prior Analyt., ii. 27) as \"a syllogism from\nprobabilities or signs\" ([Greek: syllogismos ex eikoton e semeion]).\nThe word syllogism in this connexion is a little puzzling. But it is\nplain from the examples he gives that he meant here by syllogism not\neven a correct reasoning, much less a reasoning in the explicit form\nof three terms and three propositions. He used syllogism, in fact, in\nthe same loose sense in which we use the words reasoning and argument,\napplying without distinction of good and bad.\n\nThe sign, he says, is taken in three ways, in as many ways as there\nare Syllogistic Figures.\n\n(1) A sign interpreted in the First Figure is conclusive. Thus: \"This\nperson has been drowned, for he has froth in the trachea\". Taken in\nthe First Figure with \"All who have froth in the trachea have been\ndrowned\" as a major premiss, this argument is valid. The sign is\nconclusive.\n\n(2) \"This patient is fever-stricken, for he is thirsty.\" Assumed that\n\"All fever-stricken patients are thirsty,\" this is an argument in the\nSecond Figure, but it is not a valid argument. Thirst is a sign or\nsymptom of fever, but not a conclusive sign, because it is indicative\nof other ailments also. Yet the argument has a certain probability.\n\n(3) \"Wise men are earnest ([Greek: spoudaioi]), for Pittacus is\nearnest.\" Here the suppressed premiss is that \"Pittacus is wise\".\nFully expressed, the argument is in the Third Figure:--\n\n        Pittacus is earnest.\n        Pittacus is wise.\n  [.'.] Wise men are earnest.\n\nHere again the argument is inconclusive and yet it has a certain\nprobability. The coincidence of wisdom with earnestness in one notable\nexample lends a certain air of probability to the general statement.\n\nSuch are Aristotle's examples or strict parallels to them. The\nexamples illustrate also what he says in his _Rhetoric_ as to the\nadvantages of enthymemes. For purposes of persuasion enthymemes are\nbetter than explicit syllogisms, because any inconclusiveness there\nmay be in the argument is more likely to pass undetected. As we shall\nsee, one main use of the Syllogism is to force tacit assumptions into\nlight and so make their true connexion or want of connexion apparent.\nIn Logic enthymemes are recognised only to be shown up: the elliptical\nexpression is a cover for fallacy, which it is the business of the\nlogician to strip off.\n\nIn Aristotle's examples one of the premisses is expressed. But often\nthe arguments of common speech are even less explicit than this. A\ngeneral principle is vaguely hinted at: a subject is referred to a\nclass the attributes of which are assumed to be definitely known.\nThus:--\n\n    He was too ambitious to be scrupulous in his choice of means.\n\n    He was too impulsive not to have made many blunders.\n\nEach of these sentences contains a conclusion and an enthymematic\nargument in support of it. The hearer is understood to have in his\nmind a definite idea of the degree of ambition at which a man ceases\nto be scrupulous, or the degree of impulsiveness that is incompatible\nwith accuracy.\n\nOne form of enthymeme is so common in modern rhetoric as to deserve\na distinctive name. It may be called the ENTHYMEME OF THE ABSTRACTLY\nDENOMINATED PRINCIPLE. A conclusion is declared to be at variance with\nthe principles of Political Economy, or contrary to the doctrine of\nEvolution, or inconsistent with Heredity, or a violation of the sacred\nprinciple of Freedom of Contract. It is assumed that the hearer is\nfamiliar with the principles referred to. As a safeguard against\nfallacy, it may be well to make the principle explicit in a\nproposition uniform with the conclusion.\n\n\n\n\nCHAPTER VI.\n\nTHE UTILITY OF THE SYLLOGISM.\n\nThe main use of the Syllogism is in dealing with incompletely\nexpressed or elliptical arguments from general principals. This may be\ncalled Enthymematic argument, understanding by Enthymeme an argument\nwith only one premiss put forward or hinted at, the other being held\nin the mind. In order to test whether such reasoning is sound\nor unsound, it is of advantage to make the argument explicit in\nSyllogistic form.\n\nThere have been heaps and mazes of discussion about the use of the\nSyllogism, much of it being profitable as a warning against the\nneglect of Formal Logic. Again and again it has been demonstrated that\nthe Syllogism is useless for certain purposes, and from this it has\nbeen concluded that the Syllogism is of no use at all.\n\nThe inventor of the Syllogism had a definite practical purpose, to get\nat the simplest, most convincing, undeniable and irresistible way\nof putting admitted or self-evident propositions so that their\nimplication should be apparent. His ambition was to furnish a method\nfor the Yes and No Dialectician, and the expounder of science from\nself-evident principles. A question being put up for discussion, it\nwas an advantage to analyse it, and formulate the necessary premisses:\nyou could then better direct your interrogations or guard your\nanswers. The analysis is similarly useful when you want to construct\nan argument from self-evident principles.\n\nAll that the Syllogism could show was the consistency of the premisses\nwith the conclusion. The conclusion could not go beyond the premisses,\nbecause the questioner could not go beyond the admissions of the\nrespondent. There is indeed an advance, but not an advance upon the\ntwo premisses taken together. There is an advance upon any one of\nthem, and this advance is made with the help of the other. Both must\nbe admitted: a respondent may admit one without being committed to\nthe conclusion. Let him admit both and he cannot without\nself-contradiction deny the conclusion. That is all.\n\nDialectic of the Yes and No kind is no longer practised. Does any\nanalogous use for the Syllogism remain? Is there a place for it as a\nsafeguard against error in modern debate? As a matter of fact it\nis probably more useful now than it was for its original purpose,\ninasmuch as modern discussion, aiming at literary grace and spurning\nexact formality as smacking of scholasticism and pedantry, is\nmuch more flabby and confused. In the old dialectic play there was\ngenerally a clear question proposed. The interrogative form forced\nthis much on the disputants. The modern debater of the unpedantic,\nunscholastic school is not so fettered, and may often be seen\ngalloping wildly about without any game in sight or scent, his maxim\nbeing to--\n\n  Spur boldly on, and dash through thick and thin,\n  Through sense and nonsense, never out nor in.\n\nNow the syllogistic analysis may often be of some use in helping us\nto keep a clear head in the face of a confused argument. There is a\nbrilliant defence of the syllogism as an analysis of arguments in the\n_Westminster Review_ for January, 1828. The article was a notice of\nWhately's Logic: it was written by J. S. Mill. For some reason it\nhas never been reprinted, but it puts the utility of the Syllogism on\nclearer ground than Mill afterwards sought for it.\n\nCan a fallacy in argument be detected at once? Is common-sense\nsufficient? Common-sense would require some inspection. How would\nit proceed? Does common-sense inspect the argument in a lump or\npiecemeal? All at once or step by step? It analyses. How? First, it\nseparates out the propositions which contribute to the conclusion from\nthose which do not, the essential from the irrelevant. Then it\nstates explicitly all that may have been assumed tacitly. Finally, it\nenumerates the propositions in order.\n\nSome such procedure as this would be adopted by common-sense in\nanalysing an argument. But when common-sense has done this, it has\nexhibited the argument in a series of syllogisms.\n\nSuch is Mill's early defence of the Syllogism. It is weak only in one\npoint, in failing to represent how common-sense would arrive at the\npeculiar syllogistic form. It is the peculiar form of logical analysis\nthat is the distinction of the syllogism. When you have disentangled\nthe relevant propositions you have not necessarily put them in this\nform. The arguments given in text-books to be cast into syllogistic\nform, consist only as a rule of relevant propositions, but they are\nnot yet formal syllogisms. But common-sense had only one other step to\nmake to reach the distinctive form. It had only to ask after analysing\nthe argument, Is there any form of statement specially suitable\nfor exhibiting the connexion between a conclusion and the general\nprinciple on which it is alleged to depend? Ask yourself the question,\nand you will soon see that there would be an obvious advantage in\nmaking the conclusion and the general principle uniform, in stating\nthem with the same predicate. But when you do this, as I have already\nshown (p. 197) you state the argument in the First Figure of the\nSyllogism.\n\n\nIt must, however, be admitted that it is chiefly for exhibiting, or\nforcing into light, tacit or lurking assumptions that the Syllogistic\nform is of use. Unless identity of meaning is disguised or distorted\nby puzzling difference of language, there is no special illuminative\nvirtue in the Syllogism. The argument in a Euclidean demonstration\nwould not be made clearer by being cast into formal Syllogisms.\n\nAgain, when the subject matter is simple, the Syllogistic form is not\nreally required for protection against error. In such enthymemes as\nthe following for example:--\n\n  She must be clever: she is so uncompromisingly ugly.\n  Romeo must be in love: for is he not seventeen?\n\nit is plain to the average intelligence without any knowledge of\nSyllogism that the argument takes for granted a general proposition\nand what the general proposition is.\n\nAnother thing is plain to the average intelligence, perhaps plainer\nthan to a proficient in the use of the Syllogism. Clearly we cannot\ninfer with certainty that a woman is clever because she is ugly,\nunless it is the case that all ugly women are clever. But a\nSyllogiser, seeing that no certain conclusion can be drawn except\nupon this condition, is apt to dismiss the argument as altogether\nworthless. This may be specified as an error incident to the practice\nof the Syllogism, that it inclines us to look for necessarily\nconclusive premisses, and to deny all weight to anything short of\nthis. Now in ordinary life it is comparatively seldom that such\npremisses can be found. We are obliged to proceed on maxims that are\nnot of universal scope, and which lend only a more or less strong\ncolour of probability to cases that can be brought under them. \"A\nlittle learning is a dangerous thing;\" \"Haste makes waste;\" \"Slowness\nof speech is a sign of depth of thought;\" \"Vivacity is a sign of\nshallowness:\" such are the \"endoxes\" or commonplaces of popular\nknowledge that men bring to bear in daily life. They are not true for\nall cases, but some of them are true for most or for a good many, and\nthey may be applied with a certain probability though they are not\nrigidly conclusive. The plain man's danger is that he apply them\nunthinkingly as universals: the formal logician's danger is that,\nseeing them to be inapplicable as universals, he dismisses them as\nbeing void of all argumentative force.\n\nIt helps to fix the limits of Formal Logic to remember that it lies\noutside its bounds to determine the degree of probability attaching\nto the application of approximate truths, such as are the staple of\narguments in ordinary affairs. Formal Logic, we may repeat, is\nnot concerned with degrees of truth or falsehood, probability\nor improbability. It merely shows the interdependency of certain\narguments, the consistency of conclusion with premisses.\n\nThis, however, is a function that might easily be underrated. Its\nvalue is more indirect than direct. In showing what is required for a\ncertain conclusion, it puts us on the road to a more exact estimate of\nthe premisses alleged, a sounder judgment of their worth. Well begun\nis half done: in undertaking the examination of any argument from\nauthority, a formal syllogism is a good beginning.\n\n\n\n\nCHAPTER VII.\n\nCONDITIONAL ARGUMENTS.--HYPOTHETICAL SYLLOGISM, DISJUNCTIVE SYLLOGISM,\nAND DILEMMA.\n\nThe justification of including these forms of argument in Logic is\nsimply that they are sometimes used in debate, and that confusion\nmay arise unless the precise meaning of the premisses employed\nis understood. Aristotle did not include them as now given in his\nexposition of the Syllogism, probably because they have no connexion\nwith the mode of reasoning together to which he appropriated the\ntitle. The fallacies connected with them are of such a simple kind\nthat to discuss as a question of method the precise place they should\noccupy in a logical treatise is a waste of ingenuity.[1]\n\nI.--HYPOTHETICAL SYLLOGISMS.\n\n      If A is B, C is D  |\n         A is B          } MODUS\n    [.'.]C is D          | PONENS.\n\n      If A is B, C is D  |\n         C is not D      } MODUS\n    [.'.]A is not B      | TOLLENS.\n\nA so-called Hypothetical Syllogism is thus seen to be a Syllogism in\nwhich the major premiss is a HYPOTHETICAL PROPOSITION, that is to\nsay, a complex proposition in which two propositions are given as so\nrelated that the truth of one follows necessarily from the truth of\nthe other.\n\nTwo propositions so related are technically called the ANTECEDENT or\nReason, and the CONSEQUENT.\n\nThe meaning and implication of the form, If A is B, C is D, is\nexpressed in what is known as the LAW OF REASON AND CONSEQUENT:--\n\n\"_When two propositions are related as Reason and Consequent, the\ntruth of the Consequent follows from the truth of the Antecedent,\nand the falsehood of the Antecedent, from the falsehood of the\nConsequent_\".\n\nIf A is B, C is D, implies that If C is not D, A is not B. If this\nsubject is educative, it quickens the wits; if it does not quicken the\nwits, it is not educative.\n\nAdmitted, then, that the law of Reason and Consequent holds\nbetween two propositions--that If A is B, C is D: admitted also the\nAntecedent, the truth of the Consequent follows. This is the MODUS\nPONENS or Positive Mode, where you reach a conclusion by obtaining the\nadmission of the Antecedent. Admit the Antecedent and the truth of the\nConsequent follows.\n\nWith the same Major Premiss, you may also, under the Law of Reason\nand Consequent reach a conclusion by obtaining the denial of the\nConsequent. This is the MODUS TOLLENS or Negative Mode. Deny the\nConsequent and one is bound to deny the Antecedent.\n\nBut to guard against the fallacy technically known as FALLACIA\nCONSEQUENTIS, we must observe what the relation of Reason and\nConsequent does not imply. The truth of the Consequent does not\ninvolve the truth of the Antecedent, and the falsehood of the\nAntecedent does not involve the falsehood of the Consequent.\n\n\"If the harbour is frozen, the ships cannot come in.\" If the harbour\nis not frozen, it does not follow that the ships can come in: they may\nbe excluded by other causes. And so, though they cannot come in, it\ndoes not follow that the harbour is frozen.\n\n\nQUESTIONS CONNECTED WITH HYPOTHETICAL SYLLOGISMS.\n\n(1) _Are they properly called Syllogisms?_ This is purely a question\nof Method and Definition. If we want a separate technical name for\nforms of argument in which two terms are reasoned together by means of\na third, the Hypothetical Syllogism, not being in such a form, is\nnot properly so called. The fact is that for the purposes of the\nHypothetical Argument, we do not require an analysis into terms at\nall: it is superfluous: we are concerned only with the affirmation or\ndenial of the constituent propositions as wholes.\n\nBut if we extend the word Syllogism to cover all arguments in which\ntwo propositions necessarily involve a third, the Hypothetical\nArgument is on this understanding properly enough called a Syllogism.\n\n(2) _Is the inference in the Hypothetical Syllogism Mediate or\nImmediate?_\n\nTo answer this question we have to consider whether the Conclusion\ncan be drawn from either of the two premisses without the help of the\nother. If it is possible immediately, it must be educible directly\neither from the Major Premiss or from the Minor.\n\n(_a_) Some logicians argue as if the Conclusion were immediately\npossible from the Major Premiss. The Minor Premiss and the Conclusion,\nthey urge, are simply equivalent to the Major Premiss. But this is a\nmisunderstanding. \"If A is B, C is D,\" is not equivalent to \"A is B,\n_therefore_ C is D\". \"If the harbour is frozen, the ships cannot come\nin\" is not to say that \"the harbour is frozen, and therefore,\" etc.\nThe Major Premiss merely affirms the existence of the relation of\nReason and Consequent between the two propositions. But we cannot\nthereupon assert the Conclusion unless the Minor Premiss is also\nconceded; that is, the inference of the Conclusion is Mediate, as\nbeing from two premisses and not from one alone.\n\n(_b_) Similarly with Hamilton's contention that the Conclusion\nis inferrible immediately from the Minor Premiss, inasmuch as the\nConsequent is involved in the Reason. True, the Consequent is involved\nin the Reason: but we cannot infer from \"A is B\" to \"C is D,\" unless\nit is conceded that the relation of Reason and Consequent holds\nbetween them; that is, unless the Major Premiss is conceded as well as\nthe Minor.\n\n(3) _Can Hypothetical Syllogism be reduced to the Categorical Form?_\n\nTo oppose Hypothetical Syllogisms to Categorical is misleading, unless\nwe take note of the precise difference between them. It is only in\nthe form of the Major Premiss that they differ: Minor Premiss and\nConclusion are categorical in both. And the meaning of a Hypothetical\nMajor Premiss (unless it is a mere arbitrary convention between two\ndisputants, to the effect that the Consequent will be admitted if the\nAntecedent is proved, or that the Antecedent will be relinquished\nif the Consequent is disproved), can always be put in the form of a\ngeneral proposition, from which, with the Minor Premiss as applying\nproposition, a conclusion identical with the original can be drawn in\nregular Categorical form.\n\nThus:--\n\n        If the harbour is frozen, the ships cannot come in.\n        The harbour is frozen.\n  [.'.] The ships cannot come in.\n\nThis is a Hypothetical Syllogism, _Modus Ponens_. Express the\nHypothetical Major in the form of the general proposition which it\nimplies, and you reach a conclusion (in _Barbara_) which is only\ngrammatically different from the original.\n\n        All frozen harbours exclude ships.\n        The harbour is frozen.\n  [.'.] It excludes ships.\n\nAgain, take an example of the _Modus Tollens_--\n\n        If rain has fallen, the streets are wet.\n        The streets are not wet.\n  [.'.] Rain has not fallen.\n\nThis is reducible, by formulating the underlying proposition, to\n_Camestres_ or _Baroko_ of the Second Figure.\n\n        All streets rained upon are wet.\n        The streets are not wet.\n  [.'.] They are not streets rained upon.\n\nHypothetical Syllogisms are thus reducible, by merely grammatical\nchange[2], or by the statement of self-evident implications, to the\nCategorical form. And, similarly, any Categorical Syllogism may be\nreduced to the Hypothetical form. Thus:--\n\n        All men are mortal.\n        Socrates is a man.\n  [.'.] Socrates is mortal.\n\nThis argument is not different, except in the expression of the Major\nand the Conclusion, from the following:--\n\n        If Socrates is a man, death will overtake him.\n        Socrates is a man.\n  [.'.] Death will overtake him.\n\nThe advantage of the Hypothetical form in argument is that it is\nsimpler. It was much used in Mediaeval Disputation, and is still more\npopular than the Categorical Syllogism. Perhaps the prominence\ngiven to Hypothetical Syllogisms as syllogisms in Post-Renaissance\ntext-books is due to the use of them in the formal disputations of\ngraduands in the Universities. It was the custom for the Disputant to\nexpound his argument in this form:--\n\n        If so and so is the case, such and such follows.\n        So and so is the case.\n  [.'.] Such and such follows.\n\nTo which the Respondent would reply: _Accipio antecedentem, nego\nconsequentiam_, and argue accordingly. Petrus Hispanus does not give\nthe Hypothetical Syllogism as a Syllogism: he merely explains the\ntrue law of Reason and Consequent in connexion with the Fallacia\nConsequentis in the section on Fallacies. (_Summulae. Tractatus\nSextus._)\n\n\nII.--DISJUNCTIVE SYLLOGISMS.\n\nA Disjunctive Syllogism is a syllogism in which the Major Premiss is\na DISJUNCTIVE PROPOSITION, _i.e._, one in which two propositions are\ndeclared to be mutually incompatible. It is of the form Either A is B,\nor C is D.[3]\n\nIf the disjunction between the alternatives is really complete, the\nform implies four hypothetical propositions:--\n\n  (1) If A is B, C is not D.\n  (2) If A is not B, C is D.\n  (3) If C is D, A is not B.\n  (4) If C is not D, A is B.\n\nSuppose then that an antagonist has granted you a Disjunctive\nProposition, you can, using this as a Major Premiss, extract from\nhim four different Conclusions, if you can get him also to admit the\nrequisite Minors. The Mode of two of these is technically called MODUS\nPONENDO TOLLENS, the mode that denies the one alternative by granting\nthe other--A is B, _therefore_ C is not D; C is D, _therefore_ A is\nnot B. The other Mode is also twice open, the MODUS TOLLENDO PONENS--A\nis not B, _therefore_ C is D; C is not D, _therefore_ A is B.\n\nFallacy is sometimes committed through the Disjunctive form owing to\nthe fact that in common speech there is a tendency to use it in place\nof a mere hypothetical, when there are not really two incompatible\nalternatives. Thus it may be said \"Either the witness is perjured,\nor the prisoner is guilty,\" when the meaning merely is that if the\nwitness is not perjured the prisoner is guilty. But really there is\nnot a valid disjunction and a correct use of the disjunctive form,\nunless four hypotheticals are implied, that is, unless the concession\nof either involves the denial of the other, and the denial of either\nthe concession of the other. Now the prisoner may be guilty and\nyet the witness be perjured; so that two of the four hypotheticals,\nnamely--\n\n  If the witness is perjured, the prisoner is not guilty,\n  If the prisoner is guilty, the witness is not perjured--\n\ndo not necessarily hold. If, then, we would guard against fallacy, we\nmust always make sure before assenting to a disjunctive proposition\nthat there is really a complete disjunction or mutual incompatibility\nbetween the alternatives.\n\n\nIII.--THE DILEMMA.\n\nA Dilemma is a combination of Hypothetical and Disjunctive\npropositions.\n\nThe word has passed into common speech, and its ordinary use is a clue\nto the logical structure. We are said to be in a dilemma when we\nhave only two courses open to us and both of them are attended by\nunpleasant consequences. In argument we are in this position when we\nare shut into a choice between two admissions, and either admission\nleads to a conclusion which we do not like. The statement of the\nalternatives as the consequences hypothetically of certain conditions\nis the major premiss of the dilemma: once we admit that the relations\nof Antecedent and Consequent are as stated, we are in a trap, if trap\nit is: we are on the horns of the dilemma, ready to be tossed from one\nto the other.\n\nFor example:--\n\n    If A is B, A is C, and if A is not B, A is D. But A either is\n    or is not B. Therefore, A either is C or is D.\n\n    If A acted of his own motive, he is a knave; if A did not act\n    of his own motive, he is a catspaw. But A either acted of his\n    own motive or he did not. Thereupon A is either a knave or a\n    catspaw.\n\nThis is an example of the _Constructive_ Dilemma, the form of it\ncorresponding to the common use of the word as a choice between\nequally unpleasant alternatives. The standard example is the dilemma\nin which the custodians of the Alexandrian Library are said to have\nbeen put by the Caliph Omar in 640 A.D.\n\n    If your books are in conformity with the Koran, they are\n    superfluous; if they are at variance with it, they are\n    pernicious. But they must either be in conformity with the\n    Koran or at variance with it. Therefore they are either\n    superfluous or pernicious.\n\nWhere caution has to be exercised is in accepting the clauses of the\nMajor. We must make sure that the asserted relations of Reason and\nConsequent really hold. It is there that fallacy is apt to creep in\nand hide its head. The Alexandrian Librarians were rash in accepting\nthe first clause of the conqueror's Major: it does not follow that the\nbooks are superfluous unless the doctrines of the Koran are not merely\nsound but contain all that is worth knowing. The propounder of the\ndilemma covertly assumes this. It is in the facility that it affords\nfor what is technically known as _Petitio Principii_ that the Dilemma\nis a useful instrument for the Sophist. We shall illustrate it further\nunder that head.\n\nWhat is known as the _Destructive_ Dilemma is of a somewhat different\nform. It proceeds upon the denial of the Consequent as involving the\ndenial of the Antecedent. In the Major you obtain the admission that\nif a certain thing holds, it must be followed by one or other of\ntwo consequences. You then prove by way of Minor that neither of the\nalternatives is true. The conclusion is that the antecedent is false.\n\nWe had an example of this in discussing whether the inference in the\nHypothetical Syllogism is Immediate. Our argument was in this form:--\n\n    If the inference is immediate, it must be drawn either from\n    the Major alone or from the Minor alone. But it cannot be\n    drawn from the Major alone, neither can it be drawn from the\n    Minor alone. Therefore, it is not immediate.\n\nIn this form of Dilemma, which is often serviceable for clearness\nof exposition, we must as in the other make sure of the truth of the\nMajor: we must take care that the alternatives are really the only two\nopen. Otherwise the imposing form of the argument is a convenient mask\nfor sophistry. Zeno's famous dilemma, directed to prove that motion is\nimpossible, covers a _petitio principii_.\n\n    If a body moves, it must move either where it is or where it\n    is not. But a body cannot move where it is: neither can it\n    move where it is not. Conclusion, it cannot move at all,\n    _i.e._, Motion is impossible.\n\nThe conclusion is irresistible if we admit the Major, because the\nMajor covertly assumes the point to be proved. In truth, _if_ a body\nmoves, it moves neither where it is nor where it is not, but from\nwhere it is to where it is not. Motion consists in change of place:\nthe Major assumes that the place is unchanged, that is, that there is\nno motion.\n\n    [Footnote 1: For the history of Hypothetical Syllogism see\n    Mansel's _Aldrich_, Appendix I.]\n\n    [Footnote 2: It may be argued that the change is not merely\n    grammatical, and that the implication of a general proposition\n    in a hypothetical and _vice versa_ is a strictly logical\n    concern. At any rate such an implication exists, whether it is\n    the function of the Grammarian or the Logician to expound it.]\n\n    [Footnote 3: Some logicians prefer the form Either A is, or B\n    is. But the two alternatives are propositions, and if \"A is\"\n    represents a proposition, the \"is\" is not the Syllogistic\n    copula. If this is understood it does not matter: the analysis\n    of the alternative propositions is unessential.]\n\n\n\n\nCHAPTER VIII.\n\nFALLACIES IN DEDUCTIVE ARGUMENT.--PETITIO PRINCIPII AND\nIGNORATIO ELENCHI.\n\nThe traditional treatment of Fallacies in Logic follows Aristotle's\nspecial treatise [Greek: Peri sophistikon elenchon]--Concerning\nSophistical Refutations--Pretended Disproofs--Argumentative Tricks.\n\nRegarding Logic as in the main a protection against Fallacies, I have\nbeen going on the plan of taking each fallacy in connexion with its\nspecial safeguard, and in accordance with that plan propose to deal\nhere with the two great types of fallacy in deductive argument. Both\nof them were recognised and named by Aristotle: but before explaining\nthem it is worth while to indicate Aristotle's plan as a whole.\nSome of his Argumentative Tricks were really peculiar to Yes-and-No\nDialectic in its most sportive forms: but his leading types, both\nInductive and Deductive, are permanent, and his plan as a whole has\nhistorical interest. Young readers would miss them from Logic: they\nappeal to the average argumentative boy.\n\nHe divides Fallacies broadly into Verbal Fallacies ([Greek: para ten\nlexin], _in dictione_), and Non-Verbal Fallacies ([Greek: exo tes\nlexeos], _extra dictionem_).\n\nThe first class are mere Verbal Quibbles, and hardly deserve serious\ntreatment, still less minute subdivision. The world was young when\ntime was spent upon them. Aristotle names six varieties, but they\nall turn on ambiguity of word or structure, and some of them, being\ndependent on Greek syntax, cannot easily be paralleled in another\ntongue.\n\n(1) Ambiguity of word ([Greek: homonymia]). As if one were to argue:\n\"All cold can be expelled by heat: John's illness is a cold: therefore\nit can be expelled by heat\". Or: \"Some afflictions are cheering, for\nafflictions are sometimes light, and light is always cheering\".\nThe serious confusion of ambiguous words is met by Definition, as\nexplained at length in pt. ii. c i.\n\n(2) _Ambiguity of structure_ ([Greek: amphibolia]).\n\n\"What he was beaten with was what I saw him beaten with: what I saw\nhim beaten with was my eye: therefore, what he was beaten with was my\neye.\"\n\n\"How do you do?\" \"Do? Do what?\" \"I mean, how do you feel?\" \"How do I\nfeel? With my fingers, of course; but I can see very well.\" \"No, no; I\nmean, how do you find yourself?\" \"Then why did you not say so? I never\nexactly noticed, but I will tell you next time I lose myself.\"\n\n(3) _Illicit conjunction_ ([Greek: synthesis]).\n\nSocrates is good. Socrates is a musician. Therefore Socrates is a good\nmusician.\n\n(4) _Illicit disjunction_ ([Greek: diairesis]).\n\nSocrates is a good musician. Therefore he is a good man.\n\n(5) _Ambiguity of pronunciation_ ([Greek: prosodia], _fallacia\naccentus_).\n\nAnalogies to words that differ only in accent, such as [Greek: ou-with\naccents {psili and persipomeni}] and [Greek: ou-with accents {psili\nand oxia}], may be found in differences of pronunciation. \"Hair very\nthick, sir,\" said a barber to a customer, whose hair was bushy, but\nbeginning to turn grey. \"Yes, I daresay. But I would rather have it\nthick than thin.\" \"Ah, too thick to-day, sir.\" \"But I don't want\nto dye it.\" \"Excuse me, sir, I mean the hair of the hatmosphere,\nt-o-d-a-y, to-day.\"\n\n\"He said, saddle me the ass. And they saddled _him_.\"\n\n(6) _Ambiguity of inflexion_ ([Greek: schema tes lexeos], _Figura\ndictionis_).\n\nThis is not easy to make intelligible in English. The idea is that\na termination may be ambiguously interpreted, a neuter participle,\n_e.g._, taken for an active. Thus: \"George is ailing\". \"Doing what,\ndid you say? Ailing? What is he ailing? Ginger-aleing?\"\n\nNon-Verbal Fallacies, or Fallacies in thought, are a more important\ndivision. Aristotle distinguishes seven.\n\nOf these, three are comparatively unimportant and trifling. One of\nthem, known to the Schoolmen as _Fallacia Plurium Interrogationum_,\nwas peculiar to Interrogative disputation. It is the trick of putting\nmore than one question as one, so that a simple Yes commits the\nrespondent to something implied. \"Have you left off beating your\nfather?\" If you answer Yes, that implies that you have been in the\nhabit of beating him. \"Has the practice of excessive drinking ceased\nin your part of the country?\" Such questions were unfair when the\nRespondent could answer only Yes or No. The modern disputant who\ndemands a plain answer Yes or No, is sometimes guilty of this trick.\n\nTwo others, the fallacies known as _A dicto simpliciter ad dictum\nsecundum quid_, and _A dicto secundum quid ad dictum simpliciter_,\nare as common in modern dialectic as they were in ancient. The trick,\nconscious or unconscious, consists in getting assent to a statement\nwith a qualification and proceeding to argue as if it had been\nconceded without qualification, and _vice versa_. For example, it\nbeing admitted that culture is good, a disputant goes on to argue\nas if the admission applied to some sort of culture in special,\nscientific, aesthetic, philosophical or moral. The fallacy was also\nknown as _Fallacia Accidentis_. Proving that the Syllogism is useless\nfor a certain purpose, and then claiming to have proved that it\nis useless for any purpose is another example. Getting a limited\nadmission and then extending it indefinitely is perhaps the more\ncommon of the two forms. It is common enough to deserve a shorter\nname.\n\nThe _Fallacia Consequentis_, or _Non-Sequitur_, which consists\nspecially in ignoring the possibility of a plurality of causes, has\nalready been partly explained in connexion with the Hypothetical\nSyllogism, and will be explained further in the Logic of Induction.\n\n_Post hoc ergo proper hoc_ is a purely Inductive Fallacy, and will be\nexplained in connexion with the Experimental Methods.\n\nThere remain the two typical Deductive Fallacies, PETITIO PRINCIPII\n(Surreptitious Assumption) and IGNORATIO ELENCHI (Irrelevant Argument)\nabout which we must speak more at length.\n\nThe phrase of which Petitio Principii or Begging the Question is a\ntranslation--[Greek: to en arche aiteisthai]--was applied by Aristotle\nto an argumentative trick in debate by Question and Answer. The\ntrick consisted in taking for granted a proposition necessary to\nthe refutation without having obtained the admission of it. Another\nexpression for the same thing--[Greek: to en arche lambanein]--taking\nthe principle for granted--is more descriptive.\n\nGenerally speaking, Aristotle says, Begging the Question consists in\nnot demonstrating the theorem. It would be in accordance with this\ngeneral description to extend the name to all cases of tacitly or\ncovertly, unwittingly to oneself or to one's opponent, assuming\nany premiss necessary to the conclusion. It is the fallacy of\nSurreptitious Assumption, and all cases of Enthymematic or Elliptical\nargument, where the unexpressed links in the chain of argument are not\nfully understood, are examples of it. By contrast, the articulate and\nexplicit Syllogism is an _Expositio Principii_. The only remedy for\ncovert assumptions is to force them into the light.[1]\n\n_Ignoratio Elenchi_, ignoring the refutation ([Greek: tou elenchou\nagnoia]), is simply arguing beside the point, distracting the\nattention by irrelevant considerations. It often succeeds by proving\nsome other conclusion which is not the one in dispute, but has a\nsuperficial resemblance to it, or is more or less remotely connected\nwith it.\n\nIt is easier to explain what these fallacies consist in than to\nillustrate them convincingly. It is chiefly in long arguments that the\nmischief is done. \"A Fallacy,\" says Whately, \"which when stated barely\nin a few sentences would not deceive a child, may deceive half the\nworld if diluted in a quarto volume.\" Very rarely is a series of\npropositions put before us in regular form and order, all bearing on\na definite point. A certain conclusion is in dispute, not very\ndefinitely formulated perhaps, and a mixed host of considerations\nare tumbled out before us. If we were perfectly clear-headed persons,\ncapable of protracted concentration of attention, incapable\nof bewilderment, always on the alert, never in a hurry, never\nover-excited, absolutely without prejudice, we should keep our\nattention fixed upon two things while listening to an argument, the\npoint to be proved, and the necessary premisses. We should hold\nthe point clearly in our minds, and watch indefatigably for the\ncorroborating propositions. But none of us being capable of this, all\nof us being subject to bewilderment by a rapid whirl of statements,\nand all of us biased more or less for or against a conclusion, the\nsophist has facilities for doing two things--taking for granted\nthat he has stated the required premisses (_petitio principii_), and\nproving to perfect demonstration something which is not the point\nin dispute, but which we are willing to mistake for it (_ignoratio\nelenchi_).\n\nIt is chiefly in the heat of argument that either Petitio or Ignoratio\nsucceeds. When a fallacy continues to perplex us in cold blood, it\nmust have in its favour either some deeply-rooted prejudice or some\npeculiar intricacy in the language used, or some abstruseness in the\nmatter. If we are not familiar with the matter of the argument, and\nhave but a vague hold of the words employed, we are, of course, much\nmore easily imposed upon.\n\nThe famous Sophisms of antiquity show the fascination exercised over\nus by proving something, no matter how irrelevant. If certain steps\nin an argument are sound, we seem to be fascinated by them so that we\ncannot apply our minds to the error, just as our senses are fascinated\nby an expert juggler. We have seen how plausibly Zeno's argument\nagainst the possibility of motion hides a Petitio: the Fatalist\nDilemma is another example of the same sort.\n\n    If it is fated that you die, you will die whether you call in\n    a doctor or not, and if it is fated that you will recover, you\n    will recover whether you call in a doctor or not. But it must\n    be fated either that you die or that you recover. _Therefore_,\n    you will either die or recover whether you call in a doctor or\n    not.\n\nHere it is tacitly assumed in the Major Premiss that the calling in\nof a doctor cannot be a link in the fated chain of events. In the\nstatement of both the alternative conditions, it is assumed that\nFate does not act through doctors, and the conclusion is merely a\nrepetition of this assumption, a verbal proposition after an imposing\nshow of argument. \"If Fate does not act through doctors, you will die\nwhether you call in a doctor or not.\"\n\nThe fallacy in this case is probably aided by our veneration for the\ngrand abstraction of Fate and the awful idea of Death, which absorbs\nour attention and takes it away from the artful _Petitio_.\n\nThe Sophism of Achilles and the Tortoise is the most triumphant of\nexamples of _Ignoratio Elenchi_.\n\nThe point that the Sophism undertakes to prove is that Achilles can\nnever overtake a Tortoise once it has a certain start: what it really\nproves, and proves indisputably, is that he cannot overtake the\nTortoise within a certain space or time.\n\nFor simplicity of exposition, let us assume that the Tortoise has 100\nyards start and that Achilles runs ten times as fast. Then, clearly,\nAchilles will not come up with it at the end of 100 yards, for while\nhe has run 100, the Tortoise has run 10; nor at the end of 110, for\nthen the Tortoise has run 1 more; nor at the end of 111, for then the\nTortoise has run 1/10 more; nor at the end of 111--1/10, for then the\nTortoise has gained 1/100 more. So while Achilles runs this 1/100, the\nTortoise runs 1/1000; while he runs the 1/1000, it runs 1/10000. Thus\nit would seem that the Tortoise must always keep ahead: he can never\novertake it.\n\nBut the conclusion is only a confusion of ideas: all that is really\nproved is that Achilles will not overtake the Tortoise while running\n\n  100 + 10 + 1 + 1/10 + 1/100 + 1/1000 + 1/10000, etc.\n\nThat is, that he will not overtake it till he has completed the sum of\nthis series, 111-1/9 yards. To prove this is an _ignoratio elenchi_;\nwhat the Sophist undertakes to prove is that Achilles will never\novertake it, and he really proves that Achilles passes it between the\n111th and 112th yards.\n\nThe exposure of this sophism is an example also of the value of a\ntechnical term. All attempts to expose it without using the term\n_Ignoratio Elenchi_ or something equivalent to it, succeed only in\nbewildering the student. It is customary to say that the root of the\nfallacy lies in assuming that the sum of an infinite series is equal\nto infinity. This profound error may be implied: but if any assumption\nso hard to understand were really required, the fallacy would have\nlittle force with the generality.\n\nIt has often been argued that the Syllogism involves a _petitio\nprincipii_, because the Major Premiss contains the Conclusion, and\nwould not be true unless the Conclusion were true. But this is really\nan _Ignoratio Elenchi_. The fact adduced, that the Major Premiss\ncontains the Conclusion, is indisputable; but this does not prove the\nSyllogism guilty of Petitio. _Petitio principii_ is an argumentative\ntrick, a conscious or unconscious act of deception, a covert\nassumption, and the Syllogism, so far from favouring this, is an\n_expositio principii_, an explicit statement of premisses such that,\nif they are true, the conclusion is true. The Syllogism merely shows\nthe interdependence of premisses and conclusion; its only tacit\nassumption is the _Dictum de Omni_.\n\nIf, indeed, an opponent challenges the truth of the conclusion, and\nyou adduce premisses necessarily containing it as a refutation, that\nis an _ignoratio elenchi_ unless your opponent admits those premisses.\nIf he admits them and denies the conclusion, you convict him of\ninconsistency, but you do not prove the truth of the conclusion.\nSuppose a man to take up the position: \"I am not mortal, for I have\nprocured the _elixir vitae_\". You do not disprove this by saying, \"All\nmen are mortal, and you are a man\". In denying that he is mortal, he\ndenies that all men are mortal. Whatever is sufficient evidence that\nhe is not mortal, is sufficient evidence that all men are not mortal.\nPerhaps it might be said that in arguing, \"All men are mortal, and\nyou are a man,\" it is not so much _ignoratio elenchi_ as _petitio\nprincipii_ that you commit. But be it always remembered that you may\ncommit both fallacies at once. You may both argue beside the point and\nbeg the question in the course of one and the same argument.\n\n    [Footnote 1: Cp. Mr. Sidgwick's instructive treatise on\n    Fallacies, International Scientific Series, p. 199.]\n\n\n\n\nCHAPTER IX.\n\nFORMAL OR ARISTOTELIAN INDUCTION.--INDUCTIVE ARGUMENT.\n\nThe distinction commonly drawn between Deduction and Induction is\nthat Deduction is reasoning from general to particular, and Induction\nreasoning from particular to general.\n\nBut it is really only as modes of argumentation that the two processes\ncan be thus clearly and fixedly opposed. The word Induction is used in\na much wider sense when it is the title of a treatise on the Methods\nof Scientific Investigation. It is then used to cover all the\nprocesses employed in man's search into the system of reality; and in\nthis search deduction is employed as well as induction in the narrow\nsense.\n\nWe may call Induction in the narrow sense Formal Induction or\nInductive Argument, or we may simply call it Aristotelian Induction\ninasmuch as it was the steps of Inductive argument that Aristotle\nformulated, and for which he determined the conditions of validity.\n\nLet us contrast it with Deductive argument. In this the questioner's\nprocedure is to procure the admission of a general proposition with a\nview to forcing the admission of a particular conclusion which is in\ndispute. In Inductive argument, on the other hand, it is a general\nproposition that is in dispute, and the procedure is to obtain the\nadmission of particular cases with a view to forcing the admission of\nthis general proposition.\n\nLet the question be whether All horned animals ruminate. You engage to\nmake an opponent admit this. How do you proceed? You ask him whether\nhe admits it about the various species. Does the ox ruminate? The\nsheep? The goat? And so on. The bringing in of the various particulars\nis the induction ([Greek: epagoge]).\n\nWhen is this inductive argument complete? When is the opponent bound\nto admit that all horned animals ruminate? Obviously, when he has\nadmitted it about every one. He must admit that he has admitted it\nabout every one, in other words, that the particulars enumerated\nconstitute the whole, before he can be held bound in consistency to\nadmit it about the whole.\n\nThe condition of the validity of this argument is ultimately the\nsame with that of Deductive argument, the identity for purposes of\npredication of a generic whole with the sum of its constituent parts.\nThe Axiom of Inductive Argument is, _What is predicated of every one\nof the parts is predicable of the whole._ This is the simple converse\nof the Axiom of Deductive argument, the _Dictum de Omni_, \"What is\npredicated of the whole is predicable about every one of the parts\".\nThe Axiom is simply convertible because for purposes of predication\ngeneric whole and specific or individual parts taken all together are\nidentical.\n\nPractically in inductive argument an opponent is worsted when he\ncannot produce an instance to the contrary. Suppose he admits the\npredicate in question to be true of this, that and the other, but\ndenies that this, that and the other constitute the whole class in\nquestion, he is defeated in common judgement if he cannot instance\na member of the class about which the predicate does not hold. Hence\nthis mode of induction became technically known as _Inductio per\nenumerationem simplicem ubi non reperitur instantia contradictoria_.\nWhen this phrase is applied to a generalisation of fact, Nature or\nExperience is put figuratively in the position of a Respondent unable\nto contradict the inquirer.\n\nSuch in plain language is the whole doctrine of Inductive Argument.\nAristotle's Inductive Syllogism is, in effect, an expression of this\nsimple doctrine tortuously in terms of the Deductive Syllogism. The\ngreat master was so enamoured of his prime invention that he desired\nto impress its form upon everything: otherwise, there was no reason\nfor expressing the process of Induction syllogistically. Here is his\ndescription of the Inductive Syllogism:--\n\n    \"Induction, then, and the Inductive Syllogism, consists in\n    syllogising one extreme with the middle through the other\n    extreme. For example, if B is middle to A and C, to prove\n    through C that A belongs to B.\"[1]\n\nThis may be interpreted as follows: Suppose a general proposition is\nin dispute, and that you wish to make it good by obtaining severally\nthe admission of all the particulars that it sums up. The type of a\ngeneral proposition in Syllogistic terminology is the Major Premiss,\nAll M is P. What is the type of the particulars that it sums up?\nObviously, the Conclusion, S is P. This particular is contained in the\nMajor Premiss, All M is P; its truth is accepted as contained in the\ntruth of All M is P. S is one of the parts of the generic whole M; one\nof the individuals or species contained in the class M. If you wish,\nthen, to establish P of All M by Induction, you must establish P of\nall the parts, species, or individuals contained in M, that is, of all\npossible S_s:_ you must make good that this, that and the other S is\nP, and also that this, that and the other S constitute the whole of M.\nYou are then entitled to conclude that All M is P: you have syllogised\none Extreme with the Middle through the other Extreme. The formal\nstatement of these premisses and conclusion is the Inductive\nSyllogism.\n\n      This, that and the other S is P, _Major_.\n      This, that and the other S is all M, _Minor_.\n  [.'.] All M is P, _Conclusion_.\n      This, that and the other magnet (_i.e._, magnets individually)\n          attract iron.\n      This, that and the other magnet (_i.e._, the individuals\n         separately admitted) are all magnets.\n  [.'.] All magnets attract iron.\n\nThis, that and the other S being simply convertible with All M, you\nhave only to make this conversion and you have a syllogism in Barbara\nwhere this, that and the other S figures as the Middle Term.\n\nThe practical value of this tortuous expression is not obvious.\nMediaeval logicians shortened it into what was known as the Inductive\nEnthymeme: \"This, that and the other, therefore all,\" an obvious\nconclusion when this, that and the other constitute all. It is\nmerely an evidence of the great master's intoxication with his\ngrand invention. It is a proof also that Aristotle really looked\nat Induction from the point of view of Interrogative Dialectic.\nHis question was, When is a Respondent bound to admit a general\nconclusion? And his answer was, When he has admitted a certain number\nof particulars, and cannot deny that those particulars constitute the\nwhole whose predicate is in dispute. He was not concerned primarily\nwith the analysis of the steps of an inquirer generalising from\nNature.\n\n    [Footnote 1: [Greek: epagoge men oun esti kai ho ex epagoges\n    syllogismos to dia tou eterou thateron akron to meso\n    syllogisasthai; Oion ei ton A G meson to B, dia tou G deixai\n    to A to B hyparchon.] (An. Prior., ii. 23.)]\n\n\n\n\nBOOK II.\n\nINDUCTIVE LOGIC, OR THE LOGIC OF SCIENCE.\n\n\n\n\nINTRODUCTION.\n\nPerhaps the simplest way of disentangling the leading features of\nthe departments of Logic is to take them in relation to historical\ncircumstances. These features are writ large, as it were, in history.\nIf we recognise that all bodies of doctrine have their origin in\npractical needs, we may conceive different ages as controlled each by\na distinctive spirit, which issues its mandate to the men of the age,\nassigning to them their distinctive work.\n\nThe mandate issued to the age of Plato and Aristotle was _Bring your\nbeliefs into harmony one with another_. The Aristotelian Logic\nwas framed in response to this order: its main aim was to devise\ninstruments for making clear the coherence, the concatenation, the\nmutual implication of current beliefs.\n\nThe mandate of the Mediaeval Spirit was _Bring your beliefs into\nharmony with dogma_. The mediaeval logic was contracted from\nAristotle's under this impulse. Induction as conceived by him was\nneglected, allowed to dwindle, almost to disappear from Logic. Greater\nprominence was given to Deduction.\n\nThen as Dogmatic Authority became aggressive, and the Church through\nits officials claimed to pronounce on matters outside Theology, a new\nspirit was roused, the mandate of which was, _Bring your beliefs\ninto harmony with facts_. It was under this impulse that a body of\nmethodical doctrine vaguely called Induction gradually originated.\n\nIn dealing with the genesis of the Old Logic, we began with Aristotle.\nNone can dispute his title to be called its founder. But who was the\nfounder of the New Logic? In what circumstances did it originate?\n\nThe credit of founding Induction is usually given to Francis Bacon,\nLord Verulam. That great man claimed it for himself in calling his\ntreatise on the Interpretation of Nature the _Novum Organum_. The\nclaim is generally conceded. Reid's account of the matter represents\nthe current belief since Bacon's own time.\n\n    \"After man had laboured in the search of truth near two\n    thousand years by the help of Syllogisms, [Lord] Bacon\n    proposed the method of INDUCTION as a more effectual engine\n    for that purpose. His _Novum Organum_ gave a new turn to the\n    thoughts and labours of the inquisitive, more remarkable and\n    more useful than that which the _Organon_ of Aristotle had\n    given before, and may be considered as a second grand era in\n    the progress of human nature.... Most arts have been reduced\n    to rules after they had been brought to a considerable degree\n    of perfection by the natural sagacity of artists; and the\n    rules have been drawn from the best examples of the art\n    that had been before exhibited; but the art of philosophical\n    induction was delineated by [Lord] Bacon in a very ample\n    manner before the world had seen any tolerable example of\n    it.\"[1]\n\nThere is a radical misconception here, which, for reasons that I hope\nto make plain, imperatively needs to be cleared up. It obscures the\nvery essence of \"philosophical induction\".\n\nThere are three ways in which movement in any direction may be helped\nforward, Exhortation, Example, and Precept. Exhortation: a man may\nexhort to the practice of an art and thereby give a stimulus. Example:\nhe may practise the art himself, and show by example how a thing\nshould be done. Precept: he may formulate a clear method, and so make\nplain how to do it. Let us see what was Bacon's achievement in each of\nthose three ways.\n\nUndoubtedly Bacon's powerful eloquence and high political position\ncontributed much to make the study of Nature fashionable. He was high\nin place and great in intellect, one of the commanding personalities\nof his time. Taking \"all knowledge for his province,\" though study\nwas really but his recreation, he sketched out a plan of universal\nconquest with a clearness and confidence that made the mob eager\nto range themselves under his leadership. He was the magnificent\ndemagogue of science. There had been champions of \"Induction\" before\nhim, but they had been comparatively obscure and tongue-tied.\n\nWhile, however, we admit to the full the great services of this mighty\nadvocate in making an \"Inductive\" method popular, we should not\nforget that he had pioneers even in hortatory leadership. His happiest\nwatchword, the Interpretation of Nature, as distinguished from the\nInterpretation of Authoritative Books, was not of his invention. If we\nread Whewell's _History of the Inductive Sciences_, we shall find that\nmany before him had aspired to \"give a new turn to the labors of\nthe inquisitive,\" and in particular to substitute inquisition for\ndisquisition.\n\nOne might compile from Whewell a long catalogue of eminent men before\nBacon who held that the study of Nature was the proper work of the\ninquisitive: Leonardo da Vinci (1452-1519), one of the wonders of\nmankind for versatility, a miracle of excellence in many things,\npainter, sculptor, engineer, architect, astronomer, and physicist;\nCopernicus (1473-1543), the author of the Heliocentric theory;\nTelesius (1508-1588), a theoretical reformer, whose _De Rerum Natura_\n(1565) anticipated not a little of the _Novum Organum_; Cesalpinus\n(1520-1603), the Botanist; Gilbert (1540-1603), the investigator of\nMagnetism. By all these men experiment and observation were advocated\nas the only way of really increasing knowledge. They all derided mere\nbook-learning. The conception of the world of sense as the original\nMS. of which systems of philosophy are but copies, was a familiar\nimage with them. So also was Bacon's epigrammatic retort to those\nwho wish to rest on the wisdom of the ancients, that antiquity is the\nyouth of the world and that we are the true ancients. \"We are older,\"\nsaid Giordano Bruno, \"and have lived longer than our predecessors.\"\n\nThis last argument, indeed, is much older than the sixteenth century.\nIt was used by the Doctor Mirabilis of the thirteenth, the Franciscan\nFriar, Roger Bacon (1214-1292). \"The later men are, the more\nenlightened they are; and wise men now are ignorant of much the world\nwill some day know.\" The truth is that if you are in search of a\nFather for Inductive Philosophy, the mediaeval friar has better claims\nthan his more illustrious namesake. His enthusiasm for the advancement\nof learning was not less nobly ambitious and far-reaching, and he\nwas himself an ardent experimenter and inventor. His _Opus Majus_--an\neloquent outline of his projects for a new learning, addressed in 1265\nto Pope Clement IV., through whom he offered to give to the Church the\nempire of the world as Aristotle had given it to Alexander--was almost\nincredibly bold, comprehensive and sagacious. Fixing upon Authority,\nCustom, Popular Opinion, and the Pride of Supposed Knowledge, as the\nfour causes of human ignorance, he urged a direct critical study of\nthe Scriptures, and after an acute illustration of the usefulness\nof Grammar and Mathematics (widely interpreted), concluded with\nExperimental Science as the great source of human knowledge. I have\nalready quoted (p. 15) the Friar's distinction between the two modes\nof Knowing, Argument and Experience, wherein he laid down that it is\nonly experience that makes us feel certain. It were better, he cried\nin his impatience, to burn Aristotle and make a fresh start than to\naccept his conclusions without inquiry.\n\n    Experimental Science, the sole mistress of Speculative\n    Science, has three great Prerogatives among other parts\n    of Knowledge. First, she tests by experiment the noblest\n    conclusions of all other sciences. Next, she discovers\n    respecting the notions which other sciences deal with,\n    magnificent truths to which these sciences can by no means\n    attain. Her third dignity is that she by her own power and\n    without respect to other sciences investigates the secret of\n    Nature.\n\nSo far, then, as Exhortation goes, King James's great lawyer and\nstatesman was not in advance of Pope Clement's friar. Their first\nprinciple was the same. It is only by facts that theories can be\ntested. Man must not impose his own preconceptions (_anticipationes\nmentis_) on nature. Man is only the interpreter of nature. Both\nwere also at one in holding that the secrets of nature could not be\ndiscovered by discussion, but only by observation and experiment.\n\nFrancis Bacon, however, went beyond all his predecessors in furnishing\nan elaborate Method for the interpretation of Nature. When he\nprotested against the intellect's being left to itself (_intellectus\nsibi permissus_), he meant more than speculation left unchecked by\nstudy of the facts. He meant also that the interpreter must have a\nmethod. As man, he says, cannot move rocks by the mere strength of his\nhands without instruments, so he cannot penetrate to the secrets of\nNature by mere strength of his intellect without instruments. These\ninstruments he undertakes to provide in his Inductive Method or _Novum\nOrganum_. And it is important to understand precisely what his methods\nwere, because it is on the ground of them that he is called the\nfounder of Inductive Philosophy, and because this has created a\nmisapprehension of the methods actually followed by men of science.\n\nIngenious, penetrating, wide-ranging, happy in nomenclature, the\n_Novum Organum_ is a wonderful monument of the author's subtle wit\nand restless energy; but, beyond giving a general impulse to testing\nspeculative fancies by close comparison with facts, it did nothing\nfor science. His method--with its Tables of Preliminary Muster for\nthe Intellect (_tabulae comparentiae primae instantiarum ad intellectum_,\nfacts collected and methodically arranged for the intellect to work\nupon); its Elimination upon first inspection of obviously accidental\nconcomitants (_Rejectio sive Exclusiva naturarum_); its Provisional\nHypothesis (_Vindemiatio Prima sive Interpretatio Inchoata_); its\nadvance to a true Induction or final Interpretation by examination\nof special instances (he enumerates twenty-seven, 3 x 3 x 3,\n_Prerogativas Instantiarum_, trying to show the special value of each\nfor the inquirer)[2]--was beautifully regular and imposing, but it was\nonly a vain show of a method. It was rendered so chiefly by the end\nor aim that Bacon proposed for the inquirer. In this he was not in\nadvance of his age; on the contrary, he was probably behind Roger\nBacon, and certainly far behind such patient and concentrated thinkers\nas Copernicus, Gilbert, and Galileo--no discredit to the grandeur of\nhis intellect when we remember that science was only his recreation,\nthe indulgence of his leisure from Law and State.\n\nIn effect, his method came to this. Collect as many instances as you\ncan of the effect to be investigated, and the absence of it where you\nwould expect it, arrange them methodically, then put aside guesses\nat the cause which are obviously unsuitable, then draw up a probably\nexplanation, then proceed to make this exact by further comparison\nwith instances. It is when we consider what he directed the inquirer\nto search for that we see why so orderly a method was little likely to\nbe fruitful.\n\nHe starts from the principle that the ultimate object of all knowledge\nis use, practice (_scimus ut operemur_). We want to know how Nature\nproduces things that we may produce them for ourselves, if we can.\nThe inquirer's first aim, therefore, should be to find out how the\nqualities of bodies are produced, to discover the _formae_ or formal\ncauses of each quality. An example shows what he meant by this. Gold\nis a crowd or conjugation of various qualities or \"natures\"; it is\nyellow, it has a certain weight, it is malleable or ductile to a\ncertain degree, it is not volatile (loses nothing under fire), it can\nbe melted, it is soluble. If we knew the _forma_ or formal cause of\neach of those qualities, we could make gold, provided the causes were\nwithin our control. The first object, then, of the investigator of\nNature is to discover such _formae_, in order to be able to effect the\ntransformation of bodies. It may be desirable also to know the _latens\nprocessus_, any steps not apparent to the senses by which a body grows\nfrom its first germs or rudiments, and the _schematismus_ or ultimate\ninner constitution of the body. But the discovery of the _formae_ of\nthe constituent qualities (_naturae singulae_), heat, colour, density or\nrarity, sweetness, saltness, and so forth, is the grand object of the\nInterpreter of Nature; and it is for this that Bacon prescribed his\nmethod.\n\nThe _Sylva Sylvarum_, or Natural History, a miscellaneous collection\nof facts and fictions, observations and traditions, with guesses\nat the explanation of them, affords us a measure of Bacon's own\nadvancement as an interpreter of Nature. It was a posthumous work, and\nthe editor, his secretary, tells us that he often said that if he had\nconsidered his reputation he would have withheld it from the world,\nbecause it was not digested according to his own method: yet he\npersuaded himself that the causes therein assigned were far more\ncertain than those rendered by others, \"not for any excellence of his\nown wit, but in respect of his continual conversation with Nature and\nExperience,\" and mankind might stay upon them till true Axioms were\nmore fully discovered. When, however, we examine the causes assigned,\nwe find that in practice Bacon could not carry out his own precepts:\nthat he did not attempt to creep up to an explanation by slow and\npatient ascent, but jumped to the highest generalisations: and that\nhis explanatory notions were taken not from nature, but from the\nordinary traditions of mediaeval physical science. He deceived himself,\nin short, in thinking that he could throw aside tradition and start\nafresh from observation.\n\nFor example. He is struck by the phenomenon of bubbles on water: \"It\nseemeth somewhat strange that the air should rise so swiftly, while it\nis in the water, and when it cometh to the top should be stayed by so\nweak a cover as that of the bubble is\". The swift ascent of the air he\nexplains as a \"motion of percussion,\" the water descending and forcing\nup the air, and not a \"motion of levity\" in the air itself. \"The cause\nof the enclosure of the bubble is for that the appetite to resist\nseparation or discontinuance, which is strong in solids, is also\nin liquors, though fainter and weaker.\" \"The same reason is of the\nroundness of the bubble, as well for the skin of water as for the air\nwithin. For the air likewise avoideth discontinuance, and therefore\ncasteth itself into a round figure. And for the stop and arrest of the\nair a little while, it showeth that the air of itself hath little or\nno appetite of ascending.\"[3] These notions were not taken direct from\nthe facts: they descended from Aristotle. He differs from Aristotle,\nhowever, in his explanation of the colours of birds' feathers.\n\"Aristotle giveth the cause vainly\" that birds are more in the beams\nof the sun than beasts. \"But that is manifestly untrue; for cattle are\nmore in the sun than birds, that live commonly in the woods or in some\ncovert. The true cause is that the excrementitious moisture of living\ncreatures, which maketh as well the feathers in birds as the hair in\nbeasts, passeth in birds through a finer and more delicate strainer\nthan it doth in beasts. For feathers pass through quills, and hair\nthrough skin.\" It is an instance of percolation or filtering: other\neffects of the same cause being the gums of trees, which are but a\nfine passage or straining of the juice through the wood and bark,\nand Cornish Diamonds and Rock Rubies, which are in like manner \"fine\nexudations of stone\".[4]\n\nThese examples of Bacon's Inductions are taken from the _Sylva_ at\nrandom. But the example which best of all illustrates his attitude\nas a scientific investigator is the remark he makes in the _Novum\nOrganum_ about the Copernican theory. Elsewhere he says that there\nis nothing to choose between it and the Ptolemaic; and in the _Novum\nOrganum_ (lib. ii. 5) he remarks that \"no one can hope to terminate\nthe question whether in diurnal motion it is really the earth or the\nsky that rotates, unless he shall first have comprehended the nature\nof spontaneous rotation\". That is, we must first find out the\n_forma_ or formal cause of spontaneous rotation. This is a veritable\n_instantia crucis_, as fixing Bacon's place in the mediaeval and not in\nthe new world of scientific speculation.\n\nBacon, in short, in the practice of induction did not advance an inch\nbeyond Aristotle. Rather he retrograded, inasmuch as he failed to draw\nso clear a line between the respective spheres of Inductive\ncollection of facts and Explanation. There are two sources of general\npropositions, according to Aristotle, Induction and Nous. By Induction\nhe meant the generalisation of facts open to sense, the summation of\nobserved particulars, the _inductio per enumerationem simplicem_ of\nthe schoolmen. By Nous he meant the Reason or Speculative Faculty,\nas exercised with trained sagacity by experts. Thus by Induction we\ngather that all horned animals ruminate. The explanation of this is\nfurnished by the Nous, and the explanation that commended itself to\nthe trained sagacity of his time was that Nature having but a limited\namount of hard material and having spent this on the horns, had none\nleft for teeth, and so provided four stomachs by way of compensation.\nBacon's guesses at causes are on the same scientific level with this,\nonly he rather confused matters by speaking of them as if they were\ninductions from fact, instead of being merely fancies superinduced\nupon fact. His theory of interpretation, it is true, was so far\nan advance that he insisted on the necessity of verifying every\nhypothesis by further appeal to facts, though in practice he himself\nexercised no such patience and never realised the conditions of\nverification. Against this, again, must be set the fact that by\ncalling his method induction, and laying so much stress on the\ncollection of facts, he fostered, and, indeed, fixed in the public\nmind the erroneous idea that the whole work of science consists in\nobservation. The goal of science, as Herschel said, is Explanation,\nthough every explanation must be made to conform to fact,\nand explanation is only another term for attaining to higher\ngeneralisations, higher unities.\n\nThe truth is that Induction, if that is the name we use for scientific\nmethod, is not, as Reid conceived, an exception to the usual rule of\narts in being the invention of one man. Bacon neither invented nor\npractised it. It was perfected gradually in the practice of men\nof science. The birthplace of it as a conscious method was in the\ndiscussions of the Royal Society of London, as the birthplace of the\nAristotelian Logic was in the discussions of the Athenian schools. Its\nfirst great triumph was Newton's law of Gravitation. If we are to\nname it after its first illustrious practitioner, we must call it\nthe Newtonian method, not the Baconian. Newton really stands to the\nScientific Method of Explanation as Aristotle stands to the Method\nof Dialectic and Deduction. He partly made it explicit in his _Regulae\nPhilosophandi_ (1685). Locke, his friend and fellow-member of the\nRoyal Society, who applied the method to the facts of Mind in his\n_Essay Concerning Human Understanding_ (1691), made it still further\nexplicit in the Fourth Book of that famous work.\n\nIt was, however, a century and a half later that an attempt was first\nmade to incorporate scientific method with Logic under the name of\nInduction, and add it as a new wing to the old Aristotelian building.\nThis was the work of John Stuart Mill, whose System of Logic,\nDeductive and Inductive, was first published in 1843.\n\nThe genesis of Mill's System of Logic, as of other things, throws\nlight upon its character. And in inquiries into the genesis of\nanything that man makes we may profitably follow Aristotle's division\nof causes. The Efficient Cause is the man himself, but we have also to\nfind out the Final Cause, his object or purpose in making the thing,\nthe Material Cause, the sources of his material, and the Formal Cause,\nthe reason why he shaped it as he did. In the case of Mill's system\nwe have to ask: What first moved him to formulate the methods of\nscientific investigation? Whence did he derive his materials? Why\ndid he give his scientific method the form of a supplement to the old\nAristotelian Logic? We cannot absolutely separate the three inquiries,\nbut motive, matter and form each had a traceable influence on the\nleading features of his System.\n\nFirst, then, as to his motive. It is a mistake to suppose that Mill's\nobject was to frame an organon that might assist men of science as\nordinarily understood in making discoveries. Bacon, his secretary\ntells us, was wont to complain that he should be forced to be a\nWorkman and a Labourer in science when he thought he deserved to be an\nArchitect in this building. And men of science have sometimes rebuked\nMill for his presumption in that, not being himself an investigator\nin any department of exact science, he should volunteer to teach them\ntheir business. But Mill was really guilty of no such presumption. His\nobject, on the contrary, was to learn their method with a view to\nits application to subjects that had not yet undergone scientific\ntreatment. Briefly stated, his purpose was to go to the practical\nworkers in the exact sciences, Astronomy, Chemistry, Heat, Light,\nElectricity, Molar and Molecular Physics; ascertain, not so much how\nthey made their discoveries as how they assured themselves and others\nthat their conclusions were sound; and having ascertained their tests\nof truth and principles of proof, to formulate these tests so that\nthey might be applied to propositions outside the range of the exact\nsciences, propositions in Politics, Ethics, History, Psychology.\nMore particularly he studied how scientific men verify, and when\nthey accept as proved, propositions of causation, explanations of\nthe causes of things. In effect, his survey of scientific method was\ndesigned to lead up to the Sixth Book in his System, the Logic of the\nMoral Sciences. There are multitudes of floating endoxes or current\nopinions concerning man and his concerns, assigning causes for the\nconduct and character of individuals and of communities. Mill showed\nhimself quite aware that the same modes of investigation may not be\npracticable, and that it may not be possible, though men are always\nready to assign causes with confidence, to ascertain causes with\nthe same degree of certainty: but at least the conditions of exact\nverification should be the same, and it is necessary to see what they\nare in order to see how far they can be realised.\n\nThat such was Mill's design in the main is apparent on internal\nevidence, and it was the internal evidence that first struck me. But\nthere is external evidence as well. We may first adduce some essays\non the Spirit of the Age, published in the _Examiner_ in 1831, essays\nwhich drew from Carlyle the exclamation, \"Here is a new Mystic!\" These\nessays have never been republished, but they contain Mill's first\npublic expression of the need for a method in social inquiries. He\nstarts from the Platonic idea that no state can be stable in which\nthe judgment of the wisest in political affairs is not supreme. He\nforesees danger in the prevalent anarchy of opinion. How is it to be\naverted? How are men to be brought to accept loyally the judgment of\nthe expert in public affairs? They accept at once and without question\nthe decisions of the specially skilled in the physical sciences. Why\nis this? For one reason, because there is complete agreement among\nexperts. And why is there this complete agreement? Because all accept\nthe same tests of truth, the same conditions of proof. Is it not\npossible to obtain among political investigators similar unanimity as\nto their methods of arriving at conclusions, so as to secure similar\nrespect for their authority?\n\nWe need not stop to ask whether this was a vain dream, and whether it\nmust not always be the case that to ensure confidence in a political\nor moral adviser more is needed than faith in his special knowledge\nand trained sagacity. Our point is that in 1831 Mill was in search\nof a method of reasoning in social questions. Opportunely soon after,\nearly in 1832, was published Herschel's _Discourse on the Study of\nNatural Philosophy_, the first attempt by an eminent man of science to\nmake the methods of science explicit. Mill reviewed this book in the\n_Examiner_, and there returns more definitely to the quest on which\nhe was bent. \"The uncertainty,\" he says, \"that hangs over the very\nelements of moral and social philosophy proves that the means\nof arriving at the truth in those sciences are not yet properly\nunderstood. And whither can mankind so advantageously turn, in order\nto learn the proper means and to form their minds to the proper\nhabits, as to that branch of knowledge in which by universal\nacknowledgment the greatest number of truths have been ascertained and\nthe greatest possible degree of certainty arrived at?\"\n\nWe learn from Mill himself that he made an attempt about this\ntime, while his mind was full of Herschel's Discourse, to connect a\nscientific method with the body of the Old Logic. But he could not\nmake the junction to his satisfaction, and abandoned the attempt in\ndespair. A little later, in 1837, upon the appearance of Whewell's\n_History of the Inductive Sciences_, he renewed it, and this time with\nhappier results. Whewell's _Philosophy of the Inductive Sciences_\nwas published in 1840, but by that time Mill's system was definitely\nshaped.\n\nIt was, then, to Herschel and Whewell, but especially to the former,\nthat Mill owed the raw materials of his Inductive Method. But why did\nhe desire to concatenate this with the old Logic? Probably because he\nconsidered that this also had its uses for the student of society, the\npolitical thinker. He had inherited a respect for the old Logic from\nhis father. But it was the point at which he sought to connect the\nnew material with the old, the point of junction between the two, that\ndetermined the form of his system. We find the explanation of this in\nthe history of the old Logic. It so happened that Whately's Logic was\nin the ascendant, and Whately's treatment of Induction gives the key\nto Mill's.\n\nTowards the end of the first quarter of this century there was a\ngreat revival of the study of Logic at Oxford. The study had become\nmechanical, Aldrich's Compendium, an intelligent but exceedingly brief\nabstract of the Scholastic Logic, being the text-book beyond which\nno tutor cared to go. The man who seems to have given new life to the\nstudy was a tutor who subsequently became Bishop of Llandaff, Edward\nCopleston. The first public fruits of the revival begun by him was\nWhately's article on Logic in the _Encyclopaedia Metropolitana_,\npublished as a separate book in 1827. Curiously enough, one of\nWhately's most active collaborators in the work was John Henry Newman,\nso that the common room of Oriel, which Mr. Froude describes as the\ncentre from which emanated the High Church Movement, may also be\nsaid to have been the centre from which emanated the movement that\nculminated in the revolution of Logic.\n\nThe publication of Whately's Logic made a great stir. It was reviewed\nby Mill, then a young man of twenty-one, in the _Westminster Review_\n(1828), and by Hamilton, then forty-five years of age, in the\n_Edinburgh_ (1833). There can be no doubt that it awakened Mill's\ninterest in the subject. A society formed for the discussion of\nphilosophical questions, and called the Speculative Society, met at\nGrote's house in 1825, and for some years following. Of this society\nyoung Mill was a member, and their continuous topic in 1827 was Logic,\nWhately's treatise being used as a sort of text-book.\n\nIt is remarkable that Mill's review of Whately, the outcome of these\ndiscussions, says very little about Induction. At that stage Mill's\nchief concern seems to have been to uphold the usefulness of Deductive\nLogic, and he even goes so far as to scoff at its eighteenth century\ndetractors and their ambition to supersede it with a system of\nInduction. The most striking feature of the article is the brilliant\ndefence of the Syllogism as an analysis of arguments to which I have\nalready referred. He does not deny that an Inductive Logic might be\nuseful as a supplement, but apparently he had not then formed the\ndesign of supplying such a supplement. When, however, that design\nseriously entered his mind, consequent upon the felt need of a method\nfor social investigations, it was Whately's conception of Induction\nthat he fell back upon. Historically viewed, his System of Logic was\nan attempt to connect the practical conditions of proof set forth in\nHerschel's discourse with the theoretic view of Induction propounded\nin Whately's. The tag by which he sought to attach the new material\nto the old system was the Inductive Enthymeme of the Schoolmen as\ninterpreted by Whately.\n\nWhately's interpretation--or misinterpretation--of this Enthymeme,\nand the conception of Induction underlying it, since it became Mill's\nruling conception of Induction, and virtually the formative principle\nof his system, deserves particular attention.\n\n    \"This, that and the other horned animal, ox, sheep, goat,\n    ruminate; _therefore_, all horned animals ruminate.\"\n\nThe traditional view of this Enthymeme I have given in my chapter on\nFormal Induction (p. 238). It is that a Minor Premiss is suppressed:\n\"This, that and the other constitute the whole class\". This is the\nform of the Minor in Aristotle's Inductive Syllogism.\n\nBut, Whately argued, how do we know that this, that and the other--the\nindividuals we have examined--constitute the whole class? Do we not\nassume that what belongs to the individuals examined belongs to the\nwhole class? This tacit assumption, he contended, is really at the\nbottom of the Enthymeme, and its proper completion is to take this as\nthe Major Premiss, with the enumeration of individuals as the Minor.\nThus:--\n\n  What belongs to the individuals examined belongs to\n  the whole class.\n\n  The property of the ruminating belongs to the individuals\n  examined, ox, sheep, goat, etc.\n\n  _Therefore_, it belongs to all.\n\nIn answer to this, Hamilton repeated the traditional view, treating\nWhately's view merely as an instance of the prevailing ignorance of\nthe history of Logic. He pointed out besides that Whately's Major was\nthe postulate of a different kind of inference from that contemplated\nin Aristotle's Inductive Syllogism, Material as distinguished from\nFormal inference. This is undeniable if we take this syllogism purely\nas an argumentative syllogism. The \"all\" of the conclusion simply\ncovers the individuals enumerated and admitted to be \"all\" in the\nMinor Premiss. If a disputant admits the cases produced to be all and\ncan produce none to the contrary, he is bound to admit the conclusion.\nNow the inference contemplated by Whately was not inference from\nan admission to what it implies, but inference from a series of\nobservations to all of a like kind, observed and unobserved.\n\nIt is not worth while discussing what historical justification Whately\nhad for his view of Induction. It is at least arguable that the word\nhad come to mean, if it did not mean with Aristotle himself, more\nthan a mere summation of particulars in a general statement. Even\nAristotle's respondent in the concession of his Minor admitted that\nthe individuals enumerated constituted all in the truly general sense,\nnot merely all observed but all beyond the range of observation. The\npoint, however, is insignificant. What really signifies is that\nwhile Hamilton, after drawing the line between Formal Induction and\nMaterial, fell back and entrenched himself within that line, Mill\ncaught up Whately's conception of Induction, pushed forward, and made\nit the basis of his System of Logic.\n\nIn Mill's definition, the mere summation of particulars, _Inductio per\nenumerationem simplicem ubi non reperitur instantia contradictoria_,\nis Induction improperly so called. The only process worthy of the name\nis Material Induction, inference to the unobserved. Here only is\nthere an advance from the known to the unknown, a veritable \"inductive\nhazard\".\n\nStarting then with this conception of inference to the unobserved\nas the only true inference, and with an empirical law--a generality\nextended from observed cases to unobserved--as the type of such\ninference, Mill saw his way to connecting a new Logic with the old. We\nmust examine this junction carefully, and the brilliant and plausible\narguments by which he supported it; we shall find that, biased by this\ndesire to connect the new with the old, he gave a misleading dialectic\nsetting to his propositions, and, in effect, confused the principles\nof Argumentative conclusion on the one hand and of Scientific\nObservation and Inference on the other. The conception of Inference\nwhich he adopted from Whately was too narrow on both sides for the\nuses to which he put it. Be it understood that in the central methods\nboth of Syllogistic and of Science, Mill was substantially in accord\nwith tradition; it is in his mode of junction, and the light thereby\nthrown upon the ends and aims of both, that he is most open to\ncriticism.\n\nAs regards the relation between Deduction and Induction, Mill's chief\nproposition was the brilliant paradox that all inference is at bottom\nInductive, that Deduction is only a partial and accidental stage in\na process the whole of which may be called Induction. An opinion was\nabroad--fostered by the apparently exclusive devotion of Logic to\nDeduction--that all inference is essentially Deductive. Not so,\nanswered Mill, meeting this extreme with another: all inference is\nessentially Inductive. He arrives at this through the conception\nthat Induction is a generalisation from observed particulars, while\nDeduction is merely the extension of the generalisation to a new\ncase, a new particular. The example that he used will make his meaning\nplain.\n\nTake a common Syllogism:--\n\n  All men are mortal.\n  Socrates is a man.\n  Socrates is mortal.\n\n\"The proposition,\" Mill says, \"that Socrates is mortal is evidently an\ninference. It is got at as a conclusion from something else. But do we\nin reality conclude it from the proposition, All men are mortal?\" He\nanswers that this cannot be, because if it is not true that Socrates\nis mortal it cannot be true that all men are mortal. It is clear that\nour belief in the mortality of Socrates must rest on the same ground\nas our belief in the mortality of men in general. He goes on to ask\nwhence we derive our knowledge of the general truth, and answers: \"Of\ncourse from observation. Now all which man can observe are individual\ncases.... A general truth is but an aggregate of particular truths.\nBut a general proposition is not merely a compendious form for\nrecording a number of particular facts.... It is also a process of\ninference. From instances which we have observed we feel warranted in\nconcluding that what we have found true in those instances, holds in\nall similar ones, past, present, and future. We then record all that\nwe have observed together with what we infer from our observations,\nin one concise expression.\" A general proposition is thus at once a\nsummary of particular facts and a memorandum of our right to\ninfer from them. And when we make a deduction we are, as it were,\ninterpreting this memorandum. But it is upon the particular facts\nthat the inference really rests, and Mill contends that we might if we\nchose infer to the particular conclusion at once without going through\nthe form of a general inference. Thus Mills seeks to make good his\npoint that all inference is essentially Inductive, and that it is\nonly for convenience that the word Induction has been confined to the\ngeneral induction, while the word Deduction is applied to the process\nof interpreting our memorandum.\n\nClear and consecutive as this argument is, it is fundamentally\nconfusing. It confuses the nature of Syllogistic conclusion or\nDeduction, and at the same time gives a partial and incomplete account\nof the ground of Material inference.\n\nThe root of the first confusion lies in raising the question of the\nground of material inference in connexion with the Syllogism. As\nregards the usefulness of the Syllogism, this is an IGNORATIO ELENCHI.\nThat the Major and the conclusion rest upon the same ground as\nmatters of belief is indisputable: but it is irrelevant. In so far\nas \"Socrates is mortal\" is an inference from facts, it is not the\nconclusion of a Syllogism. This is implicitly and with unconscious\ninconsistency recognised by Mill when he represents Deduction as\nthe interpretation of a memorandum. To represent Deduction as the\ninterpretation of a memorandum--a very happy way of putting it and\nquite in accordance with Roger Bacon's view--is really inconsistent\nwith regarding Deduction as an occasional step in the process of\nInduction. If Deduction is the interpretation of a memorandum, it\nis no part of the process of inference from facts. The conditions of\ncorrect interpretation as laid down in Syllogism are one thing,\nand the methods of correct inference from the facts, the methods of\nscience that he was in search of, are another.\n\nLet us emphasise this view of Deduction as the interpretation of a\nmemorandum. It corresponds exactly with the view that I have taken\nin discussing the utility of the Syllogism. Suppose we want to know\nwhether a particular conclusion is consistent with our memorandum,\nwhat have we to look to? We have to put our memorandum into such\na form that it is at once apparent whether or not it covers our\nparticular case. The Syllogism aspires to be such a form. That is\nthe end and aim of it. It does not enable us to judge whether the\nmemorandum is a legitimate memorandum or not. It only makes clear that\nif the memorandum is legitimate, so is the conclusion. How to\nmake clear and consistent memoranda of our beliefs in words is a\nsufficiently complete description of the main purpose of Deductive\nLogic.\n\nInstead, then, of trying to present Deduction and Induction as parts\nof the same process, which he was led to do by his desire to connect\nthe new and the old, Mill ought rather, in consistency as well as\nin the interests of clear system, to have drawn a line of separation\nbetween the two as having really different ends, the conditions of\ncorrect conclusion from accepted generalities on the one hand, and the\nconditions of correct inference from facts on the other. Whether the\nfirst should be called inference at all is a question of naming that\nought to have been considered by itself. We may refuse to call it\ninference, but we only confuse ourselves and others if we do not\nacknowledge that in so doing we are breaking with traditional usage.\nPerhaps the best way in the interests of clearness is to compromise\nwith tradition by calling the one Formal Inference and the other\nMaterial Inference.\n\nIt is with the latter that the Physical Sciences are mainly concerned,\nand it was the conditions and methods of its correct performance that\nMill desired to systematise in his Inductive Logic. We have next\nto see how his statement of the grounds of Material Inference was\naffected by his connexion of Deduction and Induction. Here also\nwe shall find a reason for a clearer separation between the two\ndepartments of Logic.\n\nIn his antagonism to a supposed doctrine that all reasoning is\nfrom general to particular, Mill maintained _simpliciter_ that all\nreasoning is from particulars to particulars. Now this is true only\n_secundum quid_, and although in the course of his argument Mill\nintroduced the necessary qualifications, the unqualified thesis was\nconfusing. It is perfectly true that we may infer--we can hardly be\nsaid to reason--from observed particulars to unobserved. We may even\ninfer, and infer correctly, from a single case. The village matron,\ncalled in to prescribe for a neighbour's sick child, infers that\nwhat cured her own child will cure the neighbour's, and prescribes\naccordingly. And she may be right. But it is also true that she may\nbe wrong, and that no fallacy is more common than reasoning from\nparticulars to particulars without the requisite precautions. This\nis the moral of one of the fables of Camerarius. Two donkeys were\ntravelling in the same caravan, the one laden with salt, the other\nwith hay. The one laden with salt stumbled in crossing a stream, his\npanniers dipped in the stream, the salt melted, and his burden was\nlightened. When they came to another stream, the donkey that was laden\nwith hay dipped his panniers in the water, expecting a similar\nresult. Mill's illustrations of correct inference from particulars\nto particulars were really irrelevant. What we are concerned with\nin considering the grounds of Inference, is the condition of correct\ninference, and no inference to an unobserved case is sound unless\nit is of a like kind with the observed case or cases on which it is\nfounded, that is to say, unless we are entitled to make a general\nproposition. We need not go through the form of making a general\nproposition, but if a general proposition for all particulars of\na certain description is not legitimate, no more is the particular\ninference. Mill, of course, did not deny this, he was only betrayed\nby the turn of his polemic into an unqualified form of statement that\nseemed to ignore it.\n\nBut this was not the worst defect of Mill's attempt at a junction of\nold and new through Whately's conception of Induction. A more serious\ndefect was due to the insufficiency of this conception to represent\nall the modes of scientific inference. When a certain attribute has\nbeen found in a certain connexion in this, that, and the other, to the\nextent of all observed instances, we infer that it will be found in\nall, that the connexion that has obtained within the range of our\nactual experience has obtained beyond that range and will obtain\nin the future. Call this an observed uniformity of nature: we hold\nourselves justified in expecting that the observed uniformities of\nnature will continue. Such an observed uniformity--that All animals\nhave a nervous system, that All animals die, that Quinine cures\nague--is also called an Empirical Law.\n\nBut while we are justified in extending an empirical law beyond the\nlimits within which it has been observed to hold good, it is a\nmistake to suppose that the main work of science is the collection\nof empirical laws, and that the only scientific inference is the\ninference from the observed prevalence of an empirical law to its\ncontinuance. With science the collection of empirical laws is only\na preliminary: \"the goal of science,\" in Herschel's phrase, \"is\nexplanation\". In giving such prominence to empirical laws in his\ntheory, Mill confined Induction to a narrower scope than science\nascribes to it. Science aims at reaching \"the causes of things\": it\ntries to penetrate behind observed uniformities to the explanation\nof them. In fact, as long as a science consists only of observed\nuniformities, as long as it is in the empirical stage, it is a science\nonly by courtesy. Astronomy was in this stage before the discovery of\nthe Law of Gravitation. Medicine is merely empirical as long as its\npractice rests upon such generalisations as that Quinine cures ague,\nwithout knowing why. It is true that this explanation may consist only\nin the discovery of a higher or deeper uniformity, a more recondite\nlaw of connexion: the point is that these deeper laws are not always\nopen to observation, and that the method of reaching them is not\nmerely observing and recording.\n\nIn the body of his Inductive Logic, Mill gave a sufficient account of\nthe Method of Explanation as practised in scientific inquiry. It was\nonly his mode of approaching the subject that was confusing, and\nmade it appear as if the proper work of science were merely extending\nobserved generalities, as when we conclude that all men will die\nbecause all men have died, or that all horned animals ruminate because\nall hitherto observed have had this attribute. A minor source of\nconfusion incident to the same controversy was his refusing the\ntitle of Induction proper to a mere summary of particulars. He seemed\nthereby to cast a slight upon the mere summation of particulars. And\nyet, according to his theory, it was those particulars that were the\nbasis of the Induction properly so called. That all men will die is an\ninference from the observation summed up in the proposition that\nall men have died. If we refuse the name of Induction to the general\nproposition of fact, what are we to call it? The truth is that the\nreason why the word Induction is applied indifferently to the general\nproposition of fact and the general proposition applicable to all\ntime is that, once we are sure of the facts, the transition to the\ninference is so simple an affair that it has not been found necessary\nin practice to distinguish them by different names.\n\nOur criticism of Mill would itself mislead if it were taken to mean\nthat the methods of science which he formulated are not the methods\nof science or that his system of those methods is substantially\nincomplete. His Inductive Logic as a system of scientific method was\na great achievement in organisation, a veritable _Novum Organum_ of\nknowledge. What kept him substantially right was that the methods\nwhich he systematised were taken from the practice of men of science.\nOur criticism amounts only to this, that in correlating the new system\nwith the old he went upon a wrong track. For more than two centuries\nDeduction had been opposed to Induction, the _ars disserendi_ to the\n_ars inveniendi_. In trying to reconcile them and bring them under one\nroof, Mill drew the bonds too tight. In stating the terms of the union\nbetween the two partners, he did not separate their spheres of work\nwith sufficient distinctness.\n\nMill's theory of Deduction and Induction and the voluminous criticism\nto which in its turn it has been subjected have undoubtedly been of\ngreat service in clearing up the foundations of reasoning. But the\nmoral of it is that if we are to make the methods of Science a part of\nLogic, and to name this department Induction, it is better to discard\naltogether the questions of General and Particular which are pertinent\nto Syllogism, and to recognise the new department simply as being\nconcerned with a different kind of inference, inference from facts to\nwhat lies beyond them, inference from the observed to the unobserved.\n\nThat this is the general aim and proper work of Science is evident\nfrom its history. Get at the secrets of Nature by the study of Nature,\npenetrate to what is unknown and unexperienced by help of what is\nknown and has been experienced, was the cry of the early reformers of\nScience. Thus only, in Roger Bacon's phrase, could certainty--assured,\nwell grounded, rational belief--be reached. This doctrine, like every\nother, can be understood only by what it was intended to deny. The\nway of reaching certainty that Roger Bacon repudiated was argument,\ndiscussion, dialectic. This \"concludes a question but does not make us\nfeel certain, or acquiesce in the contemplation of truth that is not\nalso found in Experience\". Argument is not necessarily useless; the\nproposition combated is only that by it alone--by discussion that does\nnot go beyond accepted theories or conceptions--rational belief about\nthe unknown cannot be reached. The proposition affirmed is that to\nthis end the conclusions of argument must be tested by experience.\n\nObservation of facts then is a cardinal part of the method of Science.\nThe facts on which our inferences are based, by which our conclusions\nare tested, must be accurate. But in thus laying emphasis on the\nnecessity of accurate observation, we must beware of rushing to the\nopposite extreme, and supposing that observation alone is enough.\nObservation, the accurate use of the senses (by which we must\nunderstand inner as well as outer sense), is not the whole work of\nScience. We may stare at facts every minute of our waking day without\nbeing a whit the wiser unless we exert our intellects to build upon\nthem or under them. To make our examination fruitful, we must have\nconceptions, theories, speculations, to bring to the test. The\ncomparison of these with the facts is the inductive verification of\nthem. Science has to exercise its ingenuity both in making hypotheses\nand in contriving occasions for testing them by observation. These\ncontrived occasions are its artificial experiments, which have come to\nbe called experiments simply by contrast with conclusive observations\nfor which Nature herself furnishes the occasion. The observations of\nScience are not passive observations. The word experiment simply means\ntrial, and every experiment, natural or artificial, is the trial of\na hypothesis. In the language of Leonardo da Vinci, \"Theory is the\ngeneral, Experiments are the soldiers\".\n\nObservation and Inference go hand in hand in the work of Science, but\nwith a view to a methodical exposition of its methods, we may divide\nthem broadly into Methods of Observation and Methods of Inference.\nThere are errors specially incident to Observation, and errors\nspecially incident to Inference. How to observe correctly and how to\nmake correct inferences from our observations are the two objects of\nour study in Inductive Logic: we study the examples of Science because\nthey have been successful in accomplishing those objects.\n\nThat all inference to the unobserved is founded on facts, on the\ndata of experience, need not be postulated. It is enough to say that\nInductive Logic is concerned with inference in so far as it is founded\non the data of experience. But inasmuch as all the data of experience\nare not of equal value as bases of inference, it is well to begin with\nan analysis of them, if we wish to take a comprehensive survey of the\nvarious modes of inference and the conditions of their validity.\n\n    [Footnote 1: Hamilton's _Reid_, p. 712.]\n\n    [Footnote 2: The _Novum Organum_ was never completed. Of\n    the nine heads of special aids to the intellect in the final\n    interpretation he completed only the first, the list of\n    Prerogative Instances.]\n\n    [Footnote 3: _Sylva Sylvarum_, Century I, 24.]\n\n    [Footnote 4: _Sylva Sylvarum_, Century I, 5.]\n\n\n\n\nCHAPTER I.\n\nTHE DATA OF EXPERIENCE AS GROUNDS OF INFERENCE OR RATIONAL BELIEF.\n\nIf we examine any of the facts or particulars on which an inference\nto the unobserved is founded, we shall find that they are not isolated\nindividuals or attributes, separate objects of perception or thought,\nbut relations among things and their qualities, constituents, or\ningredients.\n\nTake the \"particular\" from which Mill's village matron inferred, the\nfact on which she based her expectation of a cure for her neighbour's\nchild. It is a relation between things. We have the first child's\nailment, the administration of the drug, and the recovery, a series of\nevents in sequence. This observed sequence is the fact from which she\nis said to infer, the datum of experience. She expects this sequence\nto be repeated in the case of her neighbour's child.\n\nSimilarly we shall find that, in all cases where we infer, the\nfacts are complex, are not mere isolated things, but relations among\nthings--using the word thing in its widest sense--relations which we\nexpect to find repeated, or believe to have occurred before, or to be\noccurring now beyond the range of our observation. These relations,\nwhich we may call coincidences or conjunctions, are the data of\nexperience from which we start in our beliefs or inferences about the\nunexperienced.\n\nThe problem of Inductive Logic being to determine when or on what\nconditions such beliefs are rational, we may begin by distinguishing\nthe data of coincidence or conjunction accordingly. There are certain\ncoincidences that we expect to find repeated beyond the occasions on\nwhich we have observed them, and others that we do not expect to find\nrepeated. If it is a sound basis of inference that we are in search\nof, it is evidently to these first, the coincidences that we are\nassured of finding again, that we must direct our study. Let us see\nwhether they can be specified.\n\n(1) If there is no causal connexion between A and B, using these\nas symbols for the members of a coincidence--the objects that are\npresented together--we do not expect the coincidence to be repeated.\nIf A and B are connected as cause and effect, we expect the effect\nto recur in company with the cause. We expect that when the cause\nreappears in similar circumstances, the effect also will reappear.\n\nYou are hit, _e.g._, by a snowball, and the blow is followed by a\nfeeling of pain. The sun, we shall say, was shining at the moment of\nthe impact of the snowball on your body. The sunshine preceded your\nfeeling of pain as well as the blow. But you do not expect the pain\nto recur next time that the sun shines. You do expect it to recur next\ntime you are hit by a snowball.\n\nThe taking of food and a certain feeling of strength are causally\nconnected. If we go without food, we are not surprised when faintness\nor weariness supervenes.\n\nSuppose that when our village matron administered her remedy to her\nown child, a dog stood by the bedside and barked. The barking in that\ncase would precede the cure. Now, if the matron were what we should\ncall a superstitious person, and believed that this concomitant had\na certain efficacy, that the dog's barking and the cure were causally\nconnected, she would take the dog with her when she went to cure her\nneighbour's child. Otherwise she would not. She would say that the\nbarking was an accidental, casual, fortuitous coincidence, and would\nbuild no expectation upon it.\n\nThese illustrations may serve to remind us of the familiar fact that\nthe causal nexus is at least one of the things that we depend on in\nour inferences to the unobserved. To a simple sequence we attach\nno importance, but a causal sequence or consequence that has been\nobserved is a mainstay of inference.\n\nWhether the causal sequence holds or not as a matter of fact, we\ndepend upon it if we believe in it as a matter of fact. But unless\nit does hold as a matter of fact, it is valueless as a guide to the\nunknown, and our belief is irrational. Clearly, therefore, if rational\nbelief is what we aim at, it is of importance that we should make sure\nof cause and effect as matter of fact in the sequence of events.\n\nOne large department of Inductive Logic, the so-called Experimental\nMethods, is designed to help us in thus making sure, _i.e._, in\nascertaining causal sequence as a matter of fact. It is assumed\nthat by careful observation of the circumstances, we can distinguish\nbetween mere simple sequence and causal sequence or consequence,\nand methods are recommended of observing with the proper precautions\nagainst error.\n\nObserve that these methods, though called Inductive, are not concerned\nwith arriving at general propositions. The principle we go upon is\nsimply this, that if it can be ascertained as matter of fact that a\ncertain thing is related to another as cause and effect, we may count\nupon the same relation as holding in unobserved Nature, on the general\nground that like causes produce like effects in like circumstances.\n\nObserve, also, that I deliberately speak of the causal relation as\na relation among phenomena. Whether this use of the words cause and\neffect is philosophically justifiable, is a question that will be\nraised and partly discussed later on. Here I simply follow the common\nusage, in accordance with which objects of perception, _e.g._, the\nadministration of a drug and the recovery of a patient, are spoken of\nas cause and effect. Such observable sequences are causal sequences in\nthe ordinary sense, and it is part of the work of Science to observe\nthem. I do not deny that the _true_ cause, of the cause that\nscience aims ultimately at discovering, is to be found in the latent\nconstitution or composition of the things concerned. Only that, as we\nshall see more precisely, is a cause of another description. Meantime,\nlet us take the word to cover what it undoubtedly covers in ordinary\nspeech, the perceptible antecedent of a perceptible consequent.\n\nStrictly speaking, as we shall find, Science has only one method of\ndirectly observing when events are in causal sequence. But there are\nvarious indirect methods, which shall be described in some sort of\norder.\n\nFor the practical purposes of life, a single ascertained causal\nsequence is of little value as a basis of inference, because we can\ninfer only to its repetition in identical circumstances. Suppose our\nvillage matron had been able to ascertain as a matter of fact--a feat\nas we shall find not to be achieved by direct observation--that the\ndrug did cure her child, this knowledge by itself would have been\npractically valueless, because the only legitimate inference would\nhave been that an exactly similar dose would have the same effect\nin exactly similar circumstances. But, as we shall find, though\npractically valueless, a single ascertained causal sequence is of\nsupreme value in testing scientific speculations as to the underlying\ncauses.\n\n(2) We have next to see whether there are any other rational\nexpectations based on observed facts. We may lay down as a principle\nthe following:--\n\n_If a conjunction or coincidence has constantly been repeated within\nour experience, we expect it to recur and believe that it has recurred\noutside our experience._\n\nHow far such expectations are rational, and with what degrees of\nconfidence they should be entertained, are the questions for the Logic\nof Inference, but we may first note that we do as a matter of habit\nfound expectations on repeated coincidence, and indeed guide our\ndaily life in this way. If we meet a man repeatedly in the street at\na certain hour, we go out expecting to meet him: it is a shock to our\nexpectations, a surprise, when we do not. If we are walking along a\nroad and find poles set up at regular intervals, we continue our walk\nexpecting to find a pole coincident with the end of each interval.\n\nWhat Mill calls the uniformities of Nature, the uniformities expressed\nin general propositions, are from the point of view of the observer,\nexamples of repeated coincidence. Birth, growth, decay, death, are not\nisolated or variable coincidences with organised being: all are born,\nall grow, all decay, and all die. These uniformities constitute\nthe order of Nature: the coincidences observed are not occasional,\noccurring once in a way or only now and then; they turn up again and\nagain. Trees are among the uniformities on the varied face of Nature:\ncertain relations between the soil and the plant, between trunk,\nbranches, and leaves are common to them. For us who observe, each\nparticular tree that comes under our observation is a repetition of\nthe coincidence. And so with animals: in each we find certain tissues,\ncertain organs, conjoined on an invariable plan.\n\nTechnically these uniformities have been divided into uniformities\nof Sequence and uniformities of Coexistence. Thus the repeated\nalternation of day and night is a uniformity of Sequence: the\ninvariable conjunction of inertia with weight is a uniformity of\nCoexistence. But the distinction is really immaterial to Logic.\nWhat Logic is concerned with is the observation of the facts and the\nvalidity of any inference based on them: and in these respects it\nmakes no difference whether the uniformity that we observe and found\nupon is one of Sequence or of Coexistence.\n\nIt was exclusively to such inferences, inferences from observed facts\nof repeated coincidence, that Mill confined himself in his theory of\nInduction, though not in his exposition of the methods. These are the\ninferences for which we must postulate what he calls the Uniformity\nof Nature. Every induction, he says, following Whately, may be thrown\ninto the form of a Syllogism, in which the principle of the Uniformity\nof Nature is the Major Premiss, standing to the inference in the\nrelation in which the Major Premiss of a Syllogism stands to the\nconclusion. If we express this abstractly denominated principle in\npropositional form, and take it in connexion with Mill's other saying\nthat the course of Nature is not a uniformity but uniformities, we\nshall find, I think, that this postulated Major Premiss amounts to an\nassumption that the observed Uniformities of Nature continue. Mill's\nInductive Syllogism thus made explicit would be something like this:--\n\n  All the observed uniformities of Nature continue.\n  That all men have died is an observed uniformity.\n  _Therefore_, it continues; _i.e._, all men will die and did die\n  before the beginning of record.\n\nThere is no doubt that this is a perfectly sound postulate. Like all\nultimate postulates it is indemonstrable; Mill's derivation of it\nfrom Experience did not amount to a demonstration. It is simply an\nassumption on which we act. If any man cares to deny it, there is\nno argument that we can turn against him. We can only convict him of\npractical inconsistency, by showing that he acts upon this assumption\nhimself every minute of his waking day. If we do not believe in the\ncontinuance of observed uniformities, why do we turn our eyes to the\nwindow expecting to find it in its accustomed order of place? Why do\nwe not look for it in another wall? Why do we dip our pens in ink,\nand expect the application of them to white paper to be followed by a\nblack mark?\n\nThe principle is sound, but is it our only postulate in inference to\nthe unobserved, and does the continuance of empirical laws represent\nall that Science assumes in its inferences? Mill was not satisfied\nabout this question. He pointed out a difficulty which a mere belief\nin empirical continuity does not solve. Why do we believe more\nconfidently in some uniformities than in others? Why would a reported\nbreach of one be regarded with more incredulity than that of another?\nSuppose a traveller to return from a strange country and report that\nhe had met men with heads growing beneath their shoulders, why would\nthis be pronounced more incredible than a report that he had seen a\ngrey crow? All crows hitherto observed have been black, and in all men\nhitherto observed the heads have been above the shoulders: if the\nmere continuity of observed uniformities is all that we go upon in\nour inferences, a breach of the one uniformity should be just as\nimprobable as a breach of the other, neither more nor less. Mill\nadmitted the difficulty, and remarked that whoever could solve it\nwould have solved the problem of Induction. Now it seems to me that\nthis particular difficulty may be solved, and yet leave another\nbehind. It may be solved within the limits of the principle of\nemperical--meaning by that observational--continuity. The uniform\nblackness of the crow is an exception within a wider uniformity: the\ncolour of animals is generally variable. Hence we are not so much\nsurprised at the reported appearance of a grey crow: it is in\naccordance with the more general law. On the other hand, the uniform\nposition of the head relative to other parts of the body is a\nuniformity as wide as the animal kingdom: it is a coincidence repeated\nas often as animals have been repeated, and merely on the principle\nthat uniformities continue, it has an absolutely uncontradicted series\nin its favour.\n\nBut is this principle really all that we assume? Do we not also assume\nthat behind the observed fact uniformity, there is a cause for it, a\ncause that does not appear on the surface of the observation, but\nmust be sought outside of its range? And do not the various degrees\nof confidence with which we expect a repetition of the coincidence,\ndepend upon the extent of our knowledge of the producing causes and\nthe mode of their operation? At bottom our belief in the continuance\nof the observed uniformities rests on a belief in the continuance of\nthe producing causes, and till we know what these are our belief has\nan inferior warrant: there is less reason for our confidence.\n\nTo go back to the illustrations with which we started. If we have met\na man every day for months at a certain place at a certain hour, it\nis reasonable to expect to meet him there to-morrow, even if\nour knowledge does not go beyond the observed facts of repeated\ncoincidence. But if we know also what brings him there, and that this\ncause continues, we have a stronger reason for our expectation. And so\nwith the case of poles at regular intervals on a road. If we know why\nthey are placed there, and the range of the purpose, we expect their\nrecurrence more confidently within the limits of that purpose. This\nfurther knowledge is a warrant for stronger confidence, because if\nwe know the producing causes, we are in a better position for knowing\nwhether anything is likely to defeat the coincidence. A uniformity is\nsaid to be explained when its cause is known, and an inference from an\nexplained uniformity is always more certain than an inference from\na uniformity that is merely empirical in the sense of being simply\nobserved.\n\nNow, the special work of Science is to explain, in the sense of\ndiscovering the causes at work beneath what lies open to observation.\nIn so doing it follows a certain method, and obeys certain conditions\nof satisfactory explanation. Its explanations are inferences from\nfacts, inasmuch as it is conformity with observed facts, with outward\nsigns of underlying causal nexus, that is the justification of them.\nBut they are not inferences from facts in the sense above described\nas empirical inference. In its explanations also Science postulates\na principle that may be called the Uniformity of Nature. But this\nprinciple is not merely that observed uniformities continue. It may\nbe expressed rather as an assumption that the underlying causes\nare uniform in their operation, that as they have acted beneath the\nrecorded experiences of mankind, so they have acted before and will\ncontinue to act.\n\n\nThe foregoing considerations indicate a plan for a roughly systematic\narrangement of the methods of Induction. Seeing that all inference\nfrom the data of experience presupposes causal connexion among the\ndata from which we infer, all efforts at establishing sound bases of\ninference, or rational ground for expectation fall, broadly speaking,\nunder two heads: (1) Methods of ascertaining causal connexion among\nphenomena as a matter of fact, that is, Methods of Observation; and\n(2) Methods of ascertaining what the causal connexion is, that is,\nMethods of Explanation.\n\nThese constitute the body of Inductive Logic. But there is a\npreliminary and a pendant. Without raising the question of causal\nconnexion, we are liable to certain errors in ascertaining in what\nsequence and with what circumstances events really occurred. These\ntendencies to error deserve to be pointed out by way of warning, and\nthis I shall attempt in a separate chapter on observation of facts\nof simple sequence. This is preliminary to the special methods of\nobserving causal sequence. Then, by way of pendant, I shall consider\ntwo modes of empirical inference from data in which the causal\nconnexion has not been ascertained or explained--Inference from\napproximate generalisations to particular cases, and Inference from\nAnalogy.\n\nMost of these methods in one form or another were included by Mill\nin his system of Inductive Logic, and the great merit of his work was\nthat he did include them, though at some sacrifice of consistency\nwith his introductory theory. With regard to the kind of empirical\ninference which that theory, following the lead of Whately, took as\nthe type of all inference, Logic has really little to say. It was this\nprobably that was in Mill's mind when he said that there is no Logic\nof Observation, ignoring the fact that the Experimental Methods are\nreally methods of observation, as well as the Methods of Eliminating\nChance by calculation of Probability. There is no method of observing\nuniformities except simply observing them. Nor indeed is there any\n\"method\" of inferring from them: we can only point out that in\nevery particular inference from them we assume or postulate their\ncontinuance generally. As regards their observation, we may point\nout further that a special fallacy is incident to it, the fallacy of\nignoring exceptions. If we are prepossessed or prejudiced in favour of\na uniformity, we are apt to observe only the favourable instances, and\nto be blind to cases where the supposed invariable coincidence does\nnot occur. Thus, as Bacon remarked among his _Idola_, we are apt to\nremember when our dreams come true, and to forget when they do\nnot. Suppose we take up the notion that a new moon on a Saturday is\ninvariably followed by twenty days of unsettled weather, one or two\nor a few cases in which this notably holds good are apt to be borne in\nmind, while cases where the weather is neither conspicuously good\nnor bad are apt to be overlooked. But when a warning has been given\nagainst this besetting fallacy, Logic has nothing further to say about\nempirical uniformities, except that we may infer from them with some\ndegree of reasonable probability, and that if we want ground for a\nmore certain inference we should try to explain them.\n\n\n\n\nCHAPTER II.\n\nASCERTAINMENT OF SIMPLE FACTS IN THEIR ORDER.--PERSONAL OBSERVATION.\n--HEARSAY EVIDENCE--METHOD OF TESTING TRADITIONAL EVIDENCE.\n\nAll beliefs as to simple matter of fact must rest ultimately on\nobservation. But, of course, we believe many things to have happened\nthat we have never seen. As Chaucer says:--\n\n  But God forbede but men shoulde 'lieve\n  Wel more thing than men han seen with eye.\n  Man shall not weenen everything a lie\n  But if himself it seeth or else doth.\n\nFor the great bulk of matters of fact that we believe we are\nnecessarily dependent on the observations of others. And if we are\nto apply scientific method to the ascertainment of this, we must know\nwhat errors we are liable to in our recollections of what we have\nourselves witnessed, and what errors are apt to arise in the tradition\nof what purports to be the evidence of eye-witnesses.\n\n\nI.--PERSONAL OBSERVATION.\n\nIt is hard to convince anybody that he cannot trust implicitly to his\nmemory of what he has himself seen. We are ready enough to believe\nthat others may be deceived: but not our own senses. Seeing is\nbelieving. It is well, however, that we should realise that all\nobservation is fallible, even our own.\n\nThree great besetting fallacies or tendencies to error may be\nspecified:--\n\n1. Liability to have the attention fastened on special incidents, and\nso diverted from other parts of the occurrence.\n\n2. Liability to confuse and transpose the sequence of events.\n\n3. Liability to substitute inference for fact.\n\nIt is upon the first of these weaknesses in man as an observing\nmachine that jugglers chiefly depend on working their marvels. Sleight\nof hand counts for much, but diverting the spectator's eyes for a good\ndeal more. That is why they have music played and patter incessantly\nas they operate. Their patter is not purposeless: it is calculated to\nturn our eyes away from the movements of their nimble hands.\n\nIt must be borne in mind that in any field of vision there are many\nobjects, and that in any rapid succession of incidents much more\npasses before the eyes than the memory can retain in its exact\norder. It is of course in moments of excitement and hurry, when our\nobservation is distracted, that we are most subject to fallacious\nillusions of memory. Unconsciously we make a coherent picture of what\nwe have seen, and very often it happens that the sequence of events\nis not what actually passed, but what we were prejudiced in favour of\nseeing. Hence the unlikelihood of finding exact agreement among the\nwitnesses of any exciting occurrence, a quarrel, a railway accident, a\ncollision at sea, the incidents of a battle.\n\n\"It commonly happens,\" says Mr. Kinglake,[1] \"that incidents occurring\nin a battle are told by the most truthful bystanders with differences\nmore or less wide.\" In the attack on the Great Redoubt in the Battle\nof the Alma, a young officer, Anstruther, rushed forward and planted\nthe colours of the Royal Welsh--but where? Some distinctly remembered\nseeing him dig the butt-end of the flagstaff into the parapet: others\nas distinctly remembered seeing him fall several paces before he\nreached it. Similarly with the incidents of the death of the Prince\nImperial near the Italezi Hills in the Zulu War. He was out as a\nvolunteer with a reconnoitring party. They had off-saddled at a kraal\nand were resting, when a band of Zulus crept up through the long\ngrass, and suddenly opened fire and made a rush forward. Our scouts\nat once took horse, as a reconnoitring party was bound to do, and\nscampered off, but the Prince was overtaken and killed. At the\nCourt-Martial which ensued, the five troopers gave the most\nconflicting accounts of particulars which an unskilled investigator\nwould think could not possibly have been mistaken by eye-witnesses of\nthe same event. One said that the Prince had given the order to mount\nbefore the Zulus fired: another that he gave the order directly after:\na third was positive that he never gave the order at all, but that it\nwas given after the surprise by the officer in command. One said that\nhe saw the Prince vault into the saddle as he gave the order: another\nthat his horse bolted as he laid hold of the saddle, and that he ran\nalongside trying to get up.\n\nThe evidence before any Court of Inquiry into an exciting occurrence\nis almost certain to reveal similar discrepancies. But what we find it\nhard to realise is that we ourselves can possibly be mistaken in what\nwe have a distinct and positive recollection of having seen. It once\nhappened to myself in a London street to see a drunken woman\nthrown under a cab by her husband. Two cabs were running along, a\nfour-wheeler and a hansom: the woman staggered almost under the first,\nand was thrown under the second. As it happened the case never got\nbeyond the police station to which the parties were conveyed after\nfierce opposition from some neighbours, who sympathised entirely with\nthe man. The woman herself, when her wounds were dressed, acknowledged\nthe justice of her punishment, and refused to charge her husband. I\nwas all the more willing to acquiesce in this because I found\nthat while I had the most distinct impression of having seen the\nfour-wheeler run over the woman's body, and should have been obliged\nto swear accordingly, there could be no doubt that it was really\nthe hansom that had done so. This was not only the evidence of the\nneighbours, which I suspected at the time of being a trick, but of the\ncabdriver, who had stopped at the moment to abide the results of the\naccident. I afterwards had the curiosity to ask an eminent police\nmagistrate, Sir John Bridge, whether this illusion of memory on my\npart--which I can only account for by supposing that my eyes had\nbeen fixed on the sufferer and that I had unconsciously referred her\ninjuries to the heavier vehicle--would have entirely discredited my\ntestimony in his Court. His answer was that it would not; that he was\nconstantly meeting with such errors, and that if he found a number of\nwitnesses of the same occurrence exactly agreed in every particular,\nhe would suspect that they had talked the matter over and agreed upon\nwhat they were to say. This was the opinion of an experienced judge,\na skilled critic of the defects of personal observation. An Old Bailey\ncounsel for the defence, who is equally acquainted with the weakness\nof human memory, takes advantage of the fact that it is not generally\nunderstood by a Jury, and makes the fallacious assumption that glaring\ndiscrepancies are irreconcilable with the good faith of the witnesses\nwho differ.[2]\n\n\nII.--TRADITION.--HEARSAY EVIDENCE.\n\nNext in value to personal observation, we must place the report, oral\nor written, of an eye-witness. This is the best evidence we can get\nif we have not witnessed an occurrence ourselves. Yet Courts of Law,\nwhich in consideration of the defects of personal observation require\nmore than one witness to establish the truth, exclude hearsay evidence\naltogether in certain cases, and not without reason.\n\nIn hearing a report we are in the position of observers of a series\nof significant sounds, and we are subject to all the fallacies of\nobservation already mentioned. In an aggravated degree, for words are\nharder to observe than visible things. Our attention is apt to be more\nlistless than in presence of the actual events. Our minds dwell upon\nparts of the narrative to the neglect of other parts, and in the\ncoherent story or description that we retain in our memories,\nsequences are apt to be altered and missing links supplied in\naccordance with what we were predisposed to hear. Thus hearsay\nevidence is subject to all the imperfections of the original observer,\nin addition to the still more insidious imperfections of the second\nobserver.\n\nHow quickly in the course of a few such transmissions hearsay loses\nall evidentiary value is simply illustrated by the game known as\nRussian Scandal. One of a company, A, writes down a short tale or\nsketch, and reads it to B. B repeats it to C, C to D, and so on. When\nit has thus gone the round of the company, the last hearer writes\ndown his version, and it is compared with the original. With every\nwillingness to play fair, the changes are generally considerable and\nsignificant.\n\nSometimes it is possible to compare an oral tradition with a\ncontemporary written record. In one of Mr. Hayward's Essays--\"The\nPearls and Mock Pearls of History\"--there are some examples of this\ndisenchanting process. There is, for instance, a pretty story of an\nexchange of courtesies between the leaders of the French and English\nGuards at the battle of Fontenoy. The tradition runs that Lord Charles\nHay stepped in front of his men and invited the French Guards to fire,\nto which M. d'Auteroche with no less chivalry responded: \"Monsieur, we\nnever fire first; you fire\". What really passed we learn from a\nletter from Lord Charles Hay to his mother, which happens to have\nbeen preserved. \"I advanced before our regiment, and drank to the\nFrenchmen, and told them we were the English Guards, and hoped they\nwould stand till we came, and not swim the Scheldt as they did the\nMaine at Dettingen.\" Tradition has changed this lively piece of\nbuffoonery into an act of stately and romantic courtesy. The change\nwas probably made quite unconsciously by some tenth or hundredth\ntransmitter, who remembered only part of the story, and dressed the\nremainder to suit his own fancy.\n\nThe question has been raised, For how long can oral tradition be\ntrusted? Newton was of opinion that it might be trusted for eighty\nyears after the event. Others have named forty years. But if this\nmeans that we may believe a story that we find in circulation forty\nyears after the alleged events, it is wildly extravagant. It does\ninjustice to the Mythop[oe]ic Faculty of man. The period of time that\nsuffices for the creation of a full-blown myth, must be measured\nby hours rather than by years. I will give an instance from my own\nobservation, if that has not been entirely discredited by my previous\nconfessions. The bazaars of the East are generally supposed to be\nthe peculiar home of myth, hotbeds in which myths grow with the most\namazing speed, but the locality of my myth is Aberdeen. In the summer\nof 1887 our town set up in one of its steeples a very fine carillon\nof Belgian bells. There was much public excitement over the event: the\ndescriptions of enthusiastic promoters had prepared us to hear silvery\nmusic floating all over the town and filling the whole air. On the day\nfixed for the inauguration, four hours after the time announced for\nthe first ceremonial peal, not having heard the bells, I was in a shop\nand asked if anything had happened to put off the ceremony. \"Yes,\"\nI was told; \"there had been an accident; they had not been properly\nhung, and when the wife of the Lord Provost had taken hold of a string\nto give the first pull, the whole machinery had come down.\" As a\nmatter of fact all that had happened was that the sound of the bells\nwas faint, barely audible a hundred yards from the belfry, and not at\nall like what had been expected. There were hundreds of people in the\nstreets, and the myth had originated somehow among those who had\nnot heard what they went out to hear. The shop where it was repeated\ncircumstantially to me was in the main street, not more than a quarter\nof a mile from where the carillon had been played in the hearing of\na large but disappointed crowd. I could not help reflecting that if I\nhad been a mediaeval chronicler, I should have gone home and recorded\nthe story, which continued to circulate for some days in spite of\nthe newspapers: and two hundred years hence no historian would have\nventured to challenge the truth of the contemporary evidence.\n\n\nIII.--METHOD OF TESTING TRADITIONAL EVIDENCE.\n\nIt is obvious that the tests applied to descriptive testimony in\nCourts of Law cannot be applied to the assertions of History. It is\na supreme canon of historical evidence that only the statements of\ncontemporaries can be admitted: but most even of their statements must\nrest on hearsay, and even when the historian professes to have been an\neye-witness, the range of his observation is necessarily limited, and\nhe cannot be put into the witness-box and cross-examined. Is there\nthen no way of ascertaining historical fact? Must we reject history as\naltogether unworthy of credit?\n\nThe rational conclusion only is that very few facts can be established\nby descriptive testimony such as would satisfy a Court of Law. Those\nwho look for such ascertainment are on a wrong track, and are doomed\nto disappointment. It is told of Sir Walter Raleigh that when he was\nwriting his History of the World, he heard from his prison in the\nTower a quarrel outside, tried to find out the rights and the wrongs\nand the course of it, and failing to satisfy himself after careful\ninquiry, asked in despair how he could pretend to write the history\nof the world when he could not find out the truth about what occurred\nunder his own windows. But this was really to set up an impossible\nstandard of historical evidence.\n\nThe method of testing historical evidence follows rather the lines\nof the Newtonian method of Explanation, which we shall afterwards\ndescribe. We must treat any historical record as being itself in the\nfirst place a fact to be explained. The statement at least is extant:\nour first question is, What is the most rational way of accounting\nfor it? Can it be accounted for most probably by supposing the event\nstated to have really occurred with all the circumstances alleged? Or\nis it a more probable hypothesis that it was the result of an illusion\nof memory on the part of the original observer, if it professes to\nbe the record of an eye-witness, or on the part of some intermediate\ntransmitter, if it is the record of a tradition? To qualify ourselves\nto answer the latter kind of question with reasonable probability\nwe must acquaint ourselves with the various tendencies to error in\npersonal observation and in tradition, and examine how far any of\nthem are likely to have operated in the given case. We must study the\noperation of these tendencies within our experience, and apply the\nknowledge thus gained. We must learn from actual observation of facts\nwhat the Mythop[oe]ic Faculty is capable of in the way of creation\nand transmutation, and what feats are beyond its powers, and then\ndetermine with as near a probability as we can how far it has been\nactive in the particular case before us.\n\n    [Footnote 1: _The Invasion of the Crimea_, iii. 124]\n\n    [Footnote 2: The truth is, that we see much less than is\n    commonly supposed. Not every impression is attended to that\n    is made on the retina, and unless we do attend we cannot,\n    properly speaking, be said to see. Walking across to college\n    one day, I was startled by seeing on the face of a clock in\n    my way that it was ten minutes to twelve, whereas I generally\n    passed that spot about twenty minutes to twelve. I hurried\n    on, fearing to be late, and on my arrival found myself in very\n    good time. On my way back, passing the clock again, I looked\n    up to see how much it was fast. It marked ten minutes to\n    eight. It had stopped at that time. When I passed before I\n    had really seen only the minute hand. The whole dial must have\n    been on my retina, but I had looked at or attended to only\n    what I was in doubt about, taking the hour for granted. I am\n    bound to add that my business friends hint that it is only\n    absorbed students that are capable of such mistakes, and that\n    alert men of business are more circumspect. That can only be\n    because they are more alive to the danger of error.]\n\n\n\n\nCHAPTER III.\n\nASCERTAINMENT OF FACTS OF CAUSATION.\n\n\nI.--_POST HOC ERGO PROPTER HOC_.\n\nOne of the chief contributions of the Old Logic to Inductive Method\nwas a name for a whole important class of misobservations. The fallacy\nentitled _Post Hoc ergo Propter Hoc_--\"After, therefore, Because\nof\"--consisted in alleging mere sequence as a proof of consequence or\ncausal sequence. The sophist appeals to experience, to observed facts:\nthe sequence which he alleges has been observed. But the appeal is\nfallacious: the observation on which he relies amounts only to this,\nthat the one event has followed upon the other. This much must be\nobservable in all cases of causal sequence, but it is not enough for\nproof. _Post hoc ergo propter hoc_ may be taken as a generic name for\nimperfect proof of causation from observed facts of succession.\n\nThe standard example of the fallacy is the old Kentish peasant's\nargument that Tenterden Steeple was the cause of Goodwin Sands. Sir\nThomas More (as Latimer tells the story in one of his Sermons to\nridicule incautious inference) had been sent down into Kent as a\ncommissioner to inquire into the cause of the silting up of Sandwich\nHaven. Among those who came to his court was the oldest inhabitant,\nand thinking that he from his great age must at least have seen more\nthan anybody else, More asked him what he had to say as to the cause\nof the sands. \"Forsooth, sir,\" was the greybeard's answer, \"I am an\nold man: I think that Tenterden Steeple is the cause of Goodwin Sands.\nFor I am an old man, and I may remember the building of Tenterden\nSteeple, and I may remember when there was no steeple at all there.\nAnd before that Tenterden Steeple was in building, there was no\nmanner of speaking of any flats or sands that stopped the haven;\nand, therefore, I think that Tenterden Steeple is the cause of the\ndestroying and decaying of Sandwich Haven.\"\n\nThis must be taken as Latimer meant it to be, as a ridiculous example\nof a purely imbecile argument from observation, but the appeal to\nexperience may have more show of reason and yet be equally fallacious.\nThe believers in Kenelm Digby's \"Ointment of Honour\" appealed to\nexperience in support of its efficacy. The treatment was to apply the\nointment, not to the wound, but to the sword that had inflicted it, to\ndress this carefully at regular intervals, and, meantime, having bound\nup the wound, to leave it alone for seven days. It was observed that\nmany cures followed upon this treatment. But those who inferred that\nthe cure was due to the bandaging of the sword, failed to observe\nthat there was another circumstance that might have been instrumental,\nnamely, the exclusion of the air and the leaving of the wound\nundisturbed while the natural healing processes went on. And it\nwas found upon further observation that binding up the wound alone\nanswered the purpose equally well whether the sword was dressed or\nnot.\n\nIn cases where _post hoc_ is mistaken for _propter hoc_, simple\nsequence for causal sequence, there is commonly some bias of prejudice\nor custom which fixes observation on some one antecedent and diverts\nattention from other circumstances and from what may be observed to\nfollow in other cases. In the minds of Digby and his followers there\nwas probably a veneration for the sword as the weapon of honour, and a\nsuperstitious belief in some secret sympathy between the sword and its\nowner. So when the practice of poisoning was common, and suspicion was\nflurried by panic fear, observation was often at fault. Pope Clement\nVIII. was said to have been killed by the fumes of a poisoned candle\nwhich was placed in his bedroom. Undoubtedly candles were there, but\nthose who attributed the Pope's death to them took no notice of the\nfact that a brazier of burning charcoal was at the same time in the\napartment with no sufficient outlet for its fumes. Prince Eugene\nis said to have received a poisoned letter, which he suspected and\nimmediately threw from him. To ascertain whether his suspicions were\nwell founded the letter was administered to a dog, which, to make\nassurance doubly sure, was fortified by an antidote. The dog died, but\nno inquiry seems to have been made into the character of the antidote.\n\nHotspur's retort to Glendower showed a sound sense of the true value\nto be attached to mere priority.\n\n  _Glendower_.                 At my nativity\n          The front of heaven was full of fiery shapes,\n          Of burning cressets: and at my birth\n          The frame and huge foundation of the earth\n          Shaked like a coward.\n\n  _Hotspur_. Why so it would have done at the same season, if\n  your mother's cat had but kittened, though yourself had never\n  been born.\n\n  1 Hen. IV., 3, 1, 13.\n\nWe all admit at once that the retort was just. What principle of sound\nconclusion was involved in it? It is the business of Inductive Logic\nto make such principles explicit.\n\nTaking _Post Hoc ergo Propter Hoc_ as a generic name for fallacious\narguments of causation based on observed facts, for the fallacious\nproof of causation from experience, the question for Logic is, What\nmore than mere _sequence_ is required to prove _consequence?_ When do\nobservations of _Post Hoc_ warrant the conclusion _Propter Hoc?_\n\n\nII.--MEANING OF \"CAUSE\".--METHODS OF OBSERVATION--MILL'S EXPERIMENTAL\nMETHODS.\n\nThe methods formulated by Mill under the name of Experimental Methods\nare methods actually practised by men of science with satisfactory\nresults, and are perfectly sound in principle. They were, indeed, in\nsubstance, taken by him from the practice of the scientific laboratory\nand study as generalised by Herschel. In effect what Mill did was to\nrestate them and fit them into a system. But the controversies into\nwhich he was tempted in so doing have somewhat obscured their exact\nfunction in scientific inquiry. Hostile critics, finding that they did\nnot serve the ends that he seemed to claim for them, have jumped to\nthe conclusion that they are altogether illusory and serve no purpose\nat all.\n\nFirst, we must dismiss the notion, encouraged by Mill's general theory\nof Inference, that the Experimental Methods have anything special to\ndo with the observation and inferential extension of uniformities such\nas that death is common to all organised beings. One of the Methods,\nas we shall see, that named by Mill the Method of Agreement, does\nincidentally and collaterally establish empirical laws in the course\nof its observations, and this probably accounts for the prominence\ngiven to it in Mill's system. But this is not its end and aim, and\nthe leading Method, that named by him the Method of Difference,\nestablishes as fact only a particular case of causal coincidence.\nIt is with the proof of theories of causation that the Experimental\nMethods are concerned: they are methods of observing with a view to\nsuch proof.[1]\n\nThe next point to be made clear is that the facts of causation with\nwhich the Methods are concerned are observable facts, relations among\nphenomena, but that the causal relations or conditions of which they\nare the proof are not phenomena, in the meaning of being manifest\nto the senses, but rather noumena, inasmuch as they are reached by\nreasoning from what is manifest.\n\nTake, for example, what is known as the _quaquaversus_ principle in\nHydrostatics, that pressure upon a liquid is propagated equally in\nall directions. We cannot observe this extension of pressure among the\nliquid particles directly. It cannot be traced among the particles\nby any of our senses. But we can assume that it is so, consider what\nought to be visible if it is so, and then observe whether the visible\nfacts are in accordance with the hypothesis. A box can be made, filled\nwith water, and so fitted with pistons on top and bottom and on each\nof its four sides that they will indicate the amount of pressure on\nthem from within. Let pressure then be applied through a hole in\nthe top, and the pistons show that it has been communicated to them\nequally. The application of the pressure and the yielding of the\npistons are observable facts, facts in causal sequence: what happens\namong the particles of the liquid is not observed but reasonably\nconjectured, is not _phenomenal_ but _noumenal_.\n\nThis distinction, necessary to an understanding of the scope of the\nMethods, was somewhat obscured by Mill in his preliminary\ndiscussion of the meaning of \"cause\". Very rightly, though somewhat\ninconsistently with his first theory of Induction, he insists that\n\"the notion of Cause being the root of the whole theory of Induction,\nit is indispensable that this idea should at the very outset of our\ninquiry be, with the utmost practicable degree of precision, fixed\nand determined\". But in this determination, not content with simply\nrecognising that it is with phenomena that the Experimental Methods\nprimarily deal, it being indeed only phenomena that can be the\nsubjects of experimental management and observation, he starts by\ndeclaring that science has not to do with any causes except such as\nare phenomenal--\"when I speak of the cause of any phenomenon, I do not\nmean a cause which is not itself a phenomenon\"--and goes on to define\nas the only correct meaning of cause \"the sum total of conditions,\"\nincluding among them conditions which are not phenomenal, in the sense\nof being directly open to observation.\n\nWhen Mill protested that he had regard only to phenomenal causes, he\nspoke as the partisan of a philosophical tradition. It would have been\nwell if he had acted upon his own remark that the proper understanding\nof the scientific method of investigating cause is independent of\nmetaphysical analysis of what cause means. Curiously enough, this\nremark is the preface to an analysis of cause which has but slight\nrelevance to science, and is really the continuation of a dispute\nbegun by Hume. This is the key to his use of the word phenomenon: it\nmust be interpreted with reference to this: when he spoke of causes\nas phenomenal, he opposed the word to \"occult\" in some supposed\nmetaphysical sense.[2] And this irrelevant discussion, into the\nvortex of which he allowed himself to be carried, obscured the fact,\nelsewhere fully recognised by Mill himself, that science does attempt\nto get beyond phenomena at ultimate laws which are not themselves\nphenomena though they bind phenomena together. The \"colligation\"\nof the facts, to use Whewell's phrase, is not a phenomenon, but a\nnoumenon.\n\nThe truth is that a very simple analysis of \"cause\" is sufficient for\nthe purposes of scientific inquiry. It is enough to make sure that\ncausal sequence or consequence shall not be confounded with simple\nsequence. Causal sequence is simple sequence and something more, that\nsomething more being expressed by calling it causal. What we call a\ncause is not merely antecedent or prior in time to what we call its\neffect: it is so related to the effect that if it or an equivalent\nevent had not happened the effect would not have happened. Anything\nin the absence of which a phenomenon would not have come to pass as it\ndid come to pass is a cause in the ordinary sense. We may describe it\nas an indispensable antecedent, with this reservation (which will\nbe more fully understood afterwards), that if we speak of a\ngeneral effect, such as death, the antecedents must be taken with\ncorresponding generality.\n\nIt is misleading to suggest, as Mill does, by defining cause as \"the\nsum total of conditions\"--a definition given to back up his conception\nof cause as phenomenal--that science uses the word cause in a\ndifferent meaning from that of ordinary speech. It is quite true\nthat \"the cause, philosophically speaking, is the sum total of the\nconditions, positive and negative, taken together: the whole of\nthe contingencies of every description, which being realised,\nthe consequent invariably follows\". But this does not imply any\ndiscrepancy between the scientific or philosophical meaning and the\nordinary meaning. It is only another way of saying that the business\nof science or philosophy is to furnish a complete explanation of an\nevent, an account of all its indispensable antecedents. The plain\nman would not refuse the name of cause to anything that science or\nphilosophy could prove to be an indispensable antecedent, but his\ninterest in explanation is more limited. It is confined to what he\nwants to know for the purpose he has in hand. Nor could the man of\nscience consistently refuse the name of cause to what the plain man\napplies it to, if it really was something in consequence of which the\nevent took place. Only his interest in explanation is different. The\nindispensable antecedents that he wants to know may not be the same.\nScience or philosophy applies itself to the satisfaction of a wider\ncuriosity: it wants to know all the causes, the whole why, the sum\ntotal of conditions. To that end the various departments of science\ninterest themselves in various species of conditions. But all\nunderstand the word cause in the ordinary sense.\n\nWe must not conclude from accidental differences in explanation or\nstatement of cause, dependent on the purpose in view, that the word\nCause is used in different senses. In answering a question as to\nthe cause of anything, we limit ourselves to what we suppose our\ninterrogator to be ignorant of and desirous of knowing. If asked why\nthe bells are ringing, we mention a royal marriage, or a victory, or a\nchurch meeting, or a factory dinner hour, or whatever the occasion\nmay be. We do not consider it necessary to mention that the bells\nare struck by a clapper. Our hearer understands this without our\nmentioning it. Nor do we consider it necessary to mention the acoustic\ncondition, that the vibration of the bells is communicated to our ears\nthrough the air, or the physiological condition, that the vibrations\nin the drums of our ears are conveyed by a certain mechanism of bone\nand tissue to the nerves. Our hearer may not care to know this,\nthough quite prepared to admit that these conditions are indispensable\nantecedents. Similarly, a physiographer, in stating the cause of the\nperiodical inundation of the Nile, would consider it enough to mention\nthe melting of snow on the mountains in the interior of Africa,\nwithout saying anything of such conditions as the laws of gravity\nor the laws of liquefaction by heat, though he knows that these\nconditions are also indispensable. Death is explained by the doctor\nwhen referred to a gunshot wound, or a poison, or a virulent disease.\nThe Pathologist may inquire further, and the Moral Philosopher further\nstill. But all inquiries into indispensable conditions are inquiries\ninto cause. And all alike have to be on their guard against mistaking\nsimple sequence for consequence.\n\nTo speak of the sum total of conditions, as the Cause in a\ndistinctively scientific sense, is misleading in another direction. It\nrather encourages the idea that science investigates conditions in\nthe lump, merely observing the visible relations between sets of\nantecedents and their consequents. Now this is the very thing\nthat science must avoid in order to make progress. It analyses the\nantecedent situation, tries to separate the various coefficients, and\nfinds out what they are capable of singly. It must recognise that\nsome of the antecedents of which it is in search are not open to\nobservation. It is these, indeed, for the most part that constitute\nthe special subject-matter of the sciences in Molar as well as in\nMolecular Physics. For practical every-day purposes, it is chiefly\nthe visible succession of phenomena that concerns us, and we are\ninterested in the latent conditions only in as far as they provide\nsafer ground for inference regarding such visible succession. But to\nreach the latent conditions is the main work of science.\n\nIt is, however, only through observation of what is open to the senses\nthat science can reach the underlying conditions, and, therefore,\nto understand its methods we must consider generally what is open to\nobservation in causal succession. What can be observed when phenomena\nfollow one another as cause and effect, that is, when the one happens\nin consequence of the happening of the other? In Hume's theory,\nwhich Mill formally adopted with a modification,[3] there is nothing\nobservable but the constancy or invariability of the connexion. When\nwe say that Fire burns, there is nothing to be observed except that a\ncertain sensation invariably follows upon close proximity to fire. But\nthis holds good only if our observation is arbitrarily limited to the\nfacts enounced in the expression. If this theory were sound, science\nwould be confined to the observation of empirical laws. But that there\nis something wrong with it becomes apparent when we reflect that it\nhas been ascertained beyond doubt that in many observed changes, and\npresumably in all, there is a transference of energy from one form to\nanother. The paralogism really lies in the assumption from which\nHume deduced his theory, namely, that every idea is a copy of some\nimpression. As a matter of fact, we have ideas that are not copies\nof any one impression, but a binding together, colligation, or\nintellection of several impressions. Psychological analysis shows us\nthat even when we say that things exist with certain qualities, we are\nexpressing not single impressions or mental phenomena, but supposed\ncauses and conditions of such, _noumena_ in short, which connect our\nrecollections of many separate impressions and expectations of more.\n\nThe Experimental Methods proceed on the assumption that there is other\noutward and visible evidence of causal connexion than invariability of\nsequence. In the leading Method it is assumed that when events may be\nobserved to follow one another in a certain way, they are in causal\nsequence. If we can make sure that an antecedent change is the only\nchange that has occurred in an antecedent situation, we have proof\npositive that any immediately subsequent change in the situation is a\nconsequent, that the successive changes are in causal sequence. Thus\nwhen Pascal's barometer was carried to the top of Puy le Dome, and\nthe mercury in it fell, the experimenters argued that the fall of the\nmercury was causally connected with the change of elevation, all the\nother circumstances remaining the same. This is the foundation of the\nso-called Method of Difference. To determine that the latent condition\nwas a difference in the weight of the atmosphere, needed other\nobservations, calculations and inferences; but if it could be shown\nthat the elevation was the only antecedent changed in a single\ninstance, causal connexion was established between this and the\nphenomenon of the fall of the barometer.\n\nIt is obvious that in coming to this conclusion we assume what cannot\nbe demonstrated but must simply be taken as a working principle to be\nconfirmed by its accordance with experience, that nothing comes into\nbeing without some change in the antecedent circumstances. This is the\nassumption known as the Law of Causation--_ex nihilo nihil fit_.\n\nAgain, certain observable facts are taken as evidence that there is\nno causal connexion. On the assumption that any antecedent in whose\nabsence a phenomenon takes place is not causally connected with it,\nwe set aside or eliminate various antecedents as fortuitous or\nnon-causal. This negative principle, as we shall see, is the\nfoundation of what Mill called the Method of Agreement.\n\nBe it remarked, once for all, that before coming to a conclusion on\nthe Positive Method or Method of Difference, we may often have to make\nmany observations on the Negative Method. Thus Pascal's experimenters,\nbefore concluding that the change of altitude was the only influential\nchange, tried the barometer in exposed positions and in sheltered,\nwhen the wind blew and when it was calm, in rain and in fog, in order\nto prove that these circumstances were indifferent. We must expound\nand illustrate the methods separately, but every method known to\nscience may have in practice to be employed in arriving at a single\nconclusion.\n\n    [Footnote 1: This is implied, as I have already remarked, in\n    the word Experimental. An experiment is a proof or trial: of\n    what? Of a theory, a conjecture.]\n\n    [Footnote 2: If we remember, as becomes apparent on exact\n    psychological analysis, that things and their qualities are as\n    much _noumena_ and not, strictly speaking, _phenomena_ as the\n    attraction of gravity or the quaquaversus principle in liquid\n    pressure, the prejudice against occultism is mitigated.]\n\n    [Footnote 3: The modification was that causation is not only\n    \"invariable\" but also \"unconditional\" sequence. This addition\n    of unconditionality as part of the meaning of cause, after\n    defining cause as the sum total of the conditions, is very\n    much like arguing in a circle. After all, the only point\n    recognised in the theory as observable is the invariability of\n    the sequence. But this is less important than the fact that\n    in his canons of the Experimental Methods Mill recognised that\n    more is observable.]\n\n\n\n\nCHAPTER IV.\n\nMETHODS OF OBSERVATION.--SINGLE DIFFERENCE.\n\n\nI.--THE PRINCIPLE OF SINGLE DIFFERENCE.--MILL'S \"CANON\".\n\nOn what principle do we decide, in watching a succession of phenomena,\nthat they are connected as cause and effect, that one happened\nin consequence of the happening of another? It may be worded as\nfollows:--\n\n    _When the addition of an agent is followed by the appearance\n    or its subtraction by the disappearance of a certain effect,\n    no other influential circumstance having been added or\n    subtracted at the same time or in the meantime, and no change\n    having occurred among the original circumstances, that agent\n    is a cause of the effect._\n\nOn this principle we would justify our belief in the causal properties\nof common things--that fire burns, that food appeases hunger, that\nwater quenches thirst, that a spark ignites gunpowder, that taking\noff a tight shoe relieves a pinched foot. We have observed the\neffect following when there was no other change in the antecedent\ncircumstances, when the circumstance to which we refer it was simply\nadded to or subtracted from the prior situation.\n\nSuppose we doubt whether a given agent is or is not capable of\nproducing a certain effect in certain circumstances, how do we put it\nto the proof? We add it singly or subtract it singly, taking care that\neverything else remains as before, and watch the result. If we wish\nto know whether a spoonful of sugar can sweeten a cup of tea, we taste\nthe tea without the sugar, then add the sugar, and taste again. The\nisolated introduction of the agent is the proof, the experiment. If we\nwish to know whether a pain in the foot is due to a tight lacing,\nwe relax the lacing and make no other change: if the pain then\ndisappears, we refer it to the lacing as the cause. The proof is the\ndisappearance of the pain on the subtraction of the single antecedent.\n\nThe principle on which we decide that there is causal connexion is\nthe same whether we make the experimental changes ourselves or merely\nwatch them as they occur--the only course open to us with the great\nforces of nature which are beyond the power of human manipulation. In\nany case we have proof of causation when we can make sure that there\nwas only one difference in the antecedent circumstances corresponding\nto the difference of result.\n\nMill's statement of this principle, which he calls the Canon of the\nMethod of Difference, is somewhat more abstract, but the proof relied\nupon is substantially the same.\n\n    _If an instance in which the phenomenon under investigation\n    occurs, and an instance in which it does not occur, have every\n    circumstance in common save one, that one occurring only in\n    the former, the circumstance in which alone the two instances\n    differ is [the effect, or][1] the cause, or an indispensable\n    part of the cause, of the phenomenon._\n\nMill's statement has the merit of exactness, but besides being too\nabstract to be easy of application, the canon is apt to mislead in one\nrespect. The wording of it suggests that the two instances required\nmust be two separate sets of circumstances, such as may be put side\nby side and compared, one exhibiting the phenomenon and the other\nnot. Now in practice it is commonly one set of circumstances that we\nobserve with a special circumstance introduced or withdrawn: the two\ninstances, the data of observation, are furnished by the scene before\nand the scene after the experimental interference. In the case, for\nexample, of a man shot in the head and falling dead, death being the\nphenomenon in question, the instance where it does not occur is the\nman's condition before he received the wound, and the instance where\nit does occur is his condition after, the single circumstance of\ndifference being the wound, a difference produced by the addition or\nintroduction of a new circumstance. Again, take the common coin and\nfeather experiment, contrived to show that the resistance of the air\nis the cause of the feather's falling to the ground more slowly than\nthe coin. The phenomenon under investigation is the retardation of the\nfeather. When the two are dropped simultaneously in the receiver of\nan air-pump, the air being left in, the feather flutters to the ground\nafter the coin. This is the instance where the phenomenon occurs. Then\nthe air is pumped out of the receiver, and the coin and the feather\nbeing dropped at the same instant reach the ground together. This\nis the instance where the phenomenon does not occur. The single\ncircumstances of difference is the presence of air in the former\ninstance, a difference produced by the subtraction of a circumstance.\n\nMill's Canon is framed so as to suit equally whether the significant\ndifference is produced by addition to or subtraction from an existing\nsum of circumstances. But that is misleading in so far as it suggests\nthat the two instances must be separate sets of circumstances,\nis shown by the fact that it misled himself when he spoke of the\napplication of the method in social investigations, such as the effect\nof Protection on national wealth. \"In order,\" he says, \"to apply to\nthe case the most perfect of the methods of experimental inquiry, the\nMethod of Difference, we require to find two instances which tally in\nevery particular except the one which is the subject of inquiry.\nWe must have two nations alike in all natural advantages and\ndisadvantages; resembling each other in every quality physical and\nmoral; habits, usages, laws, and institutions, and differing only in\nthe circumstance that the one has a prohibitory tariff and the other\nhas not.\" It being impossible ever to find two such instances, he\nconcluded that the Method of Difference could not be applied in\nsocial inquiries. But really it is not necessary in order to have two\ninstances that we should have two different nations: the same nation\nbefore and after a new law or institution fulfils that requirement.\nThe real difficulty, as we shall see, is to satisfy the paramount\ncondition that the two instances shall differ in a single\ncircumstance. Every new enactment would be an experiment after the\nMethod of Difference, if all circumstances but it remained the same\ntill its results appeared. It is because this seldom or never occurs\nthat decisive observation is difficult or impossible, and the simple\nmethod of difference has to be supplemented by other means.\n\nTo introduce or remove a circumstance singly is the typical\napplication of the principle; but it may be employed also to compare\nthe effects of different agents, each added alone to exactly similar\ncircumstances. A simple example is seen in Mr. Jamieson's agricultural\nexperiments to determine the effects of different manures, such as\ncoprolite and superphosphate, on the growth of crops. Care is taken\nto have all the antecedent circumstances as exactly alike as possible,\nexcept as regards the agency whose effects are to be observed. A field\nis chosen of uniform soil and even exposure and divided into plots:\nit is equally drained so as to have the same degree of moisture\nthroughout; the seed is carefully selected for the whole sowing.\nBetween the sowing and the maturing of the crop all parts of the\nfield are open to the same weather. Each plot may thus be regarded as\npractically composing the same set of conditions, and any difference\nin the product may with reasonable probability be ascribed to the\nsingle difference in the antecedents, the manures which it is desired\nto compare.\n\n\nII.--APPLICATION OF THE PRINCIPLE.\n\nThe principle of referring a phenomenon to the only immediately\npreceding change in antecedent circumstances that could possibly have\naffected it, is so simple and so often employed by everybody every\nday, that at first we do not see how there can be any difficulty\nabout it or any possibility of error. And once we understand how many\ndifficulties there are in reaching exact knowledge even on this simple\nprinciple, and what care has to be taken, we are apt to overrate its\nvalue, and to imagine that it carries us further than it really does.\nThe scientific expert must know how to apply this principle, and a\nsingle application of it with the proper precautions may take him\ndays or weeks, and yet all that can be made good by it may carry but a\nlittle way towards the knowledge of which he is in search.\n\nWhen the circumstances are simple and the effect follows at once, as\nwhen hot water scalds, or a blow with a stick breaks a pane of glass,\nthere can be no doubt of the causal connexion so far, though plenty\nof room for further inquiry into the why. But the mere succession of\nphenomena may be obscure. We may introduce more than one agent\nwithout knowing it, and if some time elapses between the experimental\ninterference and the appearance of the effect, other agents may come\nin without our knowledge.\n\nWe must know exactly what it is that we introduce and all the\ncircumstances into which we introduce it. We are apt to ignore the\npresence of antecedents that are really influential in the result. A\nman heated by work in the harvest field hastily swallows a glass of\nwater, and drops down dead. There is no doubt that the drinking of the\nwater was a causal antecedent, but the influential circumstance\nmay not have been the quantity or the quality of the liquid but its\ntemperature, and this was introduced into the situation as well as a\ncertain amount of the liquid components. In making tea we put in so\nmuch tea and so much boiling water. But the temperature of the pot\nis also an influential circumstance in the resulting infusion. So in\nchemical experiments, where one might expect the result to depend only\nupon the proportions of the ingredients, it is found that the quantity\nis also influential, the degree of heat evolved entering as a\nfactor into the result. Before we can apply the principle of single\ndifference, we must make sure that there is really only a single\ndifference between the instances that we bring into comparison.\n\nThe air-pump was invented shortly before the foundation of the Royal\nSociety, and its members made many experiments with this new means\nof isolating an agent and thus discovering its potentialities.\nFor example, live animals were put into the receiver, and the air\nexhausted, with the result that they quickly died. The absence of the\nair being the sole difference, it was thus proved to be indispensable\nto life. But air is a composite agent, and when means were contrived\nof separating its components, the effects of oxygen alone and of\ncarbonic acid alone were experimentally determined.\n\nA good example of the difficulty of excluding agencies other than\nthose we are observing, of making sure that none such intrude,\nis found in the experiments that have been made in connexion with\nspontaneous generation. The question to be decided is whether life\never comes into existence without the antecedent presence of living\ngerms. And the method of determining this is to exclude all germs\nrigorously from a compound of inorganic matter, and observe whether\nlife ever appears. If we could make sure in any one case that no germs\nwere antecedently present, we should have proved that in that case at\nleast life was spontaneously generated.\n\nThe difficulty here arises from the subtlety of the agent under\nobservation. The notion that maggots are spontaneously generated in\nputrid meat, was comparatively easy to explode. It was found that when\nflies were excluded by fine wire-gauze, the maggots did not appear.\nBut in the case of microscopic organisms proof is not so easy. The\ngerms are invisible, and it is difficult to make certain of their\nexclusion. A French experimenter, Pouchet, thought he had obtained\nindubitable cases of spontaneous generation. He took infusions of\nvegetable matter, boiled them to a pitch sufficient to destroy all\ngerms of life, and hermetically sealed up the liquid in glass\nflasks. After an interval, micro-organisms appeared. Doubts as to the\nconclusion that they had been spontaneously generated turned upon two\nquestions: whether all germs in the liquid had been destroyed by the\npreliminary boiling, and whether germs could have found access in the\ncourse of the interval before life appeared. At a certain stage in\nPouchet's process he had occasion to dip the mouths of the flasks\nin mercury. It occurred to Pasteur in repeating the experiments that\ngerms might have found their way in from the atmospheric dust on the\nsurface of this mercury. That this was so was rendered probable by his\nfinding that when he carefully cleansed the surface of the mercury no\nlife appeared afterwards in his flasks.\n\nThe application of the principle in human affairs is rendered\nuncertain by the immense complication of the phenomena, the difficulty\nof experiment, and the special liability of our judgments to\nprejudice. That men and communities of men are influenced by\ncircumstances is not to be denied, and the influence of circumstances,\nif it is to be traced at all, must be traced through observed facts.\nObservation of the succession of phenomena must be part at least of\nany method of tracing cause and effect. We must watch what follows\nupon the addition of new agencies to a previously existing sum. But\nwe can seldom or never get a decisive observation from one pair of\ninstances, a clear case of difference of result preceded by a single\ndifference in the antecedents. The simple Method of Experimental\nAddition or Subtraction is practically inapplicable. We can do nothing\nwith a man analogous to putting him into a hermetically sealed retort.\nAny man or any community that is the subject of our observations\nmust be under manifold influences. Each of them probably works some\nfraction of the total change observable, but how are they to be\ndisentangled? Consider, for example, how impossible it would be\nto prove in an individual case, on the strict principle of Single\nDifference, that Evil communications corrupt good manners. Moral\ndeterioration may be observed following upon the introduction of\nan evil companion, but how can we make sure that no other degrading\ninfluence has operated, and that no original depravity has developed\nitself in the interval? Yet such propositions of moral causation can\nbe proved from experience with reasonable probability. Only it must\nbe by more extended observations than the strict Method of Difference\ntakes into account. The method is to observe repeated coincidences\nbetween evil companionship and moral deterioration, and to account for\nthis in accordance with still wider observations of the interaction of\nhuman personalities.\n\nFor equally obvious reasons the simple Method of Difference is\ninapplicable to tracing cause and effect in communities. Every new law\nor repeal of an old law is the introduction of a new agency, but the\neffects of it are intermixed with the effects of other agencies that\noperate at the same time. Thus Professor Cairnes remarks, concerning\nthe introduction of a high Protective Tariff into the United States\nin 1861, that before its results could appear in the trade and\nmanufacture of the States, there occurred (1) The great Civil War,\nattended with enormous destruction of capital; (2) Consequent upon\nthis the creation of a huge national debt, and a great increase of\ntaxation; (3) The issue of an inconvertible paper currency, deranging\nprices and wages; (4) The discovery of great mineral resources and\noil-springs; (5) A great extension of railway enterprise. Obviously in\nsuch circumstances other methods than the Method of Difference must\nbe brought into play before there can be any satisfactory reasoning on\nthe facts observed. Still what investigators aim at is the isolation\nof the results of single agencies.\n\n    [Footnote 1: Prof. Bain, who adopts Mill's Canon, silently\n    drops the words within brackets. They seem to be an\n    inadvertence. The \"circumstance,\" in all the examples\n    that Mill gives, is an antecedent circumstance. Herschel's\n    statement, of which Mill's is an adaptation, runs as follows:\n    \"If we can either find produced by nature, or produce\n    designedly for ourselves, two instances which agree exactly in\n    all but one particular and differ in that one, its influence\n    in producing the phenomenon, if it have any, must thereby be\n    rendered apparent\".]\n\n\n\n\nCHAPTER V.\n\nMETHODS OF OBSERVATION.--ELIMINATION.--SINGLE AGREEMENT.\n\n\nI.--THE PRINCIPLE OF ELIMINATION.\n\nThe essence of what Mill calls the Method of Agreement is really the\nelimination[1] of accidental, casual, or fortuitous antecedents. It\nis a method employed when we are given an effect and set to work to\ndiscover the cause. It is from the effect that we start and work back.\nWe make a preliminary analysis of the antecedents; call the roll, as\nit were, of all circumstances present before the effect appeared. Then\nwe proceed to examine other instances of the same effect, and other\ninstances of the occurrence of the various antecedents, and bring to\nbear the principle that any antecedent in the absence of which the\neffect has appeared or on the presence of which it has not appeared\nmay be set aside as fortuitous, as being not an indispensable\nantecedent. This is really the guiding principle of the method as a\nmethod of observation.\n\nLet the inquiry, for example, be into the cause of Endemic Goitre.\nInstances of the disease have been collected from the medical\nobservations of all countries over many years. Why is it endemic in\nsome localities and not in others? We proceed on the assumption that\nthe cause, whatever it is, must be some circumstance common to all\nlocalities where it is endemic. If any such circumstance is obvious\nat once, we may conclude on the mere principle of repeated coincidence\nthat there is causal connexion between it and the disease, and\ncontinue our inquiry into the nature of the connexion. But if no such\ncircumstance is obvious, then in the course of our search for it we\neliminate, as fortuitous, conditions that are present in some cases\nbut absent in others. One of the earliest theories was that endemic\ngoitre was connected with the altitude and configuration of the\nground, some notorious centres of it being deeply cleft mountain\nvalleys, with little air and wind and damp marshy soil. But wider\nobservation found it in many valleys neither narrower nor deeper than\nothers that were exempt, and also in wide exposed valleys such as\nthe Aar. Was it due to the geological formation? This also had to\nbe abandoned, for the disease is often incident within very narrow\nlimits, occurring in some villages and sparing others though the\ngeological formation is absolutely the same. Was it due to the\ncharacter of the drinking-water? Especially to the presence of lime\nor magnesia? This theory was held strongly, and certain springs\ncharacterised as goitre-springs. But the springs in some goitre\ncentres show not a trace of magnesia. The comparative immunity of\ncoast regions suggested that it might be owing to a deficiency of\niodine in the drinking-water and the air, and many instances were\nadduced in favour of this. But further inquiries made out the presence\nof iodine in considerable quantities, in the air, the water, and the\nvegetation of districts where goitre was widely prevalent; while in\nCuba it is said that not a trace of iodine is discoverable either in\nthe air or the water, and yet it is quite free from goitre. After\na huge multiplication of instances, resulting in the elimination of\nevery local condition that had been suggested as a possible cause,\nHirsch came to the conclusion that the true cause must be a morbid\npoison, and that endemic goitre has to be reckoned among the\ninfectious diseases.[2]\n\nOn this negative principle, that if a circumstance comes and goes\nwithout bringing the phenomenon in its train, the phenomenon\nis causally independent of it, common-sense is always at work\ndisconnecting events that are occasionally coincident in time. A\nbird sings at our window, for example, and the clock ticks on the\nmantelpiece. But the clock does not begin to tick when the bird begins\nto sing, nor cease to tick when the bird flies away. Accordingly, if\nthe clock should stop at any time, and we wished to inquire into the\ncause, and anybody were to suggest that the stoppage of the clock was\ncaused by the stoppage of a bird's song outside, we should dismiss\nthe suggestion at once. We should eliminate this circumstance from our\ninquiry, on the ground that from other observations we knew it to be\na casual or fortuitous concomitant. Hotspur's retort to Glendover\n(p. 297) was based on this principle. When poetic sentiment or\nsuperstition rejects a verdict of common-sense or science, it is\nbecause it imagines a causal connexion to exist that is not open to\nobservation, as in the case of the grandfather's clock which stopped\nshort never to go again when the old man died.\n\n\nII.--THE PRINCIPLE OF SINGLE AGREEMENT.\n\nThe procedure in Mill's \"Method of Agreement\" consists in thus\neliminating fortuitous antecedents or concomitants till only one\nremains. We see the nature of the proof relied upon when we ask, How\nfar must elimination be carried in order to attain proof of causal\nconnexion? The answer is that we must go on till we have eliminated\nall but one. We must multiply instances of the phenomenon, till we\nhave settled of each of the antecedents except one that it is not the\ncause. We must have taken account of all the antecedents, and we\nmust have found in our observations that all but one have been only\noccasionally present.\n\n    _When all the antecedents of an effect except one can be\n    absent without the disappearance of the effect, that one is\n    causally connected with the effect, due precautions being\n    taken that no other circumstances have been present besides\n    those taken account of._\n\nMill's Canon of the Method of Agreement is substantially identical\nwith this:--\n\n    When two or more instances of the phenomenon under\n    investigation have only one circumstance in common, the\n    circumstance in which alone all the instances agree is the\n    cause (or effect) of the given phenomenon.\n\nHerschel's statement, on which this canon is founded, runs as follows:\n\"Any circumstance in which all the facts without exception agree, may\nbe the cause in question, or if not, at least a collateral effect\nof the same cause: if there be but one such point of agreement, the\npossibility becomes a certainty\".\n\nAll the instances examined must agree in one circumstance--hence the\ntitle Method of Agreement. But it is not in the agreement merely that\nthe proof consists, but the agreement in one circumstance combined\nwith difference in all the other circumstances, when we are certain\nthat every circumstance has come within our observation. It is the\nsingleness of the agreement that constitutes the proof just as it is\nthe singleness of the difference in the Method of Difference.[3]\n\nIt has been said that Mill's Method of Agreement amounts after all\nonly to an uncontradicted _Inductio per enumerationem simplicem_,\nwhich he himself stigmatised as Induction improperly so called. But\nthis is not strictly correct. It is a misunderstanding probably caused\nby calling the method that of agreement simply, instead of calling it\nthe Method of Single Agreement, so as to lay stress upon the process\nof elimination by which the singleness is established. It is true that\nin the course of our observations we do perform an induction by simple\nenumeration. In eliminating, we at the same time generalise. That is\nto say, in multiplying instances for the elimination of non-causes, we\nnecessarily at the same time multiply instances where the true causal\nantecedent, if there is only one possible, is present. An antecedent\ncontaining the true cause must always be there when the phenomenon\nappears, and thus we may establish by our eliminating observations a\nuniformity of connexion between two facts.\n\nTake, for example, Roger Bacon's inquiry into the cause of the colours\nof the rainbow. His first notion seems to have been to connect the\nphenomenon with the substance crystal, probably from his thinking of\nthe crystal firmament then supposed to encircle the universe. He found\nthe rainbow colours produced by the passage of light through hexagonal\ncrystals. But on extending his observations, he found that the passage\nof light through other transparent mediums was also attended by the\nphenomenon. He found it in dewdrops, in the spray of waterfalls, in\ndrops shaken from the oar in rowing. He thus eliminated the substance\ncrystal, and at the same time established the empirical law that\nthe passage of light through transparent mediums of a globular or\nprismatic shape was a causal antecedent of the rainbow colours.[4]\n\nAscertainment of invariable antecedents may thus proceed side by side\nwith that of variable antecedents, the use of the elimination being\nsimply to narrow the scope of the inquiry. But the proof set forth in\nMill's Canon does not depend merely on one antecedent or concomitant\nbeing invariably present, but also on the assumption that all the\ninfluential circumstances have been within our observation. Then only\ncan we be sure that the instances have _only one_ circumstance in\ncommon.\n\nThe truth is that owing to the difficulty of fulfilling this\ncondition, proof of causation in accordance with Mill's Canon is\npractically all but impossible. It is not attained in any of the\nexamples commonly given. The want of conclusiveness is disguised\nby the fact that both elimination and positive observation of mere\nagreement or uniform concomitance are useful and suggestive in the\nsearch for causes, though they do not amount to complete proof such as\nthe Canon describes. Thus in the inquiry into the cause of goitre, the\nelimination serves some purpose though the result is purely negative.\nWhen the inquirer is satisfied that goitre is not originated by any\ndirectly observable local conditions, altitude, temperature, climate,\nsoil, water, social circumstances, habits of exertion, his search\nis profitably limited. And mere frequency, much more constancy of\nconcomitance, raises a presumption of causal connexion, and looking\nout for it is valuable as a mode of reconnoitring. The first thing\nthat an inquirer naturally asks when confronted by numerous instances\nof a phenomenon is, What have they in common? And if he finds that\nthey have some one circumstance invariably or even frequently present,\nalthough he cannot prove that they have no other circumstance in\ncommon as the Cannon of Single Agreement requires, the presumption of\ncausal connexion is strong enough to furnish good ground for further\ninquiry. If an inquirer finds an illness with marked symptoms in a\nnumber of different households, and finds also that all the households\nget their milk supply from the same source, this is not conclusive\nproof of causation, but it is a sufficient presumption to warrant him\nin examining whether there is any virulent ingredient in the milk.\n\nThus varying the circumstances so as to bring out a common antecedent,\nthough it does not end in exact proof, may indicate causal connexion\nthough it does not prove what the nature of the connexion is. Roger\nBacon's observations indicated that the production of rainbow colours\nwas connected with the passage of light through a transparent globe or\nprism. It was reserved for Newton to prove by other methods that\nwhite light was composed of rays, and that those rays were differently\nrefracted in passing through the transparent medium. We have\nanother example of how far mere agreement, revealed by varying the\ncircumstances, carries us towards discovery of the cause, in Wells's\ninvestigation of the cause of dew. Comparing the numerous instances of\ndew appearing without visible fall of moisture, Wells found that they\nall agreed in the comparative coldness of the surface dewed. This was\nall the agreement that he established by observation; he did not carry\nobservation to the point of determining that there was absolutely\nno other common circumstance: when he had simply discovered dewed\nsurfaces, he tried next to show by reasoning from other knows facts\nhow the coldness of the surface affected the aqueous vapour of the\nneighbouring air. He did not establish his Theory of Dew by the Method\nof Agreement: but the observation of an agreement or common feature in\na number of instances was a stage in the process by which he reached\nhis theory.\n\n\nIII.--MILL'S \"JOINT METHOD OF AGREEMENT AND DIFFERENCE\".\n\nAfter examining a variety of instances in which an effect appears,\nand finding that they all agree in the antecedent presence of some one\ncircumstance, we may proceed to examine instances otherwise similar\n(_in pari materia_, as Prof. Fowler puts it) where the effect does not\nappear. If these all agree in the absence of the circumstance that is\nuniformly present with the effect, we have corroborative evidence that\nthere is causal connexion between this circumstance and the effect.\n\nThe principle of this method seems to have been suggested to Mill by\nWells's investigations into Dew. Wells exposed a number of polished\nsurfaces of various substances, and compared those in which there was\na copious deposit of dew with those in which there was little or\nnone. If he could have got two surfaces, one dewed and the other\nnot, identical in every concomitant but one, he would have attained\ncomplete proof on the principle of Single Difference. But this being\nimpracticable, he followed a course which approximated to the method\nof eliminating every circumstance but one from instances of dew, and\nevery circumstance but one in the instances of no-dew. Mill sums up as\nfollows the results of his experiments: \"It appears that the instances\nin which much dew is deposited, which are very various, agree in\nthis, and, _so far as we are able to observe, in this only_, that they\neither radiate heat rapidly or conduct it slowly: qualities between\nwhich there is no other circumstance of agreement than that by virtue\nof either, the body tends to lose heat from the surface more rapidly\nthan it can be restored from within. The instances, on the contrary,\nin which no dew, or but a small quantity of it, is formed, and which\nare also extremely various, agree (_as far as we can observe_) _in\nnothing except_ in _not_ having this same property. We seem therefore\nto have detected the characteristic difference between the substances\non which the dew is produced, and those on which it is not produced.\nAnd thus have been realised the requisitions of what we have termed\nthe Indirect Method of Difference, or the Joint Method of Agreement\nand Difference.\" The Canon of this Method is accordingly stated by\nMill as follows:--\n\n    If two or more instances in which the phenomenon occurs have\n    only one circumstance in common, while two or more instances\n    in which it does not occur have nothing in common save the\n    absence of that circumstance; the circumstance in which alone\n    the two sets of instances differ, is the effect, or the cause,\n    or an indispensable part of the cause, of the phenomenon.\n\nIn practice, however, this theoretical standard of proof is never\nattained. What investigators really proceed upon is the presumption\nafforded, to use Prof. Bain's terms, by Agreement in Presence combined\nwith Agreement in Absence. When it is found that all substances which\nhave a strong smell agree in being readily oxidisable, and that the\nmarsh gas or carbonetted hydrogen which has no smell is not oxidisable\nat common temperatures, the presumption that oxidation is one of the\ncausal circumstances in smell is strengthened, even though we have not\nsucceeded in eliminating every circumstance but this one from either\nthe positive or the negative instances. So in the following examples\ngiven by Prof. Fowler there is not really a compliance with the\ntheoretical requirements of Mill's Method: there is only an increased\npresumption from the double agreement. \"The Joint Method of Agreement\nand Difference (or the Indirect Method of Difference, or, as I\nshould prefer to call it, the Double Method of Agreement) is being\ncontinually employed by us in the ordinary affairs of life. If when I\ntake a particular kind of food, I find that I invariably suffer from\nsome particular form of illness, whereas, when I leave it off, I cease\nto suffer, I entertain a double assurance that the food is the cause\nof my illness. I have observed that a certain plant is invariably\nplentiful on a particular soil; if, with a wide experience, I fail to\nfind it growing on any other soil, I feel confirmed in my belief that\nthere is in this particular soil some chemical constituent, or\nsome peculiar combination of chemical constituents, which is highly\nfavourable, if not essential, to the growth of the plant.\"\n\n    [Footnote 1: Elimination, or setting aside as being of no\n    concern, must not be confounded with the exclusion of agents\n    practised in applying the Method of Difference. We use the\n    word in its ordinary sense of putting outside the sphere of\n    an argument. By a curious slip, Professor Bain follows Mill in\n    applying the word sometimes to the process of singling out or\n    disentangling a causal circumstance. This is an inadvertent\n    departure from the ordinary usage, according to which\n    elimination means discarding from consideration as being\n    non-essential.]\n\n    [Footnote 2: Hirsch's _Geographical and Historical Pathology_,\n    Creighton's translation, vol. ii. pp. 121-202.]\n\n    [Footnote 3: The bare titles Difference and Agreement, though\n    they have the advantage of simplicity, are apt to puzzle\n    beginners inasmuch as in the Method of Difference the\n    agreement among the instances is at a maximum, and the\n    difference at a minimum, and _vice versa_ in the Method of\n    Agreement. In both Methods it is really the isolation of the\n    connexion between antecedent and sequent that constitutes the\n    proof.]\n\n    [Footnote 4: That rainbows in the sky are produced by the\n    passage of light through minute drops in the clouds was an\n    inference from this observed uniformity.]\n\n\n\n\nCHAPTER VI.\n\nMETHODS OF OBSERVATION.--MINOR METHODS.\n\n\nI.--CONCOMITANT VARIATIONS.\n\n    _Whatever phenomenon varies in any manner whenever another\n    phenomenon varies in some particular manner, is either a\n    cause or an effect of that phenomenon, or is connected with it\n    through some fact of causation._\n\nThis simple principle is constantly applied by us in connecting and\ndisconnecting phenomena. If we hear a sound which waxes and wanes with\nthe rise and fall of the wind, we at once connect the two phenomena.\nWe may not know what the causal connexion is, but if they uniformly\nvary together, there is at once a presumption that the one is causally\ndependent on the other, or that both are effects of the same cause.\n\nThis principle was employed by Wells in his researches into Dew. Some\nbodies are worse conductors of heat than others, and rough surfaces\nradiate heat more rapidly than smooth. Wells made observations on\nconductors and radiators of various degrees, and found that the\namount of dew deposited was greater or less according as the objects\nconducted heat slowly or radiated heat rapidly. He thus established\nwhat Herschel called a \"scale of intensity\" between the conducting and\nradiating properties of the bodies bedewed, and the amount of the dew\ndeposit. The explanation was that in bad conductors the surface cools\nmore quickly than in good conductors because heat is more slowly\nsupplied from within. Similarly in rough surfaces there is a more\nrapid cooling because heat is given off more quickly. But whatever\nthe explanation might be, the mere concomitant variation of the\ndew deposit with these properties showed that there was some causal\nconnexion between them.\n\nIt must be remembered that the mere fact of concomitant variation is\nonly an index that some causal connexion exists. The nature of\nthe connexion must be ascertained by other means, and may remain\na problem, one of the uses of such observed facts being indeed to\nsuggest problems, for inquiry. Thus a remarkable concomitance has been\nobserved between spots on the sun, displays of Aurora Borealis, and\nmagnetic storms. The probability is that they are causally connected,\nbut science has not yet discovered how. Similarly in the various\nsciences properties are arranged in scales of intensity, and any\ncorrespondence between two scales becomes a subject for investigation\non the assumption that it points to a causal connexion. We shall see\nafterwards how in social investigations concomitant variations in\naverages furnish material for reasoning.\n\nWhen two variants can be precisely measured, the ratio of the\nvariation may be ascertained by the Method of Single Difference. We\nmay change an antecedent in degree, and watch the corresponding change\nin the effect, taking care that no other agent influences the effect\nin the meantime. Often when we cannot remove an agent altogether,\nwe may remove it in a measurable amount, and observe the result. We\ncannot remove friction altogether, but the more it is diminished, the\nfurther will a body travel under the impulse of the same force.\n\nUntil a concomitant variation has been fully explained, it is merely\nan empirical law, and any inference that it extends at the same\nrate beyond the limits of observation must be made with due caution.\n\"Parallel variation,\" says Professor Bain, \"is sometimes interrupted\nby critical points, as in the expansion of bodies by heat, which\nsuffers a reverse near the point of cooling. Again, the energy of a\nsolution does not always follow the strength; very dilute solutions\noccasionally exercise a specific power not possessed in any degree\nby stronger. So, in the animal body, food and stimulants operate\nproportionally up to a certain point, at which their further operation\nis checked by the peculiarities in the structure of the living\norgans.... We cannot always reason from a few steps in a series to the\nwhole series, partly because of the occurrence of critical points,\nand partly from the development at the extremes of new and unsuspected\npowers. Sir John Herschel remarks that until very recently 'the\nformulae empirically deduced for the elasticity of steam, those for\nthe resistance of fluids, and on other similar subjects, have almost\ninvariably failed to support the theoretical structures that have been\nerected upon them'.\"[1]\n\n\nII.--SINGLE RESIDUE.\n\n    _Subduct from any phenomenon such part as previous induction\n    has shown to be the effect of certain antecedents, and the\n    residue of the phenomenon is the effect of the remaining\n    antecedents._\n\n\"Complicated phenomena, in which several causes concurring, opposing,\nor quite independent of each other, operate at once, so as to produce\na compound effect, may be simplified by subducting the effect of all\nthe known causes, as well as the nature of the case permits, either by\ndeductive reasoning or by appeal to experience, and thus leaving as it\nwere a _residual phenomenon_ to be explained. It is by this process,\nin fact, that science, in its present advanced state, is chiefly\npromoted. Most of the phenomena which nature presents are very\ncomplicated; and when the effects of all known causes are estimated\nwith exactness, and subducted, the residual facts are constantly\nappearing in the form of phenomena altogether new, and leading to the\nmost important conclusions.\"[2]\n\nIt is obvious that this is not a primary method of observation, but\na method that may be employed with great effect to guide observation\nwhen a considerable advance has been made in accurate knowledge\nof agents and their mode of operation. The greatest triumph of the\nmethod, the discovery of the planet Neptune, was won some years after\nthe above passage from Herschel's Discourse was written. Certain\nperturbations were observed in the movements of the planet Uranus:\nthat is to say, its orbit was found not to correspond exactly with\nwhat it should be when calculated according to the known influences\nof the bodies then known to astronomers. These perturbations were a\nresidual phenomenon. It was supposed that they might be due to\nthe action of an unknown planet, and two astronomers, Adams and Le\nVerrier, simultaneously calculated the position of a body such as\nwould account for the observed deviations. When telescopes were\ndirected to the spot thus indicated, the planet Neptune was\ndiscovered. This was in September, 1846: before its actual discovery,\nSir John Herschel exulted in the prospect of it in language that\nstrikingly expresses the power of the method. \"We see it,\" he said,\n\"as Columbus saw America from the shores of Spain. Its movements have\nbeen felt, trembling along the far-reaching line of our analysis, with\na certainty hardly inferior to that of ocular demonstration.\"[3]\n\nMany of the new elements in Chemistry have been discovered in this\nway. For example, when distinctive spectrums had been observed for all\nknown substances, then on the assumption that every substance has a\ndistinctive spectrum, the appearance of lines not referable to any\nknown substance indicated the existence of hitherto undiscovered\nsubstances and directed search for them. Thus Bunsen in 1860\ndiscovered two new alkaline metals, Caesium and Rubidium. He was\nexamining alkalies left from the evaporation of a large quantity of\nmineral water from Durkheim. On applying the spectroscope to the flame\nwhich this particular salt or mixture of salts gave off, he found that\nsome bright lines were visible which he had never observed before, and\nwhich he knew were not produced either by potash or soda. He then set\nto work to analyse the mixture, and ultimately succeeded in separating\ntwo new alkaline substances. When he had succeeded in getting them\nseparate, it was of course by the Method of Difference that he\nascertained them to be capable of producing the lines that had excited\nhis curiosity.\n\n    [Footnote 1: Bain's _Logic_, vol. ii. p. 64.]\n\n    [Footnote 2: Herschel's _Discourse_, Sec. 158.]\n\n    [Footnote 3: De Morgan's _Budget of Paradoxes_, p. 237.]\n\n\n\n\nCHAPTER VII.\n\nTHE METHOD OF EXPLANATION.\n\nGiven perplexity as to the cause of any phenomenon, what is our\nnatural first step? We may describe it as searching for a clue: we\nlook carefully at the circumstances with a view to finding some\nmeans of assimilating what perplexes us to what is already within our\nknowledge. Our next step is to make a guess, or conjecture, or, in\nscientific language, a hypothesis. We exercise our Reason or _Nous_,\nor Imagination, or whatever we choose to call the faculty, and try to\nconceive some cause that strikes us as sufficient to account for the\nphenomenon. If it is not at once manifest that this cause has really\noperated, our third step is to consider what appearances ought to\npresent themselves if it did operate. We then return to the facts in\nquestion, and observe whether those appearances do present themselves.\nIf they do, and if there is no other way of accounting for the effect\nin all its circumstances, we conclude that our guess is correct,\nthat our hypothesis is proved, that we have reached a satisfactory\nexplanation.\n\nThese four steps or stages may be distinguished in most protracted\ninquiries into cause. They correspond to the four stages of what\nMr. Jevons calls the Inductive Method _par excellence_, Preliminary\nObservation, Hypothesis, Deduction and Verification. Seeing that the\nword Induction is already an overloaded drudge, perhaps it would be\nbetter to call these four stages the Method of Explanation. The word\nInduction, if we keep near its original and most established meaning,\nwould apply strictly only to the fourth stage, the Verification, the\nbringing in of the facts to confirm our hypothesis. We might call the\nmethod the Newtonian method, for all four stages are marked in the\nprolonged process by which he made good his theory of Gravitation.\n\nTo give the name of Inductive Method simply to all the four stages\nof an orderly procedure from doubt to a sufficient explanation is\nto encourage a widespread misapprehension. There could be no greater\nerror than to suppose that only the senses are used in scientific\ninvestigation. There is no error that men of science are so apt to\nresent in the mouths of the non-scientific. Yet they have partly\nbrought it on themselves by their loose use of the word Induction,\nwhich they follow Bacon in wresting from the traditional meaning of\nInduction, using it to cover both Induction or the bringing in of\nfacts--an affair mainly of Observation--and Reasoning, the exercise of\nNous, the process of constructing satisfactory hypotheses. In reaction\nagainst the popular misconception which Bacon encouraged, it is\nfashionable now to speak of the use of Imagination in Science. This is\nwell enough polemically. Imagination as commonly understood is akin to\nthe constructive faculty in Science, and it is legitimate warfare to\nemploy the familiar word of high repute to force general recognition\nof the truth. But in common usage Imagination is appropriated to\ncreative genius in the Fine Arts, and to speak of Imagination\nin Science is to suggest that Science deals in fictions, and has\ndiscarded Newton's declaration _Hypotheses non fingo_. In a fight for\npopular respect, men of science may be right to claim for themselves\nImagination; but in the interests of clear understanding, the logician\nmust deplore that they should defend themselves from a charge due\nto their abuse of one word by making an equally unwarrantable and\nconfusing extension of another.\n\nCall it what we will, the faculty of likely guessing, of making\nprobable hypotheses, of conceiving in all its circumstances the past\nsituation or the latent and supramicroscopical situation out of\nwhich a phenomenon has emerged, is one of the most important of\nthe scientific man's special gifts. It is by virtue of it that the\ngreatest advancements of knowledge have been achieved, the cardinal\ndiscoveries in Molar and Molecular Physics, Biology, Geology, and\nall departments of Science. We must not push the idea of stages in\nexplanatory method too far: the right explanation may be reached in\na flash. The idea of stages is really useful mainly in trying to make\nclear the various difficulties in investigation, and the fact that\ndifferent men of genius may show different powers in overcoming them.\nThe right hypothesis may occur in a moment, as if by simple intuition,\nbut it may be tedious to prove, and the gifts that tell in proof,\nsuch as Newton's immense mathematical power in calculating what\na hypothesis implies, Darwin's patience in verifying, Faraday's\ningenuity in devising experiments, are all great gifts, and may be\nserviceable at different stages. But without originality and fertility\nin probable hypothesis, nothing can be done.\n\nThe dispute between Mill and Whewell as to the place and value of\nhypotheses in science was in the main a dispute about words. Mill\ndid not really undervalue hypothesis, and he gave a most luminous and\naccurate account of the conditions of proof. But here and there he\nincautiously spoke of the \"hypothetical method\" (by which he meant\nwhat we have called the method of Explanation) as if it were a\ndefective kind of proof, a method resorted to by science when the\n\"experimental methods\" could not be applied. Whether his language\nfairly bore this construction is not worth arguing, but this was\nmanifestly the construction that Whewell had in his mind when he\nretorted, as if in defence of hypotheses, that \"the inductive process\nconsists in framing successive hypotheses, the comparison of these\nwith the ascertained facts of nature, and the introduction into them\nof such modifications as the comparison may render necessary\". This is\na very fair description of the whole method of explanation. There\nis nothing really inconsistent with it in Mill's account of his\n\"hypothetical method\"; only he erred himself or was the cause of error\nin others in suggesting, intentionally or unintentionally, that\nthe Experimental Methods were different methods of proof. The\n\"hypothetical method,\" as he described it, consisting of Induction,\nRatiocination, and Verification, really comprehends the principles\nof all modes of observation, whether naturally or artificially\nexperimental. We see this at once when we ask how the previous\nknowledge is got in accordance with which hypotheses are framed. The\nanswer must be, by Observation. However profound the calculations,\nit must be from observed laws, or supposed analogues of them, that\nwe start. And it is always by Observation that the results of these\ncalculations are verified.\n\nBoth Mill and Whewell, however, confined themselves too exclusively\nto the great hypotheses of the Sciences, such as Gravitation and the\nUndulatory Theory of Light. In the consideration of scientific method,\nit is a mistake to confine our attention to these great questions,\nwhich from the multitude of facts embraced can only be verified by\nprolonged and intricate inquiry. Attempts at the explanation of the\nsmallest phenomena proceed on the same plan, and the verification\nof conjectures about them is subject to the same conditions, and the\nmethods of investigation and the conditions of verification can be\nstudied most simply in the smaller cases. Further, I venture to think\nit a mistake to confine ourselves to scientific inquiry in the narrow\nsense, meaning thereby inquiry conducted within the pale of the\nexact sciences. For not merely the exact sciences but all men in the\nordinary affairs of life must follow the same methods or at least\nobserve the same principles and conditions, in any satisfactory\nattempt to explain.\n\nTares appear among the wheat. Good seed was sown: whence, then, come\nthe tares? \"An enemy has done this.\" If an enemy has actually been\nobserved sowing the tares, his agency can be proved by descriptive\ntestimony. But if he has not been seen in the act, we must resort to\nwhat is known in Courts of Law as circumstantial evidence. This is the\n\"hypothetical method\" of science. That the tares are the work of an\nenemy is a hypothesis: we examine all the circumstances of the case in\norder to prove, by inference from our knowledge of similar cases,\nthat thus, and thus only, can those circumstances be accounted for.\nSimilarly, when a question is raised as to the authorship of an\nanonymous book. We first search for a clue by carefully noting the\ndiction, the structure of the sentences, the character and sources of\nthe illustration, the special tracks of thought. We proceed upon the\nknowledge that every author has characteristic turns of phrase and\nimagery and favourite veins of thought, and we look out for such\ninternal evidence of authorship in the work before us. Special\nknowledge and acumen may enable us to detect the authorship at once\nfrom the general resemblance to known work. But if we would have clear\nproof, we must show that the resemblance extends to all the details of\nphrase, structure and imagery: we must show that our hypothesis of the\nauthorship of XYZ explains all the circumstances. And even this is\nnot sufficient, as many erroneous guesses from internal evidence\nmay convince us. We must establish further that there is no other\nreasonable way of accounting for the matter and manner of the book;\nfor example, that it is not the work of an imitator. An imitator may\nreproduce all the superficial peculiarities of an author with such\nfidelity that the imitation can hardly be distinguished from the\noriginal: thus few can distinguish between Fenton's work and Pope's\nin the translation of the Odyssey. We must take such known facts into\naccount in deciding a hypothesis of authorship. Such hypotheses can\nseldom be decided on internal evidence alone: other circumstantial\nevidence--other circumstances that ought to be discoverable if the\nhypothesis is correct--must be searched for.\n\nThe operation of causes that are manifest only in their effects must\nbe proved by the same method as the operation of past causes that\nhave left only their effects behind them. Whether light is caused by\na projection of particles from a luminous body or by an agitation\ncommunicated through an intervening medium cannot be directly\nobserved. The only proof open is to calculate what should occur on\neither hypothesis, and observe whether this does occur. In such a\ncase there is room for the utmost calculating power and experimental\ningenuity. The mere making of the general hypothesis or guess is\nsimple enough, both modes of transmitting influence, the projection\nof moving matter and the travelling of an undulation or wave movement,\nbeing familiar facts. But it is not so easy to calculate exactly how\na given impulse would travel, and what phenomena of ray and shadow,\nof reflection, refraction and diffraction ought to be visible in\nits progress. Still, no matter how intricate the calculation, its\ncorrespondence with what can be observed is the only legitimate proof\nof the hypothesis.\n\n\nII.--OBSTACLES TO EXPLANATION.--PLURALITY OF CAUSES AND INTERMIXTURE\nOF EFFECTS.\n\nThere are two main ways in which explanation may be baffled. There may\nexist more than one cause singly capable of producing the effect in\nquestion, and we may have no means of determining which of the equally\nsufficient causes has actually been at work. For all that appears\nthe tares in our wheat may be the effect of accident or of malicious\ndesign: an anonymous book may be the work of an original author or\nof an imitator. Again, an effect may be the joint result of several\nco-operating causes, and it may be impossible to determine their\nseveral potencies. The bitter article in the _Quarterly_ may have\nhelped to kill John Keats, but it co-operated with an enfeebled\nconstitution and a naturally over-sensitive temperament, and we cannot\nassign its exact weight to each of these coefficients. Death may be\nthe result of a combination of causes; organic disease co-operating\nwith exposure, over-fatigue co-operating with the enfeeblement of the\nsystem by disease.\n\nThe technical names for these difficulties, Plurality of Causes and\nIntermixture of Effects, are apt to confuse without some clearing up.\nIn both kinds of difficulty more causes than one are involved: but\nin the one kind of case there is a plurality of possible or equally\nprobable causes, and we are at a loss to decide which: in the other\nkind of case there is a plurality of co-operating causes; the effect\nis the result or product of several causes working conjointly, and we\nare unable to assign to each its due share.\n\nIt is with a view to overcoming these difficulties that Science\nendeavours to isolate agencies and ascertain what each is capable of\nsingly. Mill and Bain treat Plurality of Causes and Intermixture of\nEffects in connexion with the Experimental Methods. It is better,\nperhaps, to regard them simply as obstacles to explanation, and the\nExperimental Methods as methods of overcoming those obstacles. The\nwhole purpose of the Experimental Methods is to isolate agencies and\neffects: unless they can be isolated, the Methods are inapplicable.\nIn situations where the effects observable may be referred with equal\nprobability to more than one cause, you cannot eliminate so as to\nobtain a single agreement. The Method of Agreement is frustrated. And\nan investigator can get no light from mixed effects, unless he\nknows enough of the causes at work to be able to apply the Method\nof Residues. If he does not, he must simply look out for or devise\ninstances where the agencies are at work separately, and apply the\nprinciple of Single Difference.\n\nGreat, however, as the difficulties are, the theory of Plurality and\nIntermixture baldly stated makes them appear greater than they are in\npractice. There is a consideration that mitigates the complication,\nand renders the task of unravelling it not altogether hopeless. This\nis that different causes have distinctive ways of operating, and leave\nbehind them marks of their presence by which their agency in a given\ncase may be recognised.\n\nAn explosion, for example, occurs. There are several explosive\nagencies, capable of causing as much destruction as meets the eye at\nthe first glance. The agent in the case before us may be gunpowder or\nit may be dynamite. But the two agents are not so alike in their mode\nof operation as to produce results identical in every circumstance.\nThe expert inquirer knows by previous observation that when gunpowder\nacts the objects in the neighbourhood are blackened; and that an\nexplosion of dynamite tears and shatters in a way peculiar to\nitself. He is thus able to interpret the traces, to make and prove a\nhypothesis.\n\nA man's body is found dead in water. It may be a question whether\ndeath came by drowning or by previous violence. He may have been\nsuffocated and afterwards thrown into the water. But the circumstances\nwill tell the true story. Death by drowning has distinctive symptoms.\nIf drowning was the cause, water will be found in the stomach and\nfroth in the trachea.\n\nThus, though there may be a plurality of possible causes, the\ncausation in the given case may be brought home to one by distinctive\naccompaniments, and it is the business of the scientific inquirer to\nstudy these. What is known as the \"ripple-mark\" in sandstone surfaces\nmay be produced in various ways. The most familiar way is by the\naction of the tides on the sand of the sea-shore, and the interpreter\nwho knows this way only would ascribe the marks at once to this\nagency. But ripple-marks are produced also by the winds on drifting\nsands, by currents of water where no tidal influence is felt, and\nin fact by any body of water in a state of oscillation. Is it, then,\nimpossible to decide between these alternative possibilities of\ncausation? No: wind-ripples and current-ripples and tidal-ripples have\neach their own special character and accompanying conditions, and the\nhypothesis of one rather than another may be made good by means of\nthese. \"In rock-formations,\" Mr. Page says,[1] \"there are many things\nwhich at first sight seem similar, and yet on more minute examination,\ndifferences are detected and conditions discovered which render\nit impossible that these appearances can have arisen from the same\ncausation.\"\n\nThe truth is that generally when we speak of plurality of causes, of\nalternative possibilities of causation, we are not thinking of\nthe effect in its individual entirety, but only of some general or\nabstract aspect of it. When we say, _e.g._, that death may be produced\nby a great many different causes, poison, gunshot wounds, disease of\nthis or that organ, we are thinking of death in the abstract, not of\nthe particular case under consideration, which as an individual case,\nhas characters so distinctive that only one combination of causes is\npossible.\n\nThe effort of science is to become less and less abstract in this\nsense, by observing agencies or combinations of agencies apart and\nstudying the special characters of their effects. That knowledge\nis then applied, on the assumption that where those characters are\npresent, the agent or combination of agencies has been at work. Given\nan effect to be explained, it is brought home to one out of several\npossible alternatives by _circumstantial evidence_.\n\nBacon's phrase, _Instantia Crucis_,[2] or Finger-post Instance, might\nbe conveniently appropriated as a technical name for a circumstance\nthat is decisive between rival hypotheses. This was, in effect,\nproposed by Sir John Herschel,[3] who drew attention to the importance\nof these crucial instances, and gave the following example: \"A curious\nexample is given by M. Fresnel, as decisive, in his mind, of the\nquestion between the two great opinions on the nature of light, which,\nsince the time of Newton and Huyghens, have divided philosophers.\nWhen two very clean glasses are laid one on the other, if they be\nnot perfectly flat, but one or both in an almost imperceptible degree\nconvex or prominent, beautiful and vivid colours will be seen between\nthem; and if these be viewed through a red glass, their appearance\nwill be that of alternate dark and bright stripes.... Now, the\ncoloured stripes thus produced are explicable on both theories, and\nare appealed to by both as strong confirmatory facts; but there is a\ndifference in one circumstance according as one or the other theory is\nemployed to explain them. In the case of the Huyghenian doctrine,\nthe intervals between the bright stripes ought to appear _absolutely\nblack_; in the other, _half bright_, when viewed [in a particular\nmanner] through a prism. This curious case of difference was tried as\nsoon as the opposing consequences of the two theories were noted by M.\nFresnel, and the result is stated by him to be decisive in favour\nof that theory which makes light to consist in the vibrations of an\nelastic medium.\"\n\n\nIII.--THE PROOF OF A HYPOTHESIS.\n\nThe completest proof of a hypothesis is when that which has been\nhypothetically assumed to exist as a means of accounting for certain\nphenomena is afterwards actually observed to exist or is proved by\ndescriptive testimony to have existed. Our argument, for example, from\ninternal evidence that Mill in writing his Logic aimed at furnishing\na method for social investigations is confirmed by a letter to Miss\nCaroline Fox, in which he distinctly avowed that object.\n\nThe most striking example of this crowning verification in Science\nis the discovery of the planet Neptune, in which case an agent\nhypothetically assumed was actually brought under the telescope as\ncalculated. Examples almost equally striking have occurred in the\nhistory of the Evolution doctrine. Hypothetical ancestors with certain\npeculiarities of structure have been assumed as links between living\nspecies, and in some cases their fossils have actually been found in\nthe geological register.\n\nSuch triumphs of verification are necessarily rare. For the most part\nthe hypothetical method is applied to cases where proof by actual\nobservation is impossible, such as prehistoric conditions of the earth\nor of life upon the earth, or conditions in the ultimate constitution\nof matter that are beyond the reach of the strongest microscope.\nIndeed, some would confine the word hypothesis to cases of this kind.\nThis, in fact, was done by Mill: hypothesis, as he defined it, was a\nconjecture not completely proved, but with a large amount of evidence\nin its favour. But seeing that the procedure of investigation is the\nsame, namely, conjecture, calculation and comparison of facts with the\ncalculated results, whether the agency assumed can be brought to the\ntest of direct observation or not, it seems better not to restrict the\nword hypothesis to incompletely proved conjectures, but to apply it\nsimply to a conjecture made at a certain stage in whatever way it may\nafterwards be verified.\n\nIn the absence of direct verification, the proof of a hypothesis is\nexclusive sufficiency to explain the circumstances. The hypothesis\nmust account for all the circumstances, and there must be no other way\nof accounting for them. Another requirement was mentioned by Newton\nin a phrase about the exact meaning of which there has been some\ncontention. The first of his Regulae Philosophandi laid down that the\ncause assumed must be a _vera causa_. \"We are not,\" the Rule runs, \"to\nadmit other causes of natural things than such as both are true, and\nsuffice for explaining their phenomena.\"[4]\n\nIt has been argued that the requirement of \"verity\" is superfluous;\nthat it is really included in the requirement of sufficiency; that if\na cause is sufficient to explain the phenomena it must _ipso facto_ be\nthe true cause. This may be technically arguable, given a sufficient\nlatitude to the word sufficiency: nevertheless, it is convenient\nto distinguish between mere sufficiency to explain the phenomena\nin question, and the proof otherwise that the cause assigned really\nexists _in rerum natura_, or that it operated in the given case. The\nfrequency with which the expression _vera causa_ has been used since\nNewton's time shows that a need is felt for it, though it may be hard\nto define \"verity\" precisely as something apart from \"sufficiency\". If\nwe examine the common usage of the expression we shall probably find\nthat what is meant by insisting on a _vera causa_ is that we must\nhave some evidence for the cause assigned outside the phenomena in\nquestion. In seeking for verification of a hypothesis we must extend\nour range beyond the limited facts that have engaged our curiosity and\nthat demand explanation.\n\nThere can be little doubt that Newton himself aimed his rule at the\nCartesian hypothesis of Vortices. This was an attempt to explain the\nsolar system on the hypothesis that cosmic space is filled with a\nfluid in which the planets are carried round as chips of wood in a\nwhirlpool, or leaves or dust in a whirlwind. Now this is so far a\n_vera causa_ that the action of fluid vortices is a familiar one: we\nhave only to stir a cup of tea with a bit of stalk in it to get an\ninstance. The agency supposed is sufficient also to account for the\nrevolution of a planet round the sun, given sufficient strength in the\nfluid to buoy up the planet. But if there were such a fluid in space\nthere would be other phenomena: and in the absence of these other\nphenomena the hypothesis must be dismissed as imaginary. The fact that\ncomets pass into and out of spaces where the vortices must be assumed\nto be in action without exhibiting any perturbation is an _instantia\ncrucis_ against the hypothesis.\n\nIf by the requirement of a _vera causa_ were meant that the cause\nassigned must be one directly open to observation, this would\nundoubtedly be too narrow a limit. It would exclude such causes as the\nether which is assumed to fill interstellar space as a medium for\nthe propagation of light. The only evidence for such a medium and\nits various properties is sufficiency to explain the phenomena. Like\nsuppositions as to the ultimate constitution of bodies, it is of the\nnature of what Professor Bain calls a \"Representative Fiction\": the\nonly condition is that it must explain all the phenomena, and that\nthere must be no other way of explaining all. When it is proved\nthat light travels with a finite velocity, we are confined to two\nalternative ways of conceiving its transmission, a projection of\nmatter from the luminous body and the transference of vibrations\nthrough an intervening medium. Either hypothesis would explain many of\nthe facts: our choice must rest with that which best explains all.\nBut supposing that all the phenomena of light were explained by\nattributing certain properties to this intervening medium, it would\nprobably be held that the hypothesis of an ether had not been fully\nverified till other phenomena than those of light had been shown to\nbe incapable of explanation on any other hypothesis. If the properties\nascribed to it to explain the phenomena of light sufficed at the same\ntime to explain otherwise inexplicable phenomena connected with Heat,\nElectricity, or Gravity, the evidence of its reality would be greatly\nstrengthened.\n\nNot only must the circumstances in hand be explained, but other\ncircumstances must be found to be such as we should expect if the\ncause assigned really operated. Take, for example, the case of Erratic\nblocks or boulders, huge fragments of rock found at a distance from\ntheir parent strata. The lowlands of England, Scotland, and Ireland,\nand the great central plain of Northern Europe contain many such\nfragments. Their composition shows indubitably that they once formed\npart of hills to the northward of their present site. They must\nsomehow have been detached and transported to where we now find them.\nHow? One old explanation is that they were carried by witches, or\nthat they were themselves witches accidentally dropped and turned\ninto stone. Any such explanation by supernatural means can neither\nbe proved nor disproved. Some logicians would exclude such hypotheses\naltogether on the ground that they cannot be rendered either more\nor less probable by subsequent examination.[5] The proper scientific\nlimit, however, is not to the making of hypotheses, but to the proof\nof them. The more hypotheses the merrier: only if such an agency as\nwitchcraft is suggested, we should expect to find other evidence\nof its existence in other phenomena that could not otherwise be\nexplained. Again, it has been suggested that the erratic boulders may\nhave been transported by water. Water is so far a _vera causa_ that\ncurrents are known to be capable of washing huge blocks to a great\ndistance. But blocks transported in this way have the edges worn off\nby the friction of their passage: and, besides, currents strong enough\nto dislodge and force along for miles blocks as big as cottages must\nhave left other marks of their presence. The explanation now received\nis that glaciers and icebergs were the means of transport. But this\nexplanation was not accepted till multitudes of circumstances were\nexamined all tending to show that glaciers had once been present in\nthe regions where the erratic blocks are found. The minute habits of\nglaciers have been studied where they still exist: how they slowly\nmove down carrying fragments of rock; how icebergs break off when they\nreach water, float off with their load, and drop it when they melt;\nhow they grind and smooth the surfaces of rocks over which they pass\nor that are frozen into them: how they undercut and mark the faces\nof precipices past which they move; how moraines are formed at the\nmelting ends of them, and so forth. When a district exhibits all the\ncircumstances that are now observed to attend the action of glaciers\nthe proof of the hypothesis that glaciers were once there is complete.\n\n    [Footnote 1: Page's _Philosophy of Geology_, p. 38.]\n\n    [Footnote 2: Crux in this phrase means a cross erected at the\n    parting of ways, with arms to tell whither each way leads.]\n\n    [Footnote 3: _Discourse_, Sec. 218.]\n\n    [Footnote 4: Causas rerum naturalium non plures admitti\n    debere quam quae et veriae sint et carum phenomenis explicandis\n    sufficiant.]\n\n    [Footnote 5: See Prof. Fowler on the Conditions of Hypotheses,\n    _Inductive Logic_, pp. 100-115.]\n\n\n\n\nCHAPTER VIII.\n\nSUPPLEMENTARY METHODS OF INVESTIGATION.\n\n\nI.--THE MAINTENANCE OF AVERAGES.--SUPPLEMENT TO THE METHOD OF\nDIFFERENCE.\n\nA certain amount of law obtains among events that are usually spoken\nof as matters of chance or accident in the individual case. Every kind\nof accident recurs with a certain uniformity. If we take a succession\nof periods, and divide the total number of any kind of event by the\nnumber of periods, we get what is called the average for that period:\nand it is observed that such averages are maintained from period to\nperiod. Over a series of years there is a fixed proportion between\ngood harvests and bad, between wet days and dry: every year nearly\nthe same number of suicides takes place, the same number of crimes, of\naccidents to life and limb, even of suicides, crimes, or injuries\nby particular means: every year in a town nearly the same number of\nchildren stray from their parents and are restored by the police:\nevery year nearly the same number of persons post letters without\nputting an address on them.\n\nThis maintenance of averages is simple matter of observation, a datum\nof experience, an empirical law. Once an average for any kind of event\nhas been noted, we may count upon its continuance as we count upon\nthe continuance of any other kind of observed uniformity. Insurance\ncompanies proceed upon such empirical laws of average in length of\nlife and immunity from injurious accidents by sea or land: their\nprosperity is a practical proof of the correctness and completeness\nof the observed facts and the soundness of their inference to the\ncontinuance of the average.\n\nThe constancy of averages is thus a guide in practice. But in\nreasoning upon them in investigations of cause, we make a further\nassumption than continued uniformity. We assume that the maintenance\nof the average is due to the permanence of the producing causes. We\nregard the average as the result of the operation of a limited sum\nof forces and conditions, incalculable as regards their particular\nincidence, but always pressing into action, and thus likely to operate\na certain number of times within a limited period.\n\nAssuming the correctness of this explanation, it would follow that\n_any change in the average is due to some change in the producing\nconditions_; and this derivative law is applied as a help in the\nobservation and explanation of social facts. Statistics are collected\nand classified: averages are struck: and changes in the average are\nreferred to changes in the concomitant conditions.\n\nWith the help of this law, we may make a near approach to the\nprecision of the Method of Difference. A multitude of unknown or\nunmeasured agents may be at work on a situation, but we may accept the\naverage as the result of their joint operation. If then a new agency\nis introduced or one of the known agents is changed in degree, and\nthis is at once followed by a change in the average, we may with\nfair probability refer the change in the result to the change in the\nantecedents.\n\nThe difficulty is to find a situation where only one antecedent has\nbeen changed before the appearance of the effect. This difficulty may\nbe diminished in practice by eliminating changes that we have reason\nto know could not have affected the circumstances in question.\nSuppose, for example, our question is whether the Education Act\nof 1872 had an influence in the decrease of juvenile crime. Such a\ndecrease took place _post hoc_; was it _propter hoc_? We may at once\neliminate or put out of account the abolition of Purchase in the Army\nor the extension of the Franchise as not having possibly exercised any\ninfluence on juvenile crime. But with all such eliminations, there may\nstill remain other possible influences, such as an improvement in\nthe organisation of the Police, or an expansion or contraction in\nemployment. \"Can you tell me in the face of chronology,\" a leading\nstatesman once asked, \"that the Crimes Act of 1887 did not diminish\ndisorder in Ireland?\" But chronological sequence alone is not a proof\nof causation as long as there are other contemporaneous changes of\ncondition that may also have been influential.\n\nThe great source of fallacy is our proneness to eliminate or isolate\nin accordance with our prejudices. This has led to the gibe that\nanything can be proved by statistics. Undoubtedly statistics may be\nmade to prove anything if you have a sufficiently low standard of\nproof and ignore the facts that make against your conclusion. But\naverages and variations in them are instructive enough if handled with\ndue caution. The remedy for rash conclusions from statistics is not no\nstatistics, but more of them and a sound knowledge of the conditions\nof reasonable proof.\n\n\nII.--THE PRESUMPTION FROM EXTRA-CASUAL COINCIDENCE.\n\nWe have seen that repeated coincidence raises a presumption of causal\nconnexion between the coinciding events. If we find two events going\nrepeatedly together, either abreast or in sequence, we infer that the\ntwo are somehow connected in the way of causation, that there is a\nreason for the coincidence in the manner of their production. It may\nnot be that the one produces the other, or even that their causes are\nin any way connected: but at least, if they are independent one of the\nother, both are tied down to happen at the same place and time,--the\ncoincidence of both with time and place is somehow fixed.\n\nBut though this is true in the main, it is not true without\nqualification. We expect a certain amount of repeated coincidence\nwithout supposing causal connexion. If certain events are repeated\nvery often within our experience, if they have great positive\nfrequency, we may observe them happening together more than once\nwithout concluding that the coincidence is more than fortuitous.\n\nFor example, if we live in a neighbourhood possessed of many black\ncats, and sally forth to our daily business in the morning, a\nmisfortune in the course of the day might more than once follow upon\nour meeting a black cat as we went out without raising in our minds\nany presumption that the one event was the result of the other.\n\nCertain planets are above the horizon at certain periods of the year\nand below the horizon at certain other periods. All through the year\nmen and women are born who afterwards achieve distinction in various\nwalks of life, in love, in war, in business, at the bar, in the\npulpit. We perceive a certain number of coincidences between\nthe ascendancy of certain planets and the birth of distinguished\nindividuals without suspecting that planetary influence was concerned\nin their superiority.\n\nMarriages take place on all days of the year: the sun shines on a good\nmany days at the ordinary time for such ceremonies; some marriages are\nhappy, some unhappy; but though in the case of many happy marriages\nthe sun has shone upon the bride, we regard the coincidence as merely\naccidental.\n\nMen often dream of calamities and often suffer calamities in real\nlife: we should expect the coincidence of a dream of calamity followed\nby a reality to occur more than once as a result of chance. There are\nthousands of men of different nationalities in business in London,\nand many fortunes are made: we should expect more than one man of any\nnationality represented there to make a fortune without arguing any\nconnexion between his nationality and his success.\n\nWe allow, then, for a certain amount of repeated coincidence without\npresuming causal connexion: can any rule be laid down for determining\nthe exact amount?\n\nProf. Bain has formulated the following rule: \"Consider the positive\nfrequency of the phenomena themselves, how great frequency of\ncoincidence must follow from that, supposing there is neither\nconnexion nor repugnance. If there be greater frequency, there is\nconnexion; if less, repugnance.\"\n\nI do not know that we can go further definite in precept. The number\nof casual coincidences bears a certain proportion to the positive\nfrequency of the coinciding phenomena: that proportion is to be\ndetermined by common-sense in each case. It may be possible, however,\nto bring out more clearly the principle on which common-sense proceeds\nin deciding what chance will and will not account for, although our\nexposition amounts only to making more clear what it is that we mean\nby chance as distinguished from assignable reason. I would suggest\nthat in deciding what chance will not account for, we make regressive\napplication of a principle which may be called the principle of Equal\nand Unequal Alternatives, and which may be worded as follows:--\n\n    Of a given number of possible alternatives, all equally\n    possible, one of which is bound to occur at a given time, we\n    expect each to have its turn an equal number of times in the\n    long run. If several of the alternatives are of the same\n    kind, we expect an alternative of that kind to recur with a\n    frequency proportioned to their greater number. If any of the\n    alternatives has an advantage, it will recur with a frequency\n    proportioned to the strength of that advantage.\n\nSituations in which alternatives are absolutely equal are rare in\nnature, but they are artificially created for games \"of chance,\" as in\ntossing a coin, throwing dice, drawing lots, shuffling and dealing a\npack of cards. The essence of all games of chance is to construct a\nnumber of equal alternatives, making them as nearly equal as possible,\nand to make no prearrangement which of the number shall come off. We\nthen say that this is determined by chance. If we ask why we believe\nthat when we go on bringing off one alternative at a time, each will\nhave its turn, part of the answer undoubtedly is that given by De\nMorgan, namely, that we know no reason why one should be chosen rather\nthan another. This, however, is probably not the whole reason for our\nbelief. The rational belief in the matter is that it is only in the\nlong run or on the average that each of the equal alternatives will\nhave its turn, and this is probably founded on the experience of\nactual trial. The mere equality of the alternatives, supposing them\nto be perfectly equal, would justify us as much in expecting that\neach would have its turn in a single revolution of the series, in one\ncomplete cycle of the alternatives. This, indeed, may be described\nas the natural and primitive expectation which is corrected by\nexperience. Put six balls in a wicker bottle, shake them up, and roll\none out: return this one, and repeat the operation: at the end of six\ndraws we might expect each ball to have had its turn of being drawn\nif we went merely on the abstract equality of the alternatives. But\nexperience shows us that in six successive draws the same ball may\ncome out twice or even three or four times, although when thousands of\ndrawings are made each comes out nearly an equal number of times.\nSo in tossing a coin, heads may turn up ten or twelve times in\nsuccession, though in thousands of tosses heads and tails are nearly\nequal. Runs of luck are thus within the rational doctrine of chances:\nit is only in the long run that luck is equalised supposing that the\nevents are pure matter of chance, that is, supposing the fundamental\nalternatives to be equal.\n\nIf three out of six balls are of the same colour, we expect a ball of\nthat colour to come out three times as often as any other colour on\nthe average of a long succession of tries. This illustrates the second\nclause of our principle. The third is illustrated by a loaded coin or\ndie.\n\nBy making regressive application of the principle thus ascertained by\nexperience, we often obtain a clue to special causal connexion. We are\nat least enabled to isolate a problem for investigation. If we find\none of a number of alternatives recurring more frequently than the\nothers, we are entitled to presume that they are not equally possible,\nthat there is some inequality in their conditions.\n\nThe inequality may simply lie in the greater possible frequency of\none of the coinciding events, as when there are three black balls in\na bottle of six. We must therefore discount the positive frequency\nbefore looking for any other cause. Suppose, for example, we find that\nthe ascendancy of Jupiter coincides more frequently with the birth of\nmen afterwards distinguished in business than with the birth of men\notherwise distinguished, say in war, or at the bar, or in scholarship.\nWe are not at liberty to conclude planetary influence till we have\ncompared the positive frequency of the different modes of distinction.\nThe explanation of the more frequently repeated coincidence may simply\nbe that more men altogether are successful in business than in war\nor law or scholarship. If so, we say that chance accounts for the\ncoincidence, that is to say, that the coincidence is casual as far as\nplanetary influence is concerned.\n\nSo in epidemics of fever, if we find on taking a long average that\nmore cases occur in some streets of a town than in others, we are not\nwarranted in concluding that the cause lies in the sanitary conditions\nof those streets or in any special liability to infection without\nfirst taking into account the number of families in the different\nstreets. If one street showed on the average ten times as many cases\nas another, the coincidence might still be judged casual if there were\nten times as many families in it.\n\nApart from the fallacy of overlooking the positive frequency, certain\nother fallacies or liabilities to error in applying this doctrine of\nchances may be specified.\n\n1. We are apt, under the influence of prepossession or prejudice, to\nremember certain coincidences better than others, and so to imagine\nextra-casual coincidence where none exists. This bias works in\nconfirming all kinds of established beliefs, superstitious and other,\nbeliefs in dreams, omens, retributions, telepathic communications, and\nso forth. Many people believe that nobody who thwarts them ever comes\nto good, and can produce numerous instances from experience in support\nof this belief.\n\n2. We are apt, after proving that there is a residuum beyond what\nchance will account for on due allowance made for positive frequency,\nto take for granted that we have proved some particular cause for\nthis residuum. Now we have not really explained the residuum by the\napplication of the principle of chances: we have only isolated a\nproblem for explanation. There may be more than chance will account\nfor: yet the cause may not be the cause that we assign off-hand. Take,\nfor example, the coincidence that has been remarked between race and\ndifferent forms of Christianity in Europe. If the distribution of\nreligious systems were entirely independent of race, it might be\nsaid that you would expect one system to coincide equally often\nwith different races in proportion to the positive number of their\ncommunities. But the Greek system is found almost solely among\nSlavonic peoples, the Roman among Celtic, and the Protestant among\nTeutonic. The coincidence is greater than chance will account for. Is\nthe explanation then to be found in some special adaptability of the\nreligious system to the character of the people? This may be the right\nexplanation, but we have not proved it by merely discounting chance.\nTo prove this we must show that there was no other cause at work, that\ncharacter was the only operative condition in the choice of system,\nthat political combinations, for example, had nothing to do with it.\nThe presumption from extra-casual coincidence is only that there is\na special cause: in determining what that is we must conform to the\nordinary conditions of explanation.\n\nSo coincidence between membership of the Government and a classical\neducation may be greater than chance would account for, and yet the\ncircumstance of having been taught Latin and Greek at school may have\nhad no special influence in qualifying the members for their duties.\nThe proportion of classically educated in the Government may be\ngreater than the proportion of them in the House of Commons, and\nyet their eminence may be in no way due to their education. Men of\na certain social position have an advantage in the competition for\noffice, and all those men have been taught Latin and Greek as a matter\nof course. Technically speaking, the coinciding phenomena may be\nindependent effects of the same cause.\n\n3. Where the alternative possibilities are very numerous, we are apt\nnot to make due allowance for the number, sometimes overrating it,\nsometimes underrating it.\n\nThe fallacy of underrating the number is often seen in games of\nchance, where the object is to create a vast number of alternatives,\nall equally possible, equally open to the player, without his being\nable to affect the advent of one more than another. In whist, for\nexample, there are some six billions of possible hands. Yet it is a\ncommon impression that, one night with another, in the course of a\nyear, a player will have dealt to him about an equal number of good\nand bad hands. This is a fallacy. A very much longer time is required\nto exhaust the possible combinations. Suppose a player to have\n2000 hands in the course of a year: this is only one \"set,\" one\ncombination, out of thousands of millions of such sets possible. Among\nthose millions of sets, if there is nothing but chance in the matter,\nthere ought to be all proportions of good and bad, some sets all good,\nsome all bad, as well as some equally divided between good and bad.[1]\n\nSometimes, however, the number of possible alternatives is overrated.\nThus, visitors to London often remark that they never go there without\nmeeting somebody from their own locality, and they are surprised at\nthis as if they had the same chance of meeting their fellow-visitors\nand any other of the four millions of the metropolis. But really the\npossible alternatives of rencounter are far less numerous. The places\nfrequented by visitors to London are filled by much more limited\nnumbers: the possible rencounters are to be counted by thousands\nrather than by millions.\n\n    [Footnote 1: See De Morgan's _Essay on Probabilities_, c. vi.,\n    \"On Common Notions of Probability\".]\n\n\n\n\nCHAPTER IX.\n\nPROBABLE INFERENCE TO PARTICULARS--THE MEASUREMENT OF PROBABILITY.\n\nUndoubtedly there are degrees of probability. Not only do we expect\nsome events with more confidence than others: we may do so, and our\nconfidence may be misplaced: but we have reason to expect some with\nmore confidence than others. There are different degrees of rational\nexpectation. Can those degrees be measured numerically?\n\nThe question has come into Logic from the mathematicians. The\ncalculation of Probabilities is a branch of Mathematics. We have seen\nhow it may be applied to guide investigation by eliminating what is\ndue to chance, and it has been vaguely conceived by logicians that\nwhat is called the calculus of probabilities might be found useful\nalso in determining by exact numerical measurement the probability\nof single events. Dr. Venn, who has written a separate treatise on the\nLogic of Chance, mentions \"accurate quantitative apportionment of our\nbelief\" as one of the goals which Logic should strive to attain. The\nfollowing passage will show his drift.[1]\n\n    A man in good health would doubtless like to know whether he\n    will be alive this time next year. The fact will be settled\n    one way or the other in due time, if he can afford to wait,\n    but if he wants a present decision, Statistics and the Theory\n    of Probability can alone give him any information. He learns\n    that the odds are, say five to one that he will survive, and\n    this is an answer to his question as far as any answer can be\n    given. Statisticians are gradually accumulating a vast mass of\n    data of this general character. What they may be said to aim\n    at is to place us in the position of being able to say, in any\n    given time or place, what are the odds for or against any at\n    present indeterminable fact which belongs to a class admitting\n    of statistical treatment.\n\n    Again, outside the regions of statistics proper--which\n    deal, broadly speaking, with events which can be numbered or\n    measured, and which occur with some frequency--there is still\n    a large field as to which some better approach to a reasoned\n    intensity of belief can be acquired. What will be the issue of\n    a coming war? Which party will win in the next election? Will\n    a patient in the crisis of a given disease recover or not?\n    That statistics are lying here in the background, and are thus\n    indirectly efficient in producing and graduating our belief, I\n    fully hold; but there is such a large intermediate process\n    of estimating, and such scope for the exercise of a practised\n    judgment, that no direct appeal to statistics in the common\n    sense can directly help us. In sketching out therefore the\n    claims of an Ideal condition of knowledge, we ought clearly to\n    include a due apportionment of belief to every event of such\n    a class as this. It is an obvious defect that one man should\n    regard as almost certain what another man regards as almost\n    impossible. Short, therefore, of certain prevision of the\n    future, we want complete agreement as to the degree of\n    probability of every future event: and for that matter of\n    every past event as well.\n\nTechnically speaking, if we extend the name Modality (see p. 78) to\nany qualification of the certainty of a statement of belief, what Dr.\nVenn here desiderates, as he has himself suggested, is a more exact\nmeasurement of the Modality of propositions. We speak of things as\nbeing certain, possible, impossible, probable, extremely probable,\nfaintly probable, and so forth: taking certainty as the highest\ndegree of probability[2] shading gradually down to the zero of\nthe impossible, can we obtain an exact numerical measure for the\ngradations of assurance?\n\nTo examine the principles of all the cases in which chances for and\nagainst an occurrence have been calculated from real or hypothetical\ndata, would be to trespass into the province of Mathematics, but a few\nsimple cases will serve to show what it is that the calculus attempts\nto measure, and what is the practical value of the measurement as\napplied to the probability of a single event.\n\nSuppose there are 100 balls in a box, 30 white and 70 black, all being\nalike except in respect of colour, we say that the chances of drawing\na black ball as against a white are as 7 to 3, and the probability of\ndrawing black is measured by the fraction 7/10. In believing this we\nproceed on the principle already explained (p. 356) of Proportional\nChances. We do not know for certain whether black or white will\nemerge, but knowing the antecedent situation we expect black rather\nthan white with a degree of assurance corresponding to the proportions\nof the two in the box. It is our degree of rational assurance that\nwe measure by this fraction, and the rationality of it depends on the\nobjective condition of the facts, and is the same for all men, however\nmuch their actual degree of confidence may vary with individual\ntemperament. That black will be drawn seven times out of every ten\non an average if we go on drawing to infinity, is as certain as any\nempirical law: it is the probability of a single draw that we measure\nby the fraction 7/10.\n\nWhen we build expectations of single events on statistics of observed\nproportions of events of that kind, it is ultimately on the same\nprinciple that rational expectation rests. That the proportion will\nobtain on the average we regard as certain: the ratio of favourable\ncases to the whole number of possible alternatives is the measure\nof rational expectation or probability in regard to a particular\noccurrence. If every year five per cent. of the children of a town\nstray from their guardians, the probability of this or that child's\ngoing astray is 1/20. The ratio is a correct measure only on the\nassumption that the average is maintained from year to year.\n\nWithout going into the combination of probabilities, we are now in a\nposition to see the practical value of such a calculus as applied to\nparticular cases. There has been some misunderstanding among logicians\non the point. Mr. Jevons rebuked Mill for speaking disrespectfully\nof the calculus, eulogised it as one of the noblest creations of the\nhuman intellect, and quoted Butler's saying that \"Probability is the\nguide of life\". But when Butler uttered this famous saying he was\nprobably not thinking of the mathematical calculus of probabilities\nas applied to particular cases, and it was this special application to\nwhich Mill attached comparatively little value.\n\nThe truth is that we seldom calculate or have any occasion to\ncalculate individual chances except as a matter of curiosity. It is\ntrue that insurance offices calculate probabilities, but it is not the\nprobability of this or that man dying at a particular age. The precise\nshade of probability for the individual, in so far as this depends on\nvital statistics, is a matter of indifference to the company as long\nas the average is maintained. Our expectations about any individual\nlife cannot be measured by a calculation of the chances because a\nvariety of other elements affect those expectations. We form beliefs\nabout individual cases, but we try to get surer grounds for them than\nthe chances as calculable from statistical data. Suppose a person were\nto institute a home for lost dogs, he would doubtless try to ascertain\nhow many dogs were likely to go astray, and in so doing would be\nguided by statistics. But in judging of the probability of the\nstraying of a particular dog, he would pay little heed to statistics\nas determining the chances, but would proceed upon empirical knowledge\nof the character of the dog and his master. Even in betting on the\nfield against a particular horse, the bookmaker does not calculate\nfrom numerical data such as the number of horses entered or the\nnumber of times the favourite has been beaten: he tries to get at\nthe pedigree and previous performances of the various horses in the\nrunning. We proceed by calculation of chances only when we cannot do\nbetter.\n\n    [Footnote 1: _Empirical Logic_, p. 556.]\n\n    [Footnote 2: Mr. Jevons held that all inference is merely\n    probable and that no inference is certain. But this is a\n    purposeless repudiation of common meaning, which he cannot\n    himself consistently adhere to. We find him saying that if a\n    penny is tossed into the air it will _certainly_ come down\n    on one side or the other, on which side being a matter of\n    probability. In common speech probability is applied to a\n    degree of belief short of certainty, but to say that certainty\n    is the highest degree of probability does no violence to the\n    common meaning.]\n\n\n\n\nCHAPTER X.\n\nINFERENCE FROM ANALOGY.\n\nThe word Analogy was appropriated by Mill, in accordance with the\nusage of the eighteenth century, to designate a ground of inference\ndistinct from that on which we proceed in extending a law, empirical\nor scientific, to a new case. But it is used in various other senses,\nmore or less similar, and in order to make clear the exact logical\nsense, it is well to specify some of these. The original word\n[Greek: analogia], as employed by Aristotle, corresponds to the word\nProportion in Arithmetic: it signified an equality of ratios, [Greek:\nisotes logon]: two compared with four is analogous to four compared\nwith eight. There is something of the same meaning in the technical\nuse of the word in Physiology, where it is used to signify similarity\nof function as distinguished from similarity of structure, which is\ncalled homology: thus the tail of a whale is analogous to the tail\nof a fish, inasmuch as it is similarly used for motion, but it\nis homologous with the hind legs of a quadruped; a man's arms are\nhomologous with a horse's fore legs, but they are not analogous\ninasmuch as they are not used for progression. Apart from these\ntechnical employments, the word is loosely used in common speech for\nany kind of resemblance. Thus De Quincey speaks of the \"analogical\"\npower in memory, meaning thereby the power of recalling things by\ntheir inherent likeness as distinguished from their casual connexions\nor their order in a series. But even in common speech, there is a\ntrace of the original meaning: generally when we speak of analogy we\nhave in our minds more than one pair of things, and what we call\nthe analogy is some resemblance between the different pairs. This\nis probably what Whately had in view when he defined analogy as\n\"resemblance of relations\".\n\nIn a strict logical sense, however, as defined by Mill, sanctioned\nby the previous usage of Butler and Kant, analogy means more than\na resemblance of relations. It means a preponderating resemblance\nbetween two things such as to warrant us in inferring that the\nresemblance extends further. This is a species of argument distinct\nfrom the extension of an empirical law. In the extension of an\nempirical law, the ground of inference is a coincidence frequently\nrepeated within our experience, and the inference is that it has\noccurred or will occur beyond that experience: in the argument from\nanalogy, the ground of inference is the resemblance between two\nindividual objects or kinds of objects in a certain number of points,\nand the inference is that they resemble one another in some other\npoint, known to belong to the one, but not known to belong to the\nother. \"Two things go together in many cases, therefore in all,\nincluding this one,\" is the argument in extending a generalisation:\n\"Two things agree in many respects, therefore in this other,\" is the\nargument from analogy.\n\nThe example given by Reid in his _Intellectual Powers_ has become the\nstandard illustration of the peculiar argument from analogy.\n\n    We may observe a very great similitude between this earth\n    which we inhabit, and the other planets, Saturn, Jupiter,\n    Mars, Venus and Mercury. They all revolve round the sun,\n    as the earth does, although at different distances and in\n    different periods. They borrow all their light from the sun,\n    as the earth does. Several of them are known to revolve\n    round their axis like the earth, and by that means have like\n    succession of day and night. Some of them have moons, that\n    serve to give them light in the absence of the sun, as our\n    moon does to us. They are all, in their motions, subject to\n    the same law of gravitation as the earth is. From all this\n    similitude it is not unreasonable to think that these planets\n    may, like our earth, be the habitation of various orders of\n    living creatures. There is some probability in this conclusion\n    from analogy.[1]\n\nThe argument from analogy is sometimes said to range through all\ndegrees of probability from certainty to zero. But this is true only\nif we take the word analogy in its loosest sense for any kind of\nresemblance. If we do this, we may call any kind of argument an\nargument from analogy, for all inferences turn upon resemblance. I\nbelieve that if I throw my pen in the air it will come down again,\nbecause it is like other ponderable bodies. But if we use the word in\nits limited logical sense, the degree of probability is much nearer\nzero than certainty. This is apparent from the conditions that\nlogicians have formulated of a strict argument from analogy.\n\n1. The resemblance must be preponderating. In estimating the value of\nan argument from analogy, we must reckon the points of difference\nas counting against the conclusion, and also the points in regard\nto which we do not know whether the two objects agree or differ. The\nnumerical measure of value is the ratio of the points of resemblance\nto the points of difference _plus_ the unknown points. Thus, in the\nargument that the planets are inhabited because they resemble the\nearth in some respects and the earth is inhabited, the force of the\nanalogy is weakened by the fact that we know very little about the\nsurface of the planets.\n\n2. In a numerical estimate all circumstances that hang together as\neffects of one cause must be reckoned as one. Otherwise, we might make\na fallaciously imposing array of points of resemblance. Thus in Reid's\nenumeration of the agreements between the earth and the planets, their\nrevolution round the sun and their obedience to the law of gravitation\nshould count as one point of resemblance. If two objects agree in _a_,\n_b_, _c_, _d_, _e_, but _b_ follows from _a_, and _d_ and _e_ from\n_c_, the five points count only as two.\n\n3. If the object to which we infer is known to possess some property\nincompatible with the property inferred, the general resemblance\ncounts for nothing. The moon has no atmosphere, and we know that air\nis an indispensable condition of life. Hence, however much the moon\nmay resemble the earth, we are debarred from concluding that there are\nliving creatures on the moon such as we know to exist on the earth. We\nknow also that life such as it is on the earth is possible only within\ncertain limits of temperature, and that Mercury is too hot for life,\nand Saturn too cold, no matter how great the resemblance to the earth\nin other respects.\n\n4. If the property inferred is known or presumed to be a concomitant\nof one or more of the points of resemblance, any argument from analogy\nis superfluous. This is, in effect, to say that we have no occasion to\nargue from general resemblance when we have reason to believe that a\nproperty follows from something that an object is known to possess.\nIf we knew that any one of the planets possessed all the conditions,\npositive and negative, of life, we should not require to reckon up\nall the respects in which it resembles the earth in order to create\na presumption that it is inhabited. We should be able to draw the\nconclusion on other grounds than those of analogy. Newton's famous\ninference that the diamond is combustible is sometimes quoted as an\nargument from analogy. But, technically speaking, it was rather,\nas Professor Bain has pointed out, of the nature of an extended\ngeneralisation. Comparing bodies in respect of their densities and\nrefracting powers, he observed that combustible bodies refract more\nthan others of the same density; and observing the exceptionally high\nrefracting power of the diamond, he inferred from this that it was\ncombustible, an inference afterwards confirmed by experiment. \"The\nconcurrence of high refracting power with inflammability was an\nempirical law; and Newton, perceiving the law, extended it to the\nadjacent case of the diamond. The remark is made by Brewster that had\nNewton known the refractive powers of the minerals _greenockite_ and\n_octohedrite_, he would have extended the inference to them, and would\nhave been mistaken.\"[2]\n\nFrom these conditions it will be seen that we cannot conclude with any\nhigh degree of probability from analogy alone. This is not to deny, as\nMr. Jevons seems to suppose, that analogies, in the sense of general\nresemblances, are often useful in directing investigation. When\nwe find two things very much alike, and ascertain that one of them\npossesses a certain property, the presumption that the other has\nthe same is strong enough to make it worth while trying whether as a\nmatter of fact it has. It is said that a general resemblance of the\nhills near Ballarat in Australia to the Californian hills where gold\nhad been found suggested the idea of digging for gold at Ballarat.\nThis was a lucky issue to an argument from analogy, but doubtless many\nhave dug for gold on similar general resemblances without finding that\nthe resemblance extended to that particular. Similarly, many of\nthe extensions of the Pharmacopeia have proceeded upon general\nresemblances, the fact that one drug resembles another in certain\nproperties being a sufficient reason for trying whether the\nresemblance goes further. The lucky guesses of what is known as\nnatural sagacity are often analogical. A man of wide experience in any\nsubject-matter such as the weather, or the conduct of men in war, in\nbusiness, or in politics, may conclude to the case in hand from some\nprevious case that bears a general resemblance to it, and very often\nhis conclusions may be perfectly sound though he has not made a\nnumerical estimate of the data.\n\nThe chief source of fallacy in analogical argument is ignoring the\nnumber of points of difference. It often happens that an amount of\nresemblance only sufficient for a rhetorical simile is made to do duty\nas a solid argument. Thus the resemblance between a living body\nand the body politic is sometimes used to support inferences from\nsuccessful therapeutic treatment to State policy. The advocates of\nannual Parliaments in the time of the Commonwealth based their case on\nthe serpent's habit of annually casting its skin.\n\n  Wisest of beasts the serpent see,\n  Just emblem of eternity,\n    And of a State's duration;\n  Each year an annual skin he takes,\n  And with fresh life and vigour wakes\n    At every renovation.\n\n  Britain! that serpent imitate.\n  Thy Commons House, that skin of State,\n    By annual choice restore;\n  So choosing thou shall live secure,\n  And freedom to thy sons inure,\n    Till Time shall be no more.\n\nCarlyle's saying that a ship could never be taken round Cape Horn if\nthe crew were consulted every time the captain proposed to alter\nthe course, if taken seriously as an analogical argument against\nRepresentative Government, is open to the objection that the\ndifferences between a ship and a State are too great for any argument\nfrom one to the other to be of value. It was such fallacious analogies\nas these that Heine had in view in his humorous prayer, \"Heaven defend\nus from the Evil One and from metaphors\".\n\n    [Footnote 1: Hamilton's _Reid_, p. 236.]\n\n    [Footnote 2: Bain's _Logic_, ii. 145.]\n\n\n\n\n\n\nPRINTED AT THE EDINBURGH PRESS, 9 AND 12 YOUNG STREET\n\n       *       *       *       *       *\n\n\n\n\nTranscriber's Note:\n\npage 113: 'aneo symplokes' corrected to 'aneu symplokes'","title":"Logic, Inductive and Deductive","tradition":"philosophy-ethics","translated_text":null,"word_count":98612}