{"collection":"philosophy-ethics","full_text_available":true,"graph_url":"https://unchartedknowledge.5gfusion.net/v2/api/page/gutenberg_18440/graph","html_url":"https://unchartedknowledge.5gfusion.net/v2/page/gutenberg_18440","id":"gutenberg_18440","license":"Public Domain (US)","rights_basis":"gutenberg_metadata_copyright_false","source":"gutenberg","source_url":"https://www.gutenberg.org/ebooks/18440","summary":null,"tags":["Category: Philosophy & Ethics","Logic","Mathematics","Philosophy"],"text":"Produced by Susan Skinner and the Online Distributed\nProofreading Team at http://www.pgdp.net\n\n\n\n\n\n\n\nLOGIC\n\nDEDUCTIVE AND INDUCTIVE\n\n\n\n\nFirst Edition, June 1898. (Grant Richards.)\nSecond Edition, November 1901. (Grant Richards.)\nThird Edition, January 1906. (A. Moring Ltd.)\nReprinted, January 1908. (A. Moring Ltd.)\nReprinted, May 1909. (A. Moring Ltd.)\nReprinted, July 1910. (A. Moring Ltd.)\nReprinted, September 1911. (A. Moring Ltd.)\nReprinted, November 1912. (A. Moring Ltd.)\nReprinted, April 1913. (A. Moring Ltd.)\nReprinted, May 1920. (Simpkin.)\n\n\n\n\nLOGIC\n\nDEDUCTIVE AND INDUCTIVE\n\n\nBY\n\nCARVETH READ, M.A.\n\n\nAUTHOR OF\n\n\"THE METAPHYSICS OF NATURE\"\n\n\"NATURAL AND SOCIAL MORALS\"\n\nETC.\n\n\nFOURTH EDITION\n\nENLARGED, AND PARTLY REWRITTEN\n\n\nSIMPKIN, MARSHALL, HAMILTON, KENT & CO. LTD.,\n4 STATIONERS' HALL COURT.\nLONDON, E.C.4\n\n\n\n[Transcriber's Note: The mathematical operator \"therefore\" is\nrepresented below by .'.]\n\nPREFACE\n\n\nIn this edition of my _Logic_, the text has been revised throughout,\nseveral passages have been rewritten, and some sections added. The chief\nalterations and additions occur in cc. i., v., ix., xiii., xvi., xvii.,\nxx.\n\nThe work may be considered, on the whole, as attached to the school of\nMill; to whose _System of Logic_, and to Bain's _Logic_, it is deeply\nindebted. Amongst the works of living writers, the _Empirical Logic_ of\nDr. Venn and the _Formal Logic_ of Dr. Keynes have given me most\nassistance. To some others acknowledgments have been made as occasion\narose.\n\nFor the further study of contemporary opinion, accessible in English,\none may turn to such works as Mr. Bradley's _Principles of Logic_, Dr.\nBosanquet's _Logic; or the Morphology of Knowledge_, Prof. Hobhouse's\n_Theory of Knowledge_, Jevon's _Principles of Science_, and Sigwart's\n_Logic_. Ueberweg's _Logic, and History of Logical Doctrine_ is\ninvaluable for the history of our subject. The attitude toward Logic of\nthe Pragmatists or Humanists may best be studied in Dr. Schiller's\n_Formal Logic_, and in Mr. Alfred Sidgwick's _Process of Argument_ and\nrecent _Elementary Logic_. The second part of this last work, on the\n\"Risks of Reasoning,\" gives an admirably succinct account of their\nposition. I agree with the Humanists that, in all argument, the\nimportant thing to attend to is the meaning, and that the most serious\ndifficulties of reasoning occur in dealing with the matter reasoned\nabout; but I find that a pure science of relation has a necessary place\nin the system of knowledge, and that the formul\u00e6 known as laws of\ncontradiction, syllogism and causation are useful guides in the framing\nand testing of arguments and experiments concerning matters of fact.\nIncisive criticism of traditionary doctrines, with some remarkable\nreconstructions, may be read in Dr. Mercier's _New Logic_.\n\nIn preparing successive editions of this book, I have profited by the\ncomments of my friends: Mr. Thomas Whittaker, Prof. Claude Thompson, Dr.\nArmitage Smith, Mr. Alfred Sidgwick, Dr. Schiller, Prof. Spearman, and\nProf. Sully, have made important suggestions; and I might have profited\nmore by them, if the frame of my book, or my principles, had been more\nelastic.\n\nAs to the present edition, useful criticisms have been received from Mr.\nS.C. Dutt, of Cotton College, Assam, and from Prof. M.A. Roy, of\nMidnapore; and, especially, I must heartily thank my colleague, Dr.\nWolf, for communications that have left their impress upon nearly every\nchapter.\n\n\nCARVETH READ.\n\nLONDON,\n_August_, 1914\n\n\n\n\nCONTENTS\n\n PAGE\n\nPREFACE v\n\n\nCHAPTER I\n\n\nINTRODUCTORY\n\n\u00a71. Definition of Logic 1\n\u00a72. General character of proof 2\n\u00a73. Division of the subject 5\n\u00a74. Uses of Logic 6\n\u00a75. Relation of Logic to other sciences 8\n to Mathematics (p. 8);\n to concrete Sciences (p. 10);\n to Metaphysics (p. 10);\n to regulative sciences (p. 11)\n\u00a76. Schools of Logicians 11\n Relation to Psychology (p. 13)\n\n\nCHAPTER II\n\nGENERAL ANALYSIS OF PROPOSITIONS\n\n\u00a71. Propositions and Sentences 16\n\u00a72. Subject, Predicate and Copula 17\n\u00a73. Compound Propositions 17\n\u00a74. Import of Propositions 19\n\u00a75. Form and Matter 22\n\u00a76. Formal and Material Logic 23\n\u00a77. Symbols used in Logic 24\n\n\nCHAPTER III\n\nOF TERMS AND THEIR DENOTATION\n\n\u00a71. Some Account of Language necessary 27\n\u00a72. Logic, Grammar and Rhetoric 28\n\u00a73. Words are Categorematic or Syncategorematic 29\n\u00a74. Terms Concrete or Abstract 30\n\u00a75. Concrete Terms, Singular, General or Collective 33\n\n\nCHAPTER IV\n\nTHE CONNOTATION OF TERMS\n\n\u00a71. Connotation of General Names 37\n\u00a72. Question of Proper Names 38\n other Singular Names (p. 40)\n\u00a73. Question of Abstract Terms 40\n\u00a74. Univocal and Equivocal Terms 41\n Connotation determined by the _suppositio_ (p. 43)\n\u00a75. Absolute and Relative Terms 43\n\u00a76. Relation of Denotation to Connotation 46\n\u00a77. Contradictory Terms 47\n\u00a78. Positive and Negative Terms 50\n Infinites; Privitives; Contraries (pp. 50-51)\n\n\nCHAPTER V\n\nCLASSIFICATION OF PROPOSITIONS\n\n\u00a71. As to Quantity 53\n Quantity of the Predicate (p. 56)\n\u00a72. As to Quality 57\n Infinite Propositions (p. 57)\n\u00a73. A. I. E. O. 58\n\u00a74. As to Relation 59\n Change of Relation (p. 60);\n Interpretation of 'either, or' (p. 63);\n Function of the hypothetical form (p. 64)\n\u00a75. As to Modality 66\n\u00a76. Verbal and Real Propositions 67\n\n\nCHAPTER VI\n\nCONDITIONS OF IMMEDIATE INFERENCE\n\n\u00a71. Meaning of Inference 69\n\u00a72. Immediate and Mediate Inference 70\n\u00a73. The Laws of Thought 72\n\u00a74. Identity 73\n\u00a75. Contradiction and Excluded Middle 74\n\u00a76. The Scope of Formal Inference 76\n\n\nCHAPTER VII\n\nIMMEDIATE INFERENCES\n\n\u00a71. Plan of the Chapter 79\n\u00a72. Subalternation 79\n\u00a73. Connotative Subalternation 80\n\u00a74. Conversion 82\n Reciprocality (p. 84)\n\u00a75. Obversion 85\n\u00a76. Contrary Opposition 87\n\u00a77. Contradictory Opposition 87\n\u00a78. Sub-contrary Opposition 88\n\u00a79. The Square of Opposition 89\n\u00a710. Secondary modes of Immediate Inference 90\n\u00a711. Immediate Inferences from Conditionals 93\n\n\nCHAPTER VIII\n\nORDER OF TERMS, EULER'S DIAGRAMS, LOGICAL EQUATIONS,\nEXISTENTIAL IMPORT OF PROPOSITIONS\n\n\u00a71. Order of Terms in a proposition 95\n\u00a72. Euler's Diagrams 97\n\u00a73. Propositions considered as Equations 101\n\u00a74. Existential Import of Propositions 104\n\n\nCHAPTER IX\n\nFORMAL CONDITIONS OF MEDIATE INFERENCE\n\n\u00a71. Nature of Mediate Inference and Syllogism 107\n\u00a72. General Canons of the Syllogism 108\n Definitions of Categorical Syllogism; Middle Term;\n Minor Term; Major Term; Minor and Major Premise (p. 109)\n Illicit Process (p. 110);\n Distribution of the Middle (p. 110);\n Negative Premises (p. 112);\n Particular Premises (p. 113)\n\u00a73. _Dictum de omni et nullo_ 115\n\u00a74. Syllogism in relation to the Laws of Thought 116\n\u00a75. Other Kinds of Mediate Inference 118\n\n\nCHAPTER X\n\nCATEGORICAL SYLLOGISMS\n\n\u00a71. Illustrations of the Syllogism 121\n\u00a72. Of Figures 122\n\u00a73. Of Moods 123\n\u00a74. How valid Moods are determined 124\n\u00a75. Special Canons of the Four Figures 126\n\u00a76. Ostensive Reduction and the Mnemonic Verses 127\n\u00a77. Another version of the Mnemonic Verses 132\n\u00a78. Indirect Reduction 132\n\u00a79. Uses of the several Figures 134\n\u00a710. Scientific Value of Reduction 135\n\u00a711. Euler's Diagrams for the Syllogism 136\n\n\nCHAPTER XI\n\nABBREVIATED AND COMPOUND ARGUMENTS\n\n\u00a71. Popular Arguments Informal 138\n\u00a72. The Enthymeme 139\n\u00a73. Monosyllogism, Polysyllogism, Prosyllogism, Episyllogism 141\n\u00a74. The Epicheirema 142\n\u00a75. The Sorites 142\n\u00a76. The Antinomy 145\n\n\nCHAPTER XII\n\nCONDITIONAL SYLLOGISMS\n\n\u00a71. The Hypothetical Syllogism 147\n\u00a72. The Disjunctive Syllogism 152\n\u00a73. The Dilemma 154\n\n\nCHAPTER XIII\n\nTRANSITION TO INDUCTION\n\n\u00a71. Formal Consistency and Material Truth 159\n\u00a72. Real General Propositions assert more than has been\n directly observed 160\n\u00a73. Hence, formally, a Syllogism's Premises seem to beg the\n Conclusion 162\n\u00a74. Materially, a Syllogism turns upon the resemblance of the\n Minor to the Middle Term; and thus extends the\n Major Premise to new cases 163\n\u00a75. Restatement of the _Dictum_ for material reasoning 165\n\u00a76. Uses of the Syllogism 167\n\u00a77. Analysis of the Uniformity of Nature, considered as the\n formal ground of all reasoning 169\n\u00a78. Grounds of our belief in Uniformity 173\n\n\nCHAPTER XIV\n\nCAUSATION\n\n\u00a71. The most important aspect of Uniformity in relation to\n Induction is Causation 174\n\u00a72. Definition of \"Cause\" explained: five marks of Causation 175\n\u00a73. How strictly the conception of Cause can be applied\n depends upon the subject under investigation 183\n\u00a74. Scientific conception of Effect. Plurality of Causes 185\n\u00a75. Some condition, but not the whole cause, may long precede\n the Effect; and some co-effect, but not the whole effect,\n may long survive the Cause 187\n\u00a76. Mechanical Causes and the homogeneous Intermixture of Effects;\n Chemical Causes and the heteropathic Intermixture of Effects 188\n\u00a77. Tendency, Resultant, Counteraction, Elimination, Resolution,\n Analysis, Reciprocity 189\n\n\nCHAPTER XV\n\nINDUCTIVE METHOD\n\n\u00a71. Outline of Inductive investigation 192\n\u00a72. Induction defined 196\n\u00a73. \"Perfect Induction\" 196\n\u00a74. Imperfect Induction methodical or immethodical 197\n\u00a75. Observation and Experiment, the material ground of\n Induction, compared 198\n\u00a76. The principle of Causation is the formal ground of Induction 201\n\u00a77. The Inductive Canons are derived from the principle of\n Causation, the more readily to detect it in facts observed 202\n\n\nCHAPTER XVI\n\nTHE CANONS OF DIRECT INDUCTION\n\n\u00a71. The Canon of Agreement 206\n Negative Instances (p. 208);\n Plurality of Causes (p. 208)\n Agreement may show connection without direct Causation (p. 209)\n\u00a72. The Canon of Agreement in Presence and in Absence 212\n It tends to disprove a Plurality of Causes (p. 213)\n\u00a73. The Canon of Difference 216\n May be applied to observations (p. 221)\n\u00a74. The Canon of Variations 222\n How related to Agreement and Difference (p. 222);\n The Graphic Method (p. 227);\n Critical points (p. 230);\n Progressive effects (p. 231);\n Gradations (p. 231)\n\u00a75. The Canon of Residues 232\n\n\nCHAPTER XVII\n\nCOMBINATION OF INDUCTION WITH DEDUCTION\n\n\u00a71. Deductive character of Formal Induction 236\n\u00a72. Further complication of Deduction with Induction 238\n\u00a73. The Direct Deductive (or Physical) Method 240\n\u00a74. Opportunities of Error in the Physical Method 243\n\u00a75. The Inverse Deductive (or Historical) Method 246\n\u00a76. Precautions in using the Historical Method 251\n\u00a77. The Comparative Method 255\n\u00a78. Historical Evidence 261\n\n\nCHAPTER XVIII\n\nHYPOTHESES\n\n\u00a71. Hypothesis defined and distinguished from Theory 266\n\u00a72. An Hypothesis must be verifiable 268\n\u00a73. Proof of Hypotheses 270\n (1) Must an hypothetical agent be directly observable? (p. 270);\n _Vera causa_ (p. 271)\n (2) An Hypothesis must be adequate to its pretensions (p. 272);\n _Exceptio probat regulam_ (p. 274)\n (3) Every competing Hypothesis must be excluded (p. 275);\n Crucial instance (p. 277)\n (4) Hypotheses must agree with the laws of Nature (p. 279)\n\u00a74. Hypotheses necessary in scientific investigation 280\n\u00a75. The Method of Abstractions 283\n Method of Limits (p. 284);\n In what sense all knowledge is hypothetical (p. 286)\n\n\nCHAPTER XIX\n\nLAWS CLASSIFIED; EXPLANATION; CO-EXISTENCE; ANALOGY\n\n\u00a71. Axioms; Primary Laws; Secondary Laws, Derivative or Empirical;\n Facts 288\n\u00a72. Secondary Laws either Invariable or Approximate Generalisations 292\n\u00a73. Secondary Laws trustworthy only in 'Adjacent Cases' 293\n\u00a74. Secondary Laws of Succession or of Co-existence 295\n Natural Kinds (p. 296);\n Co-existence of concrete things to be deduced from\n Causation (p. 297)\n\u00a75. Explanation consists in tracing resemblance, especially\n of Causation 299\n\u00a76. Three modes of Explanation 302\n Analysis (p. 302);\n Concatenation (p. 302);\n Subsumption (p. 303)\n\u00a77. Limits of Explanation 305\n\u00a78. Analogy 307\n\n\nCHAPTER XX\n\nPROBABILITY\n\n\u00a71. Meaning of Chance and Probability 310\n\u00a72. Probability as a fraction or proportion 312\n\u00a73. Probability depends upon experience and statistics 313\n\u00a74. It is a kind of Induction, and pre-supposes Causation 315\n\u00a75. Of Averages and the Law of Error 318\n\u00a76. Interpretation of probabilities 324\n Personal Equation (p. 325);\n meaning of 'Expectation' (p. 325)\n\u00a77. Rules of the combination of Probabilities 325\n Detection of a hidden Cause (p. 326);\n oral tradition (p. 327);\n circumstantial and analogical evidence (p. 328)\n\n\nCHAPTER XXI\n\nDIVISION AND CLASSIFICATION\n\n\u00a71. Classification, scientific, special and popular 330\n\u00a72. Uses of classification 332\n\u00a73. Classification, Deductive and Inductive 334\n\u00a74. Division, or Deductive Classification: its Rules 335\n\u00a75. Rules for testing a Division 337\n\u00a76. Inductive Classification 339\n\u00a77. Difficulty of Natural Classification 341\n\u00a78. Darwin's influence on the theory of Classification 342\n\u00a79. Classification of Inorganic Bodies also dependent on Causation 346\n\n\nCHAPTER XXII\n\nNOMENCLATURE, DEFINITION, PREDICABLES\n\n\u00a71. Precise thinking needs precise language 348\n\u00a72. Nomenclature and Terminology 349\n\u00a73. Definition 352\n\u00a74. Rules for testing a Definition 352\n\u00a75. Every Definition is relative to a Classification 353\n\u00a76. Difficulties of Definition 356\n Proposals to substitute the Type (p. 356)\n\u00a77. The Limits of Definition 357\n\u00a78. The five Predicables 358\n Porphyry's Tree (p. 361)\n\u00a79. Realism and Nominalism 364\n\u00a710. The Predicaments 366\n\n\nCHAPTER XXIII\n\nDEFINITION OF COMMON TERMS\n\n\u00a71. The rigour of scientific method must be qualified 369\n\u00a72. Still, Language comprises the Nomenclature of an imperfect\n Classification, to which every Definition is relative; 370\n\u00a73. and an imperfect Terminology 374\n\u00a74. Maxims and precautions of Definition 375\n\u00a75. Words of common language in scientific use 378\n\u00a76. How Definitions affect the cogency of arguments 380\n\n\nCHAPTER XXIV\n\nFALLACIES\n\n\u00a71. Fallacy defined and divided 385\n\u00a72. Formal Fallacies of Deduction 385\n\u00a73. Formal Fallacies of Induction 388\n\u00a74. Material Fallacies classified 394\n\u00a75. Fallacies of Observation 394\n\u00a76. Begging the Question 396\n\u00a77. Surreptitious Conclusion 398\n\u00a78. Ambiguity 400\n\u00a79. Fallacies, a natural rank growth of the Human mind, not\n easy to classify, or exterminate 403\n\n\nQUESTIONS 405\n\n\n\n\nLOGIC\n\n\n\n\nCHAPTER I\n\nINTRODUCTORY\n\n\n\u00a7 1. Logic is the science that explains what conditions must be\nfulfilled in order that a proposition may be proved, if it admits of\nproof. Not, indeed, every such proposition; for as to those that declare\nthe equality or inequality of numbers or other magnitudes, to explain\nthe conditions of their proof belongs to Mathematics: they are said to\nbe _quantitative_. But as to all other propositions, called\n_qualitative_, like most of those that we meet with in conversation, in\nliterature, in politics, and even in sciences so far as they are not\ntreated mathematically (say, Botany and Psychology); propositions that\nmerely tell us that something happens (as that _salt dissolves in\nwater_), or that something has a certain property (as that _ice is\ncold_): as to these, it belongs to Logic to show how we may judge\nwhether they are true, or false, or doubtful. When propositions are\nexpressed with the universality and definiteness that belong to\nscientific statements, they are called laws; and laws, so far as they\nare not laws of quantity, are tested by the principles of Logic, if they\nat all admit of proof.\n\nBut it is plain that the process of proving cannot go on for ever;\nsomething must be taken for granted; and this is usually considered to\nbe the case (1) with particular facts that can only be perceived and\nobserved, and (2) with those highest laws that are called 'axioms' or\n'first principles,' of which we can only say that we know of no\nexceptions to them, that we cannot help believing them, and that they\nare indispensable to science and to consistent thought. Logic, then, may\nbe briefly defined as the science of proof with respect to _qualitative_\nlaws and propositions, except those that are axiomatic.\n\n\u00a7 2. Proof may be of different degrees or stages of completeness.\nAbsolute proof would require that a proposition should be shown to agree\nwith all experience and with the systematic explanation of experience,\nto be a necessary part of an all-embracing and self-consistent\nphilosophy or theory of the universe; but as no one hitherto has been\nable to frame such a philosophy, we must at present put up with\nsomething less than absolute proof. Logic, assuming certain principles\nto be true of experience, or at least to be conditions of consistent\ndiscourse, distinguishes the kinds of propositions that can be shown to\nagree with these principles, and explains by what means the agreement\ncan best be exhibited. Such principles are those of Contradiction (chap.\nvi.), the Syllogism (chap. ix.), Causation (chap. xiv.), and\nProbabilities (chap. xx.). To bring a proposition or an argument under\nthem, or to show that it agrees with them, is logical proof.\n\nThe extent to which proof is requisite, again, depends upon the present\npurpose: if our aim be general truth for its own sake, a systematic\ninvestigation is necessary; but if our object be merely to remove some\noccasional doubt that has occurred to ourselves or to others, it may be\nenough to appeal to any evidence that is admitted or not questioned.\nThus, if a man doubts that _some acids are compounds of oxygen_, but\ngrants that _some compounds of oxygen are acids_, he may agree to the\nformer proposition when you point out that it has the same meaning as\nthe latter, differing from it only in the order of the words. This is\ncalled proof by immediate inference.\n\nAgain, suppose that a man holds in his hand a piece of yellow metal,\nwhich he asserts to be copper, and that we doubt this, perhaps\nsuggesting that it is really gold. Then he may propose to dip it in\nvinegar; whilst we agree that, if it then turns green, it is copper and\nnot gold. On trying this experiment the metal does turn green; so that\nwe may put his argument in this way:--\n\n _Whatever yellow metal turns green in vinegar is copper;\n This yellow metal turns green in vinegar;\n Therefore, this yellow metal is copper._\n\nSuch an argument is called proof by mediate inference; because one\ncannot see directly that the yellow metal is copper; but it is admitted\nthat any yellow metal is copper that turns green in vinegar, and we are\nshown that this yellow metal has that property.\n\nNow, however, it may occur to us, that the liquid in which the metal was\ndipped was not vinegar, or not pure vinegar, and that the greenness was\ndue to the impurity. Our friend must thereupon show by some means that\nthe vinegar was pure; and then his argument will be that, since nothing\nbut the vinegar came in contact with the metal, the greenness was due to\nthe vinegar; or, in other words, that contact with that vinegar was the\ncause of the metal turning green.\n\nStill, on second thoughts, we may suspect that we had formerly conceded\ntoo much; we may reflect that, although it had often been shown that\ncopper turned green in vinegar, whilst gold did not, yet the same might\nnot always happen. May it not be, we might ask, that just at this\nmoment, and perhaps always for the future gold turns, and will turn\ngreen in vinegar, whilst copper does not and never will again? He will\nprobably reply that this is to doubt the uniformity of causation: he may\nhope that we are not serious: he may point out to us that in every\naction of our life we take such uniformity for granted. But he will be\nobliged to admit that, whatever he may say to induce us to assent to the\nprinciple of Nature's uniformity, his arguments will not amount to\nlogical proof, because every argument in some way assumes that\nprinciple. He has come, in fact, to the limits of Logic. Just as Euclid\ndoes not try to prove that 'two magnitudes equal to the same third are\nequal to one another,' so the Logician (as such) does not attempt to\nprove the uniformity of causation and the other principles of his\nscience.\n\nEven when our purpose is to ascertain some general truth, the results of\nsystematic inquiry may have various degrees of certainty. If Logic were\nconfined to strict demonstration, it would cover a narrow field. The\ngreater part of our conclusions can only be more or less probable. It\nmay, indeed, be maintained, not unreasonably, that no judgments\nconcerning matters of fact can be more than probable. Some say that all\nscientific results should be considered as giving the average of cases,\nfrom which deviations are to be expected. Many matters can only be\ntreated statistically and by the methods of Probability. Our ordinary\nbeliefs are adopted without any methodical examination. But it is the\naim, and it is characteristic, of a rational mind to distinguish degrees\nof certainty, and to hold each judgment with the degree of confidence\nthat it deserves, considering the evidence for and against it. It takes\na long time, and much self-discipline, to make some progress toward\nrationality; for there are many causes of belief that are not good\ngrounds for it--have no value as evidence. Evidence consists of (1)\nobservation; (2) reasoning checked by observation and by logical\nprinciples; (3) memory--often inaccurate; (4) testimony--often\nuntrustworthy, but indispensable, since all we learn from books or from\nother men is taken on testimony; (5) the agreement of all our results.\nOn the other hand, belief is caused by many influences that are not\nevidence at all: such are (1) desire, which makes us believe in whatever\nserves our purpose; fear and suspicion, which (paradoxically) make us\nbelieve in whatever seems dangerous; (2) habit, which resists whatever\ndisturbs our prejudices; (3) vanity, which delights to think oneself\nalways right and consistent and disowns fallibility; (4) imitativeness,\nsuggestibility, fashion, which carry us along with the crowd. All these,\nand nobler things, such as love and fidelity, fix our attention upon\nwhatever seems to support our prejudices, and prevent our attending to\nany facts or arguments that threaten to overthrow them.\n\n\u00a7 3. Two departments of Logic are usually recognised, Deduction and\nInduction; that is, to describe them briefly, proof from principles, and\nproof from facts. Classification is sometimes made a third department;\nsometimes its topics are distributed amongst those of the former two. In\nthe present work the order adopted is, Deduction in chaps. ii. to xiii.;\nInduction in chaps. xiii. to xx.; and, lastly, Classification. But such\ndivisions do not represent fundamentally distinct and opposed aspects of\nthe science. For although, in discussing any question with an opponent\nwho makes admissions, it may be possible to combat his views with merely\ndeductive arguments based upon his admissions; yet in any question of\ngeneral truth, Induction and Deduction are mutually dependent and imply\none another.\n\nThis may be seen in one of the above examples. It was argued that a\ncertain metal must be copper, because every metal is copper that turns\ngreen when dipped in vinegar. So far the proof appealed to a general\nproposition, and was deductive. But when we ask how the general\nproposition is known to be true, experiments or facts must be alleged;\nand this is inductive evidence. Deduction then depends on Induction. But\nif we ask, again, how any number of past experiments can prove a general\nproposition, which must be good for the future as well as for the past,\nthe uniformity of causation is invoked; that is, appeal is made to a\nprinciple, and that again is deductive proof. Induction then depends\nupon Deduction.\n\nWe may put it in this way: Deduction depends on Induction, if general\npropositions are only known to us through the facts: Induction depends\non Deduction, because one fact can never prove another, except so far as\nwhat is true of the one is true of the other and of any other of the\nsame kind; and because, to exhibit this resemblance of the facts, it\nmust be stated in a general proposition.\n\n\u00a7 4. The use of Logic is often disputed: those who have not studied it,\noften feel confident of their ability to do without it; those who have\nstudied it, are sometimes disgusted with what they consider to be its\nsuperficial analysis of the grounds of evidence, or needless\ntechnicality in the discussion of details. As to those who, not having\nstudied Logic, yet despise it, there will be time enough to discuss its\nutility with them, when they know something about it; and as for those\nwho, having studied it, turn away in disgust, whether they are justified\nevery man must judge for himself, when he has attained to equal\nproficiency in the subject. Meanwhile, the following considerations may\nbe offered in its favour:\n\nLogic states, and partly explains and applies, certain abstract\nprinciples which all other sciences take for granted; namely, the axioms\nabove mentioned--the principles of Contradiction, of the Syllogism and\nof Causation. By exercising the student in the apprehension of these\ntruths, and in the application of them to particular propositions, it\neducates the power of abstract thought. Every science is a model of\nmethod, a discipline in close and consecutive thinking; and this merit\nLogic ought to possess in a high degree.\n\nFor ages Logic has served as an introduction to Philosophy that is, to\nMetaphysics and speculative Ethics. It is of old and honourable\ndescent: a man studies Logic in very good company. It is the warp upon\nwhich nearly the whole web of ancient, medi\u00e6val and modern Philosophy is\nwoven. The history of thought is hardly intelligible without it.\n\nAs the science of proof, Logic gives an account of the _general_ nature\nof evidence deductive and inductive, as applied in the physical and\nsocial sciences and in the affairs of life. The _general_ nature of such\nevidence: it would be absurd of the logician to pretend to instruct the\nchemist, economist and merchant, as to the _special_ character of the\nevidence requisite in their several spheres of judgment. Still, by\ninvestigating the general conditions of proof, he sets every man upon\nhis guard against the insufficiency of evidence.\n\nOne application of the science of proof deserves special mention:\nnamely, to that department of Rhetoric which has been the most\ndeveloped, relating to persuasion by means of oratory, leader-writing,\nor pamphleteering. It is usually said that Logic is useful to convince\nthe judgment, not to persuade the will: but one way of persuading the\nwill is to convince the judgment that a certain course is advantageous;\nand although this is not always the readiest way, it is the most\nhonourable, and leads to the most enduring results. Logic is the\nbackbone of Rhetoric.\n\nIt has been disputed whether Logic is a science or an art; and, in fact,\nit may be considered in both ways. As a statement of general truths, of\ntheir relations to one another, and especially to the first principles,\nit is a science; but it is an art when, regarding truth as an end\ndesired, it points out some of the means of attaining it--namely, to\nproceed by a regular method, to test every judgment by the principles of\nLogic, and to distrust whatever cannot be made consistent with them.\nLogic does not, in the first place, teach us to reason. We learn to\nreason as we learn to walk and talk, by the natural growth of our powers\nwith some assistance from friends and neighbours. The way to develop\none's power of reasoning is, first, to set oneself problems and try to\nsolve them. Secondly, since the solving of a problem depends upon one's\nability to call to mind parallel cases, one must learn as many facts as\npossible, and keep on learning all one's life; for nobody ever knew\nenough. Thirdly one must check all results by the principles of Logic.\nIt is because of this checking, verifying, corrective function of Logic\nthat it is sometimes called a Regulative or Normative Science. It cannot\ngive any one originality or fertility of invention; but it enables us to\ncheck our inferences, revise our conclusions, and chasten the vagaries\nof ambitious speculation. It quickens our sense of bad reasoning both in\nothers and in ourselves. A man who reasons deliberately, manages it\nbetter after studying Logic than he could before, if he is sincere about\nit and has common sense.\n\n\u00a7 5. The relation of Logic to other sciences:\n\n(a) Logic is regarded by Spencer as co-ordinate with Mathematics, both\nbeing Abstract Sciences--that is, sciences of the _relations_ in which\nthings stand to one another, whatever the particular things may be that\nare so related; and this view seems to be, on the whole, just--subject,\nhowever, to qualifications that will appear presently.\n\nMathematics treats of the relations of all sorts of things considered as\nquantities, namely, as equal to, or greater or less than, one another.\nThings may be quantitatively equal or unequal in _degree_, as in\ncomparing the temperature of bodies; or in _duration_; or in _spatial\nmagnitude_, as with lines, superficies, solids; or in _number_. And it\nis assumed that the equality or inequality of things that cannot be\ndirectly compared, may be proved indirectly on the assumption that\n'things equal to the same thing are equal,' etc.\n\nLogic also treats of the relations of all sorts of things, but not as to\ntheir quantity. It considers (i) that one thing may be like or unlike\nanother in certain attributes, as that iron is in many ways like tin or\nlead, and in many ways unlike carbon or sulphur: (ii) that attributes\nco-exist or coinhere (or do not) in the same subject, as metallic\nlustre, hardness, a certain atomic weight and a certain specific gravity\ncoinhere in iron: and (iii) that one event follows another (or is the\neffect of it), as that the placing of iron in water causes it to rust.\nThe relations of likeness and of coinherence are the ground of\nClassification; for it is by resemblance of coinhering attributes that\nthings form classes: coinherence is the ground of judgments concerning\nSubstance and Attribute, as that iron is metallic; and the relation of\nsuccession, in the mode of Causation, is the chief subject of the\ndepartment of Induction. It is usual to group together these relations\nof attributes and of order in time, and call them qualitative, in order\nto contrast them with the quantitative relations which belong to\nMathematics. And it is assumed that qualitative relations of things,\nwhen they cannot be directly perceived, may be proved indirectly by\nassuming the axiom of the Syllogism (chap. ix.) and the law of Causation\n(chap. xiv.).\n\nSo far, then, Logic and Mathematics appear to be co-ordinate and\ndistinct sciences. But we shall see hereafter that the satisfactory\ntreatment of that special order of events in time which constitutes\nCausation, requires a combination of Logic with Mathematics; and so does\nthe treatment of Probability. And, again, Logic may be said to be, in a\ncertain sense, 'prior to' or 'above' Mathematics as usually treated. For\nthe Mathematics assume that one magnitude must be either equal or\nunequal to another, and that it cannot be both equal and unequal to it,\nand thus take for granted the principles of Contradiction and Excluded\nMiddle; but the statement and elucidation of these Principles are left\nto Logic (chap. vi.). The Mathematics also classify and define\nmagnitudes, as (in Geometry) triangles, squares, cubes, spheres; but the\nprinciples of classification and definition remain for Logic to\ndiscuss.\n\n(b) As to the concrete Sciences, such as Astronomy, Chemistry, Zoology,\nSociology--Logic (as well as Mathematics) is implied in them all; for\nall the propositions of which they consist involve causation,\nco-existence, and class-likeness. Logic is therefore said to be prior to\nthem or above them: meaning by 'prior' not that it should be studied\nearlier, for that is not a good plan; meaning by 'above' not in dignity,\nfor distinctions of dignity amongst liberal studies are absurd. But it\nis a philosophical idiom to call the abstract 'prior to,' or 'higher\nthan,' the concrete (see Porphyry's Tree, chap. xxii. \u00a7 8); and Logic is\nmore abstract than Astronomy or Sociology. Philosophy may thank that\nidiom for many a foolish notion.\n\n(c) But, as we have seen, Logic does not investigate the truth,\ntrustworthiness, or validity of its own principles; nor does\nMathematics: this task belongs to Metaphysics, or Epistemology, the\ncriticism of knowledge and beliefs.\n\nLogic assumes, for example, that things are what to a careful scrutiny\nthey seem to be; that animals, trees, mountains, planets, are bodies\nwith various attributes, existing in space and changing in time; and\nthat certain principles, such as Contradiction and Causation, are true\nof things and events. But Metaphysicians have raised many plausible\nobjections to these assumptions. It has been urged that natural objects\ndo not really exist on their own account, but only in dependence on some\nmind that contemplates them, and that even space and time are only our\nway of perceiving things; or, again, that although things do really\nexist on their own account, it is in an entirely different way from that\nin which we know them. As to the principle of Contradiction--that if an\nobject has an attribute, it cannot at the same time and in the same way\nbe without it (e.g., if an animal is conscious, it is false that it is\nnot conscious)--it has been contended that the speciousness of this\nprinciple is only due to the obtuseness of our minds, or even to the\npoverty of language, which cannot make the fine distinctions that exist\nin Nature. And as to Causation, it is sometimes doubted whether events\nalways have physical causes; and it is often suggested that, granting\nthey have physical causes, yet these are such as we can neither perceive\nnor conceive; belonging not to the order of Nature as we know it, but to\nthe secret inwardness and reality of Nature, to the wells and reservoirs\nof power, not to the spray of the fountain that glitters in our\neyes--'occult causes,' in short. Now these doubts and surmises are\nmetaphysical spectres which it remains for Metaphysics to lay. Logic has\nno direct concern with them (although, of course, metaphysical\ndiscussion is expected to be logical), but keeps the plain path of plain\nbeliefs, level with the comprehension of plain men. Metaphysics, as\nexamining the grounds of Logic itself, is sometimes regarded as 'the\nhigher Logic'; and, certainly, the study of Metaphysics is necessary to\nevery one who would comprehend the nature and functions of Logic, or the\nplace of his own mind and of Reason in the world.\n\n(d) The relation of Logic to Psychology will be discussed in the next\nsection.\n\n(e) As a Regulative Science, pointing out the conditions of true\ninference (within its own sphere), Logic is co-ordinate with (i) Ethics,\nconsidered as assigning the conditions of right conduct, and with (ii)\n\u00c6sthetics, considered as determining the principles of criticism and\ngood taste.\n\n\u00a7 6. Three principal schools of Logicians are commonly recognised:\nNominalist, Conceptualist, and Materialist, who differ as to what it is\nthat Logic really treats of: the Nominalists say, 'of language'; the\nConceptualists, 'of thought'; the Materialists, 'of relations of fact.'\nTo illustrate these positions let us take authors who, if some of them\nare now neglected, have the merit of stating their contrasted views with\na distinctness that later refinements tend to obscure.\n\n(a) Whately, a well-known Nominalist, regarded Logic as the Science and\nArt of Reasoning, but at the same time as \"entirely conversant about\nlanguage\"; that is to say, it is the business of Logic to discover those\nmodes of statement which shall ensure the cogency of an argument, no\nmatter what may be the subject under discussion. Thus, _All fish are\ncold-blooded_, .'. _some cold-blooded things are fish:_ this is a sound\ninference by the mere manner of expression; and equally sound is the\ninference, _All fish are warm-blooded_, .'. _some warm-blooded things are\nfish_. The latter proposition may be false, but it follows; and\n(according to this doctrine) Logic is only concerned with the consistent\nuse of words: the truth or falsity of the proposition itself is a\nquestion for Zoology. The short-coming of extreme Nominalism lies in\nspeaking of language as if its meaning were unimportant. But Whately did\nnot intend this: he was a man of great penetration and common-sense.\n\n(b) Hamilton, our best-known Conceptualist, defined Logic as the science\nof the \"formal laws of thought,\" and \"of thought as thought,\" that is,\nwithout regard to the matter thought about. Just as Whately regarded\nLogic as concerned merely with cogent forms of statement, so Hamilton\ntreated it as concerned merely with the necessary relations of thought.\nThis doctrine is called Conceptualism, because the simplest element of\nthought is the Concept; that is, an abstract idea, such as is signified\nby the word _man, planet, colour, virtue_; not a representative or\ngeneric image, but the thought of all attributes common to any class of\nthings. Men, planets, colours, virtuous actions or characters, have,\nseverally, something in common on account of which they bear these\ngeneral names; and the thought of what they have in common, as the\nground of these names, is a Concept. To affirm or deny one concept of\nanother, as _Some men are virtuous_, or _No man is perfectly virtuous_,\nis to form a Judgment, corresponding to the Proposition of which the\nother schools of Logic discourse. Conceptualism, then, investigates the\nconditions of consistent judgment.\n\nTo distinguish Logic from Psychology is most important in connection\nwith Conceptualism. Concepts and Judgments being mental acts, or\nproducts of mental activity, it is often thought that Logic must be a\ndepartment of Psychology. It is recognised of course, that Psychology\ndeals with much more than Logic does, with sensation, pleasure and pain,\nemotion, volition; but in the region of the intellect, especially in its\nmost deliberate and elaborate processes, namely, conception, judgment,\nand reasoning, Logic and Psychology seem to occupy common ground. In\nfact, however, the two sciences have little in common except a few\ngeneral terms, and even these they employ in different senses. It is\nusual to point out that Psychology tries to explain the subjective\n_processes_ of conception, judgment and reasoning, and to give their\nnatural history; but that Logic is wholly concerned with the _results_\nof such processes, with concepts, judgments and reasonings, and merely\nwith the validity of the results, that is, with their truth or\nconsistency; whilst Psychology has nothing to do with their validity,\nbut only with their causes. Besides, the logical judgment (in Formal\nLogic at least) is quite a different thing from the psychological: the\nlatter involves feeling and belief, whereas the former is merely a given\nrelation of concepts. _S is P_: that is a model logical judgment; there\ncan be no question of believing it; but it is logically valid if _M is\nP_ and _S is M_. When, again, in Logic, one deals with belief, it\ndepends upon evidence; whereas, in Psychology belief is shown to depend\nupon causes which may have evidentiary value or may not; for Psychology\nexplains quite impartially the growth of scientific insight and the\ngrowth of prejudice.\n\n(c) Mill, Bain, and Venn are the chief Materialist logicians; and to\nguard against the error of confounding Materialism in Logic with the\nontological doctrine that nothing exists but Matter, it may suffice to\nremember that in Metaphysics all these philosophers are Idealists.\nMaterialism in Logic consists in regarding propositions as affirming or\ndenying relations (_cf._ \u00a7 5) between matters-of-fact in the widest\nsense; not only physical facts, but ideas, social and moral relations;\nit consists, in short, in attending to the meaning of propositions. It\ntreats the first principles of Contradiction and Causation as true of\nthings so far as they are known to us, and not merely as conditions or\ntendencies of thought; and it takes these principles as conditions of\nright thinking, because they seem to hold good of Nature and human life.\n\nTo these differences of opinion it will be necessary to recur in the\nnext chapter (\u00a7 4); but here I may observe that it is easy to exaggerate\ntheir importance in Logic. There is really little at issue between\nschools of logicians as such, and as far as their doctrines run\nparallel; it is on the metaphysical grounds of their study, or as to its\nscope and comprehension, that they find a battle-field. The present work\ngenerally proceeds upon the third, or Materialist doctrine. If Deduction\nand Induction are regarded as mutually dependent parts of one science,\nuniting the discipline of consistent discourse with the method of\ninvestigating laws of physical phenomena, the Materialist doctrine, that\nthe principles of Logic are founded on fact, seems to be the most\nnatural way of thinking. But if the unity of Deduction and Induction is\nnot disputed by the other schools, the Materialist may regard them as\nallies exhibiting in their own way the same body of truths. The\nNominalist may certainly claim that his doctrine is indispensable:\nconsistently cogent forms of statement are necessary both to the\nConceptualist and to the Materialist; neither the relations of thought\nnor those of fact can be arrested or presented without the aid of\nlanguage or some equivalent system of signs. The Conceptualist may urge\nthat the Nominalist's forms of statement and argument exist for the sake\nof their meaning, namely, judgments and reasonings; and that the\nMaterialist's laws of Nature are only judgments founded upon our\nconceptions of Nature; that the truth of observations and experiments\ndepends upon our powers of perception; that perception is inseparable\nfrom understanding, and that a system of Induction may be constructed\nupon the axiom of Causation, regarded as a principle of Reason, just as\nwell as by considering it as a law of Nature, and upon much the same\nlines. The Materialist, admitting all this, may say that a judgment is\nonly the proximate meaning of a proposition, and that the ultimate\nmeaning, the meaning of the judgment itself, is always some\nmatter-of-fact; that the other schools have not hitherto been eager to\nrecognise the unity of Deduction and Induction or to investigate the\nconditions of trustworthy experiments and observations within the limits\nof human understanding; that thought is itself a sort of fact, as\ncomplex in its structure, as profound in its relations, as subtle in its\nchanges as any other fact, and therefore at least as hard to know; that\nto turn away from the full reality of thought in perception, and to\nconfine Logic to artificially limited concepts, is to abandon the effort\nto push method to the utmost and to get as near truth as possible; and\nthat as to Causation being a principle of Reason rather than of Nature,\nthe distinction escapes his apprehension, since Nature seems to be that\nto which our private minds turn upon questions of Causation for\ncorrection and instruction; so that if he does not call Nature the\nUniversal Reason, it is because he loves severity of style.\n\n\n\n\nCHAPTER II\n\nGENERAL ANALYSIS OF PROPOSITIONS\n\n\n\u00a7 1. Since Logic discusses the proof or disproof, or (briefly) the\ntesting of propositions, we must begin by explaining their nature. A\nproposition, then, may first be described in the language of grammar as\n_a sentence indicative_; and it is usually expressed in the present\ntense.\n\nIt is true that other kinds of sentences, optative, imperative,\ninterrogative, exclamatory, if they express or imply an assertion, are\nnot beyond the view of Logic; but before treating such sentences, Logic,\nfor greater precision, reduces them to their equivalent sentences\nindicative. Thus, _I wish it were summer_ may be understood to mean,\n_The coming of summer is an object of my desire_. _Thou shalt not kill_\nmay be interpreted as _Murderers are in danger of the judgment_.\nInterrogatories, when used in argument, if their form is affirmative,\nhave negative force, and affirmative force if their form is negative.\nThus, _Do hypocrites love virtue?_ anticipates the answer, _No_. _Are\nnot traitors the vilest of mankind?_ anticipates the answer, _Yes_. So\nthat the logical form of these sentences is, _Hypocrites are not lovers\nof virtue_; _Traitors are the vilest of mankind_. Impersonal\npropositions, such as _It rains_, are easily rendered into logical forms\nof equivalent meaning, thus: _Rain is falling_; or (if that be\ntautology), _The clouds are raining_. Exclamations may seem capricious,\nbut are often part of the argument. _Shade of Chatham!_ usually means\n_Chatham, being aware of our present foreign policy, is much\ndisgusted_. It is in fact, an appeal to authority, without the\ninconvenience of stating what exactly it is that the authority declares.\n\n\u00a7 2. But even sentences indicative may not be expressed in the way most\nconvenient to logicians. _Salt dissolves in water_ is a plain enough\nstatement; but the logician prefers to have it thus: _Salt is soluble in\nwater_. For he says that a proposition is analysable into three\nelements: (1) a Subject (as _Salt_) about which something is asserted or\ndenied; (2) a Predicate (as _soluble in water_) which is asserted or\ndenied of the Subject, and (3) the Copula (_is_ or _are_, or _is not_ or\n_are not_), the sign of relation between the Subject and Predicate. The\nSubject and Predicate are called the Terms of the proposition: and the\nCopula may be called the sign of predication, using the verb 'to\npredicate' indefinitely for either 'to affirm' or 'to deny.' Thus _S is\nP_ means that the term _P_ is given as related in some way to the term\n_S_. We may, therefore, further define a Proposition as 'a sentence in\nwhich one term is predicated of another.'\n\nIn such a proposition as _Salt dissolves_, the copula (_is_) is\ncontained in the predicate, and, besides the subject, only one element\nis exhibited: it is therefore said to be _secundi adjacentis_. When all\nthree parts are exhibited, as in _Salt is soluble_, the proposition is\nsaid to be _tertii adjacentis_.\n\nFor the ordinary purposes of Logic, in predicating attributes of a thing\nor class of things, the copula _is_, or _is not_, sufficiently\nrepresents the relation of subject and predicate; but when it is\ndesirable to realise fully the nature of the relation involved, it may\nbe better to use a more explicit form. Instead of saying\n_Salt--is--soluble_, we may say _Solubility--coinheres with--the nature\nof salt_, or _The putting of salt in water--is a cause of--its\ndissolving_: thus expanding the copula into a full expression of the\nrelation we have in view, whether coinherence or causation.\n\n\u00a7 3. The sentences of ordinary discourse are, indeed, for the most\npart, longer and more complicated than the logical form of propositions;\nit is in order to prove them, or to use them in the proof of other\npropositions, that they are in Logic reduced as nearly as possible to\nsuch simple but explicit expressions as the above (_tertii adjacentis_).\nA Compound Proposition, reducible to two or more simple ones, is said to\nbe exponible.\n\nThe modes of compounding sentences are explained in every grammar-book.\nOne of the commonest forms is the copulative, such as _Salt is both\nsavoury and wholesome_, equivalent to two simple propositions: _Salt is\nsavoury; Salt is wholesome. Pure water is neither sapid nor odorous_,\nequivalent to _Water is not sapid; Water is not odorous_. Or, again,\n_Tobacco is injurious, but not when used in moderation_, equivalent to\n_Much tobacco is injurious; a little is not_.\n\nAnother form of Exponible is the Exceptive, as _Kladderadatsch is\npublished daily, except on week-days_, equivalent to _Kladderadatsch is\npublished on Sunday; it is not published any other day_. Still another\nExponible is the Exclusive, as _Only men use fire_, equivalent to _Men\nare users of fire; No other animals are_. Exceptive and exclusive\nsentences are, however, equivalent forms; for we may say,\n_Kladderadatsch is published only on Sunday_; and _No animals use fire,\nexcept men_.\n\nThere are other compound sentences that are not exponible, since, though\nthey contain two or more verbal clauses, the construction shows that\nthese are inseparable. Thus, _If cats are scarce, mice are plentiful_,\ncontains two verbal clauses; but _if cats are scarce_ is conditional,\nnot indicative; and _mice are plentiful_ is subject to the condition\nthat _cats are scarce_. Hence the whole sentence is called a Conditional\nProposition. For the various forms of Conditional Propositions see chap.\nv. \u00a7 4.\n\nBut, in fact, to find the logical force of recognised grammatical forms\nis the least of a logician's difficulties in bringing the discourses of\nmen to a plain issue. Metaphors, epigrams, innuendoes and other figures\nof speech present far greater obstacles to a lucid reduction whether for\napproval or refutation. No rules can be given for finding everybody's\nmeaning. The poets have their own way of expressing themselves;\nsophists, too, have their own way. And the point often lies in what is\nunexpressed. Thus, \"barbarous nations make, the civilised write\nhistory,\" means that civilised nations do not make history, which none\nis so brazen as openly to assert. Or, again, \"Alcibiades is dead, but X\nis still with us\"; the whole meaning of this 'exponible' is that X would\nbe the lesser loss to society. Even an epithet or a suffix may imply a\nproposition: _This personage_ may mean _X is a pretentious nobody_.\n\nHow shall we interpret such illusive predications except by cultivating\nour literary perceptions, by reading the most significant authors until\nwe are at home with them? But, no doubt, to disentangle the compound\npropositions, and to expand the abbreviations of literature and\nconversation, is a useful logical exercise. And if it seem a laborious\ntask thus to reduce to its logical elements a long argument in a speech\nor treatise, it should be observed that, as a rule, in a long discourse\nonly a few sentences are of principal importance to the reasoning, the\nrest being explanatory or illustrative digression, and that a close\nscrutiny of these cardinal sentences will frequently dispense us from\ngiving much attention to the rest.\n\n\u00a7 4. But now, returning to the definition of a Proposition given in \u00a7 2,\nthat it is 'a sentence in which one term is predicated of another,' we\nmust consider what is the import of such predication. For the\ndefinition, as it stands, seems to be purely Nominalist. Is a\nproposition nothing more than a certain synthesis of words; or, is it\nmeant to correspond with something further, a synthesis of ideas, or a\nrelation of facts?\n\nConceptualist logicians, who speak of judgments instead of\npropositions, of course define the judgment in their own language.\nAccording to Hamilton, it is \"a recognition of the relation of\ncongruence or confliction in which two concepts stand to each other.\" To\nlighten the sentence, I have omitted one or two qualifications\n(Hamilton's _Lectures on Logic_, xiii.). \"Thus,\" he goes on \"if we\ncompare the thoughts _water_, _iron_, and _rusting_, we find them\ncongruent, and connect them into a single thought, thus: _water rusts\niron_--in that case we form a judgment.\" When a judgment is expressed in\nwords, he says, it is called a proposition.\n\nBut has a proposition no meaning beyond the judgment it expresses? Mill,\nwho defines it as \"a portion of discourse in which a predicate is\naffirmed or denied of a subject\" (_Logic_, Book 1., chap. iv. \u00a7 1.),\nproceeds to inquire into the import of propositions (Book 1., chap. v.),\nand finds three classes of them: (a) those in which one proper name is\npredicated of another; and of these Hobbes's Nominalist definition is\nadequate, namely, that a proposition asserts or denies that the\npredicate is a name for the same thing as the subject, as _Tully is\nCicero_.\n\n(b) Propositions in which the predicate means a part (or the whole) of\nwhat the subject means, as _Horses are animals_, _Man is a rational\nanimal_. These are Verbal Propositions (see below: chap. v. \u00a7 6), and\ntheir import consists in affirming or denying a coincidence between the\nmeanings of names, as _The meaning of 'animal' is part of the meaning of\n'horse.'_ They are partial or complete definitions.\n\nBut (c) there are also Real Propositions, whose predicates do not mean\nthe same as their subjects, and whose import consists in affirming or\ndenying one of five different kinds of matter of fact: (1) That the\nsubject exists, or does not; as if we say _The bison exists_, _The great\nauk is extinct_. (2) Co-existence, as _Man is mortal_; that is, _the\nbeing subject to death coinheres with the qualities on account of which\nwe call certain objects men_. (3) Succession, as _Night follows day_.\n(4) Causation (a particular kind of Succession), as _Water rusts iron_.\n(5) Resemblance, as _The colour of this geranium is like that of a\nsoldier's coat_, or _A = B_.\n\nOn comparing this list of real predications with the list of logical\nrelations given above (chap. i. \u00a7 5 (a)), it will be seen that the two\ndiffer only in this, that I have there omitted simple Existence. Nothing\nsimply exists, unrelated either in Nature or in knowledge. Such a\nproposition as _The bison exists_ may, no doubt, be used in Logic\n(subject to interpretation) for the sake of custom or for the sake of\nbrevity; but it means that some specimens are still to be found in N.\nAmerica, or in Zoological gardens.\n\nControversy as to the Import of Propositions really turns upon a\ndifference of opinion as to the scope of Logic and the foundations of\nknowledge. Mill was dissatisfied with the \"congruity\" of concepts as the\nbasis of a judgment. Clearly, mere congruity does not justify belief. In\nthe proposition _Water rusts iron_, the concepts _water_, _rust_ and\n_iron_ may be congruous, but does any one assert their connection on\nthat ground? In the proposition _Murderers are haunted by the ghosts of\ntheir victims_, the concepts _victim_, _murderer_, _ghost_ have a high\ndegree of congruity; yet, unfortunately, I cannot believe it: there\nseems to be no such cheap defence of innocence. Now, Mill held that\nLogic is concerned with the grounds of belief, and that the scope of\nLogic includes Induction as well as Deduction; whereas, according to\nHamilton, Induction is only Modified Logic, a mere appendix to the\ntheory of the \"forms of thought as thought.\" Indeed, Mill endeavoured in\nhis _Logic_ to probe the grounds of belief deeper than usual, and\nintroduced a good deal of Metaphysics--either too much or not\nenough--concerning the ground of axioms. But, at any rate, his great\npoint was that belief, and therefore (for the most part) the Real\nProposition, is concerned not merely with the relations of words, or\neven of ideas, but with matters of fact; that is, both propositions and\njudgments point to something further, to the relations of things which\nwe can examine, not merely by thinking about them (comparing them in\nthought), but by observing them with the united powers of thought and\nperception. This is what convinces us that _water rusts iron_: and the\ndifficulty of doing this is what prevents our feeling sure that\n_murderers are haunted by the ghosts of their victims_. Hence, although\nMill's definition of a proposition, given above, is adequate for\npropositions in general; yet that kind of proposition (the Real) with\nregard to which Logic (in Mill's view) investigates the conditions of\nproof, may be more explicitly and pertinently defined as 'a predication\nconcerning the relation of matters of fact.'\n\n\u00a7 5. This leads to a very important distinction to which we shall often\nhave to refer in subsequent pages--namely, the distinction between the\nForm and the Matter of a proposition or of an argument. The distinction\nbetween Form and Matter, as it is ordinarily employed, is easily\nunderstood. An apple growing in the orchard and a waxen apple on the\ntable may have the same shape or form, but they consist of different\nmaterials; two real apples may have the same shape, but contain distinct\nounces of apple-stuff, so that after one is eaten the other remains to\nbe eaten. Similarly, tables may have the same shape, though one be made\nof marble, another of oak, another of iron. The form is common to\nseveral things, the matter is peculiar to each. Metaphysicians have\ncarried the distinction further: apples, they say, may have not only the\nsame outward shape, but the same inward constitution, which, therefore,\nmay be called the Form of apple-stuff itself--namely, a certain\npulpiness, juiciness, sweetness, etc.; qualities common to all dessert\napples: yet their Matter is different, one being here, another\nthere--differing in place or time, if in nothing else. The definition of\na species is the form of every specimen of it.\n\nTo apply this distinction to the things of Logic: it is easy to see how\ntwo propositions may have the same Form but different Matter: not using\n'Form' in the sense of 'shape,' but for that which is common to many\nthings, in contrast with that which is peculiar to each. Thus, _All male\nlions are tawny_ and _All water is liquid at 50\u00b0 Fahrenheit_, are two\npropositions that have the same form, though their matter is entirely\ndifferent. They both predicate something of the whole of their subjects,\nthough their subjects are different, and so are the things predicated of\nthem. Again, _All male lions have tufted tails_ and _All male lions have\nmanes_, are two propositions having the same form and, in their\nsubjects, the same matter, but different matter in their predicates. If,\nhowever, we take two such propositions as these: _All male lions have\nmanes_ and _Some male lions have manes_, here the matter is the same in\nboth, but the form is different--in the first, predication is made\nconcerning _every_ male lion; in the second of only _some_ male lions;\nthe first is _universal_, the second is _particular_. Or, again, if we\ntake _Some tigers are man-eaters_ and _Some tigers are not man-eaters_,\nhere too the matter is the same, but the form is different; for the\nfirst proposition is _affirmative_, whilst the second is _negative_.\n\n\u00a7 6. Now, according to Hamilton and Whately, pure Logic has to do only\nwith the Form of propositions and arguments. As to their Matter, whether\nthey are really true in fact, that is a question, they said, not for\nLogic, but for experience, or for the special sciences. But Mill desired\nso to extend logical method as to test the material truth of\npropositions: he thought that he could expound a method by which\nexperience itself and the conclusions of the special sciences may be\nexamined.\n\nTo this method it may be objected, that the claim to determine Material\nTruth takes for granted that the order of Nature will remain unchanged,\nthat (for example) water not only at present is a liquid at 50\u00b0\nFahrenheit, but will always be so; whereas (although we have no reason\nto expect such a thing) the order of Nature may alter--it is at least\nsupposable--and in that event water may freeze at such a temperature.\nAny matter of fact, again, must depend on observation, either directly,\nor by inference--as when something is asserted about atoms or ether. But\nobservation and material inference are subject to the limitations of our\nfaculties; and however we may aid observation by microscopes and\nmicrometers, it is still observation; and however we may correct our\nobservations by repetition, comparison and refined mathematical methods\nof making allowances, the correction of error is only an approximation\nto accuracy. Outside of Formal Reasoning, suspense of judgment is your\nonly attitude.\n\nBut such objections imply that nothing short of absolute truth has any\nvalue; that all our discussions and investigations in science or social\naffairs are without logical criteria; that Logic must be confined to\nsymbols, and considered entirely as mental gymnastics. In this book\nprominence will be given to the character of Logic as a formal science,\nand it will also be shown that Induction itself may be treated formally;\nbut it will be assumed that logical forms are valuable as representing\nthe actual relations of natural and social phenomena.\n\n\u00a7 7. Symbols are often used in Logic instead of concrete terms, not only\nin Symbolic Logic where the science is treated algebraically (as by Dr.\nVenn in his _Symbolic Logic_), but in ordinary manuals; so that it may\nbe well to explain the use of them before going further.\n\nIt is a common and convenient practice to illustrate logical doctrines\nby examples: to show what is meant by a Proposition we may give _salt is\nsoluble_, or _water rusts iron:_ the copulative exponible is exemplified\nby _salt is savoury and wholesome_; and so on. But this procedure has\nsome disadvantages: it is often cumbrous; and it may distract the\nreader's attention from the point to be explained by exciting his\ninterest in the special fact of the illustration. Clearly, too, so far\nas Logic is formal, no particular matter of fact can adequately\nillustrate any of its doctrines. Accordingly, writers on Logic employ\nletters of the alphabet instead of concrete terms, (say) _X_ instead of\n_salt_ or instead of _iron_, and (say) _Y_ instead of _soluble_ or\ninstead of _rusted by water_; and then a proposition may be represented\nby _X is Y_. It is still more usual to represent a proposition by _S is\n(or is not) P, S_ being the initial of Subject and _P_ of Predicate;\nthough this has the drawback that if we argue--_S is P_, therefore _P is\nS_, the symbols in the latter proposition no longer have the same\nsignificance, since the former subject is now the predicate.\n\nAgain, negative terms frequently occur in Logic, such as _not-water_, or\n_not-iron_, and then if _water_ or _iron_ be expressed by _X_, the\ncorresponding negative may be expressed by _x_; or, generally, if a\ncapital letter stand for a positive term, the corresponding small letter\nrepresents the negative. The same device may be adopted to express\ncontradictory terms: either of them being _X_, the other is _x_ (see\nchap. iv., \u00a7\u00a7 7-8); or the contradictory terms may be expressed by _x_\nand _[x]_, _y_ and _[y]_.\n\nAnd as terms are often compounded, it may be convenient to express them\nby a combination of letters: instead of illustrating such a case by\n_boiling water_ or _water that is boiling_, we may write _XY_; or since\npositive and negative terms may be compounded, instead of illustrating\nthis by _water that is not boiling_, we may write _Xy_.\n\nThe convenience of this is obvious; but it is more than convenient; for,\nif one of the uses of Logic be to discipline the power of abstract\nthought, this can be done far more effectually by symbolic than by\nconcrete examples; and if such discipline were the only use of Logic it\nmight be best to discard concrete illustrations altogether, at least in\nadvanced text-books, though no doubt the practice would be too severe\nfor elementary manuals. On the other hand, to show the practical\napplicability of Logic to the arguments and proofs of actual life, or\neven of the concrete sciences, merely symbolic illustration may be not\nonly useless but even misleading. When we speak of politics, or poetry,\nor species, or the weather, the terms that must be used can rarely have\nthe distinctness and isolation of X and Y; so that the perfunctory use\nof symbolic illustration makes argument and proof appear to be much\nsimpler and easier matters than they really are. Our belief in any\nproposition never rests on the proposition itself, nor merely upon one\nor two others, but upon the immense background of our general knowledge\nand beliefs, full of circumstances and analogies, in relation to which\nalone any given proposition is intelligible. Indeed, for this reason, it\nis impossible to illustrate Logic sufficiently: the reader who is in\nearnest about the cogency of arguments and the limitation of proofs, and\nis scrupulous as to the degrees of assent that they require, must\nconstantly look for illustrations in his own knowledge and experience\nand rely at last upon his own sagacity.\n\n\n\n\nCHAPTER III\n\nOF TERMS AND THEIR DENOTATION\n\n\n\u00a7 1. In treating of Deductive Logic it is usual to recognise three\ndivisions of the subject: first, the doctrine of Terms, words, or other\nsigns used as subjects or predicates; secondly, the doctrine of\nPropositions, analysed into terms related; and, thirdly, the doctrine of\nthe Syllogism in which propositions appear as the grounds of a\nconclusion.\n\nThe terms employed are either letters of the alphabet, or the words of\ncommon language, or the technicalities of science; and since the words\nof common language are most in use, it is necessary to give some account\nof common language as subserving the purposes of Logic. It has been\nurged that we cannot think or reason at all without words, or some\nsubstitute for them, such as the signs of algebra; but this is an\nexaggeration. Minds greatly differ, and some think by the aid of\ndefinite and comprehensive picturings, especially in dealing with\nproblems concerning objects in space, as in playing chess blindfold,\ninventing a machine, planning a tour on an imagined map. Most people\ndraw many simple inferences by means of perceptions, or of mental\nimagery. On the other hand, some men think a good deal without any\ncontinuum of words and without any imagery, or with none that seems\nrelevant to the purpose. Still the more elaborate sort of thinking, the\ngrouping and concatenation of inferences, which we call reasoning,\ncannot be carried far without language or some equivalent system of\nsigns. It is not merely that we need language to express our reasonings\nand communicate them to others: in solitary thought we often depend on\nwords--'talk to ourselves,' in fact; though the words or sentences that\nthen pass through our minds are not always fully formed or articulated.\nIn Logic, moreover, we have carefully to examine the grounds (at least\nthe proximate grounds) of our conclusions; and plainly this cannot be\ndone unless the conclusions in question are explicitly stated and\nrecorded.\n\nConceptualists say that Logic deals not with the process of thinking\n(which belongs to Psychology) but with its results; not with conceiving\nbut with concepts; not with judging but with judgments. Is the concept\nself-consistent or adequate? Logic asks; is the judgment capable of\nproof? Now, it is only by recording our thoughts in language that it\nbecomes possible to distinguish between the process and the result of\nthought. Without language, the act and the product of thinking would be\nidentical and equally evanescent. But by carrying on the process in\nlanguage and remembering or otherwise recording it, we obtain a result\nwhich may be examined according to the principles of Logic.\n\n\u00a7 2. As Logic, then, must give some account of language, it seems\ndesirable to explain how its treatment of language differs from that of\nGrammar and from that of Rhetoric.\n\nGrammar is the study of the words of some language, their classification\nand derivation, and of the rules of combining them, according to the\nusage at any time recognised and followed by those who are considered\ncorrect writers or speakers. Composition may be faultless in its\ngrammar, though dull and absurd.\n\nRhetoric is the study of language with a view to obtaining some special\neffect in the communication of ideas or feelings, such as\npicturesqueness in description, vivacity in narration, lucidity in\nexposition, vehemence in persuasion, or literary charm. Some of these\nends are often gained in spite of faulty syntax or faulty logic; but\nsince the few whom bad grammar saddens or incoherent arguments divert\nare not carried away, as they else might be, by an unsophisticated\norator, Grammar and Logic are necessary to the perfection of Rhetoric.\nNot that Rhetoric is in bondage to those other sciences; for foreign\nidioms and such figures as the ellipsis, the anacoluthon, the oxymoron,\nthe hyperbole, and violent inversions have their place in the\nmagnificent style; but authors unacquainted with Grammar and Logic are\nnot likely to place such figures well and wisely. Indeed, common idioms,\nthough both grammatically and rhetorically justifiable, both correct and\neffective, often seem illogical. 'To fall asleep,' for example, is a\nperfect English phrase; yet if we examine severally the words it\nconsists of, it may seem strange that their combination should mean\nanything at all.\n\nBut Logic only studies language so far as necessary in order to state,\nunderstand, and check the evidence and reasonings that are usually\nembodied in language. And as long as meanings are clear, good Logic is\ncompatible with false concords and inelegance of style.\n\n\u00a7 3. Terms are either Simple or Composite: that is to say, they may\nconsist either of a single word, as 'Chaucer,' 'civilisation'; or of\nmore than one, as 'the father of English poetry,' or 'modern civilised\nnations.' Logicians classify words according to their uses in forming\npropositions; or, rather, they classify the uses of words as terms, not\nthe words themselves; for the same word may fall into different classes\nof terms according to the way in which it is used. (Cf. Mr. Alfred\nSidgwick's _Distinction and the Criticism of Beliefs_, chap. xiv.)\n\nThus words are classified as Categorematic or Syncategorematic. A word\nis Categorematic if used singly as a term without the support of other\nwords: it is Syncategorematic when joined with other words in order to\nconstitute the subject or predicate of a proposition. If we say _Venus\nis a planet whose orbit is inside the Earth's_, the subject, 'Venus,'\nis a word used categorematically as a simple term; the predicate is a\ncomposite term whose constituent words (whether substantive, relative,\nverb, or preposition) are used syncategorematically.\n\nPrepositions, conjunctions, articles, adverbs, relative pronouns, in\ntheir ordinary use, can only enter into terms along with other words\nhaving a substantive, adjectival or participial force; but when they are\nthemselves the things spoken of and are used substantively (_suppositio\nmaterialis_), they are categorematic. In the proposition, _'Of' was used\nmore indefinitely three hundred years ago than it is now_, 'of' is\ncategorematic. On the other hand, all substantives may be used\ncategorematically; and the same self-sufficiency is usually recognised\nin adjectives and participles. Some, however, hold that the\ncategorematic use of adjectives and participles is due to an ellipsis\nwhich the logician should fill up; that instead of _Gold is heavy_, he\nshould say _Gold is a heavy metal_; instead of _The sun is shining_,\n_The sun is a body shining_. But in these cases the words 'metal' and\n'body' are unmistakable tautology, since 'metal' is implied in gold and\n'body' in sun. But, as we have seen, any of these kinds of word,\nsubstantive, adjective, or participle, may occur syncategorematically in\nconnection with others to form a composite term.\n\n\u00a7 4. Most terms (the exceptions and doubtful cases will be discussed\nhereafter) have two functions, a denotative and a connotative. A term's\ndenotative function is, to be the name or sign of something or some\nmultitude of things, which are said to be called or denoted by the term.\nIts connotative function is, to suggest certain qualities and\ncharacteristics of the things denoted, so that it cannot be used\nliterally as the name of any other things; which qualities and\ncharacteristics are said to be implied or connoted by the term. Thus\n'sheep' is the name of certain animals, and its connotation prevents its\nbeing used of any others. That which a term directly indicates, then,\nis its _Denotation_; that sense or customary use of it which limits the\nDenotation is its _Connotation_ (ch. iv.). Hamilton and others use\n'Extension' in the sense of Denotation, and 'Intension' or\n'Comprehension' in the sense of Connotation. Now, terms may be\nclassified, first according to what they stand for or denote; that is,\naccording to their _Denotation_. In this respect, the use of a term is\nsaid to be either Concrete or Abstract.\n\nA term is Concrete when it denotes a 'thing'; that is, any person,\nobject, fact, event, feeling or imagination, considered as capable of\nhaving (or consisting of) qualities and a determinate existence. Thus\n'cricket ball' denotes any object having a certain size, weight, shape,\ncolour, etc. (which are its qualities), and being at any given time in\nsome place and related to other objects--in the bowler's hands, on the\ngrass, in a shop window. Any 'feeling of heat' has a certain intensity,\nis pleasurable or painful, occurs at a certain time, and affects some\npart or the whole of some animal. An imagination, indeed (say, of a\nfairy), cannot be said in the same sense to have locality; but it\ndepends on the thinking of some man who has locality, and is definitely\nrelated to his other thoughts and feelings.\n\nA term is Abstract, on the other hand, when it denotes a quality (or\nqualities), considered by itself and without determinate existence in\ntime, place, or relation to other things. 'Size,' 'shape,' 'weight,'\n'colour,' 'intensity,' 'pleasurableness,' are terms used to denote such\nqualities, and are then abstract in their denotation. 'Weight' is not\nsomething with a determinate existence at a given time; it exists not\nmerely in some particular place, but wherever there is a heavy thing;\nand, as to relation, at the same moment it combines in iron with\nsolidity and in mercury with liquidity. In fact, a quality is a point of\nagreement in a multitude of different things; all heavy things agree in\nweight, all round things in roundness, all red things in redness; and an\nabstract term denotes such a point (or points) of agreement among the\nthings denoted by concrete terms. Abstract terms result from the\nanalysis of concrete things into their qualities; and conversely a\nconcrete term may be viewed as denoting the synthesis of qualities into\nan individual thing. When several things agree in more than one quality,\nthere may be an abstract term denoting the union of qualities in which\nthey agree, and omitting their peculiarities; as 'human nature' denotes\nthe common qualities of men, 'civilisation' the common conditions of\ncivilised peoples.\n\nEvery general name, if used as a concrete term, has, or may have, a\ncorresponding abstract term. Sometimes the concrete term is modified to\nform the abstract, as 'greedy--greediness'; sometimes a word is adapted\nfrom another language, as 'man--humanity'; sometimes a composite term is\nused, as 'mercury--the nature of mercury,' etc. The same concrete may\nhave several abstract correlatives, as 'man--manhood, humanity, human\nnature'; 'heavy--weight, gravity, ponderosity'; but in such cases the\nabstract terms are not used quite synonymously; that is, they imply\ndifferent ways of considering the concrete.\n\nWhether a word is used as a concrete or abstract term is in most\ninstances plain from the word itself, the use of most words being pretty\nregular one way or the other; but sometimes we must judge by the\ncontext. 'Weight' may be used in the abstract for 'gravity,' or in the\nconcrete for a measure; but in the latter sense it is syncategorematic\n(in the singular), needing at least the article 'a (or the) weight.'\n'Government' may mean 'supreme political authority,' and is then\nabstract; or, the men who happen to be ministers, and is then concrete;\nbut in this case, too, the article is usually prefixed. 'The life' of\nany man may mean his vitality (abstract), as in \"Thus following life in\ncreatures we dissect\"; or, the series of events through which he passes\n(concrete), as in 'the life of Nelson as narrated by Southey.'\n\nIt has been made a question whether the denotation of an abstract term\nmay itself be the subject of qualities. Apparently 'weight' may be\ngreater or less, 'government' good or bad, 'vitality' intense or dull.\nBut if every subject is modified by a quality, a quality is also\nmodified by making it the subject of another; and, if so, it seems then\nto become a new quality. The compound terms 'great weight,' 'bad\ngovernment,' 'dull vitality,' have not the same denotation as the simple\nterms 'weight, 'government,' 'vitality': they imply, and may be said to\nconnote, more special concrete experience, such as the effort felt in\nlifting a trunk, disgust at the conduct of officials, sluggish movements\nof an animal when irritated. It is to such concrete experiences that we\nhave always to refer in order fully to realise the meaning of abstract\nterms, and therefore, of course, to understand any qualification of\nthem.\n\n\u00a7 5. Concrete terms may be subdivided according to the number of things\nthey denote and the way in which they denote them. A term may denote one\nthing or many: if one, it is called Singular; if many, it may do so\ndistributively, and then it is General; or, as taken all together, and\nthen it is Collective: one, then; any one of many; many in one.\n\nAmong Singular Terms, each denoting a single thing, the most obvious are\nProper Names, such as Gibraltar or George Washington, which are merely\nmarks of individual things or persons, and may form no part of the\ncommon language of a country. They are thus distinguished from other\nSingular Terms, which consist of common words so combined as to restrict\ntheir denotation to some individual, such as, 'the strongest man on\nearth.'\n\nProper Terms are often said to be arbitrary signs, because their use\ndoes not depend upon any reason that may be given for them. Gibraltar\nhad a meaning among the Moors when originally conferred; but no one now\nknows what it was, unless he happens to have learned it; yet the name\nserves its purpose as well as if it were \"Rooke's Nest.\" Every Newton\nor Newport year by year grows old, but to alter the name would cause\nonly confusion. If such names were given by mere caprice it would make\nno difference; and they could not be more cumbrous, ugly, or absurd than\nmany of those that are given 'for reasons.'\n\nThe remaining kinds of Singular Terms are drawn from the common\nresources of the language. Thus the pronouns 'he,' 'she,' 'it,' are\nsingular terms, whose present denotation is determined by the occasion\nand context of discourse: so with demonstrative phrases--'the man,'\n'that horse.' Descriptive names may be more complex, as 'the wisest man\nof Gotham,' which is limited to some individual by the superlative\nsuffix; or 'the German Emperor,' which is limited by the definite\narticle--the general term 'German Emperor' being thereby restricted\neither to the reigning monarch or to the one we happen to be discussing.\nInstead of the definite, the indefinite article may be used to make\ngeneral terms singular, as 'a German Emperor was crowned at Versailles'\n(_individua vaga_).\n\nAbstract Terms are ostensively singular: 'whiteness' (e.g.) is one\nquality. But their full meaning is general: 'whiteness' stands for all\nwhite things, so far as white. Abstract terms, in fact, are only\nformally singular.\n\nGeneral Terms are words, or combinations of words, used to denote any\none of many things that resemble one another in certain respects.\n'George III.' is a Singular Term denoting one man; but 'King' is a\nGeneral Term denoting him and all other men of the same rank; whilst the\ncompound 'crowned head' is still more general, denoting kings and also\nemperors. It is the nature of a general term, then, to be used in the\nsame sense of whatever it denotes; and its most characteristic form is\nthe Class-name, whether of objects, such as 'king,' 'sheep,' 'ghost'; or\nof events, such as 'accession,' 'purchase,' 'manifestation.' Things and\nevents are known by their qualities and relations; and every such\naspect, being a point of resemblance to some other things, becomes a\nground of generalisation, and therefore a ground for the need and use of\ngeneral terms. Hence general terms are far the most important sort of\nterms in Logic, since in them general propositions are expressed and,\nmoreover (with rare exceptions), all predicates are general. For,\nbesides these typical class-names, attributive words are general terms,\nsuch as 'royal,' 'ruling,' 'woolly,' 'bleating,' 'impalpable,'\n'vanishing.'\n\nInfinitives may also be used as general terms, as '_To err is human_';\nbut for logical purposes they may have to be translated into equivalent\nsubstantive forms, as _Foolish actions are characteristic of mankind_.\nAbstract terms, too, are (as I observed) equivalent to general terms;\n'folly' is abstract for 'foolish actions.' '_Honesty is the best\npolicy_' means _people who are honest may hope to find their account in\nbeing so_; that is, in the effects of their honest actions, provided\nthey are wise in other ways, and no misfortunes attend them. The\nabstract form is often much the more succinct and forcible, but for\nlogical treatment it needs to be interpreted in the general form.\n\nBy antonomasia proper names may become general terms, as if we say _'A\nJohnson' would not have written such a book_--i.e., any man of his\ngenius for elaborate eloquence.\n\nA Collective Term denotes a multitude of similar things considered as\nforming one whole, as 'regiment,' 'flock,' 'nation': not distributively,\nthat is, not the similar things severally; to denote them we must say\n'soldiers of the regiment,' 'sheep of the flock,' and so on. If in a\nmultitude of things there is no resemblance, except the fact of being\nconsidered as parts of one whole, as 'the world,' or 'the town of\nNottingham' (meaning its streets and houses, open spaces, people, and\ncivic organisation), the term denoting them as a whole is Singular; but\n'the world' or 'town of Nottingham,' meaning the inhabitants only, is\nCollective.\n\nIn their strictly collective use, all such expressions are equivalent to\nsingular terms; but many of them may also be used as general terms, as\nwhen we speak of 'so many regiments of the line,' or discuss the\n'plurality of worlds'; and in this general use they denote any of a\nmultitude of things of the same kind--regiments, or habitable worlds.\n\nNames of substances, such as 'gold,' 'air,' 'water,' may be employed as\nsingular, collective, or general terms; though, perhaps, as singular\nterms only figuratively, as when we say _Gold is king_. If we say with\nThales, '_Water is the source of all things_,' 'water' seems to be used\ncollectively. But substantive names are frequently used as general\nterms. For example, _Gold is heavy_ means 'in comparison with other\nthings,' such as water. And, plainly, it does not mean that the\naggregate of gold is heavier than the aggregate of water, but only that\nits specific gravity is greater; that is, bulk for bulk, any piece of\ngold is heavier than water.\n\nFinally, any class-name may be used collectively if we wish to assert\nsomething of the things denoted by it, not distributively but\naltogether, as that _Sheep are more numerous than wolves_.\n\n\n\n\nCHAPTER IV\n\nTHE CONNOTATION OF TERMS\n\n\n\u00a7 1. Terms are next to be classified according to their\nConnotation--that is, according to what they imply as characteristic of\nthe things denoted. We have seen that general names are used to denote\nmany things in the same sense, because the things denoted resemble one\nanother in certain ways: it is this resemblance in certain points that\nleads us to class the things together and call them by the same name;\nand therefore the points of resemblance constitute the sense or meaning\nof the name, or its Connotation, and limit its applicability to such\nthings as have these characteristic qualities. 'Sheep' for example, is\nused in the same sense, to denote any of a multitude of animals that\nresemble one another: their size, shape, woolly coats, cloven hoofs,\ninnocent ways and edibility are well known. When we apply to anything\nthe term 'sheep,' we imply that it has these qualities: 'sheep,'\ndenoting the animal, connotes its possessing these characteristics; and,\nof course, it cannot, without a figure of speech or a blunder, be used\nto denote anything that does not possess all these qualities. It is by a\nfigure of speech that the term 'sheep' is applied to some men; and to\napply it to goats would be a blunder.\n\nMost people are very imperfectly aware of the connotation of the words\nthey use, and are guided in using them merely by the custom of the\nlanguage. A man who employs a word quite correctly may be sadly posed by\na request to explain or define it. Moreover, so far as we are aware of\nthe connotation of terms, the number and the kind of attributes we\nthink of, in any given case, vary with the depth of our interest, and\nwith the nature of our interest in the things denoted. 'Sheep' has one\nmeaning to a touring townsman, a much fuller one to a farmer, and yet a\ndifferent one to a zoologist. But this does not prevent them agreeing in\nthe use of the word, as long as the qualities they severally include in\nits meaning are not incompatible.\n\nAll general names, and therefore not only class-names, like 'sheep,' but\nall attributives, have some connotation. 'Woolly' denotes anything that\nbears wool, and connotes the fact of bearing wool; 'innocent' denotes\nanything that habitually and by its disposition does no harm (or has not\nbeen guilty of a particular offence), and connotes a harmless character\n(or freedom from particular guilt); 'edible' denotes whatever can be\neaten with good results, and connotes its suitability for mastication,\ndeglutition, digestion, and assimilation.\n\n\u00a7 2. But whether all terms must connote as well as denote something, has\nbeen much debated. Proper names, according to what seems the better\nopinion, are, in their ordinary use, not connotative. To say that they\nhave no meaning may seem violent: if any one is called John Doe, this\nname, no doubt, means a great deal to his friends and neighbours,\nreminding them of his stature and physiognomy, his air and gait, his wit\nand wisdom, some queer stories, and an indefinite number of other\nthings. But all this significance is local or accidental; it only exists\nfor those who know the individual or have heard him described: whereas a\ngeneral name gives information about any thing or person it denotes to\neverybody who understands the language, without any particular knowledge\nof the individual.\n\nWe must distinguish, in fact, between the peculiar associations of the\nproper name and the commonly recognised meaning of the general name.\nThis is why proper names are not in the dictionary. Such a name as\nLondon, to be sure, or Napoleon Buonaparte, has a significance not\nmerely local; still, it is accidental. These names are borne by other\nplaces and persons than those that have rendered them famous. There are\nLondons in various latitudes, and, no doubt, many Napoleon Buonapartes\nin Louisiana; and each name has in its several denotations an altogether\ndifferent suggestiveness. For its suggestiveness is in each application\ndetermined by the peculiarities of the place or person denoted; it is\nnot given to the different places (or to the different persons) because\nthey have certain characteristics in common.\n\nHowever, the scientific grounds of the doctrine that proper names are\nnon-connotative, are these: The peculiarities that distinguish an\nindividual person or thing are admitted to be infinite, and anything\nless than a complete enumeration of these peculiarities may fail to\ndistinguish and identify the individual. For, short of a complete\nenumeration of them, the description may be satisfied by two or more\nindividuals; and in that case the term denoting them, if limited by such\na description, is not a proper but a general name, since it is\napplicable to two or more in the same sense. The existence of other\nindividuals to whom it applies may be highly improbable; but, if it be\nlogically possible, that is enough. On the other hand, the enumeration\nof infinite peculiarities is certainly impossible. Therefore proper\nnames have no assignable connotation. The only escape from this\nreasoning lies in falling back upon time and place, the principles of\nindividuation, as constituting the connotation of proper names. Two\nthings cannot be at the same time in the same place: hence 'the man who\nwas at a certain spot on the bridge of Lodi at a certain instant in a\ncertain year' suffices to identify Napoleon Buonaparte for that instant.\nSupposing no one else to have borne the name, then, is this its\nconnotation? No one has ever thought so. And, at any rate, time and\nplace are only extrinsic determinations (suitable indeed to events like\nthe battle of Lodi, or to places themselves like London); whereas the\nconnotation of a general term, such as 'sheep,' consists of intrinsic\nqualities. Hence, then, the scholastic doctrine 'that individuals have\nno essence' (see chap. xxii. \u00a7 9), and Hamilton's dictum 'that every\nconcept is inadequate to to the individual,' are justified.\n\nGeneral names, when used as proper names, lose their connotation, as\nEuxine or Newfoundland.\n\nSingular terms, other than Proper, have connotation; either in\nthemselves, like the singular pronouns 'he,' 'she,' 'it,' which are\ngeneral in their applicability, though singular in application; or,\nderivatively, from the general names that combine to form them, as in\n'the first Emperor of the French' or the 'Capital of the British\nEmpire.'\n\n\u00a7 3. Whether Abstract Terms have any connotation is another disputed\nquestion. We have seen that they denote a quality or qualities of\nsomething, and that is precisely what general terms connote: 'honesty'\ndenotes a quality of some men; 'honest' connotes the same quality,\nwhilst denoting the men who have it.\n\nThe denotation of abstract terms thus seems to exhaust their force or\nmeaning. It has been proposed, however, to regard them as connoting the\nqualities they directly stand for, and not denoting anything; but surely\nthis is too violent. To denote something is the same as to be the name\nof something (whether real or unreal), which every term must be. It is a\nbetter proposal to regard their denotation and connotation as\ncoinciding; though open to the objection that 'connote' means 'to mark\nalong with' something else, and this plan leaves nothing else. Mill\nthought that abstract terms are connotative when, besides denoting a\nquality, they suggest a quality of that quality (as 'fault' implies\n'hurtfulness'); but against this it may be urged that one quality cannot\nbear another, since every qualification of a quality constitutes a\ndistinct quality in the total ('milk-whiteness' is distinct from\n'whiteness,' _cf._ chap. iii. \u00a7 4). After all, if it is the most\nconsistent plan, why not say that abstract, like proper, terms have no\nconnotation?\n\nBut if abstract terms must be made to connote something, should it not\nbe those things, indefinitely suggested, to which the qualities belong?\nThus 'whiteness' may be considered to connote either snow or vapour, or\nany white thing, apart from one or other of which the quality has no\nexistence; whose existence therefore it implies. By this course the\ndenotation and connotation of abstract and of general names would be\nexactly reversed. Whilst the denotation of a general name is limited by\nthe qualities connoted, the connotation of an abstract name includes all\nthe things in which its denotation is realised. But the whole difficulty\nmay be avoided by making it a rule to translate, for logical purposes,\nall abstract into the corresponding general terms.\n\n\u00a7 4. If we ask how the connotation of a term is to be known, the answer\ndepends upon how it is used. If used scientifically, its connotation is\ndetermined by, and is the same as, its definition; and the definition is\ndetermined by examining the things to be denoted, as we shall see in\nchap. xxii. If the same word is used as a term in different sciences, as\n'property' in Law and in Logic, it will be differently defined by them,\nand will have, in each use, a correspondingly different connotation. But\nterms used in popular discourse should, as far as possible, have their\nconnotations determined by classical usage, i.e., by the sense in\nwhich they are used by writers and speakers who are acknowledged masters\nof the language, such as Dryden and Burke. In this case the classical\nconnotation determines the definition; so that to define terms thus used\nis nothing else than to analyse their accepted meanings.\n\nIt must not, however, be supposed that in popular use the connotation\nof any word is invariable. Logicians have attempted to classify\nterms into Univocal (having only one meaning) and \u00c6quivocal (or\nambiguous); and no doubt some words (like 'civil,' 'natural,' 'proud,'\n'liberal,' 'humorous') are more manifestly liable to ambiguous use than\nsome others. But in truth all general terms are popularly and\nclassically used in somewhat different senses.\n\nFigurative or tropical language chiefly consists in the transfer of\nwords to new senses, as by metaphor or metonymy. In the course of years,\ntoo, words change their meanings; and before the time of Dryden our\nwhole vocabulary was much more fluid and adaptable than it has since\nbecome. Such authors as Bacon, Milton, and Sir Thomas Browne often used\nwords derived from the Latin in some sense they originally had in Latin,\nthough in English they had acquired another meaning. Spenser and\nShakespeare, besides this practice, sometimes use words in a way that\ncan only be justified by their choosing to have it so; whilst their\ncontemporaries, Beaumont and Fletcher, write the perfect modern\nlanguage, as Dryden observed. Lapse of time, however, is not the chief\ncause of variation in the sense of words. The matters which terms are\nused to denote are often so complicated or so refined in the assemblage,\ninterfusion, or gradation of their qualities, that terms do not exist in\nsufficient abundance and discriminativeness to denote the things and, at\nthe same time, to convey by connotation a determinate sense of their\nagreements and differences. In discussing politics, religion, ethics,\n\u00e6sthetics, this imperfection of language is continually felt; and the\nonly escape from it, short of coining new words, is to use such words as\nwe have, now in one sense, now in another somewhat different, and to\ntrust to the context, or to the resources of the literary art, in order\nto convey the true meaning. Against this evil the having been born since\nDryden is no protection. It behoves us, then, to remember that terms are\nnot classifiable into Univocal and \u00c6quivocal, but that all terms are\nsusceptible of being used \u00e6quivocally, and that honesty and lucidity\nrequire us to try, as well as we can, to use each term univocally in the\nsame context.\n\nThe context of any proposition always proceeds upon some assumption or\nunderstanding as to the scope of the discussion, which controls the\ninterpretation of every statement and of every word. This was called by\nDe Morgan the \"universe of discourse\": an older name for it, revived by\nDr. Venn, and surely a better one, is _suppositio_. If we are talking of\nchildren, and 'play' is mentioned, the _suppositio_ limits the\nsuggestiveness of the word in one way; whilst if Monaco is the subject\nof conversation, the same word 'play,' under the influence of a\ndifferent _suppositio_, excites altogether different ideas. Hence to\nignore the _suppositio_ is a great source of fallacies of equivocation.\n'Man' is generally defined as a kind of animal; but 'animal' is often\nused as opposed to and excluding man. 'Liberal' has one meaning under\nthe _suppositio_ of politics, another with regard to culture, and still\nanother as to the disposal of one's private means. Clearly, therefore,\nthe connotation of general terms is relative to the _suppositio_, or\n\"universe of discourse.\"\n\n\u00a7 5. Relative and Absolute Terms.--Some words go in couples or groups:\nlike 'up-down,' 'former-latter,' 'father-mother-children,'\n'hunter-prey,' 'cause-effect,' etc. These are called Relative Terms,\nand their nature, as explained by Mill, is that the connotations of the\nmembers of such a pair or group are derived from the same set of facts\n(the _fundamentum relationis_). There cannot be an 'up' without a\n'down,' a 'father' without a 'mother' and 'child'; there cannot be a\n'hunter' without something hunted, nor 'prey' without a pursuer. What\nmakes a man a 'hunter' is his activities in pursuit; and what turns a\nchamois into 'prey' is its interest in these activities. The meaning of\nboth terms, therefore, is derived from the same set of facts; neither\nterm can be explained without explaining the other, because the relation\nbetween them is connoted by both; and neither can with propriety be used\nwithout reference to the other, or to some equivalent, as 'game' for\n'prey.'\n\nIn contrast with such Relative Terms, others have been called Absolute\nor Non-relative. Whilst 'hunter' and 'prey' are relative, 'man' and\n'chamois' have been considered absolute, as we may use them without\nthinking of any special connection between their meanings. However, if\nwe believe in the unity of Nature and in the relativity of knowledge\n(that is, that all knowledge depends upon comparison, or a perception of\nthe resemblances and differences of things), it follows that nothing can\nbe completely understood except through its agreements or contrasts with\neverything else, and that all terms derive their connotation from the\nsame set of facts, namely, from general experience. Thus both man and\nchamois are animals; this fact is an important part of the meaning of\nboth terms, and to that extent they are relative terms. 'Five yards' and\n'five minutes' are very different notions, yet they are profoundly\nrelated; for their very difference helps to make both notions distinct;\nand their intimate connection is shown in this, that five yards are\ntraversed in a certain time, and that five minutes are measured by the\nmotion of an index over some fraction of a yard upon the dial.\n\nThe distinction, then, between relative and non-relative terms must\nrest, not upon a fundamental difference between them (since, in fact,\nall words are relative), but upon the way in which words are used. We\nhave seen that some words, such as 'up-down,' 'cause-effect,' can only\nbe used relatively; and these may, for distinction, be called\nCorrelatives. But other words, whose meanings are only partially\ninterdependent, may often be used without attending to their relativity,\nand may then be considered as Absolute. We cannot say 'the hunter\nreturned empty handed,' without implying that 'the prey escaped'; but we\nmay say 'the man went supperless to bed,' without implying that 'the\nchamois rejoiced upon the mountain.' Such words as 'man' and 'chamois'\nmay, then, in their use, be, as to one another, non-relative.\n\nTo illustrate further the relativity of terms, we may mention some of\nthe chief classes of them.\n\nNumerical order: 1st, 2nd, 3rd, etc.; 1st implies 2nd, and 2nd 1st;\nand 3rd implies 1st and 2nd, but these do not imply 3rd; and so on.\n\nOrder in Time or Place: before-after; early-punctual-late;\nright-middle-left; North-South, etc.\n\nAs to Extent, Volume, and Degree: greater-equal-less;\nlarge-medium-small; whole and part.\n\nGenus and Species are a peculiar case of whole and part (_cf._ chaps.\nxxi.-ii.-iii.). Sometimes a term connotes all the attributes that\nanother does, and more besides, which, as distinguishing it, are called\ndifferential. Thus 'man' connotes all that 'animal' does, and also (as\n_differenti\u00e6_) the erect gait, articulate speech, and other attributes.\nIn such a case as this, where there are well-marked classes, the term\nwhose connotation is included in the others' is called a Genus of that\nSpecies. We have a Genus, triangle; and a Species, isosceles, marked off\nfrom all other triangles by the differential quality of having two equal\nsides: again--Genus, book; Species, quarto; Difference, having each\nsheet folded into four leaves.\n\nThere are other cases where these expressions 'genus' and 'species'\ncannot be so applied without a departure from usage, as, e.g., if we\ncall snow a species of the genus 'white,' for 'white' is not a\nrecognised class. The connotation of white (i.e., whiteness) is,\nhowever, part of the connotation of snow, just as the qualities of\n'animal' are amongst those of 'man'; and for logical purposes it is\ndesirable to use 'genus and species' to express that relativity of\nterms which consists in the connotation of one being part of the\nconnotation of the other.\n\nTwo or more terms whose connotations severally include that of another\nterm, whilst at the same time exceeding it, are (in relation to that\nother term) called Co-ordinate. Thus in relation to 'white,' snow and\nsilver are co-ordinate; in relation to colour, yellow and red and blue\nare co-ordinate. And when all the terms thus related stand for\nrecognised natural classes, the co-ordinate terms are called co-ordinate\nspecies; thus man and chamois are (in Logic) co-ordinate species of the\ngenus animal.\n\n\u00a7 6. From such examples of terms whose connotations are related as whole\nand part, it is easy to see the general truth of the doctrine that as\nconnotation decreases, denotation increases: for 'animal,' with less\nconnotation than man or chamois, denotes many more objects; 'white,'\nwith less connotation than snow or silver, denotes many more things, It\nis not, however, certain that this doctrine is always true in the\nconcrete: since there may be a term connoting two or more qualities, all\nof which qualities are peculiar to all the things it denotes; and, if\nso, by subtracting one of the qualities from its connotation, we should\nnot increase its denotation. If 'man,' for example, has among mammals\nthe two peculiar attributes of erect gait and articulate speech, then,\nby omitting 'articulate speech' from the connotation of man, we could\nnot apply the name to any more of the existing mammalia than we can at\npresent. Still we might have been able to do so; there might have been\nan erect inarticulate ape, and perhaps there once was one; and, if so,\nto omit 'articulate' from the connotation of man would make the term\n'man' denote that animal (supposing that there was no other difference\nto exclude it). Hence, potentially, an increase of the connotation of\nany term implies a decrease of its denotation. And, on the other hand,\nwe can only increase the denotation of a term, or apply it to more\nobjects, by decreasing its connotation; for, if the new things denoted\nby the term had already possessed its whole connotation, they must\nalready have been denoted by it. However, we may increase the _known_\ndenotation without decreasing the connotation, if we can discover the\nfull connotation in things not formerly supposed to have it, as when\ndolphins were discovered to be mammals; or if we can impose the\nrequisite qualities upon new individuals, as when by annexing some\nmillions of Africans we extend the denotation of 'British subject'\nwithout altering its connotation.\n\nMany of the things noticed in this chapter, especially in this section\nand the preceding, will be discussed at greater length in the chapters\non Classification and Definition.\n\n\u00a7 7. Contradictory Relative Terms.--Every term has, or may have, another\ncorresponding with it in such a way that, whatever differential\nqualities (\u00a7 5) it connotes, this other connotes merely their absence;\nso that one or the other is always formally predicable of any Subject,\nbut both these terms are never predicable of the same Subject in the\nsame relation: such pairs of terms are called Contradictories. Whatever\nSubject we take, it is either visible or invisible, but not both; either\nhuman or non-human, but not both.\n\nThis at least is true formally, though in practice we should think\nourselves trifled with if any one told us that 'A mountain is either\nhuman or non-human, but not both.' It is symbolic terms, such as X and\nx, that are properly said to be contradictories in relation to any\nsubject whatever, S or M. For, as we have seen, the ordinary use of\nterms is limited by some _suppositio_, and this is true of\nContradictories. 'Human' and 'non-human' may refer to zoological\nclassification, or to the scope of physical, mental, or moral powers--as\nif we ask whether to flourish a dumbbell of a ton weight, or to know the\nfuture by intuition, or impeccability, be human or non-human. Similarly,\n'visible' and 'invisible' refer either to the power of emitting or\nreflecting light, so that the words have no hold upon a sound or a\nscent, or else to power of vision and such qualifications as 'with the\nnaked eye' or 'with a microscope.'\n\nAgain, the above definition of Contradictories tells us that they cannot\nbe predicated of the same Subject \"in the same relation\"; that is, at\nthe same time or place, or under the same conditions. The lamp is\nvisible to me now, but will be invisible if I turn it out; one side of\nit is now visible, but the other is not: therefore without this\nrestriction, \"in the same relation,\" few or no terms would be\ncontradictory.\n\nIf a man is called wise, it may mean 'on the whole' or 'in a certain\naction'; and clearly a man may for once be wise (or act wisely) who, on\nthe whole, is not-wise. So that here again, by this ambiguity, terms\nthat seem contradictory are predicable of the same subject, but not \"in\nthe same relation.\" In order to avoid the ambiguity, however, we have\nonly to construct the term so as to express the relation, as 'wise on\nthe whole'; and this immediately generates the contradictory 'not-wise\non the whole.' Similarly, at one age a man may have black hair, at\nanother not-black hair; but the difficulty is practically removable by\nstating the age referred to.\n\nStill, this case easily leads us to a real difficulty in the use of\ncontradictory terms, a difficulty arising from the continuous change or\n'flux' of natural phenomena. If things are continually changing, it may\nbe urged that contradictory terms are always applicable to the same\nsubject, at least as fast as we can utter them: for if we have just said\nthat a man's hair is black, since (like everything else) his hair is\nchanging, it must now be not-black, though (to be sure) it may still\nseem black. The difficulty, such as it is, lies in this, that the human\nmind and its instrument language are not equal to the subtlety of\nNature. All things flow, but the terms of human discourse assume a\ncertain fixity of things; everything at every moment changes, but for\nthe most part we can neither perceive this change nor express it in\nordinary language.\n\nThis paradox, however, may, I suppose, be easily over-stated. The change\nthat continually agitates Nature consists in the movements of masses or\nmolecules, and such movements of things are compatible with a\nconsiderable persistence of their qualities. Not only are the molecular\nchanges always going on in a piece of gold compatible with its remaining\nyellow, but its persistent yellowness depends on the continuance of some\nof those changes. Similarly, a man's hair may remain black for some\nyears; though, no doubt, at a certain age its colour may begin to be\nproblematical, and the applicability to it of 'black' or 'not-black' may\nbecome a matter of genuine anxiety. Whilst being on our guard, then,\nagainst fallacies of contradiction arising from the imperfect\ncorrespondence of fact with thought and language, we shall often have to\nput up with it. Candour and humility having been satisfied by the above\nacknowledgment of the subtlety of Nature, we may henceforward proceed\nupon the postulate--that it is possible to use contradictory terms such\nas cannot both be predicated of the same subject in the same relation,\nthough one of them may be; that, for example, it may be truly said of a\nman for some years that his hair is black; and, if so, that during those\nyears to call it not-black is false or extremely misleading.\n\nThe most opposed terms of the literary vocabulary, however, such as\n'wise-foolish,' 'old-young,' 'sweet-bitter,' are rarely true\ncontradictories: wise and foolish, indeed, cannot be predicated of the\nsame man in the same relation; but there are many middling men, of whom\nneither can be predicated on the whole. For the comparison of\nquantities, again, we have three correlative terms,\n'greater--equal--less,' and none of these is the contradictory of either\nof the others. In fact, the contradictory of any term is one that\ndenotes the sum of its co-ordinates (\u00a7 6); and to obtain a\ncontradictory, the surest way is to coin one by prefixing to the given\nterm the particle 'not' or (sometimes) 'non': as 'wise, not-wise,'\n'human, non-human,' 'greater, not-greater.'\n\nThe separate word 'not' is surer to constitute a contradictory than the\nusual prefixes of negation, 'un-' or 'in-,' or even 'non'; since\ncompounds of these are generally warped by common use from a purely\nnegative meaning. Thus, 'Nonconformist' does not denote everybody who\nfails to conform. 'Unwise' is not equivalent to 'not-wise,' but means\n'rather foolish'; a very foolish action is not-wise, but can only be\ncalled unwise by meiosis or irony. Still, negatives formed by 'in' or\n'un' or 'non' are sometimes really contradictory of their positives; as\n'visible, invisible,' 'equal, unequal.'\n\n\u00a7 8. The distinction between Positive and Negative terms is not of much\nvalue in Logic, what importance would else attach to it being absorbed\nby the more definite distinction of contradictories. For contradictories\nare positive and negative in essence and, when least ambiguously stated,\nalso in form. And, on the other hand, as we have seen, when positive and\nnegative terms are not contradictory, they are misleading. As with\n'wise-unwise,' so with many others, such as 'happy-unhappy'; which are\nnot contradictories; since a man may be neither happy nor unhappy, but\nindifferent, or (again) so miserable that he can only be called unhappy\nby a figure of speech. In fact, in the common vocabulary a formal\nnegative often has a limited positive sense; and this is the case with\nunhappy, signifying the state of feeling in the milder shades of\nPurgatory.\n\nWhen a Negative term is fully contradictory of its Positive it is said\nto be Infinite; because it denotes an unascertained multitude of things,\na multitude only limited by the positive term and the _suppositio_; thus\n'not-wise' denotes all except the wise, within the _suppositio_ of\n'intelligent beings.' Formally (disregarding any _suppositio_), such a\nnegative term stands for all possible terms except its positive: x\ndenotes everything but X; and 'not-wise' may be taken to include stones,\ntriangles and hippogriffs. And even in this sense, a negative term has\nsome positive meaning, though a very indefinite one, not a specific\npositive force like 'unwise' or 'unhappy': it denotes any and everything\nthat has not the attributes connoted by the corresponding positive term.\n\nPrivative Terms connote the absence of a quality that normally belongs\nto the kind of thing denoted, as 'blind' or 'deaf.' We may predicate\n'blind' or 'deaf' of a man, dog or cow that happens not to be able to\nsee or hear, because the powers of seeing and hearing generally belong\nto those species; but of a stone or idol these terms can only be used\nfiguratively. Indeed, since the contradictory of a privative carries\nwith it the privative limitation, a stone is strictly 'not-blind': that\nis, it is 'not-something-that-normally-having-sight-wants-it.'\n\nContrary Terms are those that (within a certain genus or _suppositio_)\nseverally connote differential qualities that are, in fact, mutually\nincompatible in the same relation to the same thing, and therefore\ncannot be predicated of the same subject in the same relation; and, so\nfar, they resemble Contradictory Terms: but they differ from\ncontradictory terms in this, that the differential quality connoted by\neach of them is definitely positive; no Contrary Term is infinite, but\nis limited to part of the _suppositio_ excluded by the others; so that,\npossibly, neither of two Contraries is truly predicable of a given\nsubject. Thus 'blue' and 'red' are Contraries, for they cannot both be\npredicated of the same thing in the same relation; but are not\nContradictories, since, in a given case, neither may be predicable: if a\nflower is blue in a certain part, it cannot in the same part be red; but\nit may be neither blue nor red, but yellow; though it is certainly\neither blue or not-blue. All co-ordinate terms are formal Contraries;\nbut if, in fact, a series of co-ordinates comprises only two (as\nmale-female), they are empirical Contradictories; since each includes\nall that area of the _suppositio_ which the other excludes.\n\nThe extremes of a series of co-ordinate terms are Opposites; as, in a\nlist of colours, white and black, the most strongly contrasted, are said\nto be opposites, or as among moods of feeling, rapture and misery are\nopposites. But this distinction is of slight logical importance.\nImperfect Positive and Negative couples, like 'happy and unhappy,' which\n(as we have seen) are not contradictories, are often called Opposites.\n\nThe members of any series of Contraries are all included by any one of\nthem and its contradictory, as all colours come under 'red' and\n'not-red,' all moods of feeling under 'happy' and 'not-happy.'\n\n\n\n\nCHAPTER V\n\nTHE CLASSIFICATION OF PROPOSITIONS\n\n\n\u00a7 1. Logicians classify Propositions according to Quantity, Quality,\nRelation and Modality.\n\nAs to Quantity, propositions are either Universal or Particular; that is\nto say, the predicate is affirmed or denied either of the whole subject\nor of a part of it--of _All_ or of _Some S_.\n\n _All S is P_ (that is, _P_ is predicated of _all S_).\n _Some S is P_ (that is, _P_ is predicated of _some S_).\n\nAn Universal Proposition may have for its subject a singular term, a\ncollective, a general term distributed, or an abstract term.\n\n(1) A proposition having a singular term for its subject, as _The Queen\nhas gone to France_, is called a Singular Proposition; and some\nLogicians regard this as a third species of proposition with respect to\nquantity, distinct from the Universal and Particular; but that is\nneedless.\n\n(2) A collective term may be the subject, as _The Black Watch is ordered\nto India_. In this case, as well as in singular propositions, a\npredication is made concerning the whole subject as a whole.\n\n(3) The subject may be a general term taken in its full denotation, as\n_All apes are sagacious_; and in this case a Predication is made\nconcerning the whole subject distributively; that is, of each and\neverything the subject stands for.\n\n(4) Propositions whose subjects are abstract terms, though they may\nseem to be formally Singular, are really as to their meaning\ndistributive Universals; since whatever is true of a quality is true of\nwhatever thing has that quality so far as that quality is concerned.\n_Truth will prevail_ means that _All true propositions are accepted at\nlast_ (by sheer force of being true, in spite of interests, prejudices,\nignorance and indifference). To bear this in mind may make one cautious\nin the use of abstract terms.\n\nIn the above paragraphs a distinction is implied between Singular and\nDistributive Universals; but, technically, every term, whether subject\nor predicate, when taken in its full denotation (or universally), is\nsaid to be 'distributed,' although this word, in its ordinary sense,\nwould be directly applicable only to general terms. In the above\nexamples, then, 'Queen,' 'Black Watch,' 'apes,' and 'truth' are all\ndistributed terms. Indeed, a simple definition of the Universal\nProposition is 'one whose subject is distributed.'\n\nA Particular Proposition is one that has a general term for its subject,\nwhilst its predicate is not affirmed or denied of everything the subject\ndenotes; in other words, it is one whose subject is not distributed: as\n_Some lions inhabit Africa_.\n\nIn ordinary discourse it is not always explicitly stated whether\npredication is universal or particular; it would be very natural to say\n_Lions inhabit Africa_, leaving it, as far as the words go, uncertain\nwhether we mean _all_ or _some_ lions. Propositions whose quantity is\nthus left indefinite are technically called 'preindesignate,' their\nquantity not being stated or designated by any introductory expression;\nwhilst propositions whose quantity is expressed, as _All\nfoundling-hospitals have a high death-rate_, or _Some wine is made from\ngrapes_, are said to be 'predesignate.' Now, the rule is that\npreindesignate propositions are, for logical purposes, to be treated as\nparticular; since it is an obvious precaution of the science of proof,\nin any practical application, _not to go beyond the evidence_. Still,\nthe rule may be relaxed if the universal quantity of a preindesignate\nproposition is well known or admitted, as in _Planets shine with\nreflected light_--understood of the planets of our solar system at the\npresent time. Again, such a proposition as _Man is the paragon of\nanimals_ is not a preindesignate, but an abstract proposition; the\nsubject being elliptical for _Man according to his proper nature_; and\nthe translation of it into a predesignate proposition is not _All men\nare paragons_; nor can _Some men_ be sufficient, since an abstract can\nonly be adequately rendered by a distributed term; but we must say, _All\nmen who approach the ideal_. Universal real propositions, true without\nqualification, are very scarce; and we often substitute for them\n_general_ propositions, saying perhaps--_generally, though not\nuniversally, S is P_. Such general propositions are, in strictness,\nparticular; and the logical rules concerning universals cannot be\napplied to them without careful scrutiny of the facts.\n\nThe marks or predesignations of Quantity commonly used in Logic are: for\nUniversals, _All_, _Any_, _Every_, _Whatever_ (in the negative _No_ or\n_No one_, see next \u00a7); for Particulars, _Some_.\n\nNow _Some_, technically used, does not mean _Some only,_ but _Some at\nleast_ (it may be one, or more, or all). If it meant '_Some only_,'\nevery particular proposition would be an exclusive exponible (chap. ii.\n\u00a7 3); since _Only some men are wise_ implies that _Some men are not\nwise_. Besides, it may often happen in an investigation that all the\ninstances we have observed come under a certain rule, though we do not\nyet feel justified in regarding the rule as universal; and this\nsituation is exactly met by the expression _Some_ (_it may be all_).\n\nThe words _Many_, _Most_, _Few_ are generally interpreted to mean\n_Some_; but as _Most_ signifies that exceptions are known, and _Few_\nthat the exceptions are the more numerous, propositions thus\npredesignate are in fact exponibles, mounting to _Some are_ and _Some\nare not_. If to work with both forms be too cumbrous, so that we must\nchoose one, apparently _Few are_ should be treated as _Some are not_.\nThe scientific course to adopt with propositions predesignate by _Most_\nor _Few_, is to collect statistics and determine the percentage; thus,\n_Few men are wise_--say 2 per cent.\n\nThe Quantity of a proposition, then, is usually determined entirely by\nthe quantity of the subject, whether _all_ or _some_. Still, the\nquantity of the predicate is often an important consideration; and\nthough in ordinary usage the predicate is seldom predesignate, Logicians\nagree that in every Negative Proposition (see \u00a7 2) the predicate is\n'distributed,' that is to say, is denied altogether of the subject, and\nthat this is involved in the form of denial. To say _Some men are not\nbrave_, is to declare that the quality for which men may be called brave\nis not found in any of the _Some men_ referred to: and to say _No men\nare proof against flattery_, cuts off the being 'proof against flattery'\nentirely from the list of human attributes. On the other hand, every\nAffirmative Proposition is regarded as having an undistributed\npredicate; that is to say, its predicate is not affirmed exclusively of\nthe subject. _Some men are wise_ does not mean that 'wise' cannot be\npredicated of any other beings; it is equivalent to _Some men are wise_\n(_whoever else may be_). And _All elephants are sagacious_ does not\nlimit sagacity to elephants: regarding 'sagacious' as possibly denoting\nmany animals of many species that exhibit the quality, this proposition\nis equivalent to '_All elephants are_ some _sagacious animals_.' The\naffirmative predication of a quality does not imply exclusive possession\nof it as denial implies its complete absence; and, therefore, to regard\nthe predicate of an affirmative proposition as distributed would be to\ngo beyond the evidence and to take for granted what had never been\nalleged.\n\nSome Logicians, seeing that the quantity of predicates, though not\ndistinctly expressed, is recognised, and holding that it is the part of\nLogic \"to make explicit in language whatever is implicit in thought,\"\nhave proposed to exhibit the quantity of predicates by predesignation,\nthus: 'Some men are _some_ wise (beings)'; 'some men are not _any_ brave\n(beings)'; etc. This is called the Quantification of the Predicate,\nand leads to some modifications of Deductive Logic which will be\nreferred to hereafter. (See \u00a7 3; chap. vii. \u00a7 4, and chap. viii. \u00a7 3.)\n\n\u00a7 2. As to Quality, Propositions are either Affirmative or Negative. An\nAffirmative Proposition is, formally, one whose copula is affirmative\n(or, has no negative sign), as _S--is--P, All men--are--partial to\nthemselves_. A Negative Proposition is one whose copula is negative (or,\nhas a negative sign), as _S--is not--P, Some men--are not--proof against\nflattery_. When, indeed, a Negative Proposition is of Universal\nQuantity, it is stated thus: _No S is P, No men are proof against\nflattery_; but, in this case, the detachment of the negative sign from\nthe copula and its association with the subject is merely an accident of\nour idiom; the proposition is the same as _All men--are not--proof\nagainst flattery_. It must be distinguished, therefore, from such an\nexpression as _Not every man is proof against flattery_; for here the\nnegative sign really restricts the subject; so that the meaning\nis--_Some men at most_ (it may be _none) are proof against flattery_;\nand thus the proposition is Particular, and is rendered--_Some men--are\nnot--proof against flattery_.\n\nWhen the negative sign is associated with the predicate, so as to make\nthis an Infinite Term (chap. iv. \u00a7 8), the proposition is called an\nInfinite Proposition, as _S is not-P_ (or _p), All men are--incapable of\nresisting flattery_, or _are--not-proof against flattery_.\n\nInfinite propositions, when the copula is affirmative, are formally,\nthemselves affirmative, although their force is chiefly negative; for,\nas the last example shows, the difference between an infinite and a\nnegative proposition may depend upon a hyphen. It has been proposed,\nindeed, with a view to superficial simplification, to turn all\nNegatives into Infinites, and thus render all propositions Affirmative\nin Quality. But although every proposition both affirms and denies\nsomething according to the aspect in which you regard it (as _Snow is\nwhite_ denies that it is any other colour, and _Snow is not blue_\naffirms that it is some other colour), yet there is a great difference\nbetween the definite affirmation of a genuine affirmative and the vague\naffirmation of a negative or infinite; so that materially an affirmative\ninfinite is the same as a negative.\n\nGenerally Mill's remark is true, that affirmation and denial stand for\ndistinctions of fact that cannot be got rid of by manipulation of words.\nWhether granite sinks in water, or not; whether the rook lives a hundred\nyears, or not; whether a man has a hundred dollars in his pocket, or\nnot; whether human bones have ever been found in Pliocene strata, or\nnot; such alternatives require distinct forms of expression. At the same\ntime, it may be granted that many facts admit of being stated with\nnearly equal propriety in either Quality, as _No man is proof against\nflattery_, or _All men are open to flattery_.\n\nBut whatever advantage there is in occasionally changing the Quality of\na proposition may be gained by the process of Obversion (chap. vii. \u00a7\n5); whilst to use only one Quality would impair the elasticity of\nlogical expression. It is a postulate of Logic that the negative sign\nmay be transferred from the copula to the predicate, or from the\npredicate to the copula, without altering the sense of a proposition;\nand this is justified by the experience that not to have an attribute\nand to be without it are the same thing.\n\n\u00a7 3. A. I. E. O.--Combining the two kinds of Quantity, Universal and\nParticular, with the two kinds of Quality, Affirmative and Negative, we\nget four simple types of proposition, which it is usual to symbolise by\nthe letters A. I. E. O., thus:\n\nA. Universal Affirmative -- All S is P.\nI. Particular Affirmative -- Some S is P.\nE. Universal Negative -- No S is P.\nO. Particular Negative -- Some S is not P.\n\nAs an aid to the remembering of these symbols we may observe that A. and\nI. are the first two vowels in _affirmo_ and that E. and O. are the\nvowels in _nego_.\n\nIt must be acknowledged that these four kinds of proposition recognised\nby Formal Logic constitute a very meagre selection from the list of\npropositions actually used in judgment and reasoning.\n\nThose Logicians who explicitly quantify the predicate obtain, in all,\neight forms of proposition according to Quantity and Quality:\n\n[Transcriber's Note: The Greek characters used in the original are\nrepresented below by the name of the character in square brackets.]\n\nU. Toto-total Affirmative -- All X is all Y.\nA. Toto-partial Affirmative -- All X is some Y.\nY. Parti-total Affirmative -- Some X is all Y.\nI. Parti-partial Affirmative -- Some X is some Y.\nE. Toto-total Negative -- No X is any Y.\n[eta]. Toto-partial Negative -- No X is some Y.\nO. Parti-total Negative -- Some X is not any Y.\n[omega]. Parti-partial Negative -- Some X is not some Y.\n\nHere A. I. E. O. correspond with those similarly symbolised in the usual\nlist, merely designating in the predicates the quantity which was\nformerly treated as implicit.\n\n\u00a7 4. As to Relation, propositions are either Categorical or Conditional.\nA Categorical Proposition is one in which the predicate is directly\naffirmed or denied of the subject without any limitation of time, place,\nor circumstance, extraneous to the subject, as _All men in England are\nsecure of justice_; in which proposition, though there is a limitation\nof place ('in England'), it is included in the subject. Of this kind are\nnearly all the examples that have yet been given, according to the form\n_S is P_.\n\nA Conditional Proposition is so called because the predication is made\nunder some limitation or condition not included in the subject, as _If a\nman live in England, he is secure of justice_. Here the limitation\n'living in England' is put into a conditional sentence extraneous to the\nsubject, 'he,' representing any man.\n\nConditional propositions, again, are of two kinds--Hypothetical and\nDisjunctive. Hypothetical propositions are those that are limited by an\nexplicit conditional sentence, as above, or thus: _If Joe Smith was a\nprophet, his followers have been unjustly persecuted_. Or in symbols\nthus:\n\n If A is, B is;\n If A is B, A is C;\n If A is B, C is D.\n\nDisjunctive propositions are those in which the condition under which\npredication is made is not explicit but only implied under the disguise\nof an alternative proposition, as _Joe Smith was either a prophet or an\nimpostor_. Here there is no direct predication concerning Joe Smith, but\nonly a predication of one of the alternatives conditionally on the other\nbeing denied, as, _If Joe Smith was not a prophet he was an impostor_;\nor, _If he was not an impostor, he was a prophet_. Symbolically,\nDisjunctives may be represented thus:\n\n A is either B or C,\n Either A is B or C is D.\n\nFormally, every Conditional may be expressed as a Categorical. For our\nlast example shows how a Disjunctive may be reduced to two Hypotheticals\n(of which one is redundant, being the contrapositive of the other; see\nchap. vii. \u00a7 10). And a Hypothetical is reducible to a Categorical thus:\n_If the sky is clear, the night is cold_ may be read--_The case of the\nsky being clear is a case of the night being cold_; and this, though a\nclumsy plan, is sometimes convenient. It would be better to say _The sky\nbeing clear is a sign of the night being cold_, or a condition of it.\nFor, as Mill says, the essence of a Hypothetical is to state that one\nclause of it (the indicative) may be inferred from the other (the\nconditional). Similarly, we might write: _Proof of Joe Smith's not being\na prophet is a proof of his being an impostor_.\n\nThis turning of Conditionals into Categoricals is called a Change of\nRelation; and the process may be reversed: _All the wise are virtuous_\nmay be written, _If any man is wise he is virtuous_; or, again, _Either\na man is not-wise or he is virtuous_. But the categorical form is\nusually the simplest.\n\nIf, then, as substitutes for the corresponding conditionals,\ncategoricals are formally adequate, though sometimes inelegant, it may\nbe urged that Logic has nothing to do with elegance; or that, at any\nrate, the chief elegance of science is economy, and that therefore, for\nscientific purposes, whatever we may write further about conditionals\nmust be an ugly excrescence. The scientific purpose of Logic is to\nassign the conditions of proof. Can we, then, in the conditional form\nprove anything that cannot be proved in the categorical? Or does a\nconditional require to be itself proved by any method not applicable to\nthe Categorical? If not, why go on with the discussion of Conditionals?\nFor all laws of Nature, however stated, are essentially categorical. 'If\na straight line falls on another straight line, the adjacent angles are\ntogether equal to two right angles'; 'If a body is unsupported, it\nfalls'; 'If population increases, rents tend to rise': here 'if' means\n'whenever' or 'all cases in which'; for to raise a doubt whether a\nstraight line is ever conceived to fall upon another, whether bodies are\never unsupported, or population ever increases, is a superfluity of\nscepticism; and plainly the hypothetical form has nothing to do with the\nproof of such propositions, nor with inference from them.\n\nStill, the disjunctive form is necessary in setting out the relation of\ncontradictory terms, and in stating a Division (chap. xxi.), whether\nformal (_as A is B or not-B_) or material (as _Cats are white, or black,\nor tortoiseshell, or tabby_). And in some cases the hypothetical form is\nuseful. One of these occurs where it is important to draw attention to\nthe condition, as something doubtful or especially requiring\nexamination. _If there is a resisting medium in space, the earth will\nfall into the sun; If the Corn Laws are to be re-enacted, we had better\nsell railways and buy land_: here the hypothetical form draws attention\nto the questions whether there is a resisting medium in space, whether\nthe Corn Laws are likely to be re-enacted; but as to methods of\ninference and proof, the hypothetical form has nothing to do with them.\nThe propositions predicate causation: _A resisting medium in space is a\ncondition of the earth's falling into the sun; A Corn Law is a condition\nof the rise of rents, and of the fall of railway profits_.\n\nA second case in which the hypothetical is a specially appropriate form\nof statement occurs where a proposition relates to a particular matter\nand to future time, as _If there be a storm to-morrow, we shall miss our\npicnic_. Such cases are of very slight logical interest. It is as\nexercises in formal thinking that hypotheticals are of most value;\ninasmuch as many people find them more difficult than categoricals to\nmanipulate.\n\nIn discussing Conditional Propositions, the conditional sentence of a\nHypothetical, or the first alternative of a Disjunctive, is called the\nAntecedent; the indicative sentence of a Hypothetical, or the second\nalternative of a Disjunctive, is called the Consequent.\n\nHypotheticals, like Categoricals, have been classed according to\nQuantity and Quality. Premising that the quantity of a Hypothetical\ndepends on the quantity of its Antecedent (which determines its\nlimitation), whilst its quality depends on the quality of its consequent\n(which makes the predication), we may exhibit four forms:\n\n A. _If A is B, C is D;_\n I. _Sometimes when A is B, C is D;_\n E. _If A is B, C is not D;_\n O. _Sometimes when A is B, C is not D._\n\nBut I. and O. are rarely used.\n\nAs for Disjunctives, it is easy to distinguish the two quantities thus:\n\n A. _Either A is B, or C is D;_\n I. _Sometimes either A is B or C is D._\n\nBut I. is rarely used. The distinction of quality, however, cannot be\nmade: there are no true negative forms; for if we write--\n\n _Neither is A B, nor C D,_\n\nthere is here no alternative predication, but only an Exponible\nequivalent to _No A is B, and No C is D_. And if we write--\n\n _Either A is not B, or C is not D,_\n\nthis is affirmative as to the alternation, and is for all methods of\ntreatment equivalent to A.\n\nLogicians are divided in opinion as to the interpretation of the\nconjunction 'either, or'; some holding that it means 'not both,' others\nthat it means 'it may be both.' Grammatical usage, upon which the\nquestion is sometimes argued, does not seem to be established in favour\nof either view. If we say _A man so precise in his walk and conversation\nis either a saint or a consummate hypocrite_; or, again, _One who is\nhappy in a solitary life is either more or less than man_; we cannot in\nsuch cases mean that the subject may be both. On the other hand, if it\nbe said that _the author of 'A Tale of a Tub' is either a misanthrope or\na dyspeptic_, the alternatives are not incompatible. Or, again, given\nthat _X. is a lunatic, or a lover, or a poet_, the three predicates have\nmuch congruity.\n\nIt has been urged that in Logic, language should be made as exact and\ndefinite as possible, and that this requires the exclusive\ninterpretation 'not both.' But it seems a better argument, that Logic\n(1) should be able to express all meanings, and (2), as the science of\nevidence, must not assume more than is given; to be on the safe side, it\nmust in doubtful cases assume the least, just as it generally assumes a\npreindesignate term to be of particular quantity; and, therefore\n'either, or' means 'one, or the other, or both.'\n\nHowever, when both the alternative propositions have the same subject,\nas _Either A is B, or A is C_, if the two predicates are contrary or\ncontradictory terms (as 'saint' and 'hypocrite,' or 'saint' and\n'not-saint'), they cannot in their nature be predicable in the same way\nof the same subject; and, therefore, in such a case 'either, or' means\none or the other, but not both in the same relation. Hence it seems\nnecessary to admit that the conjunction 'either, or' may sometimes\nrequire one interpretation, sometimes the other; and the rule is that it\nimplies the further possibility 'or both,' except when both alternatives\nhave the same subject whilst the predicates are contrary or\ncontradictory terms.\n\nIf, then, the disjunctive _A is either B or C_ (_B_ and _C_ being\ncontraries) implies that both alternatives cannot be true, it can only\nbe adequately rendered in hypotheticals by the two forms--(1) _If A is\nB, it is not C_, and (2)_If A is not B, it is C_. But if the disjunctive\n_A is either B or C_ (_B_ and _C_ not being contraries) implies that\nboth may be true, it will be adequately translated into a hypothetical\nby the single form, _If A is not B, it is C_. We cannot translate it\ninto--_If A is B, it is not C_, for, by our supposition, if '_A is B_'\nis true, it does not follow that '_A is C_' must be false.\n\nLogicians are also divided in opinion as to the function of the\nhypothetical form. Some think it expresses doubt; for the consequent\ndepends on the antecedent, and the antecedent, introduced by 'if,' may\nor may not be realised, as in _If the sky is clear, the night is cold_:\nwhether the sky is, or is not, clear being supposed to be uncertain. And\nwe have seen that some hypothetical propositions seem designed to draw\nattention to such uncertainty, as--_If there is a resisting medium in\nspace_, etc. But other Logicians lay stress upon the connection of the\nclauses as the important matter: the statement is, they say, that the\nconsequent may be inferred from the antecedent. Some even declare that\nit is given as a necessary inference; and on this ground Sigwart rejects\nparticular hypotheticals, such as _Sometimes when A is B, C is D_; for\nif it happens only sometimes the connexion cannot be necessary. Indeed,\nit cannot even be probably inferred without further grounds. But this is\nalso true whenever the antecedent and consequent are concerned with\ndifferent matter. For example, _If the soul is simple, it is\nindestructible_. How do you know that? Because _Every simple substance\nis indestructible_. Without this further ground there can be no\ninference. The fact is that conditional forms often cover assertions\nthat are not true complex propositions but a sort of euthymemes (chap.\nxi. \u00a7 2), arguments abbreviated and rhetorically disguised. Thus: _If\npatience is a virtue there are painful virtues_--an example from Dr.\nKeynes. Expanding this we have--\n\n Patience is painful;\n Patience is a virtue:\n .'. Some virtue is painful.\n\nAnd then we see the equivocation of the inference; for though patience\nbe painful _to learn_, it is not painful _as a virtue_ to the patient\nman.\n\nThe hypothetical, '_If Plato was not mistaken poets are dangerous\ncitizens_,' may be considered as an argument against the laureateship,\nand may be expanded (informally) thus: 'All Plato's opinions deserve\nrespect; one of them was that poets are bad citizens; therefore it\nbehoves us to be chary of encouraging poetry.' Or take this\ndisjunctive, '_Either Bacon wrote the works ascribed to Shakespeare, or\nthere were two men of the highest genius in the same age and country_.'\nThis means that it is not likely there should be two such men, that we\nare sure of Bacon, and therefore ought to give him all the glory. Now,\nif it is the part of Logic 'to make explicit in language all that is\nimplicit in thought,' or to put arguments into the form in which they\ncan best be examined, such propositions as the above ought to be\nanalysed in the way suggested, and confirmed or refuted according to\ntheir real intention.\n\nWe may conclude that no single function can be assigned to all\nhypothetical propositions: each must be treated according to its own\nmeaning in its own context.\n\n\u00a7 5. As to Modality, propositions are divided into Pure and Modal. A\nModal proposition is one in which the predicate is affirmed or denied,\nnot simply but _cum modo_, with a qualification. And some Logicians have\nconsidered any adverb occurring in the predicate, or any sign of past or\nfuture tense, enough to constitute a modal: as 'Petroleum is\n_dangerously_ inflammable'; 'English _will be_ the universal language.'\nBut far the most important kind of modality, and the only one we need\nconsider, is that which is signified by some qualification of the\npredicate as to the degree of certainty with which it is affirmed or\ndenied. Thus, 'The bite of the cobra is _probably_ mortal,' is called a\nContingent or Problematic Modal: 'Water is _certainly_ composed of\noxygen and hydrogen' is an Assertory or Certain Modal: 'Two straight\nlines _cannot_ enclose a space' is a Necessary or Apodeictic Modal (the\nopposite being inconceivable). Propositions not thus qualified are\ncalled Pure.\n\nModal propositions have had a long and eventful history, but they have\nnot been found tractable by the resources of ordinary Logic, and are now\ngenerally neglected by the authors of text-books. No doubt such\npropositions are the commonest in ordinary discourse, and in some rough\nway we combine them and draw inferences from them. It is understood\nthat a combination of assertory or of apodeictic premises may warrant an\nassertory or an apodeictic conclusion; but that if we combine either of\nthese with a problematic premise our conclusion becomes problematic;\nwhilst the combination of two problematic premises gives a conclusion\nless certain than either. But if we ask 'How much less certain?' there\nis no answer. That the modality of a conclusion follows the less certain\nof the premises combined, is inadequate for scientific guidance; so\nthat, as Deductive Logic can get no farther than this, it has abandoned\nthe discussion of Modals. To endeavour to determine the degree of\ncertainty attaching to a problematic judgment is not, however, beyond\nthe reach of Induction, by analysing circumstantial evidence, or by\ncollecting statistics with regard to it. Thus, instead of 'The cobra's\nbite is _probably_ fatal,' we might find that it is fatal 80 times in\n100. Then, if we know that of those who go to India 3 in 1000 are\nbitten, we can calculate what the chances are that any one going to\nIndia will die of a cobra's bite (chap. xx.).\n\n\u00a7 6. Verbal and Real Propositions.--Another important division of\npropositions turns upon the relation of the predicate to the subject in\nrespect of their connotations. We saw, when discussing Relative Terms,\nthat the connotation of one term often implies that of another;\nsometimes reciprocally, like 'master' and 'slave'; or by inclusion, like\nspecies and genus; or by exclusion, like contraries and contradictories.\nWhen terms so related appear as subject and predicate of the same\nproposition, the result is often tautology--e.g., _The master has\nauthority over his slave; A horse is an animal; Red is not blue; British\nis not foreign_. Whoever knows the meaning of 'master,' 'horse,' 'red,'\n'British,' learns nothing from these propositions. Hence they are called\nVerbal propositions, as only expounding the sense of words, or as if\nthey were propositions only by satisfying the forms of language, not by\nfulfilling the function of propositions in conveying a knowledge of\nfacts. They are also called 'Analytic' and 'Explicative,' when they\nseparate and disengage the elements of the connotation of the subject.\nDoubtless, such propositions may be useful to one who does not know the\nlanguage; and Definitions, which are verbal propositions whose\npredicates analyse the whole connotations of their subjects, are\nindispensable instruments of science (see chap. xxii.).\n\nOf course, hypothetical propositions may also be verbal, as _If the soul\nbe material it is extended_; for 'extension' is connoted by 'matter';\nand, therefore, the corresponding disjunctive is verbal--_Either the\nsoul is not material, or it is extended_. But a true divisional\ndisjunctive can never be verbal (chap. xxi. \u00a7 4, rule 1).\n\nOn the other hand, when there is no such direct relation between subject\nand predicate that their connotations imply one another, but the\npredicate connotes something that cannot be learnt from the connotation\nof the subject, there is no longer tautology, but an enlargement of\nmeaning--e.g., _Masters are degraded by their slaves; The horse is the\nnoblest animal; Red is the favourite colour of the British army; If the\nsoul is simple, it is indestructible_. Such propositions are called\nReal, Synthetic, or Ampliative, because they are propositions for which\na mere understanding of their subjects would be no substitute, since the\npredicate adds a meaning of its own concerning matter of fact.\n\nTo any one who understands the language, a verbal proposition can never\nbe an inference or conclusion from evidence; nor can a verbal\nproposition ever furnish grounds for an inference, except as to the\nmeaning of words. The subject of real and verbal propositions will\ninevitably recur in the chapters on Definition; but tautologies are such\ncommon blemishes in composition, and such frequent pitfalls in argument,\nthat attention cannot be drawn to them too early or too often.\n\n\n\n\nCHAPTER VI\n\nCONDITIONS OF IMMEDIATE INFERENCE\n\n\n\u00a7 1. The word Inference is used in two different senses, which are often\nconfused but should be carefully distinguished. In the first sense, it\nmeans a process of thought or reasoning by which the mind passes from\nfacts or statements presented, to some opinion or expectation. The data\nmay be very vague and slight, prompting no more than a guess or surmise;\nas when we look up at the sky and form some expectation about the\nweather, or from the trick of a man's face entertain some prejudice as\nto his character. Or the data may be important and strongly significant,\nlike the footprint that frightened Crusoe into thinking of cannibals, or\nas when news of war makes the city expect that Consols will fall. These\nare examples of the act of inferring, or of inference as a process; and\nwith inference in this sense Logic has nothing to do; it belongs to\nPsychology to explain how it is that our minds pass from one perception\nor thought to another thought, and how we come to conjecture, conclude\nand believe (_cf._ chap. i. \u00a7 6).\n\nIn the second sense, 'inference' means not this process of guessing or\nopining, but the result of it; the surmise, opinion, or belief when\nformed; in a word, the conclusion: and it is in this sense that\nInference is treated of in Logic. The subject-matter of Logic is an\ninference, judgment or conclusion concerning facts, embodied in a\nproposition, which is to be examined in relation to the evidence that\nmay be adduced for it, in order to determine whether, or how far, the\nevidence amounts to proof. Logic is the science of Reasoning in the\nsense in which 'reasoning' means giving reasons, for it shows what sort\nof reasons are good. Whilst Psychology explains how the mind goes\nforward from data to conclusions, Logic takes a conclusion and goes back\nto the data, inquiring whether those data, together with any other\nevidence (facts or principles) that can be collected, are of a nature to\nwarrant the conclusion. If we think that the night will be stormy, that\nJohn Doe is of an amiable disposition, that water expands in freezing,\nor that one means to national prosperity is popular education, and wish\nto know whether we have evidence sufficient to justify us in holding\nthese opinions, Logic can tell us what form the evidence should assume\nin order to be conclusive. What _form_ the evidence should assume: Logic\ncannot tell us what kinds of fact are proper evidence in any of these\ncases; that is a question for the man of special experience in life, or\nin science, or in business. But whatever facts constitute the evidence,\nthey must, in order to prove the point, admit of being stated in\nconformity with certain principles or conditions; and of these\nprinciples or conditions Logic is the science. It deals, then, not with\nthe subjective process of inferring, but with the objective grounds that\njustify or discredit the inference.\n\n\u00a7 2. Inferences, in the Logical sense, are divided into two great\nclasses, the Immediate and the Mediate, according to the character of\nthe evidence offered in proof of them. Strictly, to speak of inferences,\nin the sense of conclusions, as immediate or mediate, is an abuse of\nlanguage, derived from times before the distinction between inference as\nprocess and inference as result was generally felt. No doubt we ought\nrather to speak of Immediate and Mediate Evidence; but it is of little\nuse to attempt to alter the traditional expressions of the science.\n\nAn Immediate Inference, then, is one that depends for its proof upon\nonly one other proposition, which has the same, or more extensive,\nterms (or matter). Thus that _one means to national prosperity is\npopular education_ is an immediate inference, if the evidence for it is\nno more than the admission that _popular education is a means to\nnational prosperity:_ Similarly, it is an immediate inference that _Some\nauthors are vain_, if it be granted that _All authors are vain_.\n\nAn Immediate Inference may seem to be little else than a verbal\ntransformation; some Logicians dispute its claims to be called an\ninference at all, on the ground that it is identical with the pretended\nevidence. If we attend to the meaning, say they, an immediate inference\ndoes not really express any new judgment; the fact expressed by it is\neither the same as its evidence, or is even less significant. If from\n_No men are gods_ we prove that _No gods are men_, this is nugatory; if\nwe prove from it that _Some men are not gods_, this is to emasculate the\nsense, to waste valuable information, to lose the commanding sweep of\nour universal proposition.\n\nStill, in Logic, it is often found that an immediate inference expresses\nour knowledge in a more convenient form than that of the evidentiary\nproposition, as will appear in the chapter on Syllogisms and elsewhere.\nAnd by transforming an universal into a particular proposition, as _No\nmen are gods_, therefore, _Some men are not gods_,--we get a statement\nwhich, though weaker, is far more easily proved; since a single instance\nsuffices. Moreover, by drawing all possible immediate inferences from a\ngiven proposition, we see it in all its aspects, and learn all that is\nimplied in it.\n\nA Mediate Inference, on the other hand, depends for its evidence upon a\nplurality of other propositions (two or more) which are connected\ntogether on logical principles. If we argue--\n\n No men are gods;\n Alexander the Great is a man;\n .'. Alexander the Great is not a god:\n\nthis is a Mediate Inference. The evidence consists of two propositions\nconnected by the term 'man,' which is common to both (a Middle Term),\nmediating between 'gods' and 'Alexander.' Mediate Inferences comprise\nSyllogisms with their developments, and Inductions; and to discuss them\nfurther at present would be to anticipate future chapters. We must now\ndeal with the principles or conditions on which Immediate Inferences are\nvalid: commonly called the \"Laws of Thought.\"\n\n\u00a7 3. The Laws of Thought are conditions of the logical statement and\ncriticism of all sorts of evidence; but as to Immediate Inference, they\nmay be regarded as the only conditions it need satisfy. They are often\nexpressed thus: (1) The principle of Identity--'_Whatever is, is_'; (2)\nThe principle of Contradiction--'_It is impossible for the same thing to\nbe and not be_'; (3) The principle of Excluded Middle--'_Anything must\neither be or not be_.' These principles are manifestly not 'laws' of\nthought in the sense in which 'law' is used in Psychology; they do not\nprofess to describe the actual mental processes that take place in\njudgment or reasoning, as the 'laws of association of ideas' account for\nmemory and recollection. They are not natural laws of thought; but, in\nrelation to thought, can only be regarded as laws when stated as\nprecepts, the observance of which (consciously or not) is necessary to\nclear and consistent thinking: e.g., Never assume that the same thing\ncan both be and not be.\n\nHowever, treating Logic as the science of thought only as embodied in\npropositions, in respect of which evidence is to be adduced, or which\nare to be used as evidence of other propositions, the above laws or\nprinciples must be restated as the conditions of consistent argument in\nsuch terms as to be directly applicable to propositions. It was shown in\nthe chapter on the connotation of terms, that terms are assumed by\nLogicians to be capable of definite meaning, and of being used\nunivocally in the same context; if, or in so far as, this is not the\ncase, we cannot understand one another's reasons nor even pursue in\nsolitary meditation any coherent train of argument. We saw, too, that\nthe meanings of terms were related to one another: some being full\ncorrelatives; others partially inclusive one of another, as species of\ngenus; others mutually incompatible, as contraries; or alternatively\npredicable, as contradictories. We now assume that propositions are\ncapable of definite meaning according to the meaning of their component\nterms and of the relation between them; that the meaning, the fact\nasserted or denied, is what we are really concerned to prove or\ndisprove; that a mere change in the words that constitute our terms, or\nof construction, does not affect the truth of a proposition as long as\nthe meaning is not altered, or (rather) as long as no fresh meaning is\nintroduced; and that if the meaning of any proposition is true, any\nother proposition that denies it is false. This postulate is plainly\nnecessary to consistency of statement and discourse; and consistency is\nnecessary, if our thought or speech is to correspond with the unity and\ncoherence of Nature and experience; and the Laws of Thought or\nConditions of Immediate Inference are an analysis of this postulate.\n\n\u00a7 4. The principle of Identity is usually written symbolically thus: _A\nis A; not-A is not-A_. It assumes that there is something that may be\nrepresented by a term; and it requires that, in any discussion, _every\nrelevant term, once used in a definite sense, shall keep that meaning\nthroughout_. Socrates in his father's workshop, at the battle of Delium,\nand in prison, is assumed to be the same man denotable by the same name;\nand similarly, 'elephant,' or 'justice,' or 'fairy,' in the same\ncontext, is to be understood of the same thing under the same\n_suppositio_.\n\nBut, further, it is assumed that of a given term another term may be\npredicated again and again in the same sense under the same conditions;\nthat is, we may speak of the identity of meaning in a proposition as\nwell as in a term. To symbolise this we ought to alter the usual\nformula for Identity and write it thus: _If B is A, B is A; if B is\nnot-A, B is not-A_. If Socrates is wise, he is wise; if fairies frequent\nthe moonlight, they do; if Justice is not of this world, it is not.\n_Whatever affirmation or denial we make concerning any subject, we are\nbound to adhere to it for the purposes of the current argument or\ninvestigation._ Of course, if our assertion turns out to be false, we\nmust not adhere to it; but then we must repudiate all that we formerly\ndeduced from it.\n\nAgain, _whatever is true or false in one form of words is true or false\nin any other_: this is undeniable, for the important thing is identity\nof meaning; but in Formal Logic it is not very convenient. If Socrates\nis wise, is it an identity to say 'Therefore the master of Plato is\nwise'; or, further that he 'takes enlightened views of life'? If _Every\nman is fallible_, is it an identical proposition that _Every man is\nliable to error_? It seems pedantic to demand a separate proposition\nthat _Fallible is liable to error_. But, on the other hand, the\ninsidious substitution of one term for another speciously identical, is\na chief occasion of fallacy. How if we go on to argue: therefore, _Every\nman is apt to blunder, prone to confusion of thought, inured to\nself-contradiction_? Practically, the substitution of identities must be\nleft to candour and good-sense; and may they increase among us. Formal\nLogic is, no doubt, safest with symbols; should, perhaps, content itself\nwith A and B; or, at least, hardly venture beyond Y and Z.\n\n\u00a7 5. The principle of Contradiction is usually written symbolically,\nthus: _A is not not-A_. But, since this formula seems to be adapted to a\nsingle term, whereas we want one that is applicable to propositions, it\nmay be better to write it thus: _B is not both A and not-A_. That is to\nsay: _if any term may be affirmed of a subject, the contradictory term\nmay, in the same relation, be denied of it_. A leaf that is green on one\nside of it may be not-green on the other; but it is not both green and\nnot-green on the same surface, at the same time, and in the same light.\nIf a stick is straight, it is false that it is at the same time\nnot-straight: having granted that two angles are equal, we must deny\nthat they are unequal.\n\nBut is it necessarily false that the stick is 'crooked'; must we deny\nthat either angle is 'greater or less' than the other? How far is it\npermissible to substitute any other term for the formal contradictory?\nClearly, the principle of Contradiction takes for granted the principle\nof Identity, and is subject to the same difficulties in its practical\napplication. As a matter of fact and common sense, if we affirm any term\nof a Subject, we are bound to deny of that Subject, in the same\nrelation, not only the contradictory but all synonyms for this, and also\nall contraries and opposites; which, of course, are included in the\ncontradictory. But who shall determine what these are? Without an\nauthoritative Logical Dictionary to refer to, where all contradictories,\nsynonyms, and contraries may be found on record, Formal Logic will\nhardly sanction the free play of common sense.\n\nThe principle of Excluded Middle may be written: _B is either A or\nnot-A_; that is, _if any term be denied of a subject, the contradictory\nterm may, in the same relation, be affirmed_. Of course, we may deny\nthat a leaf is green on one side without being bound to affirm that it\nis not-green on the other. But in the same relation a leaf is either\ngreen or not-green; at the same time, a stick is either bent or\nnot-bent. If we deny that A is greater than B, we must affirm that it is\nnot-greater than B.\n\nWhilst, then, the principle of Contradiction (that 'of contradictory\npredicates, one being affirmed, the other is denied ') might seem to\nleave open a third or middle course, the denying of both\ncontradictories, the principle of Excluded Middle derives its name from\nthe excluding of this middle course, by declaring that the one or the\nother must be affirmed. Hence the principle of Excluded Middle does not\nhold good of mere contrary terms. If we deny that a leaf is green, we\nare not bound to affirm it to be yellow; for it may be red; and then we\nmay deny both contraries, yellow and green. In fact, two contraries do\nnot between them cover the whole predicable area, but contradictories\ndo: the form of their expression is such that (within the _suppositio_)\neach includes all that the other excludes; so that the subject (if\nbrought within the _suppositio_) must fall under the one or the other.\nIt may seem absurd to say that Mont Blanc is either wise or not-wise;\nbut how comes any mind so ill-organised as to introduce Mont Blanc into\nthis strange company? Being there, however, the principle is inexorable:\nMont Blanc is not-wise.\n\nIn fact, the principles of Contradiction and Excluded Middle are\ninseparable; they are implicit in all distinct experience, and may be\nregarded as indicating the two aspects of Negation. The principle of\nContradiction says: _B is not both A and not-A_, as if _not-A_ might be\nnothing at all; this is abstract negation. But the principle of Excluded\nMiddle says: _Granting that B is not A, it is still something_--namely,\n_not-A_; thus bringing us back to the concrete experience of a continuum\nin which the absence of one thing implies the presence of something\nelse. Symbolically: to deny that B is A is to affirm that B is not A,\nand this only differs by a hyphen from B is not-A.\n\nThese principles, which were necessarily to some extent anticipated in\nchap. iv. \u00a7 7, the next chapter will further illustrate.\n\n\u00a7 6. But first we must draw attention to a maxim (also already\nmentioned), which is strictly applicable to Immediate Inferences, though\n(as we shall see) in other kinds of proof it may be only a formal\ncondition: this is the general caution _not to go beyond the evidence_.\nAn immediate inference ought to contain nothing that is not contained\n(or formally implied) in the proposition by which it is proved. With\nrespect to quantity in denotation, this caution is embodied in the rule\n'not to distribute any term that is not given distributed.' Thus, if\nthere is a predication concerning 'Some S,' or 'Some men,' as in the\nforms I. and O., we cannot infer anything concerning 'All S.' or 'All\nmen'; and, as we have seen, if a term is given us preindesignate, we are\ngenerally to take it as of particular quantity. Similarly, in the case\nof affirmative propositions, we saw that this rule requires us to assume\nthat their predicates are undistributed.\n\nAs to the grounds of this maxim, not to go beyond the evidence, not to\ndistribute a term that is given as undistributed, it is one of the\nthings so plain that to try to justify is only to obscure them. Still,\nwe must here state explicitly what Formal Logic assumes to be contained\nor implied in the evidence afforded by any proposition, such as 'All S\nis P.' If we remember that in chap. iv. \u00a7 7, it was assumed that every\nterm may have a contradictory; and if we bear in mind the principles of\nContradiction and Excluded Middle, it will appear that such a\nproposition as 'All S is P' tells us something not only about the\nrelations of 'S' and 'P,' but also of their relations to 'not-S' and\n'not-P'; as, for example, that 'S is not not-P,' and that 'not-P is\nnot-S.' It will be shown in the next chapter how Logicians have\ndeveloped these implications in series of Immediate Inferences.\n\nIf it be asked whether it is true that every term, itself significant,\nhas a significant contradictory, and not merely a formal contradictory,\ngenerated by force of the word 'not,' it is difficult to give any better\nanswer than was indicated in \u00a7\u00a7 3-5, without venturing further into\nMetaphysics. I shall merely say, therefore, that, granting that some\nsuch term as 'Universe' or 'Being' may have no significant\ncontradictory, if it stand for 'whatever can be perceived or thought\nof'; yet every term that stands for less than 'Universe' or 'Being' has,\nof course, a contradictory which denotes the rest of the universe. And\nsince every argument or train of thought is carried on within a special\n'universe of discourse,' or under a certain _suppositio_, we may say\nthat _within the given suppositio every term has a contradictory_, and\nthat every predication concerning a term implies some predication\nconcerning its contradictory. But the name of the _suppositio_ itself\nhas no contradictory, except with reference to a wider and inclusive\n_suppositio_.\n\nThe difficulty of actual reasoning, not with symbols, but about matters\nof fact, does not arise from the principles of Logic, but sometimes from\nthe obscurity or complexity of the facts, sometimes from the ambiguity\nor clumsiness of language, sometimes from the deficiency of our own\nminds in penetration, tenacity and lucidity. One must do one's best to\nstudy the facts, and not be too easily discouraged.\n\n\n\n\nCHAPTER VII\n\nIMMEDIATE INFERENCES\n\n\n\u00a7 1. Under the general title of Immediate Inference Logicians discuss\nthree subjects, namely, Opposition, Conversion, and Obversion; to which\nsome writers add other forms, such as Whole and Part in Connotation,\nContraposition, Inversion, etc. Of Opposition, again, all recognise\nfour modes: Subalternation, Contradiction, Contrariety and\nSub-contrariety. The only peculiarities of the exposition upon which we\nare now entering are, that it follows the lead of the three Laws of\nThought, taking first those modes of Immediate Inference in which\nIdentity is most important, then those which plainly involve\nContradiction and Excluded Middle; and that this method results in\nseparating the modes of Opposition, connecting Subalternation with\nConversion, and the other modes with Obversion. To make up for this\ndeparture from usage, the four modes of Opposition will be brought\ntogether again in \u00a7 9.\n\n\u00a7 2. Subalternation.--Opposition being the relation of propositions that\nhave the same matter and differ only in form (as A., E., I., O.),\npropositions of the forms A. and I. are said to be Subalterns in\nrelation to one another, and so are E. and O.; the universal of each\nquality being distinguished as 'subalternans,' and the particular as\n'subalternate.'\n\nIt follows from the principle of Identity that, the matter of the\npropositions being the same, if A. is true I. is true, and that if E. is\ntrue O. is true; for A. and E. predicate something of _All S_ or _All\nmen_; and since I. and O. make the same predication of _Some S_ or\n_Some men_, the sense of these particular propositions has already been\npredicated in A. or E. If _All S is P, Some S is P_; if _No S is P, Some\nS is not P_; or, if _All men are fond of laughing, Some men are_; if _No\nmen are exempt from ridicule, Some men are not_.\n\nSimilarly, if I. is false A. is false; if O. is false E. is false. If we\ndeny any predication about _Some S_, we must deny it of _All S_; since\nin denying it of _Some_, we have denied it of at least part of _All_;\nand whatever is false in one form of words is false in any other.\n\nOn the other hand, if I. is true, we do not know that A. is; nor if O.\nis true, that E. is; for to infer from _Some_ to _All_ would be going\nbeyond the evidence. We shall see in discussing Induction that the great\nproblem of that part of Logic is, to determine the conditions under\nwhich we may in reality transcend this rule and infer from _Some_ to\n_All_; though even there it will appear that, formally, the rule is\nobserved. For the present it is enough that I. is an immediate inference\nfrom A., and O. from E.; but that A. is not an immediate inference from\nI., nor E. from O.\n\n\u00a7 3. Connotative Subalternation.--We have seen (chap. iv. \u00a7 6) that if\nthe connotation of one term is only part of another's its denotation is\ngreater and includes that other's. Hence genus and species stand in\nsubaltern relation, and whatever is true of the genus is true of the\nspecies: If _All animal life is dependent on vegetation, All human life\nis dependent on vegetation_. On the other hand, whatever is not true of\nthe species or narrower term, cannot be true of the whole genus: If it\nis false that '_All human life is happy_,' it is false that '_All animal\nlife is happy_.'\n\nSimilar inferences may be drawn from the subaltern relation of\npredicates; affirming the species we affirm the genus. To take Mill's\nexample, if _Socrates is a man, Socrates is a living creature_. On the\nother hand, denying the genus we deny the species: if _Socrates is not\nvicious, Socrates is not drunken_.\n\nSuch cases as these are recognised by Mill and Bain as immediate\ninferences under the principle of Identity. But some Logicians might\ntreat them as imperfect syllogisms, requiring another premise to\nlegitimate the conclusion, thus:\n\n _All animal life is dependent on vegetation;\n All human life is animal life;\n .'. All human life is dependent on vegetation._\n\nOr again:\n\n _All men are living creatures;\n Socrates is a man;\n .'. Socrates is a living creature._\n\nThe decision of this issue turns upon the question (_cf._ chap. vi. \u00a7 3)\nhow far a Logician is entitled to assume that the terms he uses are\nunderstood, and that the identities involved in their meanings will be\nrecognised. And to this question, for the sake of consistency, one of\ntwo answers is required; failing which, there remains the rule of thumb.\nFirst, it may be held that no terms are understood except those that are\ndefined in expounding the science, such as 'genus' and 'species,'\n'connotation' and 'denotation.' But very few Logicians observe this\nlimitation; few would hesitate to substitute 'not wise' for 'foolish.'\nYet by what right? Malvolio being foolish, to prove that he is not-wise,\nwe may construct the following syllogism:\n\n _Foolish is not-wise;\n Malvolio is foolish;\n .'. Malvolio is not-wise._\n\nIs this necessary? Why not?\n\nSecondly, it may be held that all terms may be assumed as understood\nunless a definition is challenged. This principle will justify the\nsubstitution of 'not-wise' for 'foolish'; but it will also legitimate\nthe above cases (concerning 'human life' and 'Socrates') as immediate\ninferences, with innumerable others that might be based upon the\ndoctrine of relative terms: for example, _The hunter missed his aim_:\ntherefore, _The prey escaped_. And from this principle it will further\nfollow that all apparent syllogisms, having one premise a verbal\nproposition, are immediate inferences (_cf._ chap. ix. \u00a7 4).\n\nClosely connected with such cases as the above are those mentioned by\nArchbishop Thomson as \"Immediate Inferences by added Determinants\"\n(_Laws of Thought_, \u00a7 87). He takes the case: '_A negro is a\nfellow-creature_: therefore, _A negro in suffering is a fellow-creature\nin suffering_.' This rests upon the principle that to increase the\nconnotations of two terms by the same attribute or determinant does not\naffect the relationship of their denotations, since it must equally\ndiminish (if at all) the denotations of both classes, by excluding the\nsame individuals, if any want the given attribute. But this principle is\ntrue only when the added attribute is not merely the same verbally, but\nhas the same significance in qualifying both terms. We cannot argue _A\nmouse is an animal_; therefore, _A large mouse is a large animal_; for\n'large' is an attribute relative to the normal magnitude of the thing\ndescribed.\n\n\u00a7 4. Conversion is Immediate Inference by transposing the terms of a\ngiven proposition without altering its quality. If the quantity is also\nunaltered, the inference is called 'Simple Conversion'; but if the\nquantity is changed from universal to particular, it is called\n'Conversion by limitation' or '_per accidens._' The given proposition is\ncalled the 'convertend'; that which is derived from it, the 'converse.'\n\nDeparting from the usual order of exposition, I have taken up Conversion\nnext to Subalternation, because it is generally thought to rest upon the\nprinciple of Identity, and because it seems to be a good method to\nexhaust the forms that come only under Identity before going on to those\nthat involve Contradiction and Excluded Middle. Some, indeed, dispute\nthe claims of Conversion to illustrate the principle of Identity; and\nif the sufficient statement of that principle be 'A is A,' it may be a\nquestion how Conversion or any other mode of inference can be referred\nto it. But if we state it as above (chap. vi. \u00a7 3), that whatever is\ntrue in one form of words is true in any other, there is no difficulty\nin applying it to Conversion.\n\nThus, to take the simple conversion of I.,\n\n _Some S is P; .'. Some P is S._\n _Some poets are business-like; .'. Some business-like men are poets._\n\nHere the convertend and the converse say the same thing, and this is\ntrue if that is.\n\nWe have, then, two cases of simple conversion: of I. (as above) and of\nE. For E.:\n\n _No S is P; .'. No P is S._\n _No ruminants are carnivores; .'. No carnivores are ruminants._\n\nIn converting I., the predicate (P) when taken as the new subject, being\npreindesignate, is treated as particular; and in converting E., the\npredicate (P), when taken as the new subject, is treated as universal,\naccording to the rule in chap. v. \u00a7 1.\n\nA. is the one case of conversion by limitation:\n\n All S is P;\n .'. Some P is S.\n\n All cats are grey in the dark;\n .'. Some things grey in the dark are cats.\n\nThe predicate is treated as particular, when taking it for the new\nsubject, according to the rule not to go beyond the evidence. To infer\nthat _All things grey in the dark are cats_ would be palpably absurd;\nyet no error of reasoning is commoner than the simple conversion of A.\nThe validity of conversion by limitation may be shown thus: if, _All S\nis P_, then, by subalternation, _Some S is P_, and therefore, by simple\nconversion, _Some P is S_.\n\nO. cannot be truly converted. If we take the proposition: _Some S is\nnot P_, to convert this into _No P is S_, or _Some P is not S_, would\nbreak the rule in chap. vi. \u00a7 6; since _S,_ undistributed in the\nconvertend, would be distributed in the converse. If we are told that\n_Some men are not cooks_, we cannot infer that _Some cooks are not men_.\nThis would be to assume that '_Some men_' are identical with '_All\nmen_.'\n\nBy quantifying the predicate, indeed, we may convert O. simply, thus:\n\n _Some men are not cooks_ .'. _No cooks are some men._\n\nAnd the same plan has some advantage in converting A.; for by the usual\nmethod _per accidens_, the converse of A. being I., if we convert this\nagain it is still I., and therefore means less than our original\nconvertend. Thus:\n\n _All S is P .'. Some P is S .'. Some S is P._\n\nSuch knowledge, as that _All S_ (the whole of it) _is P_, is too\nprecious a thing to be squandered in pure Logic; and it may be preserved\nby quantifying the predicate; for if we convert A. to Y., thus--\n\n _All S is P .'. Some P is all S--_\n\nwe may reconvert Y. to A. without any loss of meaning. It is the chief\nuse of quantifying the predicate that, thereby, every proposition is\ncapable of simple conversion.\n\nThe conversion of propositions in which the relation of terms is\ninadequately expressed (see chap. ii., \u00a7 2) by the ordinary copula (_is_\nor _is not_) needs a special rule. To argue thus--\n\n _A is followed by B_ .'. _Something followed by B is A_--\n\nwould be clumsy formalism. We usually say, and we ought to say--\n\n _A is followed by B_ .'. _B follows A_ (or _is preceded by A_).\n\nNow, any relation between two terms may be viewed from either side--_A:\nB_ or _B: A_. It is in both cases the same fact; but, with the altered\npoint of view, it may present a different character. For example, in the\nImmediate Inference--_A > B_ .'. _B < A_--a diminishing turns into an\nincreasing ratio, whilst the fact predicated remains the same. Given,\nthen, a relation between two terms as viewed from one to the other, the\nsame relation viewed from the other to the one may be called the\nReciprocal. In the cases of Equality, Co-existence and Simultaneity, the\ngiven relation and its reciprocal are not only the same fact, but they\nalso have the same character: in the cases of Greater and Less and\nSequence, the character alters.\n\nWe may, then, state the following rule for the conversion of\npropositions in which the whole relation explicitly stated is taken as\nthe copula: Transpose the terms, and for the given relation substitute\nits reciprocal. Thus--\n\n _A is the cause of B .'. B is the effect of A._\n\nThe rule assumes that the reciprocal of a given relation is definitely\nknown; and so far as this is true it may be extended to more concrete\nrelations--\n\n _A is a genus of B .'. B is a species of A\n A is the father of B .'. B is a child of A._\n\nBut not every relational expression has only one definite reciprocal. If\nwe are told that _A is the brother of B_, we can only infer that _B is\neither the brother or the sister of A_. A list of all reciprocal\nrelations is a desideratum of Logic.\n\n\u00a7 5. Obversion (otherwise called Permutation or \u00c6quipollence) is\nImmediate Inference by changing the quality of the given proposition and\nsubstituting for its predicate the contradictory term. The given\nproposition is called the 'obvertend,' and the inference from it the\n'obverse.' Thus the obvertend being--_Some philosophers are consistent\nreasoners_, the obverse will be--_Some philosophers are not inconsistent\nreasoners_.\n\nThe legitimacy of this mode of reasoning follows, in the case of\naffirmative propositions, from the principle of Contradiction, that if\nany term be affirmed of a subject, the contradictory term may be denied\n(chap. vi. \u00a7 3). To obvert affirmative propositions, then, the rule\nis--Insert the negative sign, and for the predicate substitute its\ncontradictory term.\n\n A. _All S is P .'. No S is not-P\n All men are fallible .'. No men are infallible._\n\n I. _Some S is P .'. some S is not-P\n Some philosophers are consistent .'. Some philosophers are not\n inconsistent._\n\nIn agreement with this mode of inference, we have the rule of modern\nEnglish grammar, that 'two negatives make an affirmative.'\n\nAgain, by the principle of Excluded Middle, if any term be denied of a\nsubject, its contradictory may be affirmed: to obvert negative\npropositions, then, the rule is--Remove the negative sign, and for the\npredicate substitute its contradictory term.\n\n E. _No S is P .'. All S is not-P\n No matter is destructible .'. All matter is indestructible._\n\n O. _Some S is not P .'. Some S is not-P\n Some ideals are not attainable .'. Some ideals are unattainable._\n\nThus, by obversion, each of the four propositions retains its quantity\nbut changes its quality: A. to E., I. to O., E. to A., O. to I. And all\nthe obverses are infinite propositions, the affirmative infinites having\nthe sense of negatives, and the negative infinites having the sense of\naffirmatives.\n\nAgain, having obtained the obverse of a given proposition, it may be\ndesirable to recover the obvertend; or it may at any time be requisite\nto change a given infinite proposition into the corresponding direct\naffirmative or negative; and in such cases the process is still\nobversion. Thus, if _No S is not-P_ be given us to recover the obvertend\nor to find the corresponding affirmative; the proposition being formally\nnegative, we apply the rule for obverting negatives: 'Remove the\nnegative sign, and for the predicate substitute its contradictory.' This\nyields the affirmative _All S is P_. Similarly, to obtain the obvertend\nof _All S is not-P_, apply the rule for obverting Affirmatives; and this\nyields _No S is P_.\n\n\u00a7 6. Contrariety.--We have seen in chap. iv. \u00a7 8, that contrary terms\nare such that no two of them are predicable in the same way of the same\nsubject, whilst perhaps neither may be predicable of it. Similarly,\nContrary Propositions may be defined as those of which no two are ever\nboth true together, whilst perhaps neither may be true; or, in other\nwords, both may be false. This is the relation between A. and E. when\nconcerned with the same matter: as A.--_All men are wise_; E.--_No men\nare wise_. Such propositions cannot both be true; but they may both be\nfalse, for some men may be wise and some not. They cannot both be true;\nfor, by the principle of Contradiction, if _wise_ may be affirmed of\n_All men, not-wise_ must be denied; but _All men are not-wise_ is the\nobverse of _No men are wise_, which therefore may also be denied.\n\nAt the same time we cannot apply to A. and E. the principle of Excluded\nMiddle, so as to show that one of them must be true of the same matter.\nFor if we deny that _All men are wise_, we do not necessarily deny the\nattribute 'wise' of each and every man: to say that _Not all are wise_\nmay mean no more than that _Some are not_. This gives a proposition in\nthe form of O.; which, as we have seen, does not imply its subalternans,\nE.\n\nIf, however, two Singular Propositions, having the same matter, but\ndiffering in quality, are to be treated as universals, and therefore as\nA. and E., they are, nevertheless, contradictory and not merely\ncontrary; for one of them must be false and the other true.\n\n\u00a7 7. Contradiction is a relation between two propositions analogous to\nthat between contradictory terms (one of which being affirmed of a\nsubject the other is denied)--such, namely, that one of them is false\nand the other true. This is the case with the forms A. and O., and E.\nand I., in the same matter. If it be true that _All men are wise_, it is\nfalse that _Some men are not wise_ (equivalent by obversion to _Some\nmen are not-wise_); or else, since the 'Some men' are included in the\n'All men,' we should be predicating of the same men that they are both\n'wise' and 'not-wise'; which would violate the principle of\nContradiction. Similarly, _No men are wise_, being by obversion\nequivalent to _All men are not-wise_, is incompatible with _Some men are\nwise_, by the same principle of Contradiction.\n\nBut, again, if it be false that _All men are wise_, it is always true\nthat _Some are not wise_; for though in denying that 'wise' is a\npredicate of 'All men' we do not deny it of each and every man, yet we\ndeny it of 'Some men.' Of 'Some men,' therefore, by the principle of\nExcluded Middle, 'not-wise' is to be affirmed; and _Some men are\nnot-wise_, is by obversion equivalent to _Some men are not wise_.\nSimilarly, if it be false that _No men are wise_, which by obversion is\nequivalent to _All men are not-wise_, then it is true at least that\n_Some men are wise_.\n\nBy extending and enforcing the doctrine of relative terms, certain other\ninferences are implied in the contrary and contradictory relations of\npropositions. We have seen in chap. iv. that the contradictory of a\ngiven term includes all its contraries: 'not-blue,' for example,\nincludes red and yellow. Hence, since _The sky is blue_ becomes by\nobversion, _The sky is not not-blue_, we may also infer _The sky is not\nred_, etc. From the truth, then, of any proposition predicating a given\nterm, we may infer the falsity of all propositions predicating the\ncontrary terms in the same relation. But, on the other hand, from the\nfalsity of a proposition predicating a given term, we cannot infer the\ntruth of the predication of any particular contrary term. If it be false\nthat _The sky is red_, we cannot formally infer, that _The sky is blue_\n(_cf._ chap. iv. \u00a7 8).\n\n\u00a7 8. Sub-contrariety is the relation of two propositions, concerning the\nsame matter that may both be true but are never both false. This is the\ncase with I. and O. If it be true that _Some men are wise_, it may also\nbe true that _Some (other) men are not wise_. This follows from the\nmaxim in chap. vi. \u00a7 6, not to go beyond the evidence.\n\nFor if it be true that _Some men are wise_, it may indeed be true that\n_All are_ (this being the subalternans): and if _All are_, it is (by\ncontradiction) false that _Some are not_; but as we are only told that\n_Some men are_, it is illicit to infer the falsity of _Some are not_,\nwhich could only be justified by evidence concerning _All men_.\n\nBut if it be false that _Some men are wise_, it is true that _Some men\nare not wise_; for, by contradiction, if _Some men are wise_ is false,\n_No men are wise_ is true; and, therefore, by subalternation, _Some men\nare not wise_ is true.\n\n\u00a7 9. The Square of Opposition.--By their relations of Subalternation,\nContrariety, Contradiction, and Sub-contrariety, the forms A. I. E. O.\n(having the same matter) are said to stand in Opposition: and Logicians\nrepresent these relations by a square having A. I. E. O. at its corners:\n\nA. Contraries E.\n\nS Co s S\nu nt e u\nb ra i b\na di r a\nl ct o l\nt ct o t\ne di r e\nr ra i r\nn nt e n\ns Co s s\n\nI. Sub-contraries O.\n\nAs an aid to the memory, this diagram is useful; but as an attempt to\nrepresent the logical relations of propositions, it is misleading. For,\nstanding at corners of the same square, A. and E., A. and I., E. and O.,\nand I. and O., seem to be couples bearing the same relation to one\nanother; whereas we have seen that their relations are entirely\ndifferent. The following traditional summary of their relations in\nrespect of truth and falsity is much more to the purpose:\n\n (1) If A. is true, I. is true, E. is false, O. is false.\n (2) If A. is false, I. is unknown, E. is unknown, O. is true.\n (3) If I. is true, A. is unknown, E. is false, O. is unknown.\n (4) If I. is false, A. is false, E. is true, O. is true.\n (5) If E. is true, A. is false, I. is false, O. is true.\n (6) If E. is false, A. is unknown, I. is true, O. is unknown.\n (7) If O. is true, A. is false, I. is unknown, E. is unknown.\n (8) If O. is false, A. is true, I. is true, E. is false.\n\nWhere, however, as in cases 2, 3, 6, 7, alleging either the\nfalsity of universals or the truth of particulars, it follows that two\nof the three Opposites are unknown, we may conclude further that one of\nthem must be true and the other false, because the two unknown are\nalways Contradictories.\n\n\u00a7 10. Secondary modes of Immediate Inference are obtained by applying\nthe process of Conversion or Obversion to the results already obtained\nby the other process. The best known secondary form of Immediate\nInference is the Contrapositive, and this is the converse of the obverse\nof a given proposition. Thus:\n\n DATUM. OBVERSE. CONTRAPOSITIVE.\n\n A. _All S is P_ .'. _No S is not-P_ .'. _No not-P is S_\n I. _Some S is P_ .'. _Some S is not not-P_ .'. (none)\n E. _No S is P_ .'. _All S is not-P_ .'. _Some not-P is S_\n O. _Some S is not P_ .'. _Some S is not-P_ .'. _Some not-P is S_\n\nThere is no contrapositive of I., because the obverse of I. is in the\nform of O., and we have seen that O. cannot be converted. O., however,\nhas a contrapositive (_Some not-P is S_); and this is sometimes given\ninstead of the converse, and called the 'converse by negation.'\n\nContraposition needs no justification by the Laws of Thought, as it is\nnothing but a compounding of conversion with obversion, both of which\nprocesses have already been justified. I give a table opposite of the\nother ways of compounding these primary modes of Immediate Inference.\n\n A I E O\n--------------------------------------------------------------------------------\n\n 1 All A is B Some A is B No A is B Some A is not B\n\n--------------------------------------------------------------------------------\n\nObverse 2 No A is b Some A is not b All A is b Some A is b\n\n--------------------------------------------------------------------------------\n\nConverse 3 Some B is A Some B is A No B is A\n\n--------------------------------------------------------------------------------\n\nObverse\nof 4 Some B is not a Some B is not a All B is a\nConverse\n\n--------------------------------------------------------------------------------\n\nContra-\npositive 5 No b is A Some b is A Some b is A\n\n--------------------------------------------------------------------------------\n\nObverse\nof 6 All b is a Some b is not a Some b is not a\nContrapos\n\n--------------------------------------------------------------------------------\n\nConverse\nof\nObverse 7 Some a is B\nof\nConverse\n\n--------------------------------------------------------------------------------\n\nObverse\nof\nConverse\nof 8 Some a is not b\nObverse\nof\nConverse\n\n--------------------------------------------------------------------------------\n\nConverse\nof\nObverse 9 Some a is b\nof\nContrapos\n\n--------------------------------------------------------------------------------\n\nObverse\nof\nConverse\nof 10 Some a is not B\nObverse\nof\nContrapos\n\n--------------------------------------------------------------------------------\n\nIn this table _a_ and _b_ stand for _not-A_ and _not-B_ and had better\nbe read thus: for _No A is b, No A is not-B_; for _All b is a_ (col. 6),\n_All not-B is not-A_; and so on.\n\nIt may not, at first, be obvious why the process of alternately\nobverting and converting any proposition should ever come to an end;\nthough it will, no doubt, be considered a very fortunate circumstance\nthat it always does end. On examining the results, it will be found that\nthe cause of its ending is the inconvertibility of O. For E., when\nobverted, becomes A.; every A, when converted, degenerates into I.;\nevery I., when obverted, becomes O.; O cannot be converted, and to\nobvert it again is merely to restore the former proposition: so that the\nwhole process moves on to inevitable dissolution. I. and O. are\nexhausted by three transformations, whilst A. and E. will each endure\nseven.\n\nExcept Obversion, Conversion and Contraposition, it has not been usual\nto bestow special names on these processes or their results. But the\nform in columns 7 and 10 (_Some a is B--Some a is not B_), where the\noriginal predicate is affirmed or denied of the contradictory of the\noriginal subject, has been thought by Dr. Keynes to deserve a\ndistinctive title, and he has called it the 'Inverse.' Whilst the\nInverse is one form, however, Inversion is not one process, but is\nobtained by different processes from E. and A. respectively. In this it\ndiffers from Obversion, Conversion, and Contraposition, each of which\nstands for one process.\n\nThe Inverse form has been objected to on the ground that the inference\n_All A is B .'. Some not-A is not B_, distributes _B_ (as predicate of a\nnegative proposition), though it was given as undistributed (as\npredicate of an affirmative proposition). But Dr. Keynes defends it on\nthe ground that (1) it is obtained by obversions and conversions which\nare all legitimate and (2) that although _All A is B_ does not\ndistribute _B_ in relation to _A_, it does distribute _B_ in relation to\nsome _not-A_ (namely, in relation to whatever _not-A_ is _not-B_). This\nis one reason why, in stating the rule in chap. vi. \u00a7 6, I have\nwritten: \"an immediate inference ought to contain nothing that is not\ncontained, _or formally implied_, in the proposition from which it is\ninferred\"; and have maintained that every term formally implies its\ncontradictory within the _suppositio_.\n\n\u00a7 11. Immediate Inferences from Conditionals are those which\nconsist--(1) in changing a Disjunctive into a Hypothetical, or a\nHypothetical into a Disjunctive, or either into a Categorical; and (2)\nin the relations of Opposition and the equivalences of Obversion,\nConversion, and secondary or compound processes, which we have already\nexamined in respect of Categoricals. As no new principles are involved,\nit may suffice to exhibit some of the results.\n\nWe have already seen (chap. v. \u00a7 4) how Disjunctives may be read as\nHypotheticals and Hypotheticals as Categoricals. And, as to Opposition,\nif we recognise four forms of Hypothetical A. I. E. O., these plainly\nstand to one another in a Square of Opposition, just as Categoricals do.\nThus A. and E. (_If A is B, C is D_, and _If A is B, C is not D_) are\ncontraries, but not contradictories; since both may be false (_C_ may\nsometimes be _D_, and sometimes not), though they cannot both be true.\nAnd if they are both false, their subalternates are both true, being\nrespectively the contradictories of the universals of opposite quality,\nnamely, I. of E., and O. of A. But in the case of Disjunctives, we\ncannot set out a satisfactory Square of Opposition; because, as we saw\n(chap. v. \u00a7 4), the forms required for E. and O. are not true\nDisjunctives, but Exponibles.\n\nThe Obverse, Converse, and Contrapositive, of Hypotheticals (admitting\nthe distinction of quality) may be exhibited thus:\n\n DATUM. OBVERSE.\n\nA. _If A is B, C is D_ _If A is B, C is not d_\nI. Sometimes _when A is B, C is D_ Sometimes _when A is B, C is not d_\nE. _If A is B, C is not D_ _If A is B, C is d_\nO. Sometimes _when A is B, C is not D_ Sometimes _when A is B, C is d_\n\n CONVERSE. CONTRAPOSITIVE.\n\nSometimes _when C is D, A is B_ _If C is d, A is not B_\nSometimes _when C is D, A is B_ (none)\n_If C is D, A is not B_ Sometimes _when C is d, A is B_\n (none) Sometimes _when C is d, A is B_\n\nAs to Disjunctives, the attempt to put them through these different\nforms immediately destroys their disjunctive character. Still, given any\nproposition in the form _A is either B or C_, we can state the\npropositions that give the sense of obversion, conversion, etc., thus:\n\n DATUM.--_A is either B or C;_\n OBVERSE.--_A is not both b and c;_\n CONVERSE.--_Something, either B or C, is A;_\n CONTRAPOSITIVE.--_Nothing that is both b and c is A_.\n\nFor a Disjunctive in I., of course, there is no Contrapositive. Given a\nDisjunctive in the form _Either A is B or C is D_, we may write for its\nObverse--_In no case is A b, and C at the same time d_. But no Converse\nor Contrapositive of such a Disjunctive can be obtained, except by first\ncasting it into the hypothetical or categorical form.\n\nThe reader who wishes to pursue this subject further, will find it\nelaborately treated in Dr. Keynes' _Formal Logic_, Part II.; to which\nwork the above chapter is indebted.\n\n\n\n\nCHAPTER VIII\n\nORDER OF TERMS, EULER'S DIAGRAMS, LOGICAL EQUATIONS, EXISTENTIAL IMPORT\nOF PROPOSITIONS\n\n\n\u00a7 1. Of the terms of a proposition which is the Subject and which the\nPredicate? In most of the exemplary propositions cited by Logicians it\nwill be found that the subject is a substantive and the predicate an\nadjective, as in _Men are mortal_. This is the relation of Substance and\nAttribute which we saw (chap. i. \u00a7 5) to be the central type of\nrelations of coinherence; and on this model other predications may be\nformed in which the subject is not a substance, but is treated as if it\nwere, and could therefore be the ground of attributes; as _Fame is\ntreacherous, The weather is changeable_. But, in literature, sentences\nin which the adjective comes first are not uncommon, as _Loud was the\napplause, Dark is the fate of man, Blessed are the peacemakers_, and so\non. Here, then, 'loud,' 'dark' and 'blessed' occupy the place of the\nlogical subject. Are they really the subject, or must we alter the order\nof such sentences into _The applause was loud_, etc.? If we do, and then\nproceed to convert, we get _Loud was the applause_, or (more\nscrupulously) _Some loud noise was the applause_. The last form, it is\ntrue, gives the subject a substantive word, but 'applause' has become\nthe predicate; and if the substantive 'noise' was not implied in the\nfirst form, _Loud is the applause_, by what right is it now inserted?\nThe recognition of Conversion, in fact, requires us to admit that,\nformally, in a logical proposition, the term preceding the copula is\nsubject and the one following is predicate. And, of course, materially\nconsidered, the mere order of terms in a proposition can make no\ndifference in the method of proving it, nor in the inferences that can\nbe drawn from it.\n\nStill, if the question is, how we may best cast a literary sentence into\nlogical form, good grounds for a definite answer may perhaps be found.\nWe must not try to stand upon the naturalness of expression, for _Dark\nis the fate of man_ is quite as natural as _Man is mortal_. When the\npurpose is not merely to state a fact, but also to express our feelings\nabout it, to place the grammatical predicate first may be perfectly\nnatural and most effective. But the grounds of a logical order of\nstatement must be found in its adaptation to the purposes of proof and\ninference. Now general propositions are those from which most inferences\ncan be drawn, which, therefore, it is most important to establish, if\ntrue; and they are also the easiest to disprove, if false; since a\nsingle negative instance suffices to establish the contradictory. It\nfollows that, in re-casting a literary or colloquial sentence for\nlogical purposes, we should try to obtain a form in which the subject is\ndistributed--is either a singular term or a general term predesignate as\n'All' or 'No.' Seeing, then, that most adjectives connote a single\nattribute, whilst most substantives connote more than one attribute; and\nthat therefore the denotation of adjectives is usually wider than that\nof substantives; in any proposition, one term of which is an adjective\nand the other a substantive, if either can be distributed in relation to\nthe other, it is nearly sure to be the substantive; so that to take the\nsubstantive term for subject is our best chance of obtaining an\nuniversal proposition. These considerations seem to justify the practice\nof Logicians in selecting their examples.\n\nFor similar reasons, if both terms of a proposition are substantive, the\none with the lesser denotation is (at least in affirmative\npropositions) the more suitable subject, as _Cats are carnivores_. And\nif one term is abstract, that is the more suitable subject; for, as we\nhave seen, an abstract term may be interpreted by a corresponding\nconcrete one distributed, as _Kindness is infectious_; that is, _All\nkind actions suggest imitation_.\n\nIf, however, a controvertist has no other object in view than to refute\nsome general proposition laid down by an opponent, a particular\nproposition is all that he need disentangle from any statement that\nserves his purpose.\n\n\u00a7 2. Toward understanding clearly the relations of the terms of a\nproposition, it is often found useful to employ diagrams; and the\ndiagrams most in use are the circles of Euler.\n\nThese circles represent the denotation of the terms. Suppose the\nproposition to be _All hollow-horned animals ruminate_: then, if we\ncould collect all ruminants upon a prairie, and enclose them with a\ncircular palisade; and segregate from amongst them all the hollow-horned\nbeasts, and enclose them with another ring-fence inside the other; one\nway of interpreting the proposition (namely, in denotation) would be\nfigured to us thus:\n\n[Illustration: FIG. 1.]\n\nAn Universal Affirmative may also state a relation between two terms\nwhose denotation is co-extensive. A definition always does this, as _Man\nis a rational animal_; and this, of course, we cannot represent by two\ndistinct circles, but at best by one with a thick circumference, to\nsuggest that two coincide, thus:\n\n[Illustration: FIG. 2.]\n\nThe Particular Affirmative Proposition may be represented in several\nways. In the first place, bearing in mind that 'Some' means 'some at\nleast, it may be all,' an I. proposition may be represented by Figs. 1\nand 2; for it is true that _Some horned animals ruminate_, and that\n_Some men are rational_. Secondly, there is the case in which the 'Some\nthings' of which a predication is made are, in fact, not all; whilst the\npredicate, though not given as distributed, yet might be so given if we\nwished to state the whole truth; as if we say _Some men are Chinese_.\nThis case is also represented by Fig. 1, the outside circle representing\n'Men,' and the inside one 'Chinese.' Thirdly, the predicate may\nappertain to some only of the subject, but to a great many other things,\nas in _Some horned beasts are domestic_; for it is true that some are\nnot, and that certain other kinds of animals are, domestic. This case,\ntherefore, must be illustrated by overlapping circles, thus:\n\n[Illustration: FIG. 3.]\n\nThe Universal Negative is sufficiently represented by a single Fig. (4):\ntwo circles mutually exclusive, thus:\n\n[Illustration: FIG. 4.]\n\nThat is, _No horned beasts are carnivorous_.\n\nLastly, the Particular Negative may be represented by any of the Figs.\n1, 3, and 4; for it is true that _Some ruminants are not hollow-horned_,\nthat _Some horned animals are not domestic_, and that _Some horned\nbeasts are not carnivorous_.\n\nBesides their use in illustrating the denotative force of propositions,\nthese circles may be employed to verify the results of Obversion,\nConversion, and the secondary modes of Immediate Inference. Thus the\nObverse of A. is clear enough on glancing at Figs. 1 and 2; for if we\nagree that whatever term's denotation is represented by a given circle,\nthe denotation of the contradictory term shall be represented by the\nspace outside that circle; then if it is true that _All hollow horned\nanimals are ruminants_, it is at the same time true that _No\nhollow-horned animals are not-ruminants_; since none of the\nhollow-horned are found outside the palisade that encloses the\nruminants. The Obverse of I., E. or O. may be verified in a similar\nmanner.\n\nAs to the Converse, a Definition is of course susceptible of Simple\nConversion, and this is shown by Fig. 2: 'Men are rational animals' and\n'Rational animals are men.' But any other A. proposition is presumably\nconvertible only by limitation, and this is shown by Fig. 1; where _All\nhollow-horned animals are ruminants_, but we can only say that _Some\nruminants are hollow-horned_.\n\nThat I. may be simply converted may be seen in Fig. 3, which represents\nthe least that an I. proposition can mean; and that E. may be simply\nconverted is manifest in Fig. 4.\n\nAs for O., we know that it cannot be converted, and this is made plain\nenough by glancing at Fig. 1; for that represents the O., _Some\nruminants are not hollow-horned_, but also shows this to be compatible\nwith _All hollow-horned animals are ruminants_ (A.). Now in conversion\nthere is (by definition) no change of quality. The Converse, then, of\n_Some ruminants are not hollow-horned_ must be a negative proposition,\nhaving 'hollow-horned' for its subject, either in E. or O.; but these\nwould be respectively the contrary and contradictory of _All\nhollow-horned animals are ruminants_; and, therefore, if this be true,\nthey must both be false.\n\nBut (referring still to Fig. 1) the legitimacy of contrapositing O. is\nequally clear; for if _Some ruminants are not hollow-horned_, _Some\nanimals that are not hollow-horned are ruminants_, namely, all the\nanimals between the two ring-fences. Similar inferences may be\nillustrated from Figs. 3 and 4. And the Contraposition of A. may be\nverified by Figs. 1 and 2, and the Contraposition of E. by Fig. 4.\n\nLastly, the Inverse of A. is plain from Fig. 1--_Some things that are\nnot hollow-horned are not ruminants_, namely, things that lie outside\nthe outer circle and are neither 'ruminants' nor 'hollow-horned.' And\nthe Inverse of E may be studied in Fig. 4--_Some things that are\nnot-horned beasts are carnivorous_.\n\nNotwithstanding the facility and clearness of the demonstrations thus\nobtained, it may be said that a diagrammatic method, representing\ndenotations, is not properly logical. Fundamentally, the relation\nasserted (or denied) to exist between the terms of a proposition, is a\nrelation between the terms as determined by their attributes or\nconnotation; whether we take Mill's view, that a proposition asserts\nthat the connotation of the subject is a mark of the connotation of the\npredicate; or Dr. Venn's view, that things denoted by the subject (as\nhaving its connotation) have (or have not) the attribute connoted by the\npredicate; or, the Conceptualist view, that a judgment is a relation of\nconcepts (that is, of connotations). With a few exceptions artificially\nframed (such as 'kings now reigning in Europe'), the denotation of a\nterm is never directly and exhaustively known, but consists merely in\n'all things that have the connotation.' If the value of logical training\ndepends very much upon our habituating ourselves to construe\npropositions, and to realise the force of inferences from them,\naccording to the connotation of their terms, we shall do well not to\nturn too hastily to the circles, but rather to regard them as means of\nverifying in denotation the conclusions that we have already learnt to\nrecognise as necessary in connotation.\n\n\u00a7 3. The equational treatment of propositions is closely connected with\nthe diagrammatic. Hamilton thought it a great merit of his plan of\nquantifying the predicate, that thereby every proposition is reduced to\nits true form--an equation. According to this doctrine, the proposition\n_All X is all Y_ (U.) equates X and Y; the proposition _All X is some Y_\n(A.) equates X with some part of Y; and similarly with the other\naffirmatives (Y. and I.). And so far it is easy to follow his meaning:\nthe Xs are identical with some or all the Ys. But, coming to the\nnegatives, the equational interpretation is certainly less obvious. The\nproposition _No X is Y_ (E.) cannot be said in any sense to equate X and\nY; though, if we obvert it into _All X is some not-Y_, we have (in the\nsame sense, of course, as in the above affirmative forms) X equated with\npart at least of 'not-Y.'\n\nBut what is that sense? Clearly not the same as that in which\nmathematical terms are equated, namely, in respect of some mode of\nquantity. For if we may say _Some X is some Y_, these Xs that are also\nYs are not merely the same in number, or mass, or figure; they are the\nsame in every respect, both quantitative and qualitative, have the same\npositions in time and place, are in fact identical. The proposition\n2+2=4 means that any two things added to any other two are, _in respect\nof number_, equal to any three things added to one other thing; and this\nis true of all things that can be counted, however much they may differ\nin other ways. But _All X is all Y_ means that Xs and Ys are the same\nthings, although they have different names when viewed in different\naspects or relations. Thus all equilateral triangles are equiangular\ntriangles; but in one case they are named from the equality of their\nangles, and in the other from the equality of their sides. Similarly,\n'British subjects' and 'subjects of King George V' are the same people,\nnamed in one case from the person of the Crown, and in the other from\nthe Imperial Government. These logical equations, then, are in truth\nidentities of denotation; and they are fully illustrated by the\nrelations of circles described in the previous section.\n\nWhen we are told that logical propositions are to be considered as\nequations, we naturally expect to be shown some interesting developments\nof method in analogy with the equations of Mathematics; but from\nHamilton's innovations no such thing results. This cannot be said,\nhowever, of the equations of Symbolic Logic; which are the\nstarting-point of very remarkable processes of ratiocination. As the\nsubject of Symbolic Logic, as a whole, lies beyond the compass of this\nwork, it will be enough to give Dr. Venn's equations corresponding with\nthe four propositional forms of common Logic.\n\nAccording to this system, universal propositions are to be regarded as\nnot necessarily implying the existence of their terms; and therefore,\ninstead of giving them a positive form, they are translated into symbols\nthat express what they deny. For example, the proposition _All devils\nare ugly_ need not imply that any such things as 'devils' really exist;\nbut it certainly does imply that _Devils that are not ugly do not\nexist_. Similarly, the proposition _No angels are ugly_ implies that\n_Angels that are ugly do not exist_. Therefore, writing _x_ for\n'devils,' _y_ for 'ugly,' and _[y]_ for 'not-ugly,' we may express A.,\nthe universal affirmative, thus:\n\n A. _x[y]_ = 0.\n\nThat is, _x that is not y is nothing_; or, _Devils that are not-ugly do\nnot exist_. And, similarly, writing _x_ for 'angels' and _y_ for 'ugly,'\nwe may express E., the universal negative, thus:\n\n E. _xy_ = 0.\n\nThat is, _x that is y is nothing_; or, _Angels that are ugly do not\nexist_.\n\nOn the other hand, particular propositions are regarded as implying the\nexistence of their terms, and the corresponding equations are so framed\nas to express existence. With this end in view, the symbol v is adopted\nto represent 'something,' or indeterminate reality, or more than\nnothing. Then, taking any particular affirmative, such as _Some\nmetaphysicians are obscure_, and writing _x_ for 'metaphysicians,' and\n_y_ for 'obscure,' we may express it thus:\n\n I. _xy_ = v.\n\nThat is, _x that is y is something_; or, _Metaphysicians that are\nobscure do occur in experience_ (however few they may be, or whether\nthey all be obscure). And, similarly, taking any particular negative,\nsuch as _Some giants are not cruel_, and writing _x_ for 'giants' and\n_y_ for 'not-cruel,' we may express it thus:\n\n O. _x[y]_ = v.\n\nThat is, _x that is not y is something_; or, _giants that are not-cruel\ndo occur_--in romances, if nowhere else.\n\nClearly, these equations are, like Hamilton's, concerned with\ndenotation. A. and E. affirm that the compound terms x[y] and xy have no\ndenotation; and I. and O. declare that x[y] and xy have denotation, or\nstand for something. Here, however, the resemblance to Hamilton's system\nceases; for the Symbolic Logic, by operating upon more than two terms\nsimultaneously, by adopting the algebraic signs of operations, +,-, \u00d7, \u00f7\n(with a special signification), and manipulating the symbols by\nquasi-algebraic processes, obtains results which the common Logic\nreaches (if at all) with much greater difficulty. If, indeed, the value\nof logical systems were to be judged of by the results obtainable,\nformal deductive Logic would probably be superseded. And, as a mental\ndiscipline, there is much to be said in favour of the symbolic method.\nBut, as an introduction to philosophy, the common Logic must hold its\nground. (Venn: _Symbolic Logic_, c. 7.)\n\n\u00a7 4. Does Formal Logic involve any general assumption as to the real\nexistence of the terms of propositions?\n\nIn the first place, Logic treats primarily of the _relations_ implied in\npropositions. This follows from its being the science of proof for all\nsorts of (qualitative) propositions; since all sorts of propositions\nhave nothing in common except the relations they express.\n\nBut, secondly, relations without terms of some sort are not to be\nthought of; and, hence, even the most formal illustrations of logical\ndoctrines comprise such terms as S and P, X and Y, or x and y, in a\nsymbolic or representative character. Terms, therefore, of some sort are\nassumed to exist (together with their negatives or contradictories) _for\nthe purposes of logical manipulation_.\n\nThirdly, however, that Formal Logic cannot as such directly involve the\nexistence of any particular concrete terms, such as 'man' or 'mountain,'\nused by way of illustration, is implied in the word 'formal,' that is,\n'confined to what is common or abstract'; since the only thing common to\nall terms is to be related in some way to other terms. The actual\nexistence of any concrete thing can only be known by experience, as with\n'man' or 'mountain'; or by methodically justifiable inference from\nexperience, as with 'atom' or 'ether.' If 'man' or 'mountain,' or\n'Cuzco' be used to illustrate logical forms, they bring with them an\nexistential import derived from experience; but this is the import of\nlanguage, not of the logical forms. 'Centaur' and 'El Dorado' signify to\nus the non-existent; but they serve as well as 'man' and 'London' to\nillustrate Formal Logic.\n\nNevertheless, fourthly, the existence or non-existence of particular\nterms may come to be implied: namely, wherever the very fact of\nexistence, or of some condition of existence, is an hypothesis or datum.\nThus, given the proposition _All S is P_, to be P is made a condition of\nthe existence of S: whence it follows that an S that is not P does not\nexist (_x[y]_ = 0). On the further hypothesis that S exists, it follows\nthat P exists. On the hypothesis that S does not exist, the existence of\nP is problematic; but, then, if P does exist we cannot convert the\nproposition; since _Some P is S_ (P existing) would involve the\nexistence of S; which is contrary to the hypothesis.\n\nAssuming that Universals _do not_, whilst Particulars _do_, imply the\nexistence of their subjects, we cannot infer the subalternate (I. or O.)\nfrom the subalternans (A. or E.), for that is to ground the actual on\nthe problematic; and for the same reason we cannot convert A. _per\naccidens_.\n\nAssuming, again, a certain _suppositio_ or universe, to which in a given\ndiscussion every argument shall refer, then, any propositions whose\nterms lie outside that _suppositio_ are irrelevant, and for the purposes\nof that discussion are sometimes called \"false\"; though it seems better\nto call them irrelevant or meaningless, seeing that to call them false\nimplies that they might in the same case be true. Thus propositions\nwhich, according to the doctrine of Opposition, appear to be\nContradictories, may then cease to be so; for of Contradictories one is\ntrue and the other false; but, in the case supposed, both are\nmeaningless. If the subject of discussion be Zoology, all propositions\nabout centaurs or unicorns are absurd; and such specious\nContradictories as _No centaurs play the lyre--Some centaurs do play the\nlyre_; or _All unicorns fight with lions--Some unicorns do not fight\nwith lions_, are both meaningless, because in Zoology there are no\ncentaurs nor unicorns; and, therefore, in this reference, the\npropositions are not really contradictory. But if the subject of\ndiscussion or _suppositio_ be Mythology or Heraldry, such propositions\nas the above are to the purpose, and form legitimate pairs of\nContradictories.\n\nIn Formal Logic, in short, we may make at discretion any assumption\nwhatever as to the existence, or as to any condition of the existence of\nany particular term or terms; and then certain implications and\nconclusions follow in consistency with that hypothesis or datum. Still,\nour conclusions will themselves be only hypothetical, depending on the\ntruth of the datum; and, of course, until this is empirically\nascertained, we are as far as ever from empirical reality. (Venn:\n_Symbolic Logic_, c. 6; Keynes: _Formal Logic_, Part II. c. 7: _cf._\nWolf: _Studies in Logic_.)\n\n\n\n\nCHAPTER IX\n\nFORMAL CONDITIONS OF MEDIATE INFERENCE\n\n\n\u00a7 1. A Mediate Inference is a proposition that depends for proof upon\ntwo or more other propositions, so connected together by one or more\nterms (which the evidentiary propositions, or each pair of them, have in\ncommon) as to justify a certain conclusion, namely, the proposition in\nquestion. The type or (more properly) the unit of all such modes of\nproof, when of a strictly logical kind, is the Syllogism, to which we\nshall see that all other modes are reducible. It may be exhibited\nsymbolically thus:\n\n M is P;\n S is M:\n .'. S is P.\n\nSyllogisms may be classified, as to quantity, into Universal or\nParticular, according to the quantity of the conclusion; as to quality,\ninto Affirmative or Negative, according to the quality of the\nconclusion; and, as to relation, into Categorical, Hypothetical and\nDisjunctive, according as all their propositions are categorical, or one\n(at least) of their evidentiary propositions is a hypothetical or a\ndisjunctive.\n\nTo begin with Categorical Syllogisms, of which the following is an\nexample:\n\n All authors are vain;\n Cicero is an author:\n .'. Cicero is vain.\n\nHere we may suppose that there are no direct means of knowing that\nCicero is vain; but we happen to know that all authors are vain and\nthat he is an author; and these two propositions, put together,\nunmistakably imply that he is vain. In other words, we do not at first\nknow any relation between 'Cicero' and 'vanity'; but we know that these\ntwo terms are severally related to a third term, 'author,' hence called\na Middle Term; and thus we perceive, by mediate evidence, that they are\nrelated to one another. This sort of proof bears an obvious resemblance\n(though the relations involved are not the same) to the mathematical\nproof of equality between two quantities, that cannot be directly\ncompared, by showing the equality of each of them to some third\nquantity: A = B = C .'. A = C. Here B is a middle term.\n\nWe have to inquire, then, what conditions must be satisfied in order\nthat a Syllogism may be formally conclusive or valid. A specious\nSyllogism that is not really valid is called a Parasyllogism.\n\n\u00a7 2. General Canons of the Syllogism.\n\n(1) A Syllogism contains three, and no more, distinct propositions.\n\n(2) A Syllogism contains three, and no more, distinct univocal terms.\n\nThese two Canons imply one another. Three propositions with less than\nthree terms can only be connected in some of the modes of Immediate\nInference. Three propositions with more than three terms do not show\nthat connection of two terms by means of a third, which is requisite for\nproving a Mediate Inference. If we write--\n\n All authors are vain;\n Cicero is a statesman--\n\nthere are four terms and no middle term, and therefore there is no\nproof. Or if we write--\n\n All authors are vain;\n Cicero is an author:\n .'. Cicero is a statesman--\n\nhere the term 'statesman' occurs without any voucher; it appears in the\ninference but not in the evidence, and therefore violates the maxim of\nall formal proof, 'not to go beyond the evidence.' It is true that if\nany one argued--\n\n All authors are vain;\n Cicero wrote on philosophy:\n .'. Cicero is vain--\n\nthis could not be called a bad argument or a material fallacy; but it\nwould be a needless departure from the form of expression in which the\nconnection between the evidence and the inference is most easily seen.\n\nStill, a mere adherence to the same form of words in the expression of\nterms is not enough: we must also attend to their meaning. For if the\nsame word be used ambiguously (as 'author' now for 'father' and anon for\n'man of letters'), it becomes as to its meaning two terms; so that we\nhave four in all. Then, if the ambiguous term be the Middle, no\nconnection is shown between the other two; if either of the others be\nambiguous, something seems to be inferred which has never been really\ngiven in evidence.\n\nThe above two Canons are, indeed, involved in the definition of a\ncategorical syllogism, which may be thus stated: A Categorical Syllogism\nis a form of proof or reasoning (way of giving reasons) in which one\ncategorical proposition is established by comparing two others that\ncontain together only three terms, or that have one and only one term in\ncommon.\n\nThe proposition established, derived, or inferred, is called the\nConclusion: the evidentiary propositions by which it is proved are\ncalled the Premises.\n\nThe term common to the premises, by means of which the other terms are\ncompared, is called the Middle Term; the subject of the conclusion is\ncalled the Minor Term; the predicate of the conclusion, the Major Term.\n\nThe premise in which the minor term occurs is called the Minor Premise;\nthat in which the major term occurs is called the Major Premise. And a\nSyllogism is usually written thus:\n\nMajor Premise--All authors (Middle) are vain (Major);\n\nMinor Premise--Cicero (Minor) is an author (Middle):\n\nConclusion--.'. Cicero (Minor) is vain (Major).\n\nHere we have three propositions with three terms, each term occurring\ntwice. The minor and major terms are so called, because, when the\nconclusion is an universal affirmative (which only occurs in Barbara;\nsee chap. x. \u00a7 6), its subject and predicate are respectively the less\nand the greater in extent or denotation; and the premises are called\nafter the peculiar terms they contain: the expressions 'major premise'\nand 'minor premise' have nothing to do with the order in which the\npremises are presented; though it is usual to place the major premise\nfirst.\n\n(3) No term must be distributed in the conclusion unless it is\ndistributed in the premises.\n\nIt is usual to give this as one of the General Canons of the Syllogism;\nbut we have seen (chap. vi. \u00a7 6) that it is of wider application.\nIndeed, 'not to go beyond the evidence' belongs to the definition of\nformal proof. A breech of this rule in a syllogism is the fallacy of\nIllicit Process of the Minor, or of the Major, according to which term\nhas been unwarrantably distributed. The following parasyllogism\nillicitly distributes both terms of the conclusion:\n\n All poets are pathetic;\n Some orators are not poets:\n .'. No orators are pathetic.\n\n(4) The Middle Term must be distributed at least once in the premises\n(in order to prove a conclusion in the given terms).\n\nFor the use of mediate evidence is to show the relation of terms that\ncannot be directly compared; this is only possible if the middle term\nfurnishes the ground of comparison; and this (in Logic) requires that\nthe whole denotation of the middle should be either included or excluded\nby one of the other terms; since if we only know that the other terms\nare related to _some_ of the middle, their respective relations may not\nbe with the same part of it.\n\nIt is true that in what has been called the \"numerically definite\nsyllogism,\" an inference may be drawn, though our canon seems to be\nviolated. Thus:\n\n 60 sheep in 100 are horned;\n 60 sheep in 100 are blackfaced:\n .'. at least 20 blackfaced sheep in 100 are horned.\n\nBut such an argument, though it may be correct Arithmetic, is not Logic\nat all; and when such numerical evidence is obtainable the comparatively\nindefinite arguments of Logic are needless. Another apparent exception\nis the following:\n\n Most men are 5 feet high;\n Most men are semi-rational:\n .'. Some semi-rational things are 5 feet high.\n\nHere the Middle Term (men) is distributed in neither premise, yet the\nindisputable conclusion is a logical proposition. The premises, however,\nare really arithmetical; for 'most' means 'more than half,' or more than\n50 per cent.\n\nStill, another apparent exception is entirely logical. Suppose we are\ngiven, the premises--_All P is M_, and _All S is M_--the middle term is\nundistributed. But take the obverse of the contrapositive of both\npremises:\n\n All m is p;\n All m is s:\n .'. Some s is p.\n\nHere we have a conclusion legitimately obtained; but it is not in the\nterms originally given.\n\nFor Mediate Inference depending on truly logical premises, then, it is\nnecessary that one premise should distribute the middle term; and the\nreason of this may be illustrated even by the above supposed numerical\nexceptions. For in them the premises are such that, though neither of\nthe two premises by itself distributes the Middle, yet they always\noverlap upon it. If each premise dealt with exactly half the Middle,\nthus barely distributing it between them, there would be no logical\nproposition inferrible. We require that the middle term, as used in one\npremise, should necessarily overlap the same term as used in the other,\nso as to furnish common ground for comparing the other terms. Hence I\nhave defined the middle term as 'that term common to both premises by\nmeans of which the other terms are compared.'\n\n(5) One at least of the premises must be affirmative; or, from two\nnegative premises nothing can be inferred (in the given terms).\n\nThe fourth Canon required that the middle term should be given\ndistributed, or in its whole extent, at least once, in order to afford\nsure ground of comparison for the others. But that such comparison may\nbe effected, something more is requisite; the relation of the other\nterms to the Middle must be of a certain character. One at least of them\nmust be, as to its extent or denotation, partially or wholly identified\nwith the Middle; so that to that extent it may be known to bear to the\nother term, whatever relation we are told that so much of the Middle\nbears to that other term. Now, identity of denotation can only be\npredicated in an affirmative proposition: one premise, then, must be\naffirmative.\n\nIf both premises are negative, we only know that both the other terms\nare partly or wholly excluded from the Middle, or are not identical with\nit in denotation: where they lie, then, in relation to one another we\nhave no means of knowing. Similarly, in the mediate comparison of\nquantities, if we are told that A and C are both of them unequal to B,\nwe can infer nothing as to the relation of C to A. Hence the premises--\n\n No electors are sober;\n No electors are independent--\n\nhowever suggestive, do not formally justify us in inferring any\nconnection between sobriety and independence. Formally to draw a\nconclusion, we must have affirmative grounds, such as in this case we\nmay obtain by obverting both premises:\n\n All electors are not-sober;\n All electors are not-independent:\n .'. Some who are not-independent are not-sober.\n\nBut this conclusion is not in the given terms.\n\n(6) (a) If one premise be negative, the conclusion must be negative: and\n(b) to prove a negative conclusion, one premise must be negative.\n\n(a) For we have seen that one premise must be affirmative, and that thus\none term must be partly (at least) identified with the Middle. If, then,\nthe other premise, being negative, predicates the exclusion of the\nremaining term from the Middle, this remaining term must be excluded\nfrom the first term, so far as we know the first to be identical with\nthe Middle: and this exclusion will be expressed by a negative\nconclusion. The analogy of the mediate comparison of quantities may here\nagain be noticed: if A is equal to B, and B is unequal to C, A is\nunequal to C.\n\n(b) If both premises be affirmative, the relations to the Middle of both\nthe other terms are more or less inclusive, and therefore furnish no\nground for an exclusive inference. This also follows from the function\nof the middle term.\n\nFor the more convenient application of these canons to the testing of\nsyllogisms, it is usual to derive from them three Corollaries:\n\n(i) Two particular premises yield no conclusion.\n\nFor if both premises be affirmative, _all_ their terms are\nundistributed, the subjects by predesignation, the predicates by\nposition; and therefore the middle term must be undistributed, and there\ncan be no conclusion.\n\nIf one premise be negative, its predicate is distributed by position:\nthe other terms remaining undistributed. But, by Canon 6, the conclusion\n(if any be possible) must be negative; and therefore its predicate, the\nmajor term, will be distributed. In the premises, therefore, both the\nmiddle and the major terms should be distributed, which is impossible:\ne.g.,\n\n Some M is not P;\n Some S is M:\n .'. Some S is not P.\n\nHere, indeed, the major term is legitimately distributed (though the\nnegative premise might have been the minor); but M, the middle term, is\ndistributed in neither premise, and therefore there can be no\nconclusion.\n\nStill, an exception may be made by admitting a bi-designate conclusion:\n\n Some P is M;\n Some S is not M:\n .'. Some S is not some P.\n\n(ii) If one premise be particular, so is the conclusion.\n\nFor, again, if both premises be affirmative, they only distribute one\nterm, the subject of the universal premise, and this must be the middle\nterm. The minor term, therefore, is undistributed, and the conclusion\nmust be particular.\n\nIf one premise be negative, the two premises together can distribute\nonly two terms, the subject of the universal and the predicate of the\nnegative (which may be the same premise). One of these terms must be the\nmiddle; the other (since the conclusion is negative) must be the major.\nThe minor term, therefore, is undistributed, and the conclusion must be\nparticular.\n\n(iii) From a particular major and a negative minor premise nothing can\nbe inferred.\n\nFor the minor premise being negative, the major premise must be\naffirmative (5th Canon); and therefore, being particular, distributes\nthe major term neither in its subject nor in its predicate. But since\nthe conclusion must be negative (6th Canon), a distributed major term is\ndemanded, e.g.,\n\n Some M is P;\n No S is M:\n .'. ------\n\nHere the minor and the middle terms are both distributed, but not the\nmajor (P); and, therefore, a negative conclusion is impossible.\n\n\u00a7 3. First Principle or Axiom of the Syllogism.--Hitherto in this\nchapter we have been analysing the conditions of valid mediate\ninference. We have seen that a single step of such inference, a\nSyllogism, contains, when fully expressed in language, three\npropositions and three terms, and that these terms must stand to one\nanother in the relations required by the fourth, fifth, and sixth\nCanons. We now come to a principle which conveniently sums up these\nconditions; it is called the _Dictum de omni et nullo_, and may be\nstated thus:\n\n Whatever is predicated (affirmatively or negatively) of a\n term distributed,\n\n With which term another term can be (partly or wholly)\n identified,\n\n May be predicated in like manner (affirmatively or\n negatively) of the latter term (or part of it).\n\nThus stated (nearly as by Whately in the introduction to his _Logic_)\nthe _Dictum_ follows line by line the course of a Syllogism in the First\nFigure (see chap. X. \u00a7 2). To return to our former example: _All authors\nare vain_ is the same as--Vanity is predicated of all authors; _Cicero\nis an author_ is the same as--Cicero is identified as an author;\ntherefore _Cicero is vain_, or--Vanity may be predicated of Cicero. The\n_Dictum_ then requires: (1) three propositions; (2) three terms; (3)\nthat the middle term be distributed; (4) that one premise be\naffirmative, since only by an affirmative proposition can one term be\nidentified with another; (5) that if one premise be negative the\nconclusion shall be so too, since whatever is predicated of the middle\nterm is predicated _in like manner_ of the minor.\n\nThus far, then, the _Dictum_ is wholly analytic or verbal, expressing no\nmore than is implied in the definitions of 'Syllogism' and 'Middle\nTerm'; since (as we have seen) all the General Canons (except the third,\nwhich is a still more general condition of formal proof) are derivable\nfrom those definitions. However, the _Dictum_ makes a further statement\nof a synthetic or real character, namely, that _when these conditions\nare fulfilled an inference is justified_; that then the major and minor\nterms are brought into comparison through the middle, and that the major\nterm may be predicated affirmatively or negatively of all or part of the\nminor. It is this real assertion that justifies us in calling the\n_Dictum_ an Axiom.\n\n\u00a7 4. Whether the Laws of Thought may not fully explain the Syllogism\nwithout the need of any synthetic principle has, however, been made a\nquestion. Take such a syllogism as the following:\n\n All domestic animals are useful;\n All pugs are domestic animals:\n .'. All pugs are useful.\n\nHere (an ingenious man might urge), having once identified pugs with\ndomestic animals, that they are useful follows from the Law of Identity.\nIf we attend to the meaning, and remember that what is true in one form\nof words is true in any other form, then, all domestic animals being\nuseful, of course pugs are. It is merely a case of subalternation: we\nmay put it in this way:\n\n All domestic animals are useful:\n .'. Some domestic animals (e.g., pugs) are useful.\n\nThe derivation of negative syllogisms from the Law of Contradiction (he\nmight add) may be shown in a similar manner.\n\nBut the force of this ingenious argument depends on the participial\nclause--'having once identified pugs with domestic animals.' If this is\na distinct step of the reasoning, the above syllogism cannot be reduced\nto one step, cannot be exhibited as mere subalternation, nor be brought\ndirectly under the law of Identity. If 'pug,' 'domestic,' and 'useful'\nare distinct terms; and if 'pug' and 'useful' are only known to be\nconnected because of their relations to 'domestic': this is something\nmore than the Laws of Thought provide for: it is not Immediate\nInference, but Mediate; and to justify it, scientific method requires\nthat its conditions be generalised. The _Dictum_, then, as we have seen,\ndoes generalise these conditions, and declares that when such conditions\nare satisfied a Mediate Inference is valid.\n\nBut, after all (to go back a little), consider again that proposition\n_All pugs are domestic animals_: is it a distinct step of the reasoning;\nthat is to say, is it a Real Proposition? If, indeed, 'domestic' is no\npart of the definition of 'pug,' the proposition is real, and is a\ndistinct part of the argument. But take such a case as this:\n\n All dogs are useful;\n All pugs are dogs.\n\nHere we clearly have, in the minor premise, only a verbal proposition;\nto be a dog is certainly part of the definition of 'pug.' But, if so,\nthe inference 'All pugs are useful' involves no real mediation, and the\nargument is no more than this:\n\n All dogs are useful;\n .'. Some dogs (e.g., pugs) are useful.\n\nSimilarly, if the major premise be verbal, thus:\n\n All men are rational;\n Socrates is a man--\n\nto conclude that 'Socrates is rational' is no Mediate Inference; for so\nmuch was implied in the minor premise, 'Socrates is a man,' and the\nmajor premise adds nothing to this.\n\nHence we may conclude (as anticipated in chap. vii. \u00a7 3) that 'any\napparent syllogism, having one premise a verbal proposition, is really\nan Immediate Inference'; but that, if both premises are real\npropositions, the Inference is Mediate, and demands for its explanation\nsomething more than the Laws of Thought.\n\nThe fact is that to prove the minor to be a case of the middle term may\nbe an exceedingly difficult operation (chap. xiii. \u00a7 7). The difficulty\nis disguised by ordinary examples, used for the sake of convenience.\n\n\u00a7 5. Other kinds of Mediate Inference exist, yielding valid conclusions,\nwithout being truly syllogistic. Such are mathematical inferences of\nEquality, as--\n\n A = B = C .'. A = C.\n\nHere, according to the usual logical analysis, there are strictly four\nterms--(1) A, (2) equal to B, (3) B, (4) equal to C.\n\nSimilarly with the argument _a fortiori_,\n\n A > B > C .'. (much more) A > C.\n\nThis also is said to contain four terms: (1) A, (2) greater than B, (3)\nB, (4) greater than C. Such inferences are nevertheless intuitively\nsound, may be verified by trial (within the limits of sense-perception),\nand are generalised in appropriate axioms of their own, corresponding to\nthe _Dictum_ of the syllogism; as 'Things equal to the same thing are\nequal to one another,' etc.\n\nNow, surely, this is an erroneous application of the usual logical\nanalysis of propositions. Both Logic and Mathematics treat of the\n_relations_ of terms; but whilst Mathematics employs the sign = for only\none kind of relation, and for that relation exclusive of the terms;\nLogic employs the same signs (_is_ or _is not_) for all relations,\nrecognising only a difference of quality in predication, and treating\nevery other difference of relation as belonging to one of the terms\nrelated. Thus Logicians read _A--is--equal to B_: as if _equal to B_\ncould possibly be a term co-relative with A. Whence it follows that the\nargument _A = B = C .'. A = C_ contains four terms; though everybody sees\nthat there are only three.\n\nIn fact (as observed in chap. ii. \u00a7 2) the sign of logical relation\n(_is_ or _is not_), whilst usually adequate for class-reasoning\n(coinherence) and sometimes extensible to causation (because a cause\nimplies a class of events), should never be stretched to include other\nrelations in such a way as to sacrifice intelligence to formalism. And,\nbesides mathematical or quantitative relations, there are others\n(usually considered qualitative because indefinite) which cannot be\njustly expressed by the logical copula. We ought to read propositions\nexpressing time-relations (and inferences drawn accordingly) thus:\n\n B--is before--C;\n A--is before--B:\n .'. A--is before--C.\n\nAnd in like manner _A--is simultaneous with--B; etc._ Such arguments (as\nwell as the mathematical) are intuitively sound and verifiable, and\nmight be generalised in axioms if it were worth while: but it is not,\nbecause no method could be founded on such axioms.\n\nThe customary use of relative terms justifies some Mediate Inferences,\nas, _The father of a father is a grand-father_.\n\nSome cases, however, that at first seem obvious, are really delusive\nunless further data be supplied. Thus _A co-exists with B, B with C; .'. A\nwith C_--is not sound unless _B_ is an instantaneous event; for where B\nis perdurable, _A_ may co-exist with it at one time and _C_ at another.\n\nAgain: _A is to the left of B, B of C; .'. A of C_. This may pass; but it\nis not a parallel argument that if _A is north of B and B west of C_,\nthen _A is north-west of C_: for suppose that A is a mile to the north\nof B, and B a yard to the west of C, then A is practically north of C;\nat least, its westward position cannot be expressed in terms of the\nmariner's compass. In such a case we require to know not only the\ndirections but the distances of A and C from B; and then the exact\ndirection of A from C is an affair of mathematical calculation.\n\nQualitative reasoning concerning position is only applicable to things\nin one dimension of space, or in time considered as having one\ndimension. Under these conditions we may frame the following\ngeneralisation concerning all Mediate Inferences: Two terms definitely\nrelated to a third, and one of them positively, are related to one\nanother as the other term is related to the third (that is, positively\nor negatively); provided that the relations given are of the same kind\n(that is, of Time, or Coinherence, or Likeness, or Equality).\n\nThus, to illustrate by relations of Time--\n\n B is simultaneous with C;\n A is not simultaneous with B:\n .'. A is not simultaneous with C.\n\nHere the relations are of the same kind but of different logical\nquality, and (as in the syllogism) a negative copula in the premises\nleads to a negative conclusion.\n\nAn examination in detail of particular cases would show that the above\ngeneralisation concerning all Mediate Inferences is subject to too many\nqualifications to be called an Axiom; it stands to the real Axioms (the\n_Dictum_, etc.) as the notion of the Uniformity of Nature does to the\ndefinite principles of natural order (_cf._ chap. xiii. \u00a7 9).\n\n\n\n\nCHAPTER X\n\nCATEGORICAL SYLLOGISMS\n\n\n\u00a7 1. The type of logical, deductive, mediate, categorical Inference is a\nSyllogism directly conformable with the _Dictum_: as--\n\n All carnivores (M) are excitable (P);\n Cats (S) are carnivores (M):\n .'. Cats (S) are excitable (P).\n\nIn this example P is predicated of M, a term distributed; in which term,\nM, S is given as included; so that P may be predicated of S.\n\nMany arguments, however, are of a type superficially different from the\nabove: as--\n\n No wise man (P) fears death (M);\n Balbus (S) fears death (M):\n .'. Balbus (S) is not a wise man (P).\n\nIn this example, instead of P being predicated of M, M is predicated of\nP, and yet S is given as included not in P, but in M. The divergence of\nsuch a syllogism from the _Dictum_ may, however, be easily shown to be\nsuperficial by writing, instead of _No wise man fears death_, the\nsimple, converse, _No man who fears death is wise_.\n\nAgain:\n\n Some dogs (M) are friendly to man (P);\n All dogs (M) are carnivores (S):\n .'. Some carnivores (S) are friendly to man (P).\n\nHere P is predicated of M undistributed; and instead of S being included\nin M, M is included in S: so that the divergence from the type of\nsyllogism to which the _Dictum_ directly applies is still greater than\nin the former case. But if we transpose the premises, taking first\n\n All dogs (M) are carnivores (P),\n\nthen P is predicated of M distributed; and, simply converting the other\npremise, we get--\n\n Some things friendly to man (S) are dogs (M):\n\nwhence it follows that--\n\n Some things friendly to man (S) are carnivores (P);\n\nand this is the simple converse of the original conclusion.\n\nOnce more:\n\n No pigs (P) are philosophers (M);\n Some philosophers (M) are hedonists (S):\n .'. Some hedonists (S) are not pigs (P).\n\nIn this case, instead of P being predicated of M distributed, M is\npredicated of P distributed; and instead of S (or part of it) being\nincluded in M, we are told that some M is included in S. Still there is\nno real difficulty. Simply convert both the premises, and we have:\n\n No philosophers (M) are pigs (P);\n Some hedonists (S) are philosophers (M).\n\nWhence the same conclusion follows; and the whole syllogism plainly\nconforms directly to the _Dictum_.\n\nSuch departures as these from the normal syllogistic form are said to\nconstitute differences of Figure (see \u00a7 2); and the processes by which\nthey are shown to be unessential differences are called Reduction (see \u00a7\n6).\n\n\u00a7 2. Figure is determined by the position of the Middle Term in the\npremises; of which position there are four possible variations. The\nmiddle term may be subject of the major premise, and predicate of the\nminor, as in the first example above; and this position, being directly\nconformable to the requirements of the _Dictum_, is called the First\nFigure. Or the middle term may be predicate of both premises, as in the\nsecond of the above examples; and this is called the Second Figure. Or\nthe middle term may be subject of both premises, as in the third of the\nabove examples; and this is called the Third Figure. Or, finally, the\nmiddle term may be predicate of the major premise, and subject of the\nminor, as in the fourth example given above; and this is the Fourth\nFigure.\n\nIt may facilitate the recollection of this most important point if we\nschematise the figures thus:\n\n I. II. III. IV.\n\nM---P P---M M---P P---M\n \\ | | /\n \\ | | /\n \\ | | /\nS---M S---M M---S M---S\n\nThe horizontal lines represent the premises, and at the angles formed\nwith them by the slanting or by the perpendicular lines the middle term\noccurs. The schema of Figure IV. resembles Z, the last letter of the\nalphabet: this helps one to remember it in contrast with Figure I.,\nwhich is thereby also remembered. Figures II. and III. seem to stand\nback to back.\n\n\u00a7 3. The Moods of each Figure are the modifications of it which arise\nfrom different combinations of propositions according to quantity and\nquality. In Figure I., for example, four Moods are recognised: A.A.A.,\nE.A.E., A.I.I., E.I.O.\n\n A. All M is P;\n A. All S is M:\n A. .'. All S is P.\n\n E. No M is P;\n A. All S is M:\n E. .'. No S is P.\n\n A. All M is P;\n I. Some S is M:\n I. .'. Some S is P.\n\n E. No M is P;\n I. Some S is M:\n O. .'. Some S is not P.\n\nNow, remembering that there are four Figures, and four kinds of\npropositions (A. I. E. O.), each of which propositions may be major\npremise, minor premise, or conclusion of a syllogism, it appears that in\neach Figure there may be 64 Moods, and therefore 256 in all. On\nexamining these 256 Moods, however, we find that only 24 of them are\nvalid (i.e., of such a character that the conclusion strictly follows\nfrom the premises), whilst 5 of these 24 are needless, because their\nconclusions are 'weaker' or less extensive than the premises warrant;\nthat is to say, they are particular when they might be universal. Thus,\nin Figure I., besides the above 4 Moods, A.A.I. and E.A.O. are valid in\nthe sense of being conclusive; but they are superfluous, because\nincluded in A.A.A. and E.A.E. Omitting, then, these 5 needless Moods,\nwhich are called 'Subalterns' because their conclusions are subaltern\n(chap. vii. \u00a7 2) to those of other Moods, there remain 19 Moods that are\nvalid and generally recognised.\n\n\u00a7 4. How these 19 Moods are determined must be our next inquiry. There\nare several ways more or less ingenious and interesting; but all depend\non the application, directly or indirectly, of the Six Canons, which\nwere shown in the last chapter to be the conditions of Mediate\nInference.\n\n(1) One way is to begin by finding what Moods of Figure I. conform to\nthe _Dictum_. Now, the _Dictum_ requires that, in the major premise, P\nbe predicated of a term distributed, from which it follows that no Mood\ncan be valid whose major premise is particular, as in I.A.I. or O.A.O.\nAgain, the _Dictum_ requires that the minor premise be affirmative\n(\"with which term another is identified\"); so that no Mood can be valid\nwhose minor premise is negative, as in A.E.E. or A.O.O. By such\nconsiderations we find that in Figure I., out of 64 Moods possible, only\nsix are valid, namely, those above-mentioned in \u00a7 3, including the two\nsubalterns. The second step of this method is to test the Moods of the\nSecond, Third, and Fourth Figures, by trying whether they can be reduced\nto one or other of the four Moods of the First (as briefly illustrated\nin \u00a7 1, and to be further explained in \u00a7 6).\n\n(2) Another way is to take the above six General or Common Canons, and\nto deduce from them Special Canons for testing each Figure: an\ninteresting method, which, on account of its length, will be treated of\nseparately in the next section.\n\n(3) Direct application of the Common Canons is, perhaps, the simplest\nplan. First write out the 64 Moods that are possible without regard to\nFigure, and then cross out those which violate any of the Canons or\nCorollaries, thus:\n\n[Transcriber's Note: Moods surrounded with square brackets were crossed\nout in the original text.]\n\nAAA, [AAE] (6th Can. b). AAI. [AAO] (6th Can. b).\n[AEA] (6th Can. a) AEE, [AEI] (6th Can. a) AEO,\n[AIA] (Cor. ii.) [AIE] (6th Can. b) AII, [AIO] (6th Can. b)\n[AOA] (6th Can. a) [AOE] (Cor. ii.) [AOI] (6th Can. a) AOO.\n\nWhoever has the patience to go through the remaining 48 Moods will\ndiscover that of the whole 64 only 11 are valid, namely:\n\nA.A.A., A.A.I., A.E.E., A.E.O., A.I.I., A.O.O.,\nE.A.E., E.A.O., E.I.O., I.A.I., O.A.O.\n\nThese 11 Moods have next to be examined in each Figure, and if valid in\nevery Figure there will still be 44 moods in all. We find, however, that\nin the First Figure, A.E.E., A.E.O., A.O.O. involve illicit process of\nthe major term (3rd Can.); I.A.I., O.A.O. involve undistributed Middle\n(4th Can.); and A.A.I., E.A.O. are subalterns. In the Second Figure all\nthe affirmative Moods, A.A.A., A.A.I., A.I.I., I.A.I., involve\nundistributed Middle; O.A.O. gives illicit process of the major term;\nand A.E.O., E.A.O. are subalterns. In the Third Figure, A.A.A., E.A.E.,\ninvolve illicit process of the minor term (3rd Can.); A.E.E., A.E.O.,\nA.O.O., illicit process of the major term. In the Fourth Figure, A.A.A.\nand E.A.E. involve illicit process of the minor term; A.I.I., A.O.O.,\nundistributed Middle; O.A.O. involves illicit process of the major term;\nand A.E.O. is subaltern.\n\nThose moods of each Figure which, when tried by these tests, are not\nrejected, are valid, namely:\n\nFig. I.--A.A.A., E.A.E., A.I.I., E.I.O. (A.A.I., E.A.O., Subaltern);\n\nFig. II.--E.A.E., A.E.E., E.I.O., A.O.O. (E.A.O., A.E.O., Subaltern);\n\nFig. III.--A.A.I., I.A.I., A.I.I., E.A.O., O.A.O., E.I.O.;\n\nFig. IV.--A.A.I., A.E.E., I.A.I., E.A.O., E.I.O. (A.E.O., Subaltern).\n\nThus, including subaltern Moods, there are six valid in each Figure. In\nFig. III. alone there is no subaltern Mood, because in that Figure there\ncan be no universal conclusion.\n\n\u00a7 5. Special Canons of the several Figures, deduced from the Common\nCanons, enable us to arrive at the same result by a somewhat different\ncourse. They are not, perhaps, necessary to the Science, but afford a\nvery useful means of enabling one to thoroughly appreciate the character\nof formal syllogistic reasoning. Accordingly, the proof of each rule\nwill be indicated, and its elaboration left to the reader. There is no\ndifficulty, if one bears in mind that Figure is determined by the\nposition of the middle term.\n\nFig. I., Rule (a): _The minor premise must be affirmative_.\n\nFor, if not, in negative Moods there will be illicit process of the\nmajor term. Applying this rule to the eleven possible Moods given in \u00a7\n4, as remaining after application of the Common Canons, it eliminates\nA.E.E., A.E.O., A.O.O.\n\n(b) _The major premise must be universal_.\n\nFor, if not, the minor premise being affirmative, the middle term will\nbe undistributed. This rule eliminates I.A.I., O.A.O.; leaving six\nMoods, including two subalterns.\n\nFig. II. (a) _One premise must be negative._\n\nFor else neither premise will distribute the middle term. This rule\neliminates A.A.A., A.A.I., A.I.I., I.A.I.\n\n(b) _The major premise must be universal._\n\nFor else, the conclusion being negative, there will be illicit process\nof the major term. This eliminates I.A.I., O.A.O.; leaving six Moods,\nincluding two subalterns.\n\nFig. III. (a) _The minor premise must be affirmative._\n\nFor else, in negative moods there will be illicit process of the major\nterm. This rule eliminates A.E.E., A.E.O., A.O.O.\n\n(b) _The conclusion must be particular._\n\nFor, if not, the minor premise being affirmative, there will be illicit\nprocess of the minor term. This eliminates A.A.A., A.E.E., E.A.E.;\nleaving six Moods.\n\nFig. IV. (a) _When the major premise is affirmative, the minor must be\nuniversal._\n\nFor else the middle term is undistributed. This eliminates A.I.I.,\nA.O.O.\n\n(b) _When the minor premise is affirmative the conclusion must be\nparticular._\n\nOtherwise there will be illicit process of the minor term. This\neliminates A.A.A., E.A.E.\n\n(c) _When either premise is negative, the major must be universal._\n\nFor else, the conclusion being negative, there will be illicit process\nof the major term. This eliminates O.A.O.; leaving six Moods, including\none subaltern.\n\n\u00a7 6. Reduction is either--(1) Ostensive or (2) Indirect. Ostensive\nReduction consists in showing that an argument given in one Mood can\nalso be stated in another; the process is especially used to show that\nthe Moods of the second, third, and fourth Figures are equivalent to one\nor another Mood of the first Figure. It thus proves the validity of the\nformer Moods by showing that they also essentially conform to the\n_Dictum_, and that all Categorical Syllogisms are only superficial\nvarieties of one type of proof.\n\nTo facilitate Reduction, the recognised Moods have all had names given\nthem; which names, again, have been strung together into mnemonic verses\nof great force and pregnancy:\n\n Barbara, Celarent, Darii, Ferioque prioris:\n Cesare, Camestres, Festino, Baroco, secund\u00e6:\n Tertia, Darapti, Disamis, Datisi, Felapton,\n Bocardo, Ferison, habet: Quarta insuper addit\n Bramantip, Camenes, Dimaris, Fesapo, Fresison.\n\nIn the above verses the names of the Moods of Fig. I. begin with the\nfirst four consonants B, C, D, F, in alphabetical order; and the names\nof all other Moods likewise begin with these letters, thus signifying\n(except in Baroco and Bocardo) the mood of Fig. I., to which each is\nequivalent, and to which it is to be reduced: as Bramantip to Barbara,\nCamestres to Celarent, and so forth.\n\nThe vowels A, E, I, O, occurring in the several names, give the quantity\nand quality of major premise, minor premise, and conclusion in the usual\norder.\n\nThe consonants s and p, occurring after a vowel, show that the\nproposition which the vowel stands for is to be converted either (s)\nsimply or (p) _per accidens_; except where s or p occurs after the third\nvowel of a name, the conclusion: then it refers not to the conclusion of\nthe given Mood (say Disamis), but to the conclusion of that Mood of the\nfirst Figure to which the given Mood is reduced (Darii).\n\nM (_mutare_, metathesis) means 'transpose the premises' (as of\nCa_m_estres).\n\nC means 'substitute the contradictory of the conclusion for the\nforegoing premise,' a process of the Indirect Reduction to be presently\nexplained (see Baroco, \u00a7 8).\n\nThe other consonants, r, n, t (with b and d, when not initial),\noccurring here and there, have no mnemonic significance.\n\nWhat now is the problem of Reduction? The difference of Figures depends\nupon the position of the Middle Term. To reduce a Mood of any other\nFigure to the form of the First, then, we must so manipulate its\npremises that the Middle Term shall be subject of the major premise and\npredicate of the minor premise.\n\nNow in Fig. II. the Middle Term is predicate of both premises; so that\nthe minor premise may need no alteration, and to convert the major\npremise may suffice. This is the case with Cesare, which reduces to\nCelarent by simply converting the major premise; and with Festino, which\nby the same process becomes Ferio. In Camestres, however, the minor\npremise is negative; and, as this is impossible in Fig. I., the premises\nmust be transposed, and the new major premise must be simply converted:\nthen, since the transposition of the premises will have transposed the\nterms of the conclusion (according to the usual reading of syllogisms),\nthe new conclusion must be simply converted in order to prove the\nvalidity of the original conclusion. The process may be thus represented\n(_s.c._ meaning 'simply convert')\n\n Camestres. Celarent.\n\n All P is M; ----\\ /---> No M is S;\n \\ c/\n \\/\n s/\\\n / \\\n No S is M: ----/ \\---> All P is M:\n\n s.c.\n.'. No S is P. <----------- No P is S.\n\nThe Ostensive Reduction of Baroco also needs special explanation; for as\nit used to be reduced indirectly, its name gives no indication of the\nostensive process. To reduce it ostensively let us call it Faksnoko,\nwhere k means 'obvert the foregoing premise.' By thus obverting (k) and\nsimply converting (s) (in sum, contrapositing) the major premise, and\nobverting the minor premise, we get a syllogism in Ferio, thus:\n\nBaroco or Faksnoko. Ferio.\n _contrap_\n All P is M; -----------------------> No m (not-M) is P;\n\n _obv_\n Some S is not M: -----------------------> Some S is m (not-M):\n .'. Some S is not P. .'. Some S is not P.\n\nIn Fig. III. the middle term is subject of both premises; so that, to\nreduce its Moods to the First Figure, it may be enough to convert the\nminor premise. This is the case with Darapti, Datisi, Felapton, and\nFerison. But, with Disamis, since the major premise must in the First\nFigure be universal, we must transpose the premises, and then simply\nconvert the new minor premise; and, lastly, since the major and minor\nterms have now changed places, we must simply convert the new conclusion\nin order to verify the old one. Thus:\n\n Disamis. Darii.\n\n Some M is P; ----\\ /---> All M is S;\n \\s./\n \\/\n /\\c.\n / \\\n All M is S: ----/ \\---> Some P is M:\n\n s.c.\n.'. Some S is P. <------------- .'. Some P is S.\n\nBocardo, like Baroco, indicates by its name the indirect process. To\nreduce it ostensively let its name be Doksamrosk, and proceed thus:\n\n Bocardo or Doksamrosk. Darii.\n\n Some M is not P; ----------\\ /---------> All M is S;\n \\ /\n \\/\n /\\ _contrap_\n / \\\n All M is S: ----------/ \\---------> Some p (not-P) is M:\n\n _convert & obvert_\n.'. Some S is not P. <------------------------- .'. Some p (not-P) is S.\n\nIn Fig. IV. the position of the middle term is, in both premises, the\nreverse of what it is in the First Figure; we may therefore reduce its\nMoods either by transposing the premises, as with Bramantip, Camenes,\nand Dimaris; or by converting both premises, the course pursued with\nFesapo and Fresison. It may suffice to illustrate by the case of\nBramantip:\n\nBramantip. Barbara.\n\nAll P is M; ----------\\ /------> All M is S;\n \\/\n /\\\nAll M is S: ----------/ \\------> All P is M:\n\n convert per acc.\n.'. Some S is P. <----------------------- .'. All P is S.\n\nThis case shows that a final significant consonant (s, p, or sk) in the\nname of any Mood refers to the conclusion of the new syllogism in the\nFirst Figure; since p in Bramantip cannot refer to that Mood's own\nconclusion in I.; which, being already particular, cannot be converted\n_per accidens_.\n\nFinally, in Fig. I., Darii and Ferio differ respectively from Barbara\nand Celarent only in this, that their minor premises, and consequently\ntheir conclusions, are subaltern to the corresponding propositions of\nthe universal Moods; a difference which seems insufficient to give them\nrank as distinct forms of demonstration. And as for Barbara and\nCelarent, they are easily reducible to one another by obverting their\nmajor premises and the new conclusions, thus:\n\nBarbara. Celarent.\n obv.\nAll M is P; -----------------------> No M is p (not-P);\n\nAll S is M: -----------------------> All S is M:\n\n obv.\n.'. All S is P. <------------------- .'. No S is p (not-P).\n\nThere is, then, only one fundamental syllogism.\n\n\u00a7 7. A new version of the mnemonic lines was suggested in _Mind_ No. 27,\nwith the object of (1) freeing them from all meaningless letters, (2)\nshowing by the name of each Mood the Figure to which it belongs, (3)\ngiving names to indicate the ostensive reduction of Baroco and Bocardo.\nTo obtain the first two objects, _l_ is used as the mark of Fig. I., _n_\nof Fig II., _r_ of Fig. III., _t_ of Fig. IV. The verses (to be scanned\ndiscreetly) are as follows:\n\nBalala, Celalel, Dalii, Felioque prioris:\n\n {Faksnoko}\nCesane, Camenes, Fesinon, { } secund\u00e6:\n { Banoco,}\n\nTertia, Darapri, Drisamis, Darisi, Ferapro,\n\nDoksamrosk}\n }, Ferisor habet: Quarta insuper addit.\nBocaro }\n\nBamatip, Cametes, Dimatis, Fesapto, Fesistot.\n\nDe Morgan praised the old verses as \"more full of meaning than any\nothers that ever were made\"; and in defence of the above alteration it\nmay be said that they now deserve that praise still more.\n\n\u00a7 8. Indirect reduction is the process of proving a Mood to be valid by\nshowing that the supposition of its invalidity involves a contradiction.\nTake Baroco, and (since the doubt as to its validity is concerned not\nwith the truth of the premises, but with their relation to the\nconclusion) assume the premises to be true. Then, if the conclusion be\nfalse, its contradictory is true. The conclusion being in O., its\ncontradictory will be in A. Substituting this A. for the minor premise\nof Baroco, we have the premises of a syllogism in Barbara, which will be\nfound to give a conclusion in A., contradictory of the original minor\npremise; thus:\n\n Baroco. Barbara.\n\n All P is M; -----------------> All P is M;\n\n Some S is not M: <-----\\ /-----> All S is P:\n \\ /\n contradictory \\/\n /\\ contradictory\n / \\\n.'. Some S is not P ------/ \\------ .'. All S is M.\n\nBut the original minor premise, _Some S is not M_, is true by\nhypothesis; and therefore the conclusion of Barbara, _All S is M_, is\nfalse. This falsity cannot, however, be due to the form of Barbara,\nwhich we know to be valid; nor to the major premise, which, being taken\nfrom Baroco, is true by hypothesis: it must, therefore, lie in the minor\npremise of Barbara, _All S is P_; and since this is contradictory of the\nconclusion of Baroco _Some S is not P_, that conclusion was true.\n\nSimilarly, with Bocardo, the Indirect Reduction proceeds by substituting\nfor the major premise the contradictory of the conclusion; thus again\nobtaining the premises of a syllogism in Barbara, whose conclusion is\ncontradictory of the original major premise. Hence the initial B in\nBaroco and Bocardo: it points to a syllogism in Barbara as the means of\nIndirect Reduction (_Reductio ad impossibile_).\n\nAny other Mood may be reduced indirectly: as, for example, Dimaris. If\nthis is supposed to be invalid and the conclusion false, substitute the\ncontradictory of the conclusion for the major premise, thus obtaining\nthe premises of Celarent:\n\nDimaris. Celarent.\n\n contradictory\nSome P is M; <--------- --------> No S is P;\n \\ /\n \\/\nAll M is S: -----------/\\---------> All M is S:\n / \\\n contradictory/ \\\n.'. Some S is P. ----------- -------- .'. No M is P}\n } simply converted\n .'. No P is M}\n\nThe conclusion of Celarent, simply converted, contradicts the original\nmajor premise of Dimaris, and is therefore false. Therefore the major\npremise of Celarent is false, and the conclusion of Dimaris is true. We\nmight, of course, construct mnemonic names for the Indirect Reduction of\nall the Moods: the name of Dimaris would then be Cicari.\n\n\u00a7 9. The need or use of any Figure but the First has been much discussed\nby Logicians. Since, in actual debate, arguments are rarely stated in\nsyllogistic form, and, therefore, if reduced to that form for closer\nscrutiny, generally have to be treated with some freedom; why not always\nthrow them at once into the First Figure? That Figure has manifest\nadvantages: it agrees directly with the _Dictum_; it gives conclusions\nin all four propositional forms, and therefore serves every purpose of\nfull affirmation or denial, of showing agreement or difference (total or\npartial), of establishing the contradictories of universal statements;\nand it is the only Figure in which the subject and predicate of the\nconclusion occupy the same positions in the premises, so that the course\nof argument has in its mere expression an easy and natural flow.\n\nStill, the Second Figure also has a very natural air in some kinds of\nnegative arguments. The parallelism of the two premises, with the middle\nterm as predicate in both, brings out very forcibly the necessary\ndifference between the major and minor terms that is involved in their\nopposite relations to the middle term. _P is not, whilst S is, M_, says\nCesare: that drives home the conviction that _S is not P_. Similarly in\nCamestres: _Deer do, oxen do not, shed their horns_. What is the\nconclusion?\n\nThe Third Figure, again, furnishes in Darapti and Felapton, the most\nnatural forms of stating arguments in which the middle term is singular:\n\n Socrates was truthful;\n Socrates was a Greek:\n .'. Some Greek was truthful.\n\nReducing this to Fig I., we should get for the minor premise, _Some\nGreek was Socrates_: which is certainly inelegant. Still, it might be\nurged that, in relation to proof, elegance is an extraneous\nconsideration. And as for the other advantage claimed for Fig.\nIII.--that, as it yields only particular conclusions, it is useful in\nestablishing contradictories against universals--for that purpose none\nof its Moods can be better than Darii or Ferio.\n\nAs for Fig. IV., no particular advantage has been claimed for it. It is\nof comparatively late recognition (sometimes called the 'Galenian,'\nafter Galen, its supposed discoverer); and its scientific claim to exist\nat all is disputed. It is said to be a mere inversion of Fig. I.; which\nis not true in any sense in which Figs. II. and III. may not be\ncondemned as partial inversions of Fig. I., and as having therefore\nstill less claim to recognition. It is also said to invert the order of\nthought; as if thought had only one order, or as if the order of thought\nhad anything to do with Formal Logic. Surely, if distinction of Figure\nbe recognised at all, the Fourth Figure is scientifically necessary,\nbecause it is inevitably generated by an analysis of the possible\npositions of the middle term.\n\n\u00a7 10. Is Reduction necessary, however; or have not all the Figures equal\nand independent validity? In one sense not only every Figure but each\nMood has independent validity: for any one capable of abstract thinking\nsees its validity by direct inspection; and this is true not only of the\nabstract Moods, but very frequently of particular concrete arguments.\nBut science aims at unifying knowledge; and after reducing all possible\narguments that form categorical syllogisms to the nineteen Moods, it is\nanother step in the same direction to reduce these Moods to one form.\nThis is the very nature of science: and, accordingly, the efforts of\nsome Logicians to expound separate principles of each Figure seem to be\nsupererogatory. Grant that they succeed; and what can the next step be,\nbut either to reduce these principles to the _Dictum_, or the _Dictum_\nand the rest to one of these principles? Unless this can be done there\nis no science of Formal Logic. If it is done, what is gained by reducing\nthe principles of the other Figures to the _Dictum_, instead of the\nMoods of the other Figures to those of the first Figure? It may,\nperhaps, be said that to show (1) that the Moods of the second, third,\nand fourth Figures flow from their own principles (though, in fact,\nthese principles are laboriously adapted to the Moods); and (2) that\nthese principles may be derived from the _Dictum_, is the more\nuncompromisingly gradual and regular method: but is not Formal Logic\nalready sufficiently encumbered with formalities?\n\n\u00a7 11. Euler's diagrams are used to illustrate the syllogism, though not\nvery satisfactorily, thus:\n\nBarbara--\n\n[Illustration: FIG. 5.]\n\nCelarent--\n\n[Illustration: FIG. 6.]\n\nDarii--\n\n[Illustration: FIG. 7.]\n\nRemembering that 'Some' means 'It may be all,' it is plain that any one\nof these diagrams in Fig. 7, or the one given above for Barbara, may\nrepresent the denotative relations of P, M and S in Darii; though no\ndoubt the diagram we generally think of as representing Darii is No. 1\nin Fig. 7.\n\nRemembering that A may be U, and that, therefore, wherever A occurs\nthere may be only one circle for S and P, these syllogisms may be\nrepresented by only two circles, and Barbara by only one.\n\nFerio--\n\n[Illustration: FIG. 8.]\n\nHere, again, probably, we generally think of No. 1 as the diagram\nrepresenting Ferio; but 2, or 3, or that given above for Celarent, is\ncompatible with the premises.\n\nIf instead of dealing with M, P, and S, a concrete example be taken of\nDarii or Ferio, a knowledge of the facts of the case will show what\ndiagram is suitable to it. But, then, surely it must be possible to do\nwithout the diagram. These diagrams, of course, can be used to\nillustrate Moods of the other Figures.\n\n\n\n\nCHAPTER XI\n\nABBREVIATED AND COMPOUND ARGUMENTS\n\n\n\u00a7 1. In ordinary discussion, whether oral or written, it is but rarely\nthat the forms of Logic are closely adhered to. We often leave wide gaps\nin the structure of our arguments, trusting the intelligence of those\naddressed to bridge them over; or we invert the regular order of\npropositions, beginning with the conclusion, and mentioning the\npremises, perhaps, a good while after, confident that the sagacity of\nour audience will make all smooth. Sometimes a full style, like\nMacaulay's, may, by means of amplification and illustration, spread the\nelements of a single syllogism over several pages--a pennyworth of logic\nsteeped in so much eloquence. These practices give a great advantage to\nsophists; who would find it very inconvenient to state explicitly in\nMood and Figure the pretentious antilogies which they foist upon the\npublic; and, indeed, such licences of composition often prevent honest\nmen from detecting errors into which they themselves have unwittingly\nfallen, and which, with the best intentions, they strive to communicate\nto others: but we put up with these drawbacks to avoid the inelegance\nand the tedium of a long discourse in accurate syllogisms.\n\nMany departures from the strictly logical statement of reasonings\nconsist in the use of vague or figurative language, or in the\nsubstitution for one another of expressions supposed to be equivalent,\nthough, in fact, dangerously discrepant. Against such occasions of error\nthe logician can provide no safeguard, except the advice to be careful\nand discriminating in what you say or hear. But as to any derangement\nof the elements of an argument, or the omission of them, Logic\neffectually aids the task of restoration; for it has shown what the\nelements are that enter into the explicit statement of most\nratiocinations, namely, the four forms of propositions and what that\nconnected order of propositions is which most easily and surely exposes\nthe validity or invalidity of reasoning, namely, the premises and\nconclusion of the Syllogism. Logic has even gone so far as to name\ncertain abbreviated forms of proof, which may be regarded as general\ntypes of those that actually occur in debate, in leading articles,\npamphlets and other persuasive or polemic writings--namely, the\nEnthymeme, Epicheirema and Sorites.\n\n\u00a7 2. The Enthymeme, according to Aristotle, is the Syllogism of probable\nreasoning about practical affairs and matters of opinion, in contrast\nwith the Syllogism of theoretical demonstration upon necessary grounds.\nBut, as now commonly treated, it is an argument with one of its elements\nomitted; a Categorical Syllogism, having one or other of its premises,\nor else its conclusion, suppressed. If the major premise be suppressed,\nit is called an Enthymeme of the First Order; if the minor premise be\nwanting, it is said to be of the Second Order; if the conclusion be left\nto be understood, there is an Enthymeme of the Third Order.\n\nLet the following be a complete Syllogism:\n\n All free nations are enterprising;\n The Dutch are a free nation:\n .'. The Dutch are enterprising.\n\nReduced to Enthymemes, this argument may be put thus:\n\nIn the First Order:\n\n The Dutch are a free nation:\n .'. The Dutch are enterprising.\n\nIn the Second Order--\n\n All free nations are enterprising;\n .'. The Dutch are enterprising.\n\nIn the Third Order--\n\n All free nations are enterprising;\n And the Dutch are a free nation.\n\nIt is certainly very common to meet with arguments whose statement may\nbe represented by one or other of these three forms; indeed, the\nEnthymeme is the natural substitute for a full syllogism in oratory:\nwhence the transition from Aristotle's to the modern meaning of the\nterm. The most unschooled of men readily apprehend its force; and a\nstudent of Logic can easily supply the proposition that may be wanted in\nany case to complete a syllogism, and thereby test the argument's formal\nvalidity. In any Enthymeme of the Third Order, especially, to supply the\nconclusion cannot present any difficulty at all; and hence it is a\nfavourite vehicle of innuendo, as in Hamilton's example:\n\n Every liar is a coward;\n And Caius is a liar.\n\nThe frankness of this statement and its reticence, together, make it a\nbiting sarcasm upon Caius.\n\nThe process of finding the missing premise in an Enthymeme of either the\nFirst or the Second Order, so as to constitute a syllogism, is sometimes\ncalled Reduction; and for this a simple rule may be given: Take that\nterm of the given premise which does not occur in the conclusion (and\nwhich must therefore be the Middle), and combine it with that term of\nthe conclusion which does not occur in the given premise; the\nproposition thus formed is the premise which was requisite to complete\nthe Syllogism. If the premise thus constituted contain the predicate of\nthe conclusion, the Enthymeme was of the First Order; if it contain the\nsubject of the conclusion, the Enthymeme was of the Second Order.\n\nThat a statement in the form of a Hypothetical Proposition may really be\nan Enthymeme (as observed in chap. v. \u00a7 4) can easily be shown by\nrecasting one of the above Enthymemes thus: _If all free nations are\nenterprising, the Dutch are enterprising_. Such statements should be\ntreated according to their true nature.\n\nTo reduce the argument of any ordinary discourse to logical form, the\nfirst care should be to make it clear to oneself what exactly the\nconclusion is, and to state it adequately but as succinctly as possible.\nThen look for the evidence. This may be of an inductive character,\nconsisting of instances, examples, analogies; and, if so, of course its\ncogency must be evaluated by the principles of Induction, which we\nshall presently investigate. But if the evidence be deductive, it will\nprobably consist of an Enthymeme, or of several Enthymemes one depending\non another. Each Enthymeme may be isolated and expanded into a\nsyllogism. And we may then inquire: (1) whether the syllogisms are\nformally correct according to Barbara (or whatever the appropriate\nMood); (2) whether the premises, or the ultimate premises, are true in\nfact.\n\n\u00a7 3. A Monosyllogism is a syllogism considered as standing alone or\nwithout relation to other arguments. But, of course, a disputant may be\nasking to prove the premises of any syllogism; in which case other\nsyllogisms may be advanced for that purpose. When the conclusion of one\nsyllogism is used to prove another, we have a chain-argument which,\nstated at full length, is a Polysyllogism. In any Polysyllogism, again,\na syllogism whose conclusion is used as the premise of another, is\ncalled in relation to that other a Prosyllogism; whilst a syllogism one\nof whose premises is the conclusion of another syllogism, is in relation\nto that other an Episyllogism. Two modes of abbreviating a\nPolysyllogism, are usually discussed, the Epicheirema and the Sorites.\n\n\u00a7 4. An Epicheirema is a syllogism for one or both of whose premises a\nreason is added; as--\n\n All men are mortal, for they are animals;\n Socrates is a man, for rational bipeds are men:\n .'. Socrates is mortal.\n\nThe Epicheirema is called Single or Double, says Hamilton, according as\nan \"adscititious proposition\" attaches to one or both of the premises.\nThe above example is of the double kind. The Single Epicheirema is said\nto be of the First Order, if the adscititious proposition attach to the\nmajor premise; if to the minor, of the Second Order. (Hamilton's\n_Logic_: Lecture xix.)\n\nAn Epicheirema, then, is an abbreviated chain of reasoning, or\nPolysyllogism, comprising an Episyllogism with one or two enthymematic\nProsyllogisms. The major premise in the above case, _All men are mortal,\nfor they are animals,_ is an Enthymeme of the First Order, suppressing\nits own major premise, and may be restored thus:\n\n All animals are mortal;\n All men are animals:\n .'. All men are mortal.\n\nThe minor premise, _Socrates is a man, for rational bipeds are men_, is\nan Enthymeme of the Second Order, suppressing its own minor premise, and\nmay be restored thus:\n\n All rational bipeds are men;\n Socrates is a rational biped:\n .'. Socrates is a man.\n\n\u00a7 5. The Sorites is a Polysyllogism in which the Conclusions, and even\nsome of the Premises, are suppressed until the arguments end. If the\nchain of arguments were freed of its enthymematic character, the\nsuppressed conclusions would appear as premises of Episyllogisms.\n\nTwo varieties of Sorites are recognised, the Aristotelian (so called,\nthough not treated of by Aristotle), and the Goclenian (named after its\ndiscoverer, Goclenius of Marburg, who flourished about 1600 A.D.). In\norder to compare these two forms of argument, it will be convenient to\nplace side by side Hamilton's classical examples of them.\n\n Aristotelian. Goclenian.\n Bucephalus is a horse; An animal is a substance;\n A horse is a quadruped; A quadruped is an animal;\n A quadruped is an animal; A horse is a quadruped;\n An animal is a substance: Bucephalus is a horse:\n .'. Bucephalus is a substance. .'. Bucephalus is a substance.\n\nThe reader wonders what is the difference between these two forms. In\nthe Aristotelian Sorites the minor term occurs in the first premise, and\nthe major term in the last; whilst in the Goclenian the major term\noccurs in the first premise, and the minor in the last. But since the\ncharacter of premises is fixed by their terms, not by the order in which\nthey are written, there cannot be a better example of a distinction\nwithout a difference. At a first glance, indeed, there may seem to be a\nmore important point involved; the premises of the Aristotelian Sorites\nseem to proceed in the order of Fig. IV. But if that were really so the\nconclusion would be, _Some Substance is Bucephalus_. That, on the\ncontrary, every one writes the conclusion, _Bucephalus is a substance_,\nproves that the logical order of the premises is in Fig. I. Logically,\ntherefore, there is absolutely no difference between these two forms,\nand pure reason requires either that the \"Aristotelian Sorites\"\ndisappear from the text-books, or that it be regarded as in Fig. IV.,\nand its conclusion converted. It is the shining merit of Goclenius to\nhave restored the premises of the Sorites to the usual order of Fig. I.:\nwhereby he has raised to himself a monument more durable than brass, and\nsecured indeed the very cheapest immortality.\n\nThe common Sorites, then, being in Fig. I., its rules follow from those\nof Fig. I:\n\n(1) Only one premise can be particular; and, if any, only that in which\nthe minor term occurs.\n\nFor, just as in Fig I., a particular premise anywhere else involves\nundistributed Middle.\n\n(2) Only one premise can be negative; and, if any, only that in which\nthe major term occurs.\n\nFor if there were two negative premises, at the point where the second\nentered the chain of argument there must be a syllogism with two\nnegative premises, which is contrary to Rule 5; whilst if one premise be\nnegative it must be that which contains the major term, for the same\nreason as in Fig. I., namely, that the conclusion will be negative, and\nthat therefore only a negative major premise can prevent illicit process\nof the major term.\n\nIf we expand a Sorites into its constituent syllogisms, the conclusions\nsuccessively suppressed will reappear as major premises; thus:\n\n (1) An animal is a substance;\n A quadruped is an animal:\n .'. A quadruped is a substance.\n\n (2) A quadruped is a substance;\n A horse is a quadruped:\n .'. A horse is a substance.\n\n (3) A horse is a substance:\n Bucephalus is a horse:\n .'. Bucephalus is a substance.\n\nThis suffices to show that the Protosyllogism of a Goclenian Sorites is\nan Enthymeme of the Third Order; after which the argument is a chain of\nEnthymemes of the First Order, or of the First and Third combined, since\nthe conclusions as well as the major premises are omitted, except in the\nlast one.\n\nLest it should be thought that the Sorites is only good for arguments so\nfrivolous as the above, I subjoin an example collected from various\nparts of Mill's _Political Economy_:--\n\n The cost of labour depends on the efficiency of labour;\n The rate of profits depends on the cost of labour;\n The investment of capital depends on the rate of profits;\n Wages depend on the investment of capital:\n .'. Wages depend on the efficiency of labour.\n\nHad it occurred to Mill to construct this Sorites, he would have\nmodified his doctrine of the wages-fund, and would have spared many\ncritics the malignant joy of refuting him.\n\n\u00a7 6. The Antinomy is a combination of arguments by which contradictory\nattributes are proved to be predicable of the same subject. In symbols,\nthus:\n\n All M is P; All N is p;\n All S is M: All S is N:\n .'. All S is P. .'. All S is p.\n\nNow, by the principle of Contradiction, S cannot be P and p (not-P):\ntherefore, if both of the above syllogisms are sound, S, as the subject\nof contradictory attributes, is logically an impossible thing. The\ncontradictory conclusions are called, respectively, Thesis and\nAntithesis.\n\nTo come to particulars, we may argue: (1) that a constitution which is\nat once a monarchy, an aristocracy and a democracy, must comprise the\nbest elements of all three forms; and must, therefore, be the best of\nall forms of government: the British Constitution is, therefore, the\nbest of all. But (2) such a constitution must also comprise the worst\nelements of monarchy, aristocracy and democracy; and, therefore, must be\nthe worst of all forms. Are we, then, driven to conclude that the\nBritish Constitution, thus proved to be both the best and worst, does\nnot really exist at all, being logically impossible? The proofs seem\nequally cogent; but perhaps neither the best nor the worst elements of\nthe simpler constitutions need be present in our own in sufficient force\nto make it either good or bad.\n\nAgain:\n\n (1) Every being who is responsible for his actions is free;\n Man is responsible for his actions:\n .'. Man is free.\n\n (2) Every being whose actions enter into the course of nature is not free;\n Man is such a being:\n .'. Man is not free.\n\nDoes it, then, follow that 'Man,' as the subject of contradictory\nattributes, is a nonentity? This doctrine, or something like it, has\nbeen seriously entertained; but if to any reader it seem extravagant (as\nit certainly does to me), he will no doubt find an error in the above\narguments. Perhaps the major term is ambiguous.\n\nFor other examples it is enough to refer to the _Critique of Pure\nReason_, where Kant sets out the Antinomies of Rational Cosmology. But\neven if we do not agree with Kant that the human understanding, in\nattempting to deal with certain subjects beyond its reach, inevitably\nfalls into such contradictory reasonings; yet it can hardly be doubted\nthat we not unfrequently hold opinions which, if logically developed,\nresult in Antinomies. And, accordingly, the Antinomy, if it cannot be\nimputed to Reason herself, may be a very fair, and a very wholesome\n_argumentum ad hominem_. It was the favourite weapon of the Pyrrhonists\nagainst the dogmatic philosophies that flourished after the death of\nAristotle.\n\n\n\n\nCHAPTER XII\n\nCONDITIONAL SYLLOGISMS\n\n\n\u00a7 1. Conditional Syllogisms may be generally described as those that\ncontain conditional propositions. They are usually divided into two\nclasses, Hypothetical and Disjunctive.\n\nA Hypothetical Syllogism is one that consists of a Hypothetical Major\nPremise, a Categorical Minor Premise, and a Categorical Conclusion. Two\nMoods are usually recognised the _Modus ponens_, in which the antecedent\nof the hypothetical major premise is affirmed; and the _Modus tollens_,\nin which its consequent is denied.\n\n(1) _Modus ponens_, or Constructive.\n\n If A is B, C is D;\n A is B:\n .'. C is D.\n\nIf Aristotle's reasoning is conclusive, Plato's theory of Ideas is\nerroneous;\n\n Aristotle's reasoning is conclusive:\n .'. Plato's theory of Ideas is erroneous.\n\nRule of the _Modus ponens_: The antecedent of the major premise being\naffirmed in the minor premise, the consequent is also affirmed in the\nconclusion.\n\n(2) _Modus tollens_, or Destructive.\n\n If A is B, C is D;\n C is not D:\n .'. A is not B.\n\n If Pythagoras is to be trusted, Justice is a number;\n Justice is not a number:\n .'. Pythagoras is not to be trusted.\n\nRule of the _Modus tollens_: The consequent of the major premise being\ndenied in the minor premise, the antecedent is denied in the conclusion.\n\nBy using negative major premises two other forms are obtainable: then,\neither by affirming the antecedent or by denying the consequent, we draw\na negative conclusion.\n\n Thus (_Modus ponens_): (_Modus tollens_):\n\n If A is B, C is not D; If A is B, C is not D;\n A is B: C is D:\n .'. C is not D. .'. A is not B.\n\nFurther, since the antecedent of the major premise, taken by itself, may\nbe negative, it seems possible to obtain four more forms, two in each\nMood, from the following major premises:\n\n (1) If A is not B, C is D;\n (2) If A is not B, C is not D.\n\nBut since the quality of a Hypothetical Proposition is determined by the\nquality of its consequent, not at all by the quality of its antecedent,\nwe cannot get from these two major premises any really new Moods, that\nis to say, Moods exhibiting any formal difference from the four\npreviously expounded.\n\nIt is obvious that, given the hypothetical major premise--\n\n If A is B, C is D--\n\nwe cannot, by denying the antecedent, infer a denial of the consequent.\nThat A is B, is a mark of C being D; but we are not told that it is the\nsole and indispensable condition of it. If men read good books, they\nacquire knowledge; but they may acquire knowledge by other means, as by\nobservation. For the same reason, we cannot by affirming the consequent\ninfer the affirmation of the antecedent: Caius may have acquired\nknowledge; but we cannot thence conclude that he has read good books.\n\nTo see this in another light, let us recall chap. v. \u00a7 4, where it was\nshown that a hypothetical proposition may be translated into a\ncategorical one; whence it follows that a Hypothetical Syllogism may be\ntranslated into a Categorical Syllogism. Treating the above examples\nthus, we find that the _Modus ponens_ (with affirmative major premise)\ntakes the form of Barbara, and the _Modus tollens_ the form of\nCamestres:\n\n _Modus ponens._ Barbara.\n\n If A is B, C is D; The case of A being B is a case of C being D;\n A is B: This is a case of A being B:\n .'. C is D. .'. This is a case of C being D.\n\nNow if, instead of this, we affirm the consequent, to form the new minor\npremise,\n\n This is a case of C being D,\n\nthere will be a Syllogism in the Second Figure with two affirmative\npremises, and therefore the fallacy of undistributed Middle. Again:\n\n _Modus tollens._ Camestres.\n\n If A is B, C is D; The case of A being B is a case of C being D:\n C is not D: This is not a case of C being D:\n .'. A is not B. .'. This is not a case of A being B.\n\nBut if, instead of this, we deny the antecedent, to form the new minor\npremise,\n\n This is not a case of A being B,\n\nthere arises a syllogism in the First Figure with a negative minor\npremise, and therefore the fallacy of illicit process of the major term.\n\nBy thus reducing the Hypothetical Syllogism to the Categorical form,\nwhat is lost in elegance is gained in intelligibility. For, first, we\nmay justify ourselves in speaking of the hypothetical premise as the\nmajor, and of the categorical premise as the minor; since in the\ncategorical form they contain respectively the major and minor terms.\nAnd, secondly, we may justify ourselves in treating the Hypothetical\nSyllogism as a kind of Mediate Inference, in spite of the fact that it\ndoes not exhibit two terms compared by means of a third; since in the\nCategorical form such terms distinctly appear: a new term ('This')\nemerges in the position of the minor; the place of the Middle is filled\nby the antecedent of the major premise in the _Modus ponens_, and by the\nconsequent in the _Modus tollens_.\n\nThe mediate element of the inference in a Hypothetical Syllogism\nconsists in asserting, or denying, the fulfilment of a given condition;\njust as in a Categorical syllogism to identify the minor term with the\nMiddle is a condition of the major term's being predicated of it. In the\nhypothetical proposition--\n\n If A is B, C is D--\n\nthe Antecedent, _A is B_, is the _conditio sufficiens_, or mark, of the\nConsequent, _C is D_; and therefore the Consequent, _C is D_, is a\n_conditio sine qua non_ of the antecedent, _A is B_; and it is by means\nof affirming the former condition, or else denying the latter, that a\nconclusion is rendered possible.\n\nIndeed, we need not say that the element of mediation consists in\naffirming, _or denying_, the fulfilment of a given condition: it is\nenough to say 'in affirming.' For thus to explain the _Modus tollens_,\nreduce it to the _Modus ponens_ (contrapositing the major premise and\nobverting the minor):\n\n Celarent.\n\n If A is B, C is D: The case of C being not-D is\n .'. If C is not-D, A is not B; not a case of A being B;\n C is not-D: This is a case of C being\n .'. A is not B. not-D:\n .'. This is not a case of A\n being B.\n\nThe above four forms commonly treated of as Hypothetical Syllogisms, are\ncalled by Ueberweg and Dr. Keynes 'Hypothetico-Categorical.' Ueberweg\nrestricts the name 'Hypothetical' simply (and Dr. Keynes the name\n'Conditional') to such Syllogisms as the following, having two\nHypothetical Premises:\n\n If C is D, E is F;\n If A is B, C is D:\n .'. If A is B, E is F.\n\nIf we recognise particular hypothetical propositions (see chap. v. \u00a7 4),\nit is obvious that such Syllogisms may be constructed in all the Moods\nand Figures of the Categorical Syllogism; and of course they may be\ntranslated into Categoricals. We often reason in this hypothetical way.\nFor example:\n\n If the margin of cultivation be extended, rents will rise;\n If prices of produce rise, the margin of cultivation will be extended:\n .'. If prices of produce rise, rents will rise.\n\nBut the function of the Hypothetical Syllogism (commonly so called), as\nalso of the Disjunctive Syllogism (to be discussed in the next section)\nis to get rid of the conditional element of the premises, to pass from\nsuspense to certainty, and obtain a decisive categorical conclusion;\nwhereas these Syllogisms with two hypothetical premises leave us still\nwith a hypothetical conclusion. This circumstance seems to ally them\nmore closely with Categorical Syllogisms than with those that are\ndiscussed in the present chapter. That they are Categoricals in disguise\nmay be seen by considering that the above syllogism is not materially\nsignificant, unless in each proposition the word 'If' is equivalent to\n'Whenever.' Accordingly, the name 'Hypothetical Syllogism,' is here\nemployed in the older usage.\n\n\u00a7 2. A Disjunctive Syllogism consists of a Disjunctive Major Premise, a\nCategorical Minor Premise, and a Categorical Conclusion.\n\nHow many Moods are to be recognised in this kind of argument depends on\nwhether the alternatives of the Disjunctive Premise are regarded as\nmutually exclusive or possibly coincident. In saying '_Either_ A is B,\n_or_ C is D,' do we mean 'either, but not both,' or 'either, it may be\nboth'? (See chap. v. \u00a7 4.)\n\nWhen the alternatives of the Disjunctive are not exclusive, we have only\nthe\n\n _Modus tollendo ponens._\n\n Either A is B, or C is D;\n A is not B (or C is not D):\n .'. C is D (or A is B).\n\nEither wages fall, or the weaker hands are dismissed;\n\n Wages do not fall:\n .'. The weaker hands are dismissed.\n\nBut we cannot argue--\n\n Wages fall:\n .'. The weaker hands are not dismissed;\n\nsince in 'hard times' both events may happen together.\n\nRule of the _Modus tollendo ponens_: If one alternative be denied, the\nother is affirmed.\n\nWhen, however, the alternatives of the Disjunctive are mutually\nexclusive, we have also the\n\n _Modus ponendo tollens._\n\n Either A is B, or C is D;\n A is B (or C is D):\n .'. C is not D (or A is not B).\n\nEither the Tories or the Whigs win the election;\n\n The Tories win:\n .'. The Whigs do not win.\n\nWe may also, of course, argue as above in the _Modus tollendo ponens_--\n\n The Tories do not win:\n .'. The Whigs do.\n\nBut in this example, to make the _Modus tollendo ponens_ materially\nvalid, it must be impossible that the election should result in a tie.\nThe danger of the Disjunctive Proposition is that the alternatives may\nnot, between them, exhaust the possible cases. Only contradictory\nalternatives are sure to cover the whole ground.\n\nRule of the _Modus ponendo tollens:_ If one alternative be affirmed, the\nother is denied.\n\nSince a disjunctive proposition may be turned into a hypothetical\nproposition (chap. v. \u00a7 4,) a Disjunctive Syllogism may be turned into a\nHypothetical Syllogism:\n\n _Modus tollendo ponens._ _Modus ponens._\n\n Either A is B, or C is D; If A is not B, C is D;\n A is not B: A is not B:\n .'. C is D. .'. C is D.\n\nSimilarly the _Modus ponendo tollens_ is equivalent to that kind of\n_Modus ponens_ which may be formed with a negative major premise; for if\nthe alternatives of a disjunctive proposition be exclusive, the\ncorresponding hypothetical be affirmative or negative:\n\n _Modus ponendo tollens._ _Modus ponens._\n\n Either A is B, or C is D; If A is B, C is not D;\n A is B: A is B:\n .'. C is not D. .'. C is not D.\n\nHence, finally, a Disjunctive Syllogism being equivalent to a\nHypothetical, and a Hypothetical to a Categorical; a Disjunctive\nSyllogism is equivalent and reducible to a Categorical. It is a form of\nMediate Inference in the same sense as the Hypothetical Syllogism is;\nthat is to say, the conclusion depends upon an affirmation, or denial,\nof the fulfilment of a condition implied in the disjunctive major\npremise.\n\n\u00a7 3. The Dilemma is perhaps the most popularly interesting of all forms\nof proof. It is a favourite weapon of orators and wits; and \"impaled\nupon the horns of a dilemma\" is a painful situation in which every one\ndelights to see his adversary. It seems to have been described by\nRhetoricians before finding its way into works on Logic; and Logicians,\nto judge from their diverse ways of defining it, have found some\ndifficulty in making up their minds as to its exact character.\n\nThere is a famous Dilemma employed by Demosthenes, from which the\ngeneral nature of the argument may be gathered:\n\n If \u00c6schines joined in the public rejoicings, he is\n inconsistent; if he did not, he is unpatriotic;\n\n But either he joined, or he did not join:\n\n Therefore he is either inconsistent or unpatriotic.\n\nThat is, reduced to symbols:\n\n If A is B, C is D; and if E is F, G is H:\n But either A is B, or E is F;\n .'. Either C is D or G is H (_Complex Constructive_).\n\nThis is a compound Conditional Syllogism, which may be analysed as\nfollows:\n\n Either A is B or E is F.\n\n Suppose that E is not F: Suppose that A is not B:\n Then A is B. Then E is F.\n But if A is B, C is D; But if E is F, G is H;\n (A is B): (E is F):\n .'. C is D. .'. G is H.\n\n .'. Either C is D or G is H.\n\nA Dilemma, then, is a compound Conditional Syllogism, having for its\nMajor Premise two Hypothetical Propositions, and for its Minor Premise a\nDisjunctive Proposition, whose alternative terms either affirm the\nAntecedents or deny the Consequents of the two Hypothetical Propositions\nforming the Major Premise.\n\nThe hypothetical propositions in the major premise, may have all four\nterms distinct (as in the above example); and then the conclusion is a\ndisjunctive proposition, and the Dilemma is said to be Complex. Or the\ntwo hypothetical propositions may have a common antecedent or a common\nconsequent; and then the conclusion is a categorical proposition, and\nthe Dilemma is said to be Simple.\n\nAgain, the alternatives of the disjunctive minor premise may be\naffirmative or negative: if affirmative, the Dilemma is called\nConstructive; and if negative, Destructive.\n\nUsing, then, only affirmative hypothetical propositions in the major\npremise, there are four Moods:\n\n1. The Simple Constructive--\n\n If A is B, C is D; and if E is F, C is D:\n But either A is B, or E is F:\n .'. C is D.\n\n If the Tories win the election, the Government will avoid\n innovation; and if the Whigs win, the House of Lords will\n prevent them innovating:\n\n But either the Tories or the Whigs will win:\n\n .'. There will be no innovation.\n\n2. The Complex Constructive--\n\n If A is B, C is D; and if E is F, G is H:\n But either A is B, or E is F:\n .'. Either C is D or G is H.\n\n If appearance is all that exists, reality is a delusion; and\n if there is a substance beyond consciousness, knowledge of\n reality is impossible:\n\n But either appearance is all, or there is a substance beyond\n consciousness:\n\n .'. Either reality is a delusion, or a knowledge of it is\n impossible.\n\n3. Simple Destructive--\n\n If A is B, C is D; and if A is B, E is F:\n But either C is not D, or E is not F:\n .'. A is not B.\n\n If table-rappers are to be trusted, the departed are spirits;\n and they also exert mechanical energy:\n\n But either the departed are not spirits, or they do not\n exert mechanical energy:\n\n .'. Table-rappers are not to be trusted.\n\n4. Complex Destructive--\n\n If A is B, C is D; and if E is F, G is H:\n But either C is not D, or G is not H:\n .'. Either A is not B, or E is not F.\n\n If poetic justice is observed, virtue is rewarded; and if the\n mirror is held up to Nature, the villain triumphs:\n\n But either virtue is not rewarded, or the villain does not\n triumph:\n\n .'. Either poetic justice is not observed, or the mirror is\n not held up to Nature.\n\nSuch are the four Moods of the Dilemma that emerge if we only use\naffirmative hypotheticals for the major premise; but, certainly, it is\noften quite as natural to employ two negative hypotheticals (indeed,\none might be affirmative and the other negative; but waive that); and\nthen four more moods emerge, all having negative conclusions. It is\nneedless to intimidate the reader by drawing up these four moods in\nbattle array: they always admit of reduction to the foregoing moods by\nobverting the hypotheticals. Still, by the same process we may greatly\ndecrease the number of moods of the Categorical Syllogism; and just as\nsome Syllogisms are most simply expressed in Celarent or Cesare, so some\nDilemmas are most simply stated with negative major premises--e.g.,\nThe example of a Simple Constructive Dilemma above given would run more\nnaturally thus: _If the Tories win, the Government will not innovate;\nand if the Whigs, the Lords will not let them_: and similarly\nDemosthenes' Dilemma--_If \u00c6schines joined, he is not consistent; and if\nhe did not, he is not patriotic_. Moreover, the propriety of recognising\nDilemmas with negative major premises, follows from the above analysis\nof the Dilemma into a combination of Conditional Syllogisms, even if (as\nin \u00a7 1 of this chapter) we take account of only four Moods of the\nHypothetical Syllogism.\n\nIn the rhetorical use of the Dilemma, it may be observed that the\ndisjunction in the minor premise ought to be obvious, or (at any rate)\neasily acceptable to the audience. Thus, _Either the Tories or the Whigs\nwill win; Either \u00c6schines joined in the rejoicings, or he did not_; such\npropositions are not likely to be disputed. But if the orator must stop\nto prove his minor premise, the smacking effect of this figure (if the\nexpression be allowed) will be lost. Hence the minor premises of other\nexamples given above are only fit for a select audience. That _Either\nghosts are not spirits, or they do not exert mechanical energy_,\nsupposes a knowledge of the principle, generally taught by physical\nphilosophers, that only matter is the vehicle of energy; and that\n_Either appearance is all, or there is substance beyond consciousness_,\nis a doctrine which only metaphysical philosophers could be expected to\nunderstand, and upon which they could not be expected to agree. However,\nthe chief danger is that a plausible disjunction may not be really such\nas to exclude any middle ground: _Either the Tories or the Whigs win_,\nis bad, if a tie be possible; though in the above argument this is\nnegligible, seeing that a tie cannot directly cause innovations. _Either\n\u00c6schines joined in the rejoicings, or he did not_, does not allow for a\ndecent conformity with the public movement where resistance would be\nvain; yet such conformity as need not be inconsistent with subsequent\ncondemnation of the proceedings, nor incompatible with patriotic reserve\nfounded on a belief that the rejoicings are premature and ominous.\n\nAnother rhetorical consideration is, that the alternatives of the\ndisjunctive conclusion of a Complex Dilemma should both point the same\nway, should be equally distasteful or paradoxical. 'Either inconsistent\nor unpatriotic': horrid words to a politician! 'Either no reality or no\npossible knowledge of it': very disappointing to an anxious inquirer!\nThus the disjunctive conclusion is as bad for an opponent as the\ncategorical one in a Simple Dilemma.\n\nLogicians further speak of the Trilemma, with three Hypotheticals and a\ncorresponding triple Disjunction; and of a Polylemma, with any further\nnumber of perplexities. But anyone who has a taste for logical forms may\nhave it amply gratified in numerous text-books.\n\n\n\n\nCHAPTER XIII\n\nTRANSITION TO INDUCTION\n\n\n\u00a7 1. Having now discussed Terms, Propositions, Immediate and Mediate\nInferences, and investigated the conditions of formal truth or\nconsistency, we have next to consider the conditions of material truth:\nwhether (or how far) it is possible to arrive at propositions that\naccurately represent the course of nature or of human life. Hitherto we\nhave dealt with no sort of proof that gives any such assurance. A valid\nsyllogism guarantees the truth of its conclusion, provided the premises\nbe true: but what of the premises? The relation between the premises of\na valid syllogism and its conclusion is the same as the relation between\nthe antecedent and consequent of a hypothetical proposition. If A is B,\nC is D: grant that A is B, and it follows that C is D; and, similarly,\ngrant the premises of a syllogism, and the conclusion follows. Again,\ngrant that C is not D, and it follows that A is not B; and, similarly,\nif the conclusion of a valid syllogism be false, it follows that one, or\nother, or both of the premises must be false. But, once more, grant that\nC is D, and it does not follow that A is B; so neither, if the\nconclusion of a syllogism be true, does it follow that the premises are.\nFor example:--\n\n Sociology is an exact science;\n Mathematics is a branch of Sociology:\n .'. Mathematics is an exact science.\n\nHere the conclusion is true although the premises are absurd. Or\nagain:--\n\n Mathematics is an exact science;\n Sociology is a branch of Mathematics:\n .'. Sociology is an exact science.\n\nHere the major premise is true, but the minor is false, and the\nconclusion is false. In both cases, however, whether the conclusion be\ntrue or false, it equally follows from the premises, if there is any\ncogency in Barbara. The explanation of this is, that Barbara has only\nformal cogency; and that whether the conclusion of that, or any other\nvalid mood, shall be true according to fact and experience, depends upon\nhow the form is filled up. How to establish the premises, then, is a\nmost important problem; and it still remains to be solved.\n\n\u00a7 2. We may begin by recalling the distinction between the denotation\nand connotation of a general term: the denotation comprising the things\nor events which the term is a name for; the connotation comprising the\ncommon qualities on account of which these things are called by the same\nname. Obviously, there are very few general terms whose denotation is\nexhaustively known; since the denotation of a general term comprises all\nthe things that have its connotation, or that ever have had, or that\never will have it, whether they exist here, or in Australia, or in the\nMoon, or in the utmost stars. No one has examined all men, all mammoths,\nall crystals, all falling bodies, all cases of fever, all revolutions,\nall stars--nor even all planets, since from time to time new ones are\ndiscerned. We have names for animals that existed long before there were\nmen to observe them, and of which we know only a few bones, the remains\nof multitudinous species; and for others that may continue to exist when\nmen have disappeared from the earth.\n\nIf, indeed, we definitely limit the time, or place, or quantity of\nmatter to be explored, we may sometimes learn, within the given limits,\nall that there is to know: as all the bones of a particular animal, or\nthe list of English monarchs hitherto, or the names of all the members\nof the House of Commons at the present time. Such cases, however, do not\ninvalidate the above logical truth that few general terms are\nexhaustively known in their denotation; for the very fact of assigning\nlimits of time and place impairs the generality of a term. The bones of\na certain animal may be all examined, but not the bones of all animals,\nnor even of one species. The English monarchs that have reigned hitherto\nmay be known, but there may be many still to reign.\n\nThe general terms, then, with which Logic is chiefly concerned, the\nnames of Causes and Kinds, such as gravitation, diseases, social events,\nminerals, plants and animals, stand for some facts that are, or have\nbeen, known, and for a great many other similar ones that have not been,\nand never will be, known. The use of a general term depends not upon our\ndirect knowledge of everything comprised in its denotation, but upon our\nreadiness to apply it to anything that has its connotation, whether we\nhave seen the thing or not, and even though we never can perceive it; as\nwhen a man talks freely of the ichthyosaurus, or of the central heat of\nplanets, or of atoms and ether.\n\nHence Universal Propositions, which consist of general terms, deceive\nus, if we suppose that their predicates are directly known to be related\nto all the facts denoted by their subjects. In exceptional cases, in\nwhich the denotation of a subject is intentionally limited, such\nexhaustive direct knowledge may be possible; as that \"all the bones of a\ncertain animal consist of phosphate of lime,\" or that every member of\nthe present Parliament wears a silk hat. But what predication is\npossible concerning the hats of all members of Parliament from the\nbeginning? Ordinarily, then, whilst the relation of predicate to subject\nhas been observed in some cases, in much the greater number of cases\nour belief about it depends upon something besides observation, or may\nbe said (in a certain sense) to be taken on trust.\n\n'All rabbits are herbivorous': why do we believe that? We may have seen\na few wild rabbits feeding: or have kept tame ones, and tried\nexperiments with their diet; or have read of their habits in a book of\nNatural History; or have studied the anatomy and physiology of the\ndigestive system in many sorts of animals: but with whatever care we add\ntestimony and scientific method to our own observation, it still remains\ntrue that the rabbits observed by ourselves and others are few in\ncomparison with those that live, have lived and will live. Similarly of\nany other universal proposition; that it 'goes beyond the evidence' of\ndirect observation plainly follows from the fact that the general terms,\nof which such propositions consist, are never exhaustively known in\ntheir denotation. What right have we then to state Universal\nPropositions? That is the problem of Inductive Logic.\n\n\u00a7 3. Universal Propositions, of course, cannot always be proved by\nsyllogisms; because to prove a universal proposition by a syllogism, its\npremises must be universal propositions; and, then, these must be proved\nby others. This process may sometimes go a little way, thus: _All men\nare mortal_, because _All animals are_; and _All animals are mortal_,\nbecause _All composite bodies are subject to dissolution._ Were there no\nlimit to such sorites, proof would always involve a _regressus ad\ninfinitum_, for which life is too short; but, in fact, prosyllogisms\nsoon fail us.\n\nClearly, the form of the Syllogism must itself be misleading if the\nuniversal proposition is so: if we think that premises prove the\nconclusion because they themselves have been established by detailed\nobservation, we are mistaken. The consideration of any example will show\nthis. Suppose any one to argue:\n\n All ruminants are herbivorous;\n Camels are ruminants:\n .'. Camels are herbivorous.\n\nHave we, then, examined all ruminants? If so, we must have examined all\ncamels, and cannot need a syllogism to prove their herbivorous nature:\ninstead of the major premise proving the conclusion, the proof of the\nconclusion must then be part of the proof of the major premise. But if\nwe have not examined all ruminants, having omitted most giraffes, most\ndeer, most oxen, etc., how do we know that the unexamined (say, some\ncamels) are not exceptional? Camels are vicious enough to be\ncarnivorous; and indeed it is said that Bactrian camels will eat flesh\nrather than starve, though of course their habit is herbivorous.\n\nOr, again, it is sometimes urged that--\n\n All empires decay:\n .'. Britain will decay.\n\nThis is manifestly a prediction: at present Britain flourishes, and\nshows no signs of decay. Yet a knowledge of its decay seems necessary,\nto justify any one in asserting the given premise. If it is a question\nwhether Britain will decay, to attempt (while several empires still\nflourish) to settle the matter by asserting that _all_ empires decay,\nseems to be 'a begging of the question.' But although this latter case\nis a manifest prediction, it does not really differ from the former one;\nfor the proof that camels are herbivorous has no limits in time. If\nvalid, it shows not only that they are, but also that they will be,\nherbivorous.\n\nHence, to resort to a dilemma, it may be urged: If _all_ the facts of\nthe major premise of any syllogism have been examined, the syllogism is\nneedless; and if _some_ of them have not been examined, it is a _petitio\nprincipii_. But either all have been examined, or some have not.\nTherefore; the syllogism is either useless or fallacious.\n\n\u00a7 4. A way of escape from this dilemma is provided by distinguishing\nbetween the formal and material aspects of the syllogism considered as a\nmeans of proof. It begs the question formally, but not materially; that\nis to say, if it be a question whether camels are herbivorous, and to\ndecide it we are told that '_all_ ruminants are,' laying stress upon the\n'all,' as if all had been examined, though in fact camels have not been,\nthen the question as to camels is begged. The form of a universal\nproposition is then offered as evidence, when in fact the evidence has\nnot been universally ascertained. But if in urging that 'all ruminants\nare herbivorous' no more is meant than that so many other ruminants of\ndifferent species are known to be herbivorous, and that the ruminant\nstomach is so well adapted to a coarse vegetable diet, that the same\nhabit may be expected in other ruminants, such as camels, the argument\nthen rests upon material evidence without unfairly implying the case in\nquestion. Now the nature of the material evidence is plainly this, that\nthe resemblance of camels to deer, oxen, etc., in chewing the cud,\njustifies us in believing that they have a further resemblance in\nfeeding on herbs; in other words, we assume that _resemblance is a\nground of inference_.\n\nAnother way of putting this difficulty which we have just been\ndiscussing, with regard to syllogistic evidence, is to urge that by the\nLaws of Syllogism a conclusion must never go beyond the premises, and\nthat therefore no progress in knowledge can ever be established, except\nby direct observation. Now, taking the syllogism formally, this is true:\nif the conclusion go beyond the premises, there must be either four\nterms, or illicit process of the major or minor term. But, taking it\nmaterially, the conclusion may cover facts which were not in view when\nthe major premise was laid down; facts of which we predicate something\nnot as the result of direct observation, but because they resemble in a\ncertain way those facts which had been shown to carry the predicate when\nthe major premise was formed.\n\n'What sort of resemblance is a sufficient ground of inference?' is,\ntherefore, the important question alike in material Deduction and in\nInduction; and in endeavouring to answer it we shall find that the\nsurest ground of inference is resemblance of causation. For example, it\nis due to causation that ruminants are herbivorous. Their instincts make\nthem crop the herb, and their stomachs enable them easily to digest it;\nand in these characters camels are like the other ruminants.\n\n\u00a7 5. In ch. ix, \u00a7 3, the _Dictum de omni et nullo_ was stated: 'Whatever\nmay be predicated of a term distributed may be predicated of anything\nthat can be identified with that term.' Nothing was there said (as\nnothing was needed) of the relations that might be implied in the\npredication. But now that it comes to the ultimate validity of\npredication, we must be clear as to what these relations are; and it\nwill also be convenient to speak no longer of terms, as in Formal Logic,\nbut of the things denoted. What relations, then, can be determined\nbetween concrete facts or phenomena (physical or mental) with the\ngreatest certainty of general truth; and what axioms are there that\nsanction mediate inferences concerning those relations?\n\nIn his _Logic_ (B. II. c. 2, \u00a7 3) Mill gives as the axiom of syllogistic\nreasoning, instead of the _Dictum_: \"A thing which co-exists with\nanother thing, which other co-exists with a third thing, also co-exists\nwith that third thing.\" Thus the peculiar properties of Socrates\nco-exist with the attributes of man, which co-exist with mortality:\ntherefore, Socrates is mortal. But, again, he says that the ground of\nthe syllogism is Induction; that man is mortal is an induction. And,\nfurther, the ground of Induction is causation; the law of causation is\nthe ultimate major premise of every sound induction. Now causation is\nthe principle of the succession of phenomena: how, then, can the\nsyllogism rest on an axiom concerning co-existence? On reflection, too,\nit must appear that 'Man is mortal' predicates causation: the human\nconstitution issues in death.\n\nThe explanation of this inconsistency may perhaps be found in the\nhistory of Mill's work. Books I. and II. were written in 1831; but being\nunable at that time to explain Induction, he did not write Book III.\nuntil 1837-8. Then, no doubt, he revised the earlier Books, but not\nenough to bring his theory of the syllogism into complete agreement with\nthe theory of Induction; so that the axiom of co-existence was allowed\nto stand.\n\nMill also introduced the doctrine of Natural Kinds as a ground of\nInduction supplementary, at least provisionally, to causation; and to\nreasoning about Kinds, or Substance and Attribute, his axiom of\nco-existence is really adapted. Kinds are groups of things that agree\namongst themselves and differ from all others in a multitude of\nqualities: these qualities co-exist, or co-inhere, with a high degree of\nconstancy; so that where some are found others may be inferred. Their\nco-inherence is not to be considered an ultimate fact; for, \"since\neverything which occurs is determined by laws of causation and\ncollocations of the original causes, it follows that the co-existences\nobservable amongst effects cannot themselves be the subject of any\nsimilar set of laws distinct from laws of causation\" (B. III. c. 5, \u00a7\n9). According to the theory of evolution (worked out since Mill wrote),\nKinds--that is, species of plants, animals and minerals--with their\nqualities are all due to causation. Still, as we can rarely, or never,\ntrace the causes with any fullness or precision, a great deal of our\nreasoning, as, e.g., about men and camels, does in fact trust to the\nrelative permanence of natural Kinds as defined by co-inhering\nattributes.\n\nTo see this more clearly, we should consider that causation and natural\nKinds are not at present separable; propositions about causation in\nconcrete phenomena (as distinct from abstract 'forces') always involve\nthe assumption of Kinds. For example--'Water rusts iron,' or the oxygen\nof water combines with iron immersed in it to form rust: this statement\nof causation assumes that water, oxygen, iron, and iron-rust are known\nKinds. On the other hand, the constitution of every concrete thing, and\nmanifestly of every organised body, is always undergoing change, that\nis, causation, upon which fact its properties depend.\n\nHow, then, can we frame principles of mediate reasoning, about such\nthings? So far as we consider them as Kinds, it is enough to say:\n_Whatever can be identified as a specimen of a known substance or Kind\nhas the properties of that Kind_. So far as we consider them as in the\nrelation of causation, we may say: _Whatever relation of events can be\nidentified with the relation of cause and effect is constant_. And these\nprinciples may be generalised thus: _Whatever is constantly related to a\nphenomenon (cause or Kind), determined by certain characters, is related\nin the same way to any phenomenon, that has the same characters_. Taking\nthis as axiom of the syllogism materially treated, we see that\nherbivorousness, being constantly related to ruminants, is constantly\nrelated to camels; mortality to man and, therefore, to Socrates; rusting\nto the immersion of iron in water generally and, therefore, to this\npiece of iron. _Nota not\u00e6, nota rei ipsius_ is another statement of the\nsame principle; still another is Mill's axiom, \"Whatever has a mark has\nwhat it is a mark of.\" A mark is anything (A) that is never found\nwithout something else (B)--a phenomenon constantly related to another\nphenomenon--so that wherever A is found, B may be expected: human nature\nis a mark of mortality.\n\n\u00a7 6. The Syllogism has sometimes been discarded by those who have only\nseen that, as formally stated, it is either useless or fallacious: but\nthose who also perceive its material grounds retain and defend it. In\nfact, great advantages are gained by stating an argument as a formal\nsyllogism. For, in the first place, we can then examine separately the\nthree conditions on which the validity of the argument depends:\n\n(1) Are the Premises so connected that, _if they are true_, the\nConclusion follows? This depends upon the formal principles of chap. x.\n\n(2) Is the Minor Premise true? This question can only arise when the\nminor premise is a real proposition; and then it may be very difficult\nto answer. Water rusts iron; but is the metal we are now dealing with a\nfair specimen of iron? Few people, comparatively, know how to determine\nwhether diamonds, or even gold or silver coins, are genuine. That\n_Camels are ruminants_ is now a verbal proposition to a Zoologist, but\nnot to the rest of us; and to the Zoologist the ascertaining of the\nrelation in which camels stand to such ruminants as oxen and deer, was\nnot a matter of analysing words but of dissecting specimens. What a long\ncontroversy as to whether the human race constitutes a Family of the\nPrimates! That 'the British Empire is an empire' affords no matter for\ndoubt or inquiry; but how difficult to judge whether the British Empire\nresembles Assyria, Egypt, Rome, Spain in those characters and\ncircumstances that caused their downfall!\n\n(3) Is the Major Premise true? Are all ruminants herbivorous? If there\nbe any exceptions to the rule, camels are likely enough to be among the\nexceptions. And here the need of Inductive Logic is most conspicuous:\nhow can we prove our premises when they are universal propositions?\nUniversal propositions, however, are also involved in proving the minor\npremise: to prove a thing to be iron, we must know the constant\nreactions of iron.\n\nA second advantage of the syllogism is, that it makes us fully aware of\nwhat an inference implies. An inference must have some grounds, or else\nit is a mere prejudice; but whatever the grounds, if sufficient in a\nparticular case, they must be sufficient for all similar cases, they\nmust admit of being generalised; and to generalise the grounds of the\ninference, is nothing else than to state the major premise. If the\nevidence is sufficient to justify the argument that camels are\nherbivorous _because_ they are ruminants, it must also justify the major\npremise, _All ruminants are herbivorous_; for else the inference cannot\nreally depend merely upon the fact of ruminating. To state our evidence\nsyllogistically, then, must be possible, if the evidence is mediate and\nof a logical kind; and to state it in this formal way, as depending on\nthe truth of a general principle (the major premise), increases our\nsense of responsibility for the inference that is thus seen to imply so\nmuch; and if any negative instances lie within our knowledge, we are the\nmore likely to remember them. The use of syllogisms therefore tends to\nstrengthen our reasonings.\n\nA third advantage is, that to formulate an accurate generalisation may\nbe useful to others: it is indeed part of the systematic procedure of\nscience. The memoranda of our major premises, or reasons for believing\nanything, may be referred to by others, and either confirmed or refuted.\nWhen such a memorandum is used for further inferences, these inferences\nare said, in the language of Formal Logic, to be drawn _from_ it, as if\nthe conclusion were contained in our knowledge of the major premise;\nbut, considering the limited extent of the material evidence, it is\nbetter to say that the inference is drawn _according to_ the memorandum\nor major premise, since the grounds of the major premise and of the\nconclusion are in fact the same (Mill: _Logic_, B. II. c. 3). Inductive\nproofs may be stated in Syllogisms, and inductive inferences are drawn\n_according to_ the Law of Causation.\n\n\u00a7 7. To assume that resemblance is a ground of inference, and that\nsubstance and attribute, or cause and effect, are phenomena constantly\nrelated, implies belief in the Uniformity of Nature. The Uniformity of\nNature cannot be defined, and is therefore liable to be misunderstood.\nIn many ways Nature seems not to be uniform: there is great variety in\nthe sizes, shapes, colours and all other properties of things: bodies\nfalling in the open air--pebbles, slates, feathers--descend in different\nlines and at different rates; the wind and weather are proverbially\nuncertain; the course of trade or of politics, is full of surprises. Yet\ncommon maxims, even when absurd, testify to a popular belief that the\nrelations of things are constant: the doctrine of St. Swithin and the\nrhyme beginning 'Evening red and morning grey,' show that the weather is\nheld to be not wholly unpredictable; as to human affairs, it is\nsaid that 'a green Yule makes a fat churchyard,' that 'trade follows the\nflag,' and that 'history repeats itself'; and Superstition knows that\nwitches cannot enter a stable-door if a horse-shoe is nailed over it,\nand that the devil cannot cross a threshold inscribed with a perfect\npentagram. But the surest proof of a belief in the uniformity of nature\nis given by the conduct of men and animals; by that adherence to habit,\ncustom and tradition, to which in quiet times they chiefly owe their\nsafety, but which would daily disappoint and destroy them, if it were\nnot generally true that things may be found where they have been left\nand that in similar circumstances there are similar events.\n\nNow this general belief, seldom distinctly conceived, for the most part\nquite unconscious (as a principle), merely implied in what men do, is\nalso the foundation of all the Sciences; which are entirely occupied in\nseeking the Laws (that is, the Uniformities) of Nature. As the\nuniformity of nature cannot be defined, it cannot be proved; the most\nconvincing evidence in its favour is the steady progress made by Science\nwhilst trusting in it. Nevertheless, what is important is not the\ncomprehensive but indeterminate notion of Uniformity so much as a number\nof First Principles, which may be distinguished in it as follows:\n\n(1) The Principles of Contradiction and Excluded Middle (ch. vi. \u00a7 3)\ndeclare that in a given relation to a given phenomenon any two or more\nother phenomena are incompatible (_B is not A and a_); whilst the given\nphenomenon either stands related to another phenomenon or not (_B is\neither A or a_). It is not only a matter of Logic but of fact that, if a\nleaf is green, it is not under the same conditions red or blue, and that\nif it is not green it is some other colour.\n\n(2) Certain Axioms of Mediate Evidence: as, in Mathematics, 'that\nmagnitudes equal to the same magnitude are equal to one another'; and,\nin Logic, the _Dictum_ or its material equivalent.\n\n(3) That all Times and all Spaces are commensurable; although in certain\nrelations of space (as [pi]) the unit of measurement must be infinitely\nsmall.--If Time really trotted with one man and galloped with another,\nas it seems to; if space really swelled in places, as De Quincey dreamed\nthat it did; life could not be regulated, experience could not be\ncompared and science would be impossible. The Mathematical Axioms would\nthen never be applicable to space or time, or to the objects or\nprocesses that fill them.\n\n(4) The Persistence of Matter and Energy: the physical principle that,\nin all changes of the universe, the quantities of Matter and Energy\n(actual and potential, so-called) remain the same.--For example, as to\nmatter, although dew is found on the grass at morning without any\napparent cause, and although a candle seems to burn away to a scrap of\nblackened wick, yet every one knows that the dew has been condensed from\nvapour in the air, and that the candle has only turned into gas and\nsmoke. As to energy, although a stone thrown up to the housetop and\nresting there has lost actual energy, it has gained such a position that\nthe slightest touch may bring it to the earth again in the same time as\nit took to travel upwards; so on the house-top it is said to have\npotential energy. When a boiler works an engine, every time the piston\nis thrust forward (mechanical energy), an equivalent in heat (molecular\nenergy) is lost. But for the elucidation of these principles, readers\nmust refer to treatises of Chemistry and Physics.\n\n(5) Causation, a special form of the foregoing principles of the\npersistence of matter and energy, we shall discuss in the next chapter.\nIt is not to be conceived of as anything occult or noumenal, but merely\nas a special mode of the uniformity of Nature or experience.\n\n(6) Certain Uniformities of Co-existence; but for want of a general\nprinciple of Co-existence, corresponding to Causation (the principle of\nSuccession), we can only classify these uniformities as follows:\n\n(a) The Geometrical; as that, in a four-sided figure, if the opposite\nangles are equal, the opposite sides are equal and parallel.--Countless\nsimilar uniformities of co-existence are disclosed by Geometry. The\nco-existent facts do not cause one another, nor are they jointly caused\nby something else; they are mutually involved: such is the nature of\nspace.\n\n(b) Universal co-inherences among the properties of concrete\nthings.--The chief example is the co-inherence of gravity with inertia\nin all material bodies. There is, I believe, no other entirely\nsatisfactory case; but some good approximations to such uniformity are\nknown to physical science.\n\n(c) Co-existence due to Causation; such as the positions of objects in\nspace at any time.--The houses of a town are where they are, because\nthey were put there; and they remain in their place as long as no other\ncauses arise strong enough to remove or destroy them. Similarly, the\nrelative positions of rocks in geological strata, and of trees in a\nforest, are due to causes.\n\n(d) The co-inherence of properties in Natural Kinds; which we call the\nconstitution, defining characters, or specific nature of such\nthings.--Oxygen, platinum, sulphur and the other elements; water, common\nsalt, alcohol and other compounds; the various species of plants and\nanimals: all these are known to us as different groups of co-inherent\nproperties. It may be conjectured that these groupings of properties are\nalso due to causation, and sometimes the causes can be traced: but very\noften the causes are still unknown; and, until resolved into their\ncauses, they must be taken as necessary data in the investigation of\nnature. Laws of the co-inherence of the properties of Kinds do not, like\nlaws of causation, admit of methodical proof upon their own principles,\nbut only by constancy in experience and statistical probability (c. xix,\n\u00a7 4).\n\n(e) There are also a few cases in which properties co-exist in an\nunaccountable way, without being co-extensive with any one species,\ngenus, or order: as most metals are whitish, and scarlet flowers are\nwanting in fragrance. (On this \u00a7 7, see Venn's _Empirical Logic_, c. 4.)\n\n\u00a7 8. Inasmuch as Axioms of Uniformity are ultimate truths, they cannot\nbe deduced; and inasmuch as they are universal, no proof by experience\ncan ever be adequate. The grounds of our belief in them seem to be\nthese:\n\n(1) Every inference takes for granted an order of Nature corresponding\nwith it; and every attempt to explain the origin of anything assumes\nthat it is the transformation of something else: so that uniformity of\norder and conservation of matter and energy are necessary\npresuppositions of reasoning.\n\n(2) On the rise of philosophic reflection, these tacit presuppositions\nare first taken as dogmas, and later as postulates of scientific\ngeneralisation, and of the architectonic unification of science. Here\nthey are indispensable.\n\n(3) The presuppositions or postulates are, in some measure, verifiable\nin practical life and in scientific demonstration, and the better\nverifiable as our methods become more exact.\n\n(4) There is a cause of this belief that cannot be said to contain any\nevidence for it, namely, the desire to find in Nature a foundation for\nconfidence in our own power to foresee and to control events.\n\n\n\n\nCHAPTER XIV\n\nCAUSATION\n\n\n\u00a7 1. For the theory of Induction, the specially important aspect of the\nUniformity of Nature is Causation.\n\nFor (1) the Principles of Contradiction and Excluded Middle are implied\nin all logical operations, and need no further explication.\n\n(2) That one thing is a mark of another or constantly related to it,\nmust be established by Induction; and the surest of all marks is a\nCause. So that the application of the axiom of the Syllogism in\nparticular cases requires, when most valid, a previous appeal to\nCausation.\n\n(3) The uniformity of Space and of Time is involved in Causation, so far\nas we conceive Causation as essentially matter in motion--for motion is\nonly known as a traversing of space in time; and so far as forces vary\nin any way according to the distance between bodies; so that if space\nand time were not uniform, causation would be irregular. Not that time\nand space are agents, but they are conditions of every agent's\noperation.\n\n(4) The persistence of Matter and Energy, being nothing else than\nCausation in the general movement of the world, is applied under the\nname of that principle in explaining any particular limited phenomenon,\nsuch as a soap-bubble, or a thunderstorm, or the tide.\n\n(5) As to co-existences, the Geometrical do not belong to Logic: those\ninvolved in the existence of plants, animals, and inorganic bodies,\nmust, as far as possible, be traced to causes; and so, of course, must\nthe relative positions of objects in space at any time: and what\nCo-existences remain do not admit of methodical inductive treatment;\nthey will be briefly discussed in chap. xix.\n\nCausation, then, is that mode or aspect of the Uniformity of Nature\nwhich especially concerns us in Induction; and we must make it as\ndefinite as possible. It is nothing occult, but merely a convenient name\nfor phenomena in a particular relation to other phenomena, called their\neffect. Similarly, if the word 'force' is sometimes used for convenience\nin analysing causation, it means nothing more than something in time and\nspace, itself moving, or tending to move, or hindering or accelerating\nother things. If any one does not find these words convenient for the\npurpose, he can use others.\n\n\u00a7 2. A Cause, according to Mill, is \"the invariable unconditional\nantecedent\" of a given phenomenon. To enlarge upon this:\n\n(1) A Cause is _relative to a given phenomenon_, called the Effect.\nLogic has no method for investigating the cause of the universe as a\nwhole, but only of a part or epoch of it: we select from the infinite\ncontinuum of Nature any portion that is neither too large nor too small\nfor a trained mind to comprehend. The magnitude of the phenomenon may be\na matter of convenience. If the cause of disease in general be too wide\na problem, can fevers be dealt with; or, if that be too much, is typhus\nwithin the reach of inquiry? In short, how much can we deal with\naccurately?\n\n(2) The given phenomenon is always _an event_; that is to say, not a new\nthing (nothing is wholly new), but a change in something, or in the\nrelative position of things. We may ask the cause of the phases of the\nmoon, of the freezing of water, of the kindling of a match, of a deposit\nof chalk, of the differentiation of species. To inquire the cause of\nFrance being a republic, or Russia an autocracy, implies that these\ncountries were once otherwise governed, or had no government: to inquire\nthe cause of the earth being shaped like an orange, implies that the\nmatter of the earth had once another shape.\n\n(3) The Cause is _antecedent_ to the Effect, which accordingly is often\ncalled its _consequent_. This is often misunderstood and sometimes\ndisputed. It has been said that the meaning of 'cause' implies an\n'effect,' so that until an effect occurs there can be no cause. But this\nis a blunder; for whilst the word 'cause' implies 'effect,' it also\nimplies the relative futurity of the effect; and effect implies the\nrelative priority of the cause. The connotation of the words, therefore,\nagrees well enough with Mill's doctrine. In fact, the danger is that any\npair of contrasted words may suggest too strongly that the phenomena\ndenoted are separate in Nature; whereas every natural process is\ncontinuous. If water, dripping from the roof wears away a stone, it fell\non the roof as rain; the rain came from a condensing cloud; the cloud\nwas driven by the wind from the sea, whence it exhaled; and so on. There\nis no known beginning to this, and no break in it. We may take any one\nof these changes, call it an effect, and ask for its cause; or call it a\ncause, and ask for its effect. There is not in Nature one set of things\ncalled causes and another called effects; but every change is both cause\n(or a condition) of the future and effect of the past; and whether we\nconsider an event as the one or the other, depends upon the direction of\nour curiosity or interest.\n\nStill, taking the event as effect, its cause is the antecedent process;\nor, taking it as a cause, its effect is the consequent process. This\nfollows from the conception of causation as essentially motion; for that\n_motion takes time_ is (from the way our perceptive powers grow) an\nultimate intuition. But, for the same reason, there is no interval of\ntime between cause and effect; since all the time is filled up with\nmotion.\n\nNor must it be supposed that the whole cause is antecedent to the\neffect as a whole: for we often take the phenomenon on such a scale that\nminutes, days, years, ages, may elapse before we consider the cause as\nexhausted (e.g., an earthquake, a battle, an expansion of credit,\nnatural selection operating on a given variety); and all that time the\neffect has been accumulating. But we may further consider such a cause\nas made up of moments or minute factors, and the effect as made up of\ncorresponding moments; and then the cause, taken in its moments, is\nantecedent throughout to the effect, taken in its corresponding moments.\n\n(4) The Cause is the _invariable_ antecedent of the effect; that is to\nsay, whenever a given cause occurs it always has the same effect: in\nthis, in fact, consists the Uniformity of Causation. Accordingly, not\nevery antecedent of an event is its Cause: to assume that it is so, is\nthe familiar fallacy of arguing '_post hoc ergo propter hoc_.' Every\nevent has an infinite number of antecedents that have no ascertainable\nconnection with it: if a picture falls from the wall in this room, there\nmay have occurred, just previously, an earthquake in New Zealand, an\nexplosion in a Japanese arsenal, a religious riot in India, a political\nassassination in Russia and a vote of censure in the House of Commons,\nbesides millions of other less noticeable events, between none of which\nand the falling of the picture can any direct causation be detected;\nthough, no doubt, they are all necessary occurrences in the general\nworld-process, and remotely connected. The cause, however, was that a\ndoor slammed violently in the room above and shook the wall, and that\nthe picture was heavy and the cord old and rotten. Even if two events\ninvariably occur one after the other, as day follows night, or as the\nreport follows the flash of a gun, they may not be cause and effect,\nthough it is highly probable that they are closely connected by\ncausation; and in each of these two examples the events are co-effects\nof a common cause, and may be regarded as elements of its total effect.\nStill, whilst it is not true that every antecedent, or that every\ninvariable antecedent, of an event is its cause, the cause is conceived\nof as some change in certain conditions, or some state and process of\nthings, such that should it exactly recur the same event would\ninvariably follow. If we consider the antecedent state and process of\nthings very widely or very minutely, it never does exactly recur; nor\ndoes the consequent. But the purpose of induction is to get as near the\ntruth as possible within the limits set by our faculties of observation\nand calculation. Complex causal instances that are most unlikely to\nrecur as a whole, may be analysed into the laws of their constituent\nconditions.\n\n(5) The Cause is the Unconditional Antecedent. A cause is never simple,\nbut may be analysed into several conditions; and 'Condition' means any\nnecessary factor of a Cause: any thing or agent that exerts, absorbs,\ntransforms, or deflects energy; or any relation of time or space in\nwhich agents stand to one another. A positive condition is one that\ncannot be omitted without frustrating the effect; a negative condition\nis one that cannot be introduced without frustrating the effect. In the\nfalling of the picture, e.g., the positive conditions were the picture\n(as being heavy), the slamming of the door, and the weakness of the\ncord: a negative condition was that the picture should have no support\nbut the cord. When Mill, then, defines the Cause of any event as its\n\"unconditional\" antecedent, he means that it is that group of conditions\n(state and process of things) which, without any further condition, is\nfollowed by the event in question: it is the least antecedent that\nsuffices, positive conditions being present and negative absent.\n\nWhatever item of the antecedent can be left out, then, without affecting\nthe event, is no part of the cause. Earthquakes have happened in New\nZealand and votes of censure in the House of Commons without a picture's\nfalling in this room: they were not unconditional antecedents;\nsomething else was needed to bring down a picture. Unconditionality also\ndistinguishes a true cause from an invariable antecedent that is only a\nco-effect: for when day follows night something else happens; the Earth\nrotates upon her axis: a flash of gunpowder is not an unconditional\nantecedent of a report; the powder must be ignited in a closed chamber.\n\nBy common experience, and more precisely by experiment, it is found\npossible to select from among the antecedents of an event a certain\nnumber upon which, so far as can be perceived, it is dependent, and to\nneglect the rest: to purge the cause of all irrelevant antecedents is\nthe great art of inductive method. Remote or minute conditions may\nindeed modify the event in ways so refined as to escape our notice.\nSubject to the limitations of our human faculties, however, we are able\nin many cases to secure an unconditional antecedent upon which a certain\nevent invariably follows. Everybody takes this for granted: if the gas\nwill not burn, or a gun will not go off, we wonder 'what can be wrong\nwith it,' that is, what positive condition is wanting, or what negative\none is present. No one now supposes that gunnery depends upon those\n\"remotest of all causes,\" the stars, or upon the sun being in\nSagittarius rather than in Aquarius, or that one shoots straightest with\na silver bullet, or after saying the alphabet backwards.\n\n(6) That the Cause of any event is an Immediate Antecedent follows from\nits being an unconditional one. For if there are three events, A B C,\ncausally connected, it is plain that A is not the unconditional\nantecedent of C, but requires the further condition of first giving rise\nto B. But that is not all; for the B that gives rise to C is never\nmerely the effect of A; it involves something further. Take such a\nsimple case as the motion of the earth round the sun (neglecting all\nother conditions, the other planets, etc.); and let the earth's\nmotion at three successive moments be A B C: A is not the whole cause of\nB in velocity and direction; we must add relation to the sun, say x. But\nthen, again, the cause of C will not be merely Bx, for the relation to\nthe sun will have altered; so that we must represent it as Bx'. The\nseries, therefore, is Ax Bx' C. What is called a \"remote cause\" is,\ntherefore, doubly conditional; first, because it supposes an intervening\ncause; and secondly, because it only in part determines the conditions\nthat constitute this intervening cause.\n\nThe immediacy of a cause being implied in its unconditionalness, is an\nimportant clue to it; but as far as the detection of causes depends upon\nsense-perception, our powers (however aided by instruments) are unequal\nto the subtlety of Nature. Between the event and what seems to us the\nimmediate antecedent many things (molecular or etherial changes) may\nhappen in Chemistry or Physics. The progress of science would be\nimpossible were not observation supplemented by hypothesis and\ncalculation. And where phenomena are treated upon a large scale, as in\nthe biological and social sciences, immediacy, as a mark of causation,\nmust be liberally interpreted. So far, then, as to the qualitative\ncharacter of Causation.\n\n(7) But to complete our account of it, we must briefly consider its\nquantitative character. As to the Matter contained, and as to the Energy\nembodied, Cause and Effect are conceived to be _equal_. As to matter,\nindeed, they may be more properly called identical; since the effect is\nnothing but the cause redistributed. When oxygen combines with hydrogen\nto form water, or with mercury to form red precipitate, the weight of\nthe compound is exactly equal to the weight of the elements combined in\nit; when a shell explodes and knocks down a wall, the materials of the\nshell and wall are scattered about. As to energy, we see that in the\nheavenly bodies, which meet with no sensible impediment, it remains the\nsame from age to age: with things 'below the moon' we have to allow for\nthe more or less rapid conversion of the visible motion of a mass into\nother forms of energy, such as sound and heat. But the right\nunderstanding of this point involves physical considerations of some\ndifficulty, as to which the reader must refer to appropriate books, such\nas Balfour Stewart's on _The Conservation of Energy_.\n\nThe comprehension of the quantitative aspect of causation is greatly\naided by Bain's analysis of any cause into a 'Moving or an Inciting\nPower' and a 'Collocation' of circumstances. When a demagogue by making\na speech stirs up a mob to a riot, the speech is the moving or inciting\npower; the mob already in a state of smouldering passion, and a street\nconvenient to be wrecked, are the collocation. When a small quantity of\nstrychnine kills a man, the strychnine is the inciting power; the nature\nof his nervo-muscular system, apt to be thrown into spasms by that drug,\nand all the organs of his body dependent on that system, are the\ncollocation. Now any one who thinks only of the speech, or the drug, in\nthese cases, may express astonishment at the disproportion of cause and\neffect:\n\n \"What great events from trivial causes spring!\"\n\nBut, remembering that the whole cause of the riot included the excited\nmob, every one sees that its muscular power is enough to wreck a street;\nand remembering that breathing depends upon the normal action of the\nintercostal muscles, it is plain that if this action is stopped by\nstrychnine, a man must die. Again, a slight rise of temperature may be a\nsufficient inciting power to occasion extensive chemical changes in a\ncollocation of elements otherwise stable; a spark is enough to explode a\npowder magazine. Hence, when sufficient energy to account for any effect\ncannot be found in the inciting power, or manifestly active condition,\nwe must look for it in the collocation which is often supposed to be\npassive.\n\nAnd that reminds us of another common misapprehension, namely, that in\nNature some things are passive and others active: the distinction\nbetween 'agent' and 'patient.' This is a merely relative distinction: in\nNature all things are active. To the eye some things seem at rest and\nothers in motion; but we know that nothing is really at rest, that\neverything palpitates with molecular change, and whirls with the planet\nthrough space. Everything that is acted upon reacts according to its own\nnature: the quietest-looking object (say, a moss-covered stone), if we\ntry to push or lift it, pushes or pulls us back, assuring us that\n'action and reaction are equal and opposite.' 'Inertia' does not mean\nwant of vigour, but may be metaphorically described as the inexpugnable\nresolve of everything to have its own way.\n\nThe equality of cause and effect defines and interprets the\nunconditionality of causation. The cause, we have seen, is that group of\nconditions which, without any further condition, is followed by a given\nevent. But how is such a group to be conceived? Unquantified, it admits\nonly of a general description: quantified, it must mean a group of\nconditions equal to the effect in mass and energy, the essence of the\nphysical world. Apparently, a necessary conception of the human mind:\nfor if a cause seem greater than its effect, we ask what has become of\nthe surplus matter and energy; or if an effect seem greater than its\ncause, we ask whence the surplus matter and energy has arisen. So\nconvinced of this truth is every experimenter, that if his results\npresent any deviation from it, he always assumes that it is he who has\nmade some mistake or oversight, never that there is indeterminism or\ndiscontinuity in Nature.\n\nThe transformation of matter and energy, then, is the essence of\ncausation: because it is continuous, causation is immediate; and because\nin the same circumstances the transformation always follows the same\ncourse, a cause has invariably the same effect. If a fire be lit\nmorning after morning in the same grate, with coal, wood, and paper of\nthe same quality and similarly arranged, there will be each day the same\nflaming of paper, crackling of wood and glowing of coal, followed in\nabout the same time by the same reduction of the whole mass partly to\nashes and partly to gases and smoke that have gone up the chimney. The\nflaming, crackling and glowing are, physically, modes of energy; and the\nchange of materials into gas and ashes is a chemical and physical\nredistribution: and, if some one be present, he will be aware of all\nthis; and then, besides the physical changes, there will be sensations\nof light, sound and heat; and these again will be always the same in the\nsame circumstances.\n\nThe Cause of any event, then, when exactly ascertainable, has five\nmarks: it is (quantitatively) _equal_ to the effect, and (qualitatively)\n_the immediate, unconditional, invariable antecedent of the effect_.\n\n\u00a7 3. This scientific conception of causation has been developed and\nrendered definite by the investigations of those physical sciences that\ncan avail themselves of exact experiments and mathematical calculation;\nand it is there, in Chemistry and Physics, that it is most at home. The\nconception can indeed be carried into the Biological and Social\nSciences, even in its quantitative form, by making the proper\nallowances. For the limbs of animals are levers, and act upon mechanical\nprinciples; and digestion and the aeration of the blood by breathing are\npartly chemical processes. There is a quantitative relation between the\nfood a man eats and the amount of work he can do. The numbers of any\nspecies of plant or animal depend upon the food supply. The value of a\ncountry's imports is equal to the value of its exports and of the\nservices it renders to foreigners. But, generally, the less experiment\nand exact calculation are practicable in any branch of inquiry, the less\nrigorously can the conception of causation be applied there, the more\nwill its application depend upon the qualitative marks, and the more\nneed there will be to use it judiciously. In every inquiry the greatest\npossible precision must be aimed at; but it is unreasonable to expect in\nany case more precise proof than the subject admits of in the existing\nstate of culture.\n\nWherever mental action is involved, there is a special difficulty in\napplying the physical notion of causation. For if a Cause be conceived\nof as matter in motion, a thought, or feeling, or volition can be\nneither cause nor effect. And since mental action is involved in all\nsocial affairs, and in the life of all men and animals, it may seem\nimpossible to interpret social or vital changes according to laws of\ncausation. Still, animals and men are moving bodies; and it is\nrecognised that their thoughts and feelings are so connected with their\nmovements and with the movements of other things acting upon them, that\nwe can judge of one case by another; although the connection is by no\nmeans well understood, and the best words (such as all can agree to use)\nhave not yet been found to express even what we know about it. Hence, a\nregular connection being granted, I have not hesitated, to use\nbiological and social events and the laws of them, to illustrate\ncausation and induction; because, though less exact than chemical or\nmechanical examples, they are to most people more familiar and\ninteresting.\n\nIn practical affairs, it is felt that everything depends upon causation;\nhow to play the fiddle, or sail a yacht, or get one's living, or defeat\nthe enemy. The price of pig-iron six months hence, the prospects of the\nharvest, the issue in a Coroner's Court, Home Rule and Socialism, are\nall questions of causation. But, in such cases, the conception of a\ncause is rarely applied in its full scientific acceptation, as the\nunconditional antecedent, or 'all the conditions' (neither more nor\nless) upon which the event depends. This is not because men of affairs\nare bad logicians, or incapable of scientific comprehension; for very\noften the reverse is conspicuously true; but because practical affairs\ncall for promptitude and a decisive seizing upon what is predominantly\nimportant. How learn to play the fiddle? \"Go to a good teacher.\" (Then,\nbeginning young enough, with natural aptitude and great diligence, all\nmay be well.) How defeat the enemy? \"Be two to one at the critical\njuncture.\" (Then, if the men are brave, disciplined, well armed and well\nfed, there is a good chance of victory.) Will the price of iron improve?\n\"Yes: for the market is oversold\": (that is, many have sold iron who\nhave none to deliver, and must at some time buy it back; and that will\nput up the price--if the stock is not too great, if the demand does not\nfall off, and if those who have bought what they cannot pay for are not\nin the meanwhile obliged to sell.) These prompt and decisive judgments\n(with the parenthetic considerations unexpressed) as to what is the\nCause, or predominantly important condition, of any event, are not as\ngood as a scientific estimate of all the conditions, when this can be\nobtained; but, when time is short, the insight of trained sagacity may\nbe much better than an imperfect theoretical treatment of such problems.\n\n\u00a7 4. To regard the Effect of certain antecedents in a narrow selective\nway, is another common mistake. In the full scientific conception of an\nEffect it is the sum of the unconditional consequences of a given state\nand process of things: the consequences immediately flowing from that\nsituation without further conditions. Always to take account of all the\nconsequences of any cause would no doubt be impracticable; still the\npractical, as well as the scientific interest, often requires that we\nshould enlarge our views of them; and there is no commoner error in\nprivate effort or in legislation than to aim at some obvious good,\nwhilst overlooking other consequences of our action, the evil of which\nmay far outweigh that good. An important consequence of eating is to\nsatisfy hunger, and this is the ordinary motive to eat; but it is a\npoor account of the physiological consequences. An important consequence\nof firing a gun is the propulsion of the bullet or shell; but there are\nmany other consequences in the whole effect, and one of them is the\nheating of the barrel, which, accumulating with rapid firing, may at\nlast put the gun out of action. The tides have consequences to shipping\nand in the wear and tear of the coast that draw every one's attention;\nbut we are told that they also retard the rotation of the earth, and at\nlast may cause it to present always the same face to the sun, and,\ntherefore, to be uninhabitable. Such concurrent consequences of any\ncause may be called its Co-effects: the Effect being the sum of them.\n\nThe neglect to take account of the whole effect (that is, of all the\nco-effects) in any case of causation is perhaps the reason why many\nphilosophers have maintained the doctrine of a \"Plurality of Causes\":\nmeaning not that more than one condition is operative in the antecedent\nof every event (which is true), but that the same event may be due at\ndifferent times to different antecedents, that in fact there may be\n_vicarious_ causes. If, however, we take any effect as a whole, this\ndoes not seem to be true. A fire may certainly be lit in many ways: with\na match or a flint and steel, or by rubbing sticks together, or by a\nflash of lightning: have we not here a plurality of causes? Not if we\ntake account of the whole effect; for then we shall find it modified in\neach case according to the difference of the cause. In one case there\nwill be a burnt match, in another a warm flint, in the last a changed\nstate of electrical tension. And similar differences are found in cases\nof death under different conditions, as stabbing, hanging, cholera; or\nof shipwreck from explosion, scuttling, tempest. Hence a Coroner's Court\nexpects to find, by examining a corpse, the precise cause of death. In\nshort, if we knew the facts minutely enough, it would be found that\nthere is only one Cause (sum of conditions) for each Effect (sum of\nco-effects), and that the order of events is as uniform backwards as\nforwards.\n\nStill, as we are far from knowing events minutely, it is necessary in\npractical affairs, and even in the more complex and unmanageable\nscientific investigations, especially those that deal with human life,\nto acknowledge a possible plurality of causes for any effect. Indeed,\nforgetfulness of this leads to many rash generalisations; as that\n'revolutions always begin in hunger'; or that 'myths are a disease of\nlanguage.' Then there is great waste of ingenuity in reconciling such\npropositions with the recalcitrant facts. A scientific method recognises\nthat there may be other causes of effects thus vaguely conceived, and\nthen proceeds to distinguish in each class of effects the peculiarities\ndue to different causes.\n\n\u00a7 5. The understanding of the complex nature of Causes and Effects helps\nus to overcome some other difficulties that perplex the use of these\nwords. We have seen that the true cause is an _immediate_ antecedent;\nbut if the cause is confounded with _one_ of its constituent conditions,\nit may seem to have long preceded the event which is regarded as its\neffect. Thus, if one man's death is ascribed to another's desire of\nrevenge, this desire may have been entertained for years before the\nassassination occurred: similarly, if a shipwreck is ascribed to a\nsunken reef, the rock was waiting for ages before the ship sailed that\nway. But, of course, neither the desire of revenge nor the sunken rock\nwas 'the sum of the conditions' on which the one or the other event\ndepended: as soon as this is complete the effect appears.\n\nWe have also seen the true effect of any state and process of things is\nthe immediate consequence; but if the effect be confounded with _one_ of\nits constituent factors, it may seem to long outlive the cessation of\nthe cause. Thus, in nearly every process of human industry and art, one\nfactor of the effect--a road, a house, a tool, a picture--may, and\ngenerally does, remain long after the work has ceased: but such a\nresult is not the whole effect of the operations that produce it. The\nother factors may be, and some always are, evanescent. In most of such\nworks some heat is produced by hammering or friction, and the labourers\nare fatigued; but these consequences soon pass off. Hence the effect as\na whole only momentarily survives the cause. Consider a pendulum which,\nhaving been once set agoing, swings to and fro in an arc, under the\njoint control of the shaft, gravitation and its own inertia: at every\nmoment its speed and direction change; and each change may be considered\nas an effect, of which the antecedent change was one condition. In such\na case as this, which, though a very simple, is a perfectly fair example\nof all causation, the duration of either cause or effect is quite\ninsensible: so that, as Dr. Venn says, an Effect, rigorously conceived,\nis only \"the initial tendency\" of its Cause.\n\n\u00a7 6. Mill contrasted two forms under which causation appears to us: that\nis to say, the conditions constituting a cause may be modified, or\n'intermixed' in the effect, in two ways, which are typified respectively\nby Mechanical and Chemical action. In mechanical causation, which is\nfound in Astronomy and all branches of Physics, the effects are all\nreducible to modes of energy, and are therefore commensurable with their\ncauses. They are either directly commensurable, as in the cases treated\nof in the consideration of the mechanical powers; or, if different forms\nof energy enter into cause and effect, such as mechanical energy,\nelectrical energy, heat, these different forms are severally reducible\nto units, between which equivalents have been established. Hence Mill\ncalls this the \"homogeneous intermixture of effects,\" because the\nantecedents and consequents are fundamentally of the same kind.\n\nIn chemical causation, on the other hand, cause and effect (at least, as\nthey present themselves to us) differ in almost every way: in the act of\ncombination the properties of elements (except weight) disappear, and\nare superseded by others in the compound. If, for example, mercury (a\nheavy, silvery liquid) be heated in contact with oxygen (a colourless\ngas), oxide of mercury is formed (red precipitate, which is a powder).\nThis compound presents very different phenomena from those of its\nelements; and hence Mill called this class of cases \"the heteropathic\nintermixture of effects.\" Still, in chemical action, the effect is not\n(in Nature) heterogeneous with the cause: for the weight of a compound\nis equal to the sum of the weights of the elements that are merged in\nit; and an equivalence has been ascertained between the energy of\nchemical combination and the heat, light, etc., produced in the act of\ncombination.\n\nThe heteropathic intermixture of effects is also found in organic\nprocesses (which, indeed, are partly chemical): as when a man eats bread\nand milk, and by digestion and assimilation converts them into nerve,\nmuscle and bone. Such phenomena may make us wonder that people should\never have believed that 'effects resemble their causes,' or that 'like\nproduces like.' A dim recognition of the equivalence of cause and effect\nin respect of matter and motion may have aided the belief; and the\nresemblance of offspring to parents may have helped: but it is probably\na residuum of magical rites; in which to whistle may be regarded as a\nmeans of raising the wind, because the wind whistles; and rain-wizards\nmay make a victim shed tears that the clouds also may weep.\n\n\u00a7 7. Another consideration arises out of the complex character of causes\nand effects. When a cause consists of two or more conditions or forces,\nwe may consider what effect any one of them would have if it operated\nalone, that is to say, its _Tendency_. This is best illustrated by the\nParallelogram of Forces: if two forces acting upon a point, but not in\nthe same direction, be represented by straight lines drawn in the\ndirection of the forces, and in length proportional to their\nmagnitudes, these lines, meeting in an angle, represent severally the\ntendencies of the forces; whilst if the parallelogram be completed on\nthese lines, the diagonal drawn from the point in which they meet\nrepresents their _Resultant_ or effect.\n\nAgain, considering the tendency of any force if it operated alone, we\nmay say that, when combined with another force (not in the same\ndirection) in any resultant, its tendency is _counteracted_: either\npartially, when the direction of the resultant is different; or wholly\nwhen, the other force being equal and opposite, the resultant is\nequilibrium. If the two forces be in the same direction, they are merely\nadded together. Counteraction is only one mode of combination; in no\ncase is any force destroyed.\n\nSometimes the separate tendencies of combined forces can only be\ntheoretically distinguished: as when the motion of a projectile is\nanalysed into a tendency to travel in the straight line of its\ndischarge, and a tendency to fall straight to the ground. But sometimes\na tendency can be isolated: as when,--after dropping a feather in some\nplace sheltered from the wind, and watching it drift to and fro, as the\nair, offering unequal resistances to its uneven surface, counteracts its\nweight with varying success, until it slowly settles upon the\nground,--we take it up and drop it again in a vacuum, when it falls like\nlead. Here we have the tendency of a certain cause (namely, the relation\nbetween the feather and the earth) free from counteraction: and this is\ncalled the _Elimination_ of the counteracting circumstances. In this\ncase indeed there is physical elimination; whereas, in the case of a\nprojectile, when we say that its actual motion is resolvable (neglecting\nthe resistance of the air) into two tendencies, one in the line of\ndischarge, the other earthwards, there is only theoretical elimination\nof either tendency, considered as counteracting the other; and this is\nmore specifically called the _Resolution_ or Analysis of the total\neffect into its component conditions. Now, Elimination and Resolution\nmay be said to be the essential process of Induction in the widest sense\nof the term, as including the combination of Induction with Deduction.\n\nThe several conditions constituting any cause, then, by aiding or\ncounteracting one another's tendencies, jointly determine the total\neffect. Hence, viewed in relation one to another, they may be said to\nstand in _Reciprocity_ or mutual influence. This relation at any moment\nis itself one of co-existence, though it is conceived with reference to\na possible effect. As Kant says, all substances, as perceived in space\nat the same time, are in reciprocal activity. And what is true of the\nworld of things at any moment (as connected, say, by gravity), is true\nof any selected group of circumstances which we regard as the particular\ncause of any event to come. The use of the concept of reciprocity, then,\nlies in the analysis of a cause: we must not think of reciprocity as\nobtaining in the succession of cause and effect, as if the effect could\nturn back upon its cause; for as the effect arises its cause disappears,\nand is irrecoverable by Nature or Magic. There are many cases of\nrhythmic change and of moving equilibria, in which one movement or\nprocess produces another, and this produces something closely resembling\nthe former, and so on in long series; as with the swing of a pendulum or\nthe orbit of a planet: but these are series of cause and effect, not of\nreciprocity.\n\n\n\n\nCHAPTER XV\n\nINDUCTIVE METHOD\n\n\n\u00a7 1. It is necessary to describe briefly the process of investigating\nlaws of causation, not with the notion of teaching any one the Art of\nDiscovery, which each man pursues for himself according to his natural\ngifts and his experience in the methods of his own science, but merely\nto cast some light upon the contents of the next few chapters. Logic is\nhere treated as a process of proof; proof supposes that some general\nproposition or hypothesis has been suggested as requiring proof; and the\nsearch for such propositions may spring from scientific curiosity or\nfrom practical interests.\n\nWe may, as Bain observes (_Logic_: B. iii. ch. 5), desire to detect a\nprocess of causation either (1) amidst circumstances that have no\ninfluence upon the process but only obscure it; as when, being pleased\nwith a certain scent in a garden, we wish to know from what flower it\nrises; or, being attracted by the sound of some instrument in an\norchestra, we desire to know which it is: or (2) amidst circumstances\nthat alter the effect from what it would have been by the sole operation\nof some cause; as when the air deflects a falling feather; or in some\nmore complex case, such as a rise or fall of prices that may extend over\nmany years.\n\nTo begin with, we must form definite ideas as to what the phenomenon is\nthat we are about to investigate; and in a case of any complexity this\nis best done by writing a detailed description of it: e.g., to\ninvestigate the cause of a recent fall of prices, we must describe\nexactly the course of the phenomenon, dating the period over which it\nextends, recording the successive fluctuations of prices, with their\nmaxima and minima, and noting the classes of goods or securities that\nwere more or less affected, etc.\n\nThen the first step of elimination (as Bain further observes) is \"to\nanalyse the situation mentally,\" in the light of analogies suggested by\nour experience or previous knowledge. Dew, for example, is moisture\nformed upon the surface of bodies from no apparent source. But two\npossible sources are easily suggested by common experience: is it\ndeposited from the air, like the moisture upon a mirror when we breathe\nupon it; or does it exude from the bodies themselves, like gum or\nturpentine? Or, again, as to a fall of prices, a little experience in\nbusiness, or knowledge of Economics, readily suggests two possible\nexplanations: either cheaper production in making goods or carrying\nthem; or a scarcity of that in which the purchasing power of the chief\ncommercial nations is directly expressed, namely, gold.\n\nHaving thus analysed the situation and considered the possibility of\none, two, three, or more possible causes, we fix upon one of them for\nfurther investigation; that is to say, we frame an hypothesis that this\nis the cause. When an effect is given to find its cause, an inquirer\nnearly always begins his investigations by thus framing an hypothesis as\nto the cause.\n\nThe next step is to try to _verify_ this Hypothesis. This we may\nsometimes do by _varying the circumstances_ of the phenomenon, according\nto the Canons of direct Inductive Proof to be discussed in the next\nchapter; that is to say, by _observing_ or _experimenting_ in such a way\nas to get rid of or eliminate the obscuring or disturbing conditions.\nThus, to find out which flower in a garden gives a certain scent, it is\nusually enough to rely on observation, going up to the likely flowers\none after the other and smelling them: at close quarters, the greater\nrelative intensity of the scent is sufficiently decisive. Or we may\nresort to a sort of experiment, plucking a likely flower, as to which we\nframe the hypothesis (this is the cause), and carrying it to some place\nwhere the air is free from conflicting odours. Should observation or\nexperiment disprove our first hypothesis we try a second; and so on\nuntil we succeed, or exhaust the known possibilities.\n\nBut if the phenomenon is so complex and extensive as a continuous fall\nof prices, direct observation or experiment is a useless or impossible\nmethod; and we must then resort to Deduction; that is, to indirect\nInduction. If, for example, we take the hypothesis that the fall is due\nto a scarcity of gold, we must show that there is a scarcity; what\neffect such a scarcity may be expected to have upon prices from the\nacknowledged laws of prices, and from the analogy of other cases of an\nexpanded or restricted currency; that this expectation agrees with the\nstatistics of recent commerce: and finally, that the alternative\nhypothesis that the fall is due to cheaper production is not true;\neither because there has not been a sufficient cheapening of general\nproduction; or because, if there has been, the results to be rationally\nexpected from it are not such as to agree with the statistics of recent\ncommerce. (Ch. xviii.)\n\nBut now suppose that, a phenomenon having been suggested for\nexplanation, we are unable at the time to think of any cause--to frame\nany hypothesis about it; we must then wait for the phenomenon to occur\nagain, and, once more observing its course and accompaniments and trying\nto recall its antecedents, do our best to conceive an hypothesis, and\nproceed as before. Thus, in the first great epidemic of influenza, some\ndoctors traced it to a deluge in China, others to a volcanic eruption\nnear Java; some thought it a mild form of Asiatic plague, and others\ncaught a specific microbe. As the disease often recurred, there were\nfresh opportunities of framing hypotheses; and the microbe was\nidentified.\n\nAgain, the investigation may take a different form: given a supposed\nCause to find its Effect; e.g., a new chemical element, to find what\ncompounds it forms with other elements; or, the spots on the sun--have\nthey any influence upon our weather?\n\nHere, if the given cause be under control, as a new element may be, it\nis possible to try experiments with it according to the Canons of\nInductive Proof. The inquirer may form some hypothesis or expectation as\nto the effects, to guide his observation of them, but will be careful\nnot to hold his expectation so confidently as to falsify his observation\nof what actually happens.\n\nBut if the cause be, like the sun-spots, not under control, the inquirer\nwill watch on all sides what events follow their appearance and\ndevelopment; he must watch for consequences of the new cause he is\nstudying in many different circumstances, that his observations may\nsatisfy the canons of proof. But he will also resort for guidance to\ndeduction; arguing from the nature of the cause, if anything is known of\nits nature, what consequences may be expected, and comparing the results\nof this deduction with any consequent which he suspects to be connected\nwith the cause. And if the results of deduction and observation agree,\nhe will still consider whether the facts observed may not be due to some\nother cause.\n\nA cause, however, may be under control and yet be too dangerous to\nexperiment with; such as the effects of a poison--though, if too\ndangerous to experiment with upon man, it may be tried upon animals; or\nsuch as a proposed change of the constitution by legislation; or even\nsome minor Act of Parliament, for altering the Poor Law, or regulating\nthe hours of labour. Here the first step must be deductive. We must ask\nwhat consequences are to be expected from the nature of the change\n(comparing it with similar changes), and from the laws of the special\ncircumstances in which it is to operate? And sometimes we may partially\nverify our deduction by trying experiments upon a small scale or in a\nmild form. There are conflicting deductions as to the probable effect of\ngiving Home Rule to Ireland; and experiments have been made in more or\nless similar cases, as in the Colonies and in some foreign countries. As\nto the proposal to make eight hours the legal limit of a day's labour in\nall trades, we have all tried to forecast the consequences of this; and\nby way of verification we might begin with nine hours; or we might\ninduce some other country to try the experiment first. Still, no\nverification by experiments on a small scale, or in a mild form, or in\nsomewhat similar yet different circumstances, can be considered\nlogically conclusive. What proofs are conclusive we shall see in the\nfollowing chapters.\n\n\u00a7 2. To begin with the conditions of direct Induction.--An Induction is\nan universal real proposition, based on observation, in reliance on the\nuniformity of Nature: when well ascertained, it is called a Law. Thus,\nthat all life depends on the presence of oxygen is (1) an universal\nproposition; (2) a real one, since the 'presence of oxygen' is not\nconnoted by 'life'; (3) it is based on observation; (4) it relies on the\nuniformity of Nature, since all cases of life have not been examined.\n\nSuch a proposition is here called 'an induction,' when it is inductively\nproved; that is, proved by facts, not merely deduced from more general\npremises (except the premise of Nature's uniformity): and by the\n'process of induction' is meant the method of inductive proof. The\nphrase 'process of induction' is often used in another sense, namely for\nthe inference or judgment by which such propositions are arrived at. But\nit is better to call this 'the process of hypothesis,' and to regard it\nas a preliminary to the process of induction (that is, proof), as\nfurnishing the hypothesis which, if it can stand the proper tests,\nbecomes an induction or law.\n\n\u00a7 3. Inductive proofs are usually classed as Perfect and Imperfect.\nThey are said to be perfect when all the instances within the scope of\nthe given proposition have been severally examined, and the proposition\nhas been found true in each case. But we have seen (chap. xiii. \u00a7 2)\nthat the instances included in universal propositions concerning Causes\nand Kinds cannot be exhaustively examined: we do not know all planets,\nall heat, all liquids, all life, etc.; and we never can, since a man's\nlife is never long enough. It is only where the conditions of time,\nplace, etc., are arbitrarily limited that examination can be exhaustive.\nPerfect induction might show (say) that every member of the present\nHouse of Commons has two Christian names. Such an argument is sometimes\nexhibited as a Syllogism in Darapti with a Minor premise in U., which\nlegitimates a Conclusion in A., thus:\n\n A.B. to Z have two Christian names;\n A.B. to Z are all the present M.P.'s:\n .'. All the present M.P.'s have two Christian names.\n\nBut in such an investigation there is no need of logical method to find\nthe major premise; it is mere counting: and to carry out the syllogism\nis a hollow formality. Accordingly, our definition of Induction excludes\nthe kind unfortunately called Perfect, by including in the notion of\nInduction a reliance on the uniformity of Nature; for this would be\nsuperfluous if every instance in question had been severally examined.\nImperfect Induction, then, is what we have to deal with: the method of\nshowing the credibility of an universal real proposition by an\nexamination of _some_ of the instances it includes, generally a small\nfraction of them.\n\n\u00a7 4. Imperfect Induction is either Methodical or Immethodical. Now,\nMethod is procedure upon a principle; and if the method is to be precise\nand conclusive, the principle must be clear and definite.\n\nThere is a Geometrical Method, because the axioms of Geometry are clear\nand definite, and by their means, with the aid of definitions, laws are\ndeduced of the equality of lines and angles and other relations of\nposition and magnitude in space. The process of proof is purely\nDeductive (the axioms and definitions being granted). Diagrams are used\nnot as facts for observation, but merely to fix our attention in\nfollowing the general argument; so that it matters little how badly they\nare drawn, as long as their divergence from the conditions of the\nproposition to be proved is not distracting. Even the appeal to\n\"superposition\" to prove the equality of magnitudes (as in Euclid I. 4),\nis not an appeal to observation, but to our judgment of what is implied\nin the foregoing conditions. Hence no inference is required from the\nspecial case to all similar ones; for they are all proved at once.\n\nThere is also, as we have seen, a method of Deductive Logic resting on\nthe Principles of Consistency and the _Dictum de omni et nullo_. And we\nshall find that there is a method of Inductive Logic, resting on the\nprinciple of Causation.\n\nBut there are a good many general propositions, more or less trustworthy\nwithin a certain range of conditions, which cannot be methodically\nproved for want of a precise principle by which they may be tested; and\nthey, therefore, depend upon Immethodical Induction, that is, upon the\nexamination of as many instances as can be found, relying for the rest\nupon the undefinable principle of the Uniformity of Nature, since we are\nnot able to connect them with any of its definite modes enumerated in\nchap. xiii. \u00a7 7. To this subject we shall return in chap. xix., after\ntreating of Methodical Induction, or the means of determining that a\nrelation of events is of the nature of cause and effect, because the\nrelation can be shown to have the marks of causation, or some of them.\n\n\u00a7 5. Observations and Experiments are the _material_ grounds of\nInduction. An experiment is an observation made under prepared, and\ntherefore known, conditions; and, when obtainable, it is much to be\npreferred. Simple observation shows that the burning of the fire\ndepends, for one thing, on the supply of air; but it cannot show us that\nit depends on oxygen. To prove this we must make experiments as by\nobtaining pure oxygen and pure nitrogen (which, mixed in the proportion\nof one to four, form the air) in separate vessels, and then plunging a\nburning taper into the oxygen--when it will blaze fiercely; and again\nplunging it into the nitrogen--when it will be extinguished. This shows\nthat the greater part of the air does nothing to keep the fire alight,\nexcept by diminishing its intensity and so making it last longer.\nExperiments are more perfect the more carefully they are prepared, and\nthe more completely the conditions are known under which the given\nphenomenon is to be observed. Therefore, they become possible only when\nsome knowledge has already been gained by observation; for else the\npreparation which they require could not be made.\n\nObservation, then, was the first material ground of Induction, and in\nsome sciences it remains the chief ground. The heavenly bodies, the\nwinds and tides, the strata of the earth, and the movements of history,\nare beyond our power to experiment with. Experiments upon the living\nbody or mind are indeed resorted to when practicable, even in the case\nof man, as now in all departments of Psychology; but, if of a grave\nnature, they are usually thought unjustifiable. And in political affairs\nexperiments are hindered by the reflection, that those whose interests\nare affected must bear the consequences and may resent them. Hence, it\nis in physical and chemical inquiries and in the physiology of plants\nand animals (under certain conditions) that direct experiment is most\nconstantly practised.\n\nWhere direct experiment is possible, however, it has many advantages\nover unaided observation. If one experiment does not enable us to\nobserve the phenomenon satisfactorily, we may try again and again;\nwhereas the mere observer, who wishes to study the bright spots on Mars,\nor a commercial crisis, must wait for a favourable opportunity. Again,\nin making experiments we can vary the conditions of the phenomenon, so\nas to observe its different behaviour in each case; whereas he who\ndepends solely on observation must trust the bounty of nature to supply\nhim with a suitable diversity of instances. It is a particular advantage\nof experiment that a phenomenon may sometimes be 'isolated,' that is,\nremoved from the influence of all agents except that whose operation we\ndesire to observe, or except those whose operation is already known:\nwhereas a simple observer, who has no control over the conditions of the\nsubject he studies, can never be quite sure that its movements or\nchanges are not due to causes that have never been conspicuous enough to\ndraw his attention. Finally, experiment enables us to observe coolly and\ncircumspectly and to be precise as to what happens, the time of its\noccurrence, the order of successive events, their duration, intensity\nand extent.\n\nBut whether we proceed by observation or experiment, the utmost\nattainable exactness of measurements and calculation is requisite; and\nthese presuppose some Unit, in multiples or divisions of which the\nresult may be expressed. This unit cannot be an abstract number as in\nArithmetic, but must be one something--an hour, or a yard, or a\npound--according to the nature of the phenomenon to be measured. But\nwhat is an hour, or a yard or a pound? There must in each case be some\nconstant Standard of reference to give assurance that the unit may\nalways have the same value. \"The English pound is defined by a certain\nlump of platinum preserved at Westminster.\" The unit may be identical\nwith the standard or some division or multiple of it; and, in measuring\nthe same kind of phenomena, different units may be used for different\npurposes as long as each bears a constant relation to the standard.\nThus, taking the rotation of the earth as the standard of Time, the\nconvenient unit for long periods is a year (which is a multiple); for\nshorter periods, a day (which is identical); for shorter still, an hour\n(which is a division), or a second, or a thousandth of a second. (See\nJevons' _Principles of Science_, ch. 14.)\n\n\u00a7 6. The principle of Causation is the _formal_ ground of Induction; and\nthe Inductive Canons derived from it are means of testing the formal\nsufficiency of observations to justify the statement of a Law. If we can\nobserve the process of cause and effect in nature we may generalise our\nobservation into a law, because that process is invariable. First, then,\ncan we observe the course of cause and effect? Our power to do so is\nlimited by the refinement of our senses aided by instruments, such as\nlenses, thermometers, balances, etc. If the causal process is\nessentially molecular change, as in the maintenance of combustion by\noxygen, we cannot directly observe it; if the process is partly cerebral\nor mental, as in social movements which depend on feeling and opinion,\nit can but remotely be inferred; even if the process is a collision of\nmoving masses (billiard-balls), we cannot really observe what happens,\nthe elastic yielding, and recoil and the internal changes that result;\nthough no doubt photography will throw some light upon this, as it has\ndone upon the galloping of horses and the impact of projectiles. Direct\nobservation is limited to the effect which any change in a phenomenon\n(or its index) produces upon our senses; and what we believe to be the\ncausal process is a matter of inference and calculation. The meagre and\nabstract outlines of Inductive Logic are apt to foster the notion, that\nthe evidence on which Science rests is simple; but it is amazingly\nintricate and cumulative.\n\nSecondly, so far as we can observe the process of nature, how shall we\njudge whether a true causal instance, a relation of cause and effect,\nis before us? By looking for the five marks of Causation. Thus, in the\nexperiment above described, showing that oxygen supports combustion, we\nfind--(1) that the taper which only glowed before being plunged into the\noxygen, bursts into flame when there--Sequence; (2) that this begins to\nhappen at once without perceptible interval--Immediacy; (3) that no\nother agent or disturbing circumstance was present (the preparation of\nthe experiment having excluded any such thing)--Unconditionalness; (4)\nthe experiment may be repeated as often as we like with the same\nresult--Invariableness. Invariableness, indeed, I do not regard as\nformally necessary to be shown, supposing the other marks to be clear;\nfor it can only be proved within our experience; and the very object of\nInduction is to find grounds of belief beyond actual experience.\nHowever, for material assurance, to guard against his own liability to\nerror, the inquirer will of course repeat his experiments.\n\nThe above four are the qualitative marks of Causation: the fifth and\nquantitative mark is the Equality of Cause and Effect; and this, in the\nabove example, the Chemist determines by showing that, instead of the\noxygen and wax that have disappeared during combustion, an equivalent\nweight of carbon dioxide, water, etc., has been formed.\n\nHere, then, we have all the marks of causation; but in the ordinary\njudgments of life, in history, politics, criticism, business, we must\nnot expect such clear and direct proofs; in subsequent chapters it will\nappear how different kinds of evidence are combined in different\ndepartments of investigation.\n\n\u00a7 7. The Inductive Canons, to be explained in the next chapter, describe\nthe character of observations and experiments that justify us in drawing\nconclusions about causation; and, as we have mentioned, they are derived\nfrom the principle of Causation itself. According to that principle,\ncause and effect are invariably, immediately and unconditionally\nantecedent and consequent, and are equal as to the matter and energy\nembodied.\n\nInvariability can only be observed, in any of the methods of induction,\nby collecting more and more instances, or repeating experiments. Of\ncourse it can never be exhaustively observed.\n\nImmediacy, too, in direct Induction, is a matter for observation the\nmost exact that is possible.\n\nSuccession, or the relation itself of antecedent and consequent, must\neither be directly observed (or some index of it); or else ascertained\nby showing that energy gained by one phenomenon has been lost by\nanother, for this implies succession.\n\nBut to determine the unconditionality of causation, or the\nindispensability of some condition, is the great object of the methods,\nand for that purpose the meaning of unconditionality may be further\nexplicated by the following rules for the determination of a Cause.\n\n\nA. QUALITATIVE DETERMINATION\n\n_I.--For Positive Instances._\n\nTo prove a supposed Cause: (a) Any agent whose introduction among\ncertain conditions (without further change) is followed by a given\nphenomenon; or, (b) whose removal is followed by the cessation (or\nmodification) of that phenomenon, is (so far) the cause or an\nindispensable condition of it.\n\nTo find the Effect: (c) Any event that follows a given phenomenon, when\nthere is no further change; or, (d) that does not occur when the\nconditions of a former occurrence are exactly the same, except for the\nabsence of that phenomenon, is the effect of it (or is dependent on\nit).\n\n\n_II.--For Negative Instances._\n\nTo exclude a supposed Cause: (a) Any agent that can be introduced among\ncertain conditions without being followed by a given phenomenon (or that\nis found without that phenomenon); or (b) that can be removed when that\nphenomenon is present without impairing it (or that is absent when that\nphenomenon is present), is not the cause, or does not complete the\ncause, of that phenomenon in those circumstances.\n\nTo exclude a supposed Effect: (c) Any event that occurs without the\nintroduction (or presence) of a given phenomenon; or (d) that does not\noccur when that phenomenon is introduced (or is present), is not the\neffect of that phenomenon.\n\n * * * * *\n\nSubject to the conditions thus stated, the rules may be briefly put as\nfollows:\n\nI. (a) That which (without further change) is followed by a given event\nis its cause.\n\nII. (a) That which is not so followed is not the cause.\n\nI. (b) That which cannot be left out without impairing a phenomenon is a\ncondition of it.\n\nII. (b) That which can be left out is not a condition of it.\n\n\nB. QUANTITATIVE DETERMINATION\n\nThe Equality of Cause and Effect may be further explained by these\nrules:\n\nIII. (a) When a cause (or effect) increases or decreases, so does its\neffect (or cause).\n\nIII. (b) If two phenomena, having the other marks of cause and effect,\nseem unequal, the less contains an unexplored factor.\n\nIII. (c) If an antecedent and consequent do not increase or decrease\ncorrespondingly, they are not cause and effect, so far as they vary.\n\nIt will next be shown that these propositions are variously combined in\nMill's five Canons of Induction: Agreement, the Joint Method,\nDifference, Variations, Residues. The first three are sometimes called\nQualitative Methods, and the two last Quantitative; and although this\ngrouping is not quite accurate, seeing that Difference is often used\nquantitatively, yet it draws attention to an important distinction\nbetween a mere description of conditions and determination by exact\nmeasurement.\n\nTo avoid certain misunderstandings, some slight alterations have been\nmade in the wording of the Canons. It may seem questionable whether the\nCanons add anything to the above propositions: I think they do. They are\nnot discussed in the ensuing chapter merely out of reverence for Mill,\nor regard for a nascent tradition; but because, as describing the\ncharacter of observations and experiments that justify us in drawing\nconclusions about causation, they are guides to the analysis of\nobservations and to the preparation of experiments. To many eminent\ninvestigators the Canons (as such) have been unknown; but they prepared\ntheir work effectively so far only as they had definite ideas to the\nsame purport. A definite conception of the conditions of proof is the\nnecessary antecedent of whatever preparations may be made for proving\nanything.\n\n\n\n\nCHAPTER XVI\n\nTHE CANONS OF DIRECT INDUCTION\n\n\n\u00a7 1. Let me begin by borrowing an example from Bain (_Logic_: B. III. c.\n6). The North-East wind is generally detested in this country: as long\nas it blows few people feel at their best. Occasional well-known causes\nof a wind being injurious are violence, excessive heat or cold,\nexcessive dryness or moisture, electrical condition, the being laden\nwith dust or exhalations. Let the hypothesis be that the last is the\ncause of the North-East wind's unwholesome quality; since we know it is\na ground current setting from the pole toward the equator and bent\nwestward by the rotation of the earth; so that, reaching us over\nthousands of miles of land, it may well be fraught with dust, effluvia,\nand microbes. Now, examining many cases of North-East wind, we find that\nthis is the only circumstance in which all the instances agree: for it\nis sometimes cold, sometimes hot; generally dry, but sometimes wet;\nsometimes light, sometimes violent, and of all electrical conditions.\nEach of the other circumstances, then, can be omitted without the N.E.\nwind ceasing to be noxious; but one circumstance is never absent,\nnamely, that it is a ground current. That circumstance, therefore, is\nprobably the cause of its injuriousness. This case illustrates:--\n\n\n(I) THE CANON OF AGREEMENT.\n\n_If two or more instances of a phenomenon under investigation have only\none other circumstance (antecedent or consequent) in common, that\ncircumstance is probably the cause (or an indispensable condition) or\nthe effect of the phenomenon, or is connected with it by causation._\n\nThis rule of proof (so far as it is used to establish direct causation)\ndepends, first, upon observation of an invariable connection between the\ngiven phenomenon and one other circumstance; and, secondly, upon I. (a)\nand II. (b) among the propositions obtained from the unconditionality of\ncausation at the close of the last chapter.\n\nTo prove that A is causally related to _p_, suppose two instances of the\noccurrence of A, an antecedent, and _p_, a consequent, with concomitant\nfacts or events--and let us represent them thus:\n\n Antecedents: A B C A D E\n Consequents: _p q r_ _p s t_;\n\nand suppose further that, in this case, the immediate succession of\nevents can be observed. Then A is probably the cause, or an\nindispensable condition, of _p_. For, as far as our instances go, A is\nthe invariable antecedent of _p_; and _p_ is the invariable consequent\nof A. But the two instances of A or _p_ agree in no other circumstance.\nTherefore A is (or completes) the unconditional antecedent of _p_. For B\nand C are not indispensable conditions of _p_, being absent in the\nsecond instance (Rule II. (b)); nor are D and E, being absent in the\nfirst instance. Moreover, _q_ and _r_ are not effects of A, being absent\nin the second instance (Rule II. (d)); nor are _s_ and _t_, being absent\nin the first instance.\n\nIt should be observed that the cogency of the proof depends entirely\nupon its tending to show the unconditionality of the sequence A-_p_, or\nthe indispensability of A as a condition of _p_. That _p_ follows A,\neven immediately, is nothing by itself: if a man sits down to study and,\non the instant, a hand-organ begins under his window, he must not infer\nmalice in the musician: thousands of things follow one another every\nmoment without traceable connection; and this we call 'accidental.' Even\ninvariable sequence is not enough to prove direct causation; for, in\nour experience does not night invariable follow day? The proof requires\nthat the instances be such as to show not merely what events _are_ in\ninvariable sequence, but also what _are not_. From among the occasional\nantecedents of _p_ (or consequents of A) we have to eliminate the\naccidental ones. And this is done by finding or making 'negative\ninstances' in respect of each of them. Thus the instance\n\n A D E\n _p s t_\n\nis a negative instance of B and C considered as supposable causes of _p_\n(and of _q_ and _r_ as supposable effects of A); for it shows that they\nare absent when _p_ (or A) is present.\n\nTo insist upon the cogency of 'negative instances' was Bacon's great\ncontribution to Inductive Logic. If we neglect them, and merely collect\nexamples of the sequence A-_p_, this is 'simple enumeration'; and\nalthough simple enumeration, when the instances of agreement are\nnumerous enough, may give rise to a strong belief in the connection of\nphenomena, yet it can never be a methodical or logical proof of\ncausation, since it does not indicate the unconditionalness of the\nsequence. For simple enumeration of the sequence A-_p_ leaves open the\npossibility that, besides A, there is always some other antecedent of\n_p_, say X; and then X may be the cause of _p_. To disprove it, we must\nfind, or make, a negative instance of X--where _p_ occurs, but X is\nabsent.\n\nSo far as we recognise the possibility of a plurality of causes, this\nmethod of Agreement cannot be quite satisfactory. For then, in such\ninstances as the above, although D is absent in the first, and B in the\nsecond, it does not follow that they are not the causes of _p_; for they\nmay be alternative causes: B may have produced _p_ in the first\ninstance, and D in the second; A being in both cases an accidental\ncircumstance in relation to _p_. To remedy this shortcoming by the\nmethod of Agreement itself, the only course is to find more instances of\n_p_. We may never find a negative instance of A; and, if not, the\nprobability that A is the cause of _p_ increases with the number of\ninstances. But if there be no antecedent that we cannot sometimes\nexclude, yet the collection of instances will probably give at last all\nthe causes of _p_; and by finding the proportion of instances in which\nA, B, or X precedes _p_, we may estimate the probability of any one of\nthem being the cause of _p_ in any given case of its occurrence.\n\nBut this is not enough. Since there cannot really be vicarious causes,\nwe must define the effect (_p_) more strictly, and examine the cases to\nfind whether there may not be varieties of _p_, with each of which one\nof the apparent causes is correlated: A with _p_^{1} B with _p_^{11}, X\nwith _p_^{111}. Or, again, it may be that none of the recognised\nantecedents is effective: as we here depend solely on observation, the\ntrue conditions may be so recondite and disguised by other phenomena as\nto have escaped our scrutiny. This may happen even when we suppose that\nthe chief condition has been isolated: the drinking of foul water was\nlong believed to cause dysentery, because it was a frequent antecedent;\nwhilst observation had overlooked the bacillus, which was the\nindispensable condition.\n\nAgain, though we have assumed that, in the instances supposed above,\nimmediate sequence is observable, yet in many cases it may not be so, if\nwe rely only on the canon of Agreement; if instances cannot be obtained\nby experiment, and we have to depend on observation. The phenomena may\nthen be so mixed together that A and _p_ seem to be merely concomitant;\nso that, though connection of some sort may be rendered highly probable,\nwe may not be able to say which is cause and which is effect. We must\nthen try (as Bain says) to trace the expenditure of energy: if _p_ gains\nwhen A loses, the course of events if from A to _p_.\n\nMoreover, where succession cannot be traced, the method of Agreement may\npoint to a connection between two or more facts (perhaps as co-effects\nof a remote cause) where direct causation seems to be out of the\nquestion: e.g., that Negroes, though of different tribes, different\nlocalities, customs, etc., are prognathous, woolly-haired and\ndolichocephalic.\n\nThe Method of Agreement, then, cannot by itself prove causation. Its\nchief use (as Mill says) is to suggest hypotheses as to the cause; which\nmust then be used (if possible) experimentally to try if it produces the\ngiven effect. A bacillus, for example, being always found with a certain\ndisease, is probably the chief condition of it: give it to a guinea-pig,\nand observe whether the disease appears in that animal.\n\nMen often use arguments which, if they knew it, might be shown to\nconform more or less to this canon; for they collect many instances to\nshow that two events are connected; but usually neglect to bring out the\nnegative side of the proof; so that their arguments only amount to\nsimple enumeration. Thus Ascham in his _Toxophilus_, insisting on the\nnational importance of archery, argues that victory has always depended\non superiority in shooting; and, to prove it, he shows how the Parthians\nchecked the Romans, Sesostris conquered a great part of the known world,\nTiberius overcame Arminius, the Turks established their empire, and the\nEnglish defeated the French (with many like examples)--all by superior\narchery. But having cited these cases to his purpose, he is content;\nwhereas he might have greatly strengthened his proof by showing how one\nor the other instance excludes other possible causes of success. Thus:\nthe cause was not discipline, for the Romans were better disciplined\nthan the Parthians; nor yet the boasted superiority of a northern\nhabitat, for Sesostris issued from the south; nor better manhood, for\nhere the Germans probably had the advantage of the Romans; nor superior\ncivilisation, for the Turks were less civilised than most of those they\nconquered; nor numbers, nor even a good cause, for the French were more\nnumerous than the English, and were shamefully attacked by Henry V. on\ntheir own soil. Many an argument from simple enumeration may thus be\nturned into an induction of greater plausibility according to the Canon\nof Agreement.\n\nStill, in the above case, the effect (victory) is so vaguely conceived,\nthat a plurality of causes must be allowed for: although, e.g.,\ndiscipline did not enable the Romans to conquer the Parthians, it may\nhave been their chief advantage over the Germans; and it was certainly\nimportant to the English under Henry V. in their war with the French.\n\nHere is another argument, somewhat similar to the above, put forward by\nH. Spencer with a full consciousness of its logical character. States\nthat make war their chief object, he says, assume a certain type of\norganisation, involving the growth of the warrior class and the\ntreatment of labourers as existing solely to sustain the warriors; the\ncomplete subordination of individuals to the will of the despotic\nsoldier-king, their property, liberty and life being at the service of\nthe State; the regimentation of society not only for military but also\nfor civil purposes; the suppression of all private associations, etc.\nThis is the case in Dahomey and in Russia, and it was so at Sparta, in\nEgypt, and in the empire of the Yncas. But the similarity of\norganisation in these States cannot have been due to race, for they are\nall of different races; nor to size, for some are small, some large; nor\nto climate or other circumstances of habitat, for here again they differ\nwidely: the one thing they have in common is the military purpose; and\nthis, therefore, must be the cause of their similar organisation.\n(_Political Institutions._)\n\nBy this method, then, to prove that one thing is causally connected with\nanother, say A with _p_, we show, first, that in all instances of _p_, A\nis present; and, secondly, that any other supposable cause of _p_ may be\nabsent without disturbing _p_. We next come to a method the use of which\ngreatly strengthens the foregoing, by showing that where _p_ is absent\nA is also absent, and (if possible) that A is the only supposable cause\nthat is always absent along with _p_.\n\n\n\u00a7 2. THE CANON OF THE JOINT METHOD OF AGREEMENT IN PRESENCE AND IN\nABSENCE.\n\n_If_ (1) _two or more instances in which a phenomenon occurs have only\none other circumstance (antecedent or consequent) in common, while_ (2)\n_two or more instances in which it does not occur (though in important\npoints they resemble the former set of instances) have nothing else in\ncommon save the absence of that circumstance--the circumstance in which\nalone the two sets of instances differ throughout (being present in the\nfirst set and absent in the second) is probably the effect, or the\ncause, or an indispensable condition of the phenomenon._\n\nThe first clause of this Canon is the same as that of the method of\nAgreement, and its significance depends upon the same propositions\nconcerning causation. The second clause, relating to instances in which\nthe phenomenon is absent, depends for its probative force upon Prop. II.\n(a), and I. (b): its function is to exclude certain circumstances (whose\nnature or manner of occurrence gives them some claim to consideration)\nfrom the list of possible causes (or effects) of the phenomenon\ninvestigated. It might have been better to state this second clause\nseparately as the Canon of the Method of Exclusions.\n\nTo prove that A is causally related to _p_, let the two sets of\ninstances be represented as follows:\n\nInstances of Presence. Instances of Absence.\n A B C C H F\n _p q r_ _r x v_\n A D E B D K\n _p s t_ _q y s_\n A F G E G M\n _p u v_ _t f u_\n\nThen A is probably the cause or a condition of _p_, or _p_ is dependent\nupon A: first, by the Canon of Agreement in Presence, as represented by\nthe first set of instances; and, secondly, by Agreement in Absence in\nthe second set of instances. For there we see that C, H, F, B, D, K, E,\nG, M occur without the phenomenon _p_, and therefore (by Prop. II. (a))\nare not its cause, or not the whole cause, unless they have been\ncounteracted (which is a point for further investigation). We also see\nthat _r, v, q, s, t, u_ occur without A, and therefore are not the\neffects of A. And, further, if the negative instances represent all\npossible cases, we see that (according to Prop. I. (b)) A is the cause\nof _p_, because it cannot be omitted without the cessation of _p_. The\ninference that A and _p_ are cause and effect, suggested by their being\npresent throughout the first set of instances, is therefore strengthened\nby their being both absent throughout the second set.\n\nSo far as this Double Method, like the Single Method of Agreement,\nrelies on observation, sequence may not be perceptible in the instances\nobserved, and then, direct causation cannot be proved by it, but only\nthe probability of causal connection; and, again, the real cause, though\npresent, may be so obscure as to evade observation. It has, however, one\npeculiar advantage, namely, that if the second list of instances (in\nwhich the phenomenon and its supposed antecedent are both absent) can be\nmade exhaustive, it precludes any hypothesis of a plurality of causes;\nsince all possible antecedents will have been included in this list\nwithout producing the phenomenon. Thus, in the above symbolic example,\ntaking the first set of instances, the supposition is left open that B,\nC, D, E, F, G may, at one time or another, have been a condition of _p_;\nbut, in the second list, these antecedents all occur, here or there,\nwithout producing _p_, and therefore (unless counteracted somehow)\ncannot be a condition of _p_. A, then, stands out as the one thing that\nis present whenever _p_ is present, and absent whenever _p_ is absent.\n\nStated in this abstract way, the Double Method may seem very elaborate\nand difficult; yet, in fact, its use may be very simple. Tyndall, to\nprove that dispersed light in the air is due to motes, showed by a\nnumber of cases (1) that any gas containing motes is luminous; (2) that\nair in which the motes had been destroyed by heat, and any gas so\nprepared as to exclude motes, are not luminous. All the instances are of\ngases, and the result is: motes--luminosity; no motes--no luminosity.\nDarwin, to show that cross-fertilisation is favourable to flowers,\nplaced a net about 100 flower-heads, and left 100 others of the same\nvarieties exposed to the bees: the former bore no seed, the latter\nnearly 3,000. We must assume that, in Darwin's judgment, the net did not\nscreen the flowers from light and heat sufficiently to affect the\nresult.\n\nThere are instructive applications of this Double Method in Wallace's\n_Darwinism_. In chap. viii., on _Colour in Animals_, he observes, that\nthe usefulness of their coloration to animals is shown by the fact that,\n\"as a rule, colour and marking are constant in each species of wild\nanimal, while, in almost every domesticated animal, there arises great\nvariability. We see this in our horses and cattle, our dogs and cats,\nour pigeons and poultry. Now the essential difference between the\nconditions of life of domesticated and wild animals is, that the former\nare protected by man, while the latter have to protect themselves.\" Wild\nanimals protect themselves by acquiring qualities adapted to their mode\nof life; and coloration is a very important one, its chief, though not\nits only use, being concealment. Hence a useful coloration having been\nestablished in any species, individuals that occasionally may vary from\nit, will generally, perish; whilst, among domestic animals, variation of\ncolour or marking is subject to no check except the taste of owners. We\nhave, then, two lists of instances; first, innumerable species of wild\nanimals in which the coloration is constant and which depend upon their\nown qualities for existence; secondly, several species of domestic\nanimals in which the coloration is _not_ constant, and which do _not_\ndepend upon their own qualities for existence. In the former list two\ncircumstances are present together (under all sorts of conditions); in\nthe latter they are absent together. The argument may be further\nstrengthened by adding a third list, parallel to the first, comprising\ndomestic animals in which coloration is approximately constant, but\nwhere (as we know) it is made a condition of existence by owners, who\nonly breed from those specimens that come up to a certain standard of\ncoloration.\n\nWallace goes on to discuss the colouring of arctic animals. In the\narctic regions, he says, some animals are wholly white all the year\nround, such as the polar bear, the American polar hare, the snowy owl\nand the Greenland falcon: these live amidst almost perpetual snow.\nOthers, that live where the snow melts in summer, only turn white in\nwinter, such as the arctic hare, the arctic fox, the ermine and the\nptarmigan. In all these cases the white colouring is useful, concealing\nthe herbivores from their enemies, and also the carnivores in\napproaching their prey; this usefulness, therefore, is a condition of\nthe white colouring. Two other explanations have, however, been\nsuggested: first, that the prevalent white of the arctic regions\ndirectly colours the animals, either by some photographic or chemical\naction on the skin, or by a reflex action through vision (as in the\nchameleon); secondly, that a white skin checks radiation and keeps the\nanimals warm. But there are some exceptions to the rule of white\ncolouring in arctic animals which refute these hypotheses, and confirm\nthe author's. The sable remains brown throughout the winter; but it\nfrequents trees, with whose bark its colour assimilates. The musk-sheep\nis brown and conspicuous; but it is gregarious, and its safety depends\nupon its ability to recognise its kind and keep with the herd. The raven\nis always black; but it fears no enemy and feeds on carrion, and\ntherefore does not need concealment for either defence or attack. The\ncolour of the sable, then, though not white, serves for concealment; the\ncolour of the musk-sheep serves a purpose more important than\nconcealment; the raven needs no concealment. There are thus two sets of\ninstances:--in one set the animals are white (a) all the year, (b) in\nwinter; and white conceals them (a) all the year, (b) in winter; in the\nother set, the animals are _not_ white, and to them either whiteness\nwould _not_ give concealment, or concealment would _not_ be\nadvantageous. And this second list refutes the rival hypotheses: for the\nsable, the musk-sheep and the raven are as much exposed to the glare of\nthe snow, and to the cold, as the other animals are.\n\n\n\u00a7 3. THE CANON OF DIFFERENCE.\n\n_If an instance in which a phenomenon occurs, and an instance in which\nit does not occur, have every other circumstance in common save one,\nthat one (whether consequent or antecedent) occurring only in the\nformer; the circumstance in which alone the two instances differ is the\neffect, or the cause, or an indispensable condition of the phenomenon._\n\nThis follows from Props. I (a) and (b), in chapter xv. \u00a7 7. To prove\nthat A is a condition of _p_, let two instances, such as the Canon\nrequires, be represented thus:\n\n A B C B C\n _p q r_ _q r_\n\nThen A is the cause or a condition of _p_. For, in the first instance, A\nbeing introduced (without further change), _p_ arises (Prop. I. (a));\nand, in the second instance, A having been removed (without other\nchange), _p_ disappears (Prop. I. (b)). Similarly we may prove, by the\nsame instances, that _p_ is the effect of A.\n\nThe order of the phenomena and the immediacy of their connection is a\nmatter for observation, aided by whatever instruments and methods of\ninspection and measurement may be available.\n\nAs to the invariability of the connection, it may of course be tested by\ncollecting more instances or making more experiments; but it has been\nmaintained, that a single perfect experiment according to this method is\nsufficient to prove causation, and therefore implies invariability\n(since causation is uniform), though no other instances should ever be\nobtainable; because it establishes once for all the unconditionality of\nthe connection\n\n A B C\n _p q r_.\n\nNow, formally this is true; but in any actual investigation how shall we\ndecide what is a satisfactory or perfect experiment? Such an experiment\nrequires that in the negative instance\n\n B C\n _q r_,\n\nBC shall be the least assemblage of conditions necessary to co-operate\nwith A in producing _p_; and that it is so cannot be ascertained without\neither general prior knowledge of the nature of the case or special\nexperiments for the purpose. So that invariability will not really be\ninferred from a single experiment; besides that every prudent inquirer\nrepeats his experiments, if only to guard against his own liability to\nerror.\n\nThe supposed plurality of causes does not affect the method of\nDifference. In the above symbolic case, A is clearly _one_ cause (or\ncondition) of _p_, whatever other causes may be possible; whereas with\nthe Single Method of Agreement, it remained doubtful (admitting a\nplurality of causes) whether A, in spite of being always present with\n_p_, was ever a cause or condition of it.\n\nThis method of Difference without our being distinctly aware of it, is\noftener than any other the basis of ordinary judgments. That the sun\ngives light and heat, that food nourishes and fire burns, that a stone\nbreaks a window or kills a bird, that the turning of a tap permits or\nchecks the flow of water or of gas, and thousands of other propositions\nare known to be true by rough but often emphatic applications of this\nmethod in common experience.\n\nThe method of Difference may be applied either (1) by observation, on\nfinding two instances (distinct assemblages of conditions) differing\nonly in one phenomenon together with its antecedent or consequent; or\n(2) by experiment, and then, either (a) by preparing two instances that\nmay be compared side by side, or (b) by taking certain conditions, and\nthen introducing (or subtracting) some agent, supposed to be the cause,\nto see what happens: in the latter case the \"two instances\" are the same\nassemblage of conditions considered before and, again, after, the\nintroduction of the agent. As an example of (a) there is an experiment\nto show that radium gives off heat: take two glass tubes, in one put\nsome chloride of radium, in both thermometers, and close them with\ncotton-wool. Soon the thermometer in the tube along with radium reads\n54\u00b0 F. higher than the other one. The tube without the radium, whose\ntemperature remains unaltered, is called the \"control\" experiment. Most\nexperiments are of the type (b); and since the Canon, which describes\ntwo co-existing instances, does not readily apply to this type, an\nalternative version may be offered: _Any agent whose introduction into\nknown circumstances (without further change) is immediately followed by\na definite phenomenon is a condition of the occurrence of that\nphenomenon._\n\nThe words _into known circumstances_ are necessary to emphasise what is\nrequired by this Method, namely, that the two instances differ in only\none thing; for this cannot be ascertained unless all the other\nconditions are known; and this further implies that they have been\nprepared. It is, therefore, not true (as Sigwart asserts) that this\nmethod determines only one condition of a phenomenon, and that it is\nthen necessary to inquire into the other conditions. If they were not\nknown they must be investigated; but then the experiment would not have\nbeen made upon this method. Practically, experiments have to be made in\nall degrees of imperfection, and the less perfect they are, that is, the\nless the circumstances are known beforehand, the more remains to be\ndone. A common imperfection is delay, or the occurrence of a latent\nperiod between the introduction of an agent and the manifestation of its\neffects; it cannot then be the unconditional cause; though it may be an\nindispensable remote condition of whatever change occurs. If, feeling\nout of sorts, you take a drug and some time afterwards feel better, it\nis not clear on this ground alone that the drug was the cause of\nrecovery, for other curative processes may have been active\nmeanwhile--food, or sleep, or exercise.\n\nAny book of Physics or of Chemistry will furnish scores of examples of\nthe method of Difference: such as Galileo's experiment to show that air\nhas weight, by first weighing a vessel filled with ordinary air, and\nthen filling it with condensed air and weighing it again; when the\nincreased weight can only be due to the greater quantity of air\ncontained. The melting-point of solids is determined by heating them\nuntil they do melt (as silver at 1000\u00b0 C., gold at 1250\u00b0, platinum at\n2000\u00b0); for the only difference between bodies at the time of melting\nand just before is the addition of so much heat. Similarly with the\nboiling point of liquids. That the transmission of sound depends upon\nthe continuity of an elastic ponderable medium, is proved by letting a\nclock strike in a vacuum (under a glass from which the air has been\nwithdrawn by an air pump), and standing upon a non-elastic pedestal:\nwhen the clock be seen to strike, but makes only such a faint sound as\nmay be due to the imperfections of the vacuum and the pedestal.\n\nThe experiments by which the chemical analysis or synthesis of various\nforms of matter is demonstrated are simple or compound applications of\nthis method of Difference, together with the quantitative mark of\ncausation (that cause and effect are equal); since the bodies resulting\nfrom an analysis are equal in weight to the body analysed, and the body\nresulting from a synthesis is equal in weight to the bodies synthesised.\nThat an electric current resolves water into oxygen and hydrogen may be\nproved by inserting the poles of a galvanic battery in a vessel of\nwater; when this one change is followed by another, the rise of bubbles\nfrom each pole and the very gradual decrease of the water. If the\nbubbles are caught in receivers placed over them, it can be shown that\nthe joint weight of the two bodies of gas thus formed is equal to the\nweight of the water that has disappeared; and that the gases are\nrespectively oxygen and hydrogen may then be shown by proving that they\nhave the properties of those gases according to further experiments by\nthe method of Difference; as (e.g.) that one of them is oxygen because\nit supports combustion, etc.\n\nWhen water was first decomposed by the electric current, there appeared\nnot only oxygen and hydrogen, but also an acid and an alkali. These\nproducts were afterwards traced to impurities of the water and of the\noperator's hands. Mill observes that in any experiment the effect, or\npart of it, may be due, not to the supposed agent, but to the means\nemployed in introducing it. We should know not only the other conditions\nof an experiment, but that the agent or change introduced is nothing\nelse than what it is supposed to be.\n\nIn the more complex sciences the method of Difference is less easily\napplicable, because of the greater difficulty of being sure that only\none circumstance at a time has altered; still, it is frequently used.\nThus, if by dividing a certain nerve certain muscles are paralysed, it\nis shown that normally that nerve controls those muscles. That the sense\nof smell in flies and cockroaches is connected with the antennae has\nbeen shown by cutting them off: whereupon the insects can no longer find\ncarrion. In his work on _Earthworms_, Darwin shows that, though\nsensitive to mechanical tremors, they are deaf (or, at least, not\nsensitive to sonorous vibrations transmitted through the air), by the\nfollowing experiment. He placed a pot containing a worm that had come to\nthe surface, as usual at night, upon a table, whilst close by a piano\nwas violently played; but the worm took no notice of the noise. He then\nplaced the pot upon the piano, whilst it was being played, when the\nworm, probably feeling mechanical vibrations, hastily slid back into its\nburrow.\n\nWhen, instead of altering one circumstance in an instance (which we have\ndone our best not otherwise to disturb) and then watching what follows,\nwe try to find two ready-made instances of a phenomenon, which only\ndiffer in one other circumstance, it is, of course, still more difficult\nto be sure that there is only one other circumstance in which they\ndiffer. It may be worth while, however, to look for such instances.\nThus, that the temperature of ocean currents influences the climate of\nthe shores they wash, seems to be shown by the fact that the average\ntemperature of Newfoundland is lower than that of the Norwegian coast\nsome 15\u00b0 farther north. Both regions have great continents at their\nback; and as the mountains of Norway are higher and capped with\nperennial snow, we might expect a colder climate there: but the shore of\nNorway is visited by the Gulf Stream, whilst the shore of Newfoundland\nis traversed by a cold current from Greenland. Again, when in 1841 the\nrailway from Rouen to Paris was being built, gangs of English and gangs\nof French workmen were employed upon it, and the English got through\nabout one-third more work per man than the French. It was suspected that\nthis difference was due to one other difference, namely, that the\nEnglish fed better, preferring beef to thin soup. Now, logically, it\nmight have been objected that the evidence was unsatisfactory, seeing\nthat the men differed in other things besides diet--in 'race' (say),\nwhich explains so much and so easily. But the Frenchmen, having been\ninduced to try the same diet as the English, were, in a few days, able\nto do as much work: so that the \"two instances\" were better than they\nlooked. It often happens that evidence, though logically questionable,\nis good when used by experts, whose familiarity with the subject makes\nit good.\n\n\n\u00a7 4. THE CANON OF CONCOMITANT VARIATIONS.\n\n_Whatever phenomenon varies in any manner whenever another phenomenon\n(consequent or antecedent) varies in some particular manner [no other\nchange having concurred] is either the cause or effect of that\nphenomenon [or is connected with it through some fact of causation]._\n\nThis is not an entirely fresh method, but may be regarded as a special\ncase either of Agreement or of Difference, to prove the cause or effect,\nnot of a phenomenon as a whole, but of some increment of it (positive or\nnegative). There are certain forces, such as gravitation, heat,\nfriction, that can never be eliminated altogether, and therefore can\nonly be studied in their degrees. To such phenomena the method of\nDifference cannot be applied, because there are no negative instances.\nBut we may obtain negative instances of a given quantity of such a\nphenomenon (say, heat), and may apply the method of Difference to that\nquantity. Thus, if the heat of a body increases 10 degrees, from 60 to\n70, the former temperature of 60 was a negative instance in respect of\nthose 10 degrees; and if only one other circumstance (say, friction)\nhas altered at the same time, that circumstance (if an antecedent) is\nthe cause. Accordingly, if in the above Canon we insert, after\n'particular manner,' \"[no other change having concurred,]\" it is a\nstatement of the method of Difference as applicable to the increment of\na phenomenon, instead of to the phenomenon as a whole; and we may then\nomit the last clause--\"[or is connected, etc.].\" For these words are\ninserted to provide for the case of co-effects of a common cause (such\nas the flash and report of a gun); but if no other change (such as the\ndischarge of a gun) has concurred with the variations of two phenomena,\nthere cannot have been a common cause, and they are therefore cause and\neffect.\n\nIf, on the other hand, we omit the clause \"[no other change having\nconcurred,]\" the Canon is a statement of the method of Agreement as\napplicable to the increment of a phenomenon instead of to the phenomenon\nas a whole; and it is then subject to the imperfections of that method:\nthat is to say, it leaves open the possibilities, that an inquirer may\noverlook a plurality of causes; or may mistake a connection of two\nphenomena, which (like the flash and report of a gun) are co-effects of\na common cause, for a direct relation of cause and effect.\n\nIt may occur to the reader that we ought also to distinguish Qualitative\nand Quantitative Variations as two orders of phenomena to which the\npresent method is applicable. But, in fact, Qualitative Variations may\nbe adequately dealt with by the foregoing methods of Agreement, Double\nAgreement, and Difference; because a change of quality or property\nentirely gets rid of the former phase of that quality, or substitutes\none for another; as when the ptarmigan changes from brown to white in\nwinter, or as when a stag grows and sheds its antlers with the course of\nthe seasons. The peculiar use of the method of Variations, however, is\nto formulate the conditions of proof in respect of those causes or\neffects which cannot be entirely got rid of, but can be obtained only in\ngreater or less amount; and such phenomena are or course, quantitative.\n\nEven when there are two parallel series of phenomena the one\nquantitative and the other qualitative--like the rate of air-vibration\nand the pitch of sound, or the rate of ether-vibration and the\ncolour-series of the spectrum--the method of Variations is not\napplicable. For (1) two such series cannot be said to vary together,\nsince the qualitative variations are heterogeneous: 512: 576 is a\ndefinite ratio; but the corresponding notes, C, D, in the treble clef,\npresent only a difference. Hence (2) the correspondence of each note\nwith each number is a distinct fact. Each octave even is a distinct\nfact; there is a difference between C 64 and C 128 that could never have\nbeen anticipated without the appropriate experience. There is,\ntherefore, no such law of these parallel series as there is for\ntemperature and change of volume (say) in mercury. Similar remarks apply\nto the physical and sensitive light-series.\n\nWe may illustrate the two cases of the method thus (putting a dash\nagainst any letter, A' or _p_', to signify an increase or decrease of\nthe phenomenon the letter stands for): Agreement in Variations (other\nchanges being admissible)--\n\n A B C A' D E A'' F G\n _p q r_ _p' s t_ _p'' u v_\n\nHere the accompanying phenomena (_B C q r, D E s t, F G u v_) change\nfrom time to time, and the one thing in which the instances agree\nthroughout is that any increase of A (A' or A'') is followed or\naccompanied by an increase of _p (p' or p'')_: whence it is argued that\nA is the cause of _p_, according to Prop. III. (a) (ch. xv. \u00a7 7). Still,\nit is supposable that, in the second instance, D or E may be the cause\nof the increment of _p_; and that, in the third instance, F or G may be\nits cause: though the probability of such vicarious causation decreases\nrapidly with the increase of instances in which A and _p_ vary together.\nAnd, since an actual investigation of this type must rely on\nobservation, it is further possible that some undiscovered cause, X, is\nthe real determinant of both A and _p_ and of their concomitant\nvariations.\n\nProfessor Ferri, in his _Criminal Sociology_, observes: \"I have shown\nthat in France there is a manifest correspondence of increase and\ndecrease between the number of homicides, assaults and malicious\nwounding, and the more or less abundant vintage, especially in the years\nof extraordinary variations, whether of failure of the vintage (1853-5,\n1859, 1867, 1873, 1878-80), attended by a remarkable diminution of crime\n(assaults and wounding), or of abundant vintages (1850, 1856-8, 1862-3,\n1865, 1868, 1874-5), attended by an increase of crime\" (p. 117, Eng.\ntrans.). And earlier he had remarked that such crimes also \"in their\noscillations from month to month display a characteristic increase\nduring the vintage periods, from June to December, notwithstanding the\nconstant diminution of other offences\" (p. 77). This is necessarily an\nappeal to the canon of Concomitant Variations, because France is never\nwithout her annual vintage, nor yet without her annual statistics of\ncrime. Still, it is an argument whose cogency is only that of Agreement,\nshowing that probably the abuse of the vintage is a cause of crimes of\nviolence, but leaving open the supposition, that some other circumstance\nor circumstances, arising or varying from year to year, may determine\nthe increase or decrease of crime; or that there is some unconsidered\nagent which affects both the vintage and crimes of violence. French\nsunshine, it might be urged, whilst it matures the generous grape, also\nexcites a morbid fermentation in the human mind.\n\nDifference in Variations may be symbolically represented thus (no other\nchange having concurred):\n\n A B A' B A'' B\n _p q_, _p' q_, _p'' q_.\n\nHere the accompanying phenomena are always the same B/q; and the only\npoint in which the successive instances differ is in the increments of A\n(A', A'') followed by corresponding increments of _p_ (_p', p''_): hence\nthe increment of A is the cause of the increment of _p_.\n\nFor examples of the application of this method, the reader should refer\nto some work of exact science. He will find in Deschanel's _Natural\nPhilosophy_, c. 32, an account of some experiments by which the\nconnection between heat and mechanical work has been established. It is\nthere shown that \"whenever work is performed by the agency of heat\" [as\nin driving an engine], \"an amount of heat disappears equivalent to the\nwork performed; and whenever mechanical work is spent in generating\nheat\" [as in rubbing two sticks together], \"the heat generated is\nequivalent to the work thus spent.\" And an experiment of Joule's is\ndescribed, which consisted in fixing a rod with paddles in a vessel of\nwater, and making it revolve and agitate the water by means of a string\nwound round the rod, passed over a pulley and attached to a weight that\nwas allowed to fall. The descent of the weight was measured by a\ngraduated rule, and the rise of the water's temperature by a\nthermometer. \"It was found that the heat communicated to the water by\nthe agitation amounted to one pound-degree Fahrenheit for every 772\nfoot-pounds of work\" expended by the falling weight. As no other\nmaterial change seems to take place during such an experiment, it shows\nthat the progressive expenditure of mechanical energy is the cause of\nthe progressive heating of the water.\n\nThe thermometer itself illustrates this method. It has been found that\nthe application of heat to mercury expands it according to a law; and\nhence the volume of the mercury, measured by a graduated index, is used\nto indicate the temperature of the air, water, animal body, etc., in\nwhich the thermometer is immersed, or with which it is brought into\ncontact. In such cases, if no other change has taken place, the heat of\nthe air, water, or body is the cause of the rise of the mercury in its\ntube. If some other substance (say spirit) be substituted for mercury in\nconstructing a thermometer, it serves the same purpose, provided the\nindex be graduated according to the law of the expansion of that\nsubstance by heat, as experimentally determined.\n\nInstances of phenomena that do not vary together indicate the exclusion\nof a supposed cause (by Prop. III (c)). The stature of the human race\nhas been supposed to depend on temperature; but there is no\ncorrespondence. The \"not varying together,\" however, must not be\nconfused with \"varying inversely,\" which when regular indicates a true\nconcomitance. It is often a matter of convenience whether we regard\nconcomitant phenomena as varying directly or inversely. It is usual to\nsay--'the greater the friction the less the speed'; but it is really\nmore intelligible to say--'the greater the friction the more rapidly\nmolar is converted into molecular motion.'\n\nThe Graphic Method exhibits Concomitant Variations to the eye, and is\nextensively used in physical and statistical inquiries. Along a\nhorizontal line (the abscissa) is measured one of the conditions (or\nagents) with which the inquiry is concerned, called the Variable; and\nalong perpendiculars (ordinates) is measured some phenomenon to be\ncompared with it, called the Variant.\n\nThus, the expansion of a liquid by heat may be represented by measuring\ndegrees of temperature along the horizontal, and the expansion of a\ncolumn of the liquids in units of length along the perpendicular.\n\n[Illustration: FIG. 9.]\n\nIn the next diagram (Fig. 10), reduced from one given by Mr. C.H. Denyer\nin an article on the Price of Tea (_Economic Journal_, No. 9), the\ncondition measured horizontally is Time; and, vertically, three variants\nare measured simultaneously, so that their relations to one another from\ntime to time may be seen at a glance. From this it is evident that, as\nthe duty on tea falls, the price of tea falls, whilst the consumption of\ntea rises; and, in spite of some irregularity of correspondence in the\ncourses of the three phenomena, their general causal connection can\nhardly be mistaken. However, the causal connection may also be inferred\nby general reasoning; the statistical Induction can be confirmed by a\nDeduction; thus illustrating the combined method of proof to be\ndiscussed in the next chapter. Without such confirmation the proof by\nConcomitant Variations would not be complete; because, from the\ncomplexity of the circumstances, social statistics can only yield\nevidence according to the method of Agreement in Variations. For,\nbesides the agents that are measured, there may always be some other\nimportant influence at work. During the last fifty years, for example,\ncrime has decreased whilst education has increased: true, but at the\nsame time wages have risen and many other things have happened.\n\n[Illustration: FIG. 10.]\n\nIt will be noticed that in the diagram the three lines, especially those\nof Price and Consumption (which may be considered _natural_ resultants,\nin contrast with the arbitrary fixation of a Tax), do not depart widely\nfrom regular curves; and accordingly, assuming the causes at work to\nvary continuously during the intervals between points of measurement,\ncurves may be substituted. In fact, a curve often represents the course\nof a phenomenon more truthfully than can be done by a line that zigzags\nalong the exact measurements; because it is less influenced by temporary\nand extraordinary causes that may obscure the operation of those that\nare being investigated. On the other hand, the abrupt deviations of a\npunctilious zigzag may have their own logical value, as will appear in\nthe next section.\n\nIn working with the Method of Variations one must allow for the\noccurrence in a series of 'critical points,' at which sudden and\nsometimes heterogeneous changes may take place. Every substance exists\nat different temperatures in three states, gaseous, liquid, solid; and\nwhen the change takes place, from one state to another, the series of\nvariations is broken. Water, e.g., follows the general law that\ncooling is accompanied by decrease of volume between 212\u00b0 and 39\u00b0 F.:\nbut above 212\u00b0, undergoes a sudden expansion in becoming a gas; and\nbelow 39\u00b0 begins to expand, until at 32\u00b0 the expansion is considerable\non its becoming solid. This illustrates a common experience that\nconcomitant variations are most regular in the 'median range,' and are\napt to become irregular at the extremities of the series, where new\nconditions begin to operate.\n\nThe Canon of Variations, again, deals not with sudden irruptions of a\ncause, force or agent, but with some increase or decrease of an agent\nalready present, and a corresponding increase or decrease of some other\nphenomenon--say an increase of tax and a rise of price. But there are\ncases in which the energy of a cause is not immediately discharged and\ndissipated. Whilst a tax of 6_d._ per lb. on tea raises the price per\nlb. by about 6_d._, however long it lasts, the continuous application of\nfriction to a body may gradually raise its temperature to the point of\ncombustion; because heat is received faster than it is radiated, and\ntherefore accumulates. Such cases are treated by Mill under the title of\n'progressive effects' (_Logic_: B. III., c. 15): he gives as an example\nof it the acceleration of falling bodies. The storage of effects is a\nfact of the utmost importance in all departments of nature, and is\nespecially interesting in Biology and Sociology, where it is met with as\nheredity, experience, tradition. Evolution of species of plants and\nanimals would (so far as we know) be impossible, if the changes (however\ncaused) that adapt some individuals better than others to the conditions\nof life were not inherited by, and accumulated in, their posterity. The\neyes in the peacock's tail are supposed to have reached their present\nperfection gradually, through various stages that may be illustrated by\nthe ocelli in the wings of the Argus pheasant and other genera of\n_Phasianid\u00e6_. Similarly the progress of societies would be impossible\nwithout tradition, whereby the improvements made in any generation may\nbe passed on to the next, and the experience of mankind may be gradually\naccumulated in various forms of culture. The earliest remains of culture\nare flint implements and weapons; in which we can trace the effect of\ntradition in the lives of our remote forefathers, as they slowly through\nthousands of years learnt to improve the chipping of flints, until the\nfirst rudely shaped lumps gave place to works of unmistakable design,\nand these to the beautiful weapons contemporary with the Bronze Age.\n\nThe Method of Gradations, the arranging of any phenomena to be studied\nin series, according to the degree in which some character is exhibited,\nis, perhaps, the most definite device in the Art of Discovery. (Bain:\n_Induction_, c. 6, and App. II.) If the causes are unknown it is likely\nto suggest hypotheses: and if the causes are partly known, variation in\nthe character of the series is likely to indicate a corresponding\nvariation of the conditions.\n\n\n\u00a7 5. THE CANON OF RESIDUES.\n\n_Subduct from any phenomenon such part as previous inductions have shown\nto be the effect of certain antecedents, and the residue of the\nphenomenon is the effect of the remaining antecedents_.\n\nThe phenomenon is here assumed to be an effect: a similar Canon may be\nframed for residuary causes.\n\nThis also is not a fresh method, but a special case of the method of\nDifference. For if we suppose the phenomenon to be _p q r_, and the\nantecedent to be A B C, and that we already know B and C to have (either\nseverally or together) the consequents _q r_, in which their efficacy is\nexhausted; we may regard\n\n B C\n_q r_\n\nas an instance of the absence of _p_ obtained deductively from the whole\nphenomenon\n\n A B C\n_p q r_\n\nby our knowledge of the laws of B and C; so that\n\n A B C\n_p q r_\n\nis an instance of the presence of _p_, differing otherwise from\n\n B C\n_q r_\n\nin nothing except that A is also present. By the Canon of Difference,\ntherefore A is the cause of _p_. Or, again, when phenomena thus treated\nare strictly quantitative, the method may be based on Prop. III. (b),\nch. xv. \u00a7 7.\n\nOf course, if A can be obtained apart from B C and directly experimented\nwith so as to produce _p_, so much the better; and this may often be\ndone; but the special value of the method of Residues appears, when some\ncomplex phenomenon has been for the most part accounted for by known\ncauses, whilst there remains some excess, or shortcoming, or deviation\nfrom the result which those causes alone would lead us to expect, and\nthis residuary fact has to be explained in relation to the whole. Here\nthe negative instance is constituted by deduction, showing what would\nhappen but for the interference of some unknown cause which is to be\ninvestigated; and this prominence of the deductive process has led some\nwriters to class the method as deductive. But we have seen that all the\nCanons involve deduction; and, considering how much in every experiment\nis assumed as already known (what circumstances are 'material,' and when\nconditions may be called 'the same'), the wonder is that no one has\ninsisted upon regarding every method as concerned with residues. In\nfact, as scientific explanation progresses, the phenomena that may be\nconsidered as residuary become more numerous and the importance of this\nmethod increases.\n\nExamples: The recorded dates of ancient eclipses having been found to\ndiffer from those assigned by calculation, it appears that the average\nlength of a day has in the meanwhile increased. This is a residuary\nphenomenon not accounted for by the causes formerly recognised as\ndetermining the rotation of the earth on its axis; and it may be\nexplained by the consideration that the friction of the tides reduces\nthe rate of the earth's rotation, and thereby lengthens the day.\nAstronomy abounds in examples of the method of Residues, of which the\ndiscovery of Neptune is the most famous.\n\nCapillarity seems to be a striking exception to the principle that water\n(or any liquid) 'finds its level,' that being the condition of\nequilibrium; yet capillarity proves to be only a refined case of\nequilibrium when account is taken of the forces of adhesion exerted by\ndifferent kinds of bodies in contact.\n\n\"Many of the new elements of Chemistry,\" says Herschel, \"have been\ndetected in the investigation of residual phenomena.\" Thus, Lord\nRayleigh and Sir W. Ramsay found that nitrogen from the atmosphere was\nslightly heavier than nitrogen got from chemical sources; and, seeking\nthe cause of this difference, discovered argon.\n\nThe Economist shows that when a country imports goods the chief means of\npaying for them is to export other goods. If this were all, imports and\nexports would be of equal value: yet the United Kingdom imports about\n\u00a3400,000,000 annually, and exports about \u00a3300,000,000. Here, then, is a\nresiduary phenomenon of \u00a3100,000,000 to be accounted for. But foreign\ncountries owe us about \u00a350,000,000 for the use of shipping, and\n\u00a370,000,000 as interest on the capital we have lent them, and\n\u00a315,000,000 in commissions upon business transacted for them. These sums\nadded together amount to \u00a3135,000,000; and that is \u00a335,000,000 too much.\nThus another residuary phenomenon emerges; for whilst foreigners seem to\nowe us \u00a3435,000,000 they only send us \u00a3400,000,000 of imports. These\n\u00a335,000,000 are accounted for by the annual investment of our capital\nabroad, in return for which no immediate payment is due; and, these\nbeing omitted, exports and imports balance. Since this was written the\nfigures of our foreign trade have greatly risen; but the character of\nthe explanation remains the same.\n\nWhen, in pursuing the method of Variations, the phenomena compared do\nnot always correspond in their fluctuations, the irregular movements of\nthat phenomenon which we regard as the effect may often be explained by\ntreating them as residuary phenomena, and then seeking for exceptional\ncauses, whose temporary interference has obscured the influence of the\ngeneral cause. Thus, returning to the diagram of the Price of Tea in \u00a7\n4, it is clear that generally the price falls as the duty falls; but in\nMr. Denyer's more minutely wrought diagram, from which this is reduced,\nit may be seen that in 1840 the price of tea rose from 3_s._ 9_d._ to\n4_s._ 9_d._ without any increase of duty. This, however, is readily\nexplained by the Chinese War of that year, which checked the supply.\nAgain, from 1869 to 1889 the duty was constant, whilst the price of tea\nfell as much as 8_d._ per lb.; but this residuary phenomenon is\nexplained by the prodigiously increased production of tea during that\nperiod in India and Ceylon.\n\nThe above examples of the method of Residues are all quantitative; but\nthe method is often employed where exact estimates are unobtainable.\nThus Darwin, having found certain modifications of animals in form,\ncoloration and habits, that were not clearly derivable from their\nstruggle for existence in relation to other species or to external\nconditions, suggested that they were due to Sexual Selection.\n\nThe 'vestiges' and 'survivals' so common in Biology and Sociology are\nresiduary phenomena. It is a general inference from the doctrine of\nNatural Selection that every organ of a plant, animal, or society is in\nsome way useful to it. There occur, however, organs that have at present\nno assignable utility, are at least wasteful, and sometimes even\ninjurious. And the explanation is that formerly they were useful; but\nthat, their uses having lapsed, they are now retained by the force of\nheredity or tradition. Either they are not injurious enough to be\neliminated by natural selection; or they are correlated with other\norgans, whose utility outweighs their disutility.\n\n\n\n\nCHAPTER XVII\n\nCOMBINATION OF INDUCTION WITH DEDUCTION\n\n\n\u00a7 1. We have now reviewed Mill's five Canons of Inductive Proof. At\nbottom, as he observes, there are only two, namely, Agreement and\nDifference: since the Double Method, Variations and Residues are only\nspecial forms of the other two. Indeed, in their function of _proof_,\nthey are all reducible to one, namely, Difference; for the cogency of\nthe method of Agreement (as distinguished from a simple enumeration of\ninstances agreeing in the coincidence of a supposed cause and its\neffect), depends upon the omission, in one instance after another, of\nall other circumstances; which omission is a point of difference.\n\nThe Canons are an analysis of the conditions of proving directly (where\npossible), by means of observation or experiment, any proposition that\npredicates causation. But if we say 'by means of observation or\nexperiment,' it is not to be understood that these are the only means\nand that nothing else is involved; for it has been shown that the Law of\nCausation is itself an indispensable foundation of the evidence. In fact\nInductive Logic may be considered as having a purely formal character.\nIt consists (1) in a statement of the Law of Cause and Effect; (2) in\ncertain immediate inferences from this Law, expanded into the Canons;\n(3) in the syllogistic application of the Canons to special predications\nof causation by means of minor premises, showing that certain instances\nsatisfy the Canons.\n\nAt the risk of some pedantry, we may exhibit the process as follows\n(_cf._ Prof. Ray's _Logic_: Appendix D):\n\nWhatever relation of events has certain marks is a case of causation;\n\n The relation A: _p_ has some or all of these marks (as shown\n by observation and by the conformity of instances to such or\n such a Canon):\n\nTherefore, the relation A: _p_ is a case of causation. Now, the\nparenthesis, \"as shown by the conformity, etc.,\" is an adscititious\nmember of an Epicheirema, which may be stated, as a Prosyllogism, thus:\n\n If an instance, etc. (Canon of Difference);\n\n The instances A B C B C are of the kind required:\n _p q r' q r_\n\n Therefore, A, present where _p_ occurs and absent where it\n does not occur, is an indispensable antecedent of _p_.\n\nSuch is the bare Logic of Induction: so that, strictly speaking,\nobservation or experiment is no part of the logic, but a means of\napplying the logic to actual, that is, not merely symbolical,\npropositions. The Formal Logic of Induction is essentially deductive;\nand it has been much questioned whether any transition from the formal\nto the material conditions of proof is possible. As long as we are\ncontent to illustrate the Canons with symbols, such as A and _p_, all\ngoes well; but can we in any actual investigation show that the relevant\nfacts or 'instances' correspond with those symbols?\n\nIn the first place, as Dr. Venn shows, natural phenomena want the\ndistinctness and capability of isolation that belong to symbols.\nSecondly, the observing whether instances conform to a Canon, must\nalways be subject at last to the limits of our faculties. How can we\nascertain exact equality, immediate sequence? The Canon of Difference,\nin its experimental application, is usually considered the most cogent\nsort of proof: yet when can the two sequent instances, before and after\nthe introduction of a certain agent, be said to differ in nothing else?\nAre not earth and stars always changing position; is not every molecule\nin the room and apparatus always oscillating? It is true that our senses\nare now aided by elaborate instruments; but the construction of these\ndepends on scientific theories, which again depend on experiments.\n\nIt is right to touch upon this well-known sceptical topic; but to insist\nmuch upon it is not a sign of good sense. The works of Herschel,\nWhewell, and Jevons should be consulted for the various methods of\ncorrecting observations, by repeating them, averaging them, verifying\none experimental process by another, always refining the methods of\nexact measurement, multiplying the opportunities of error (that if any\nexist it may at last show itself), and by other devices of what may be\ncalled Material Logic or Methodology. But only direct experience and\npersonal manipulation of scientific processes, can give a just sense of\ntheir effectiveness; and to stand by, suggesting academic doubts, is\neasier and more amusing.\n\n\u00a7 2. Still, it is not so much in laws based upon direct observation or\nexperiment, that the material validity of scientific reasoning appears,\nas in the cumulative evidence that arises from the co-ordination of laws\nwithin each science, and the growing harmony and coherence of all\nsciences. This requires a more elaborate combination of deduction with\nobservation and experiment. During the last three hundred years many\ndepartments of science have been reduced under principles of the\ngreatest generality, such as the Conservation of Energy, the Law of\nGravitation, the Undulatory theory of Light, the Law of combining\nEquivalents, and the Theory of Natural Selection; connecting and\nexplaining the less general laws, which, again, are said to connect and\nexplain the facts. Meanwhile, those sciences that were the first to make\nprogress have helped to develop others which, like Biology and\nSociology, present greater difficulties; and it becomes more and more\napparent that the distinctions drawn among sciences are entirely for the\nconvenience of study, and that all sciences tend to merge in one\nuniversal Science of Nature. Now, this process of the 'unification of\nknowledge' is almost another name for deduction; but at the same time it\ndepends for its reality and solidity upon a constant reference to\nobservation and experiment. Only a very inadequate notion of it can be\ngiven in the ensuing chapters.\n\nWe saw in chap. xiv. \u00a7 6, that when two or more agents or forces combine\nto produce a phenomenon, their effects are intermixed in it, and this in\none of two ways according to their nature. In chemical action and in\nvegetable and animal life, the causal agents concerned are blended in\ntheir results in such a way that most of the qualities which they\nexhibited severally are lost, whilst new qualities appear instead. Thus\nchlorine (a greenish-yellow gas) and sodium (a metal) unite to form\ncommon salt NaCl; which is quite unlike either of them: a man eats\nbread, and it becomes muscle, nerve and bone. In such cases we cannot\ntrace the qualities of the causal agents in the qualities of the\neffects; given such causes, we can prove experimentally, according to\nthe canons of induction, that they have such effects; but we may not be\nable in any new case to calculate what the effects will be.\n\nOn the other hand, in Astronomy and Physics, the causes treated of are\nmechanical; at least, it is the aim of Physics to attain to a mechanical\nconception of phenomena; so that, in every new combination of forces,\nthe intermixed effect, or resultant, may be calculated beforehand;\nprovided that the forces concerned admit of being quantitatively\nestimated, and that the conditions of their combination are not so\ncomplex as to baffle the powers of mathematicians. In such cases, when\ndirect observation or experiment is insufficient to resolve an effect\ninto the laws of its conditions, the general method is to calculate\nwhat may be expected from a combination of its conditions, as either\nknown or hypothetically assumed, and to compare this anticipation with\nthe actual phenomenon.\n\n\u00a7 3. This is what Mill calls the Direct Deductive Method; or, the\nPhysical Method, because it is so much relied on in treating of Light,\nHeat, Sound, etc.; it is also the method of Astronomy and much used in\nEconomics: Deduction leads the way, and its results are tested\ninductively by experiments or observations. Given any complex mechanical\nphenomenon, the inquirer considers--(1) what laws already ascertained\nseem likely to apply to it (in default of known laws, hypotheses are\nsubstituted: _cf._ chap. xviii.); he then--(2) computes the effect that\nwill follow from these laws in circumstances similar to the case before\nhim; and (3) he verifies his conclusion by comparing it with the actual\nphenomenon.\n\nA simple example of this method is the explanation of the rise of water\nin the 'common pump.' We know three laws applicable to this case: (a)\nthat the atmosphere weighs upon the water outside the pump with a\npressure of 15 lb. to the square inch; (b) that a liquid (and therefore\nthe water) transmits pressure equally in all directions (upwards as well\nas downwards and sideways); and (c) that pressure upon a body in any\ndirection, if not counteracted by an opposite pressure, produces motion.\nHence, when the rise of the piston of the pump removes the pressure upon\nthe water within the cylinder, tending to produce a vacuum there, this\nwater is pushed up by the pressure of the air upon the water outside the\ncylinder, and follows the rising piston, until the column of water\ninside the cylinder exerts a pressure equal to that of the atmosphere\nupon an equal area. So much for the computation; does it correspond with\nthe fact? It is found that at the sea level water can be pumped to the\nheight of 33 ft; and that such a column of water has a pressure of 15\nlb. to the square inch. We may show further that, at the sea level,\nspirits of wine may be pumped higher according to its less specific\ngravity; and that if we attempt to pump water at successive altitudes\nabove the sea level, we can only raise it to less and less heights,\ncorresponding with the lessened atmospheric pressure at those altitudes,\nwhere the column of air producing the pressure is shorter. Finally, if\nwe try to work a pump, having first produced a vacuum over the water\noutside the cylinder, we shall find that the water inside will not rise\nat all; the piston can be raised, but the water does not follow it. The\nverification thus shows that the computed effect corresponds with the\nphenomenon to be explained; that the result does not depend upon the\nnature of water only, but is true (allowing for differences of specific\ngravity) of other liquids; that if the pressure of the outside air is\ndiminished, the height of pumping is so too (canon of Variations); and\nthat if that pressure is entirely removed, pumping becomes impossible\n(canon of Difference).\n\nAny text-book of Astronomy or Physics furnishes numerous illustrations\nof the deductive method. Take, for example, the first chapter of\nDeschanel's _Optics_, where are given three methods of determining the\nvelocity of Light. This was first deduced from observation of Jupiter's\nsatellites. The one nearest the planet passes behind it, or into its\nshadow, and is eclipsed, at intervals of about 42-1/2 hours. But it can\nbe shown that, when Jupiter and the Earth are nearest together on the\nsame side of the Sun, an eclipse of this satellite is visible from the\nearth 16 min. 26.6 sec. earlier than when Jupiter and the earth are\nfurthest apart on opposite sides of the Sun: 16 min. 26.6 sec, then, is\nthe time in which light traverses the diameter of the Earth's orbit.\nTherefore, supposing the Earth's distance from the Sun to be 92 millions\nof miles, light travels about 186,000 miles a second. Another deduction,\nagreeing with this, starts from the fact of aberration, or the\ndisplacement of the apparent from the actual position of the stars in\nthe direction of the earth's motion. Aberration depends partly on the\nvelocity of light, partly on the velocity of the Earth; and the latter\nbeing known, the former can be computed. Now, these two deductive\narguments, verifying each other, have also been verified experimentally.\nFoucault's experiment to measure the velocity of light is too elaborate\nto be described here: a full account of it will be found in the treatise\nabove cited, \u00a7 687.\n\nWhen the phenomena to be explained are of such a character, so vast in\nextent, power or duration, that it is impossible, in the actual\ncircumstances of the case, to frame experiments in order to verify a\ndeductive explanation, it may still be possible to reproduce a similar\nphenomenon upon a smaller scale. Thus Monge's explanation of mirage by\nthe great heat of the desert sand, which makes the lowest stratum of air\nless dense than those above it, so that rays of light from distant\nobjects are refracted in descending, until they are actually turned\nupwards again to the eye of the beholders, giving him inverted images of\nthe objects as if they were reflected in water, is manifestly incapable\nof being verified by experiment in the natural conditions of the\nphenomenon. But by heating the bottom of \"a sheet-iron box, with its\nends cut away,\" the rarefied air at the bottom of the box may sometimes\nbe made to yield reflections; and this shows at least that the supposed\ncause is a possible one (Deschanel, _Optics,_ \u00a7 726). Similarly as to\nthe vastest of all phenomena, the evolution of the stellar system, and\nof the solar system as part of it, from an immense cloudlike volume of\nmatter: H. Spencer, in his Essay on _The Nebular Hypothesis_, says,\namidst a great array of deductive arguments from mechanical principles,\nthat \"this _a priori_ reasoning harmonises with the results of\nexperiment. Dr. Plateau has shown that when a mass of fluid is, as far\nas may be, protected from the action of external forces, it will, if\nmade to rotate with adequate velocity, form detached rings; and that\nthese rings will break up into spheroids, which turn on their axes in\nthe same direction with the central mass.\" The theory of the evolution\nof species of plants and animals by Natural Selection, again, though, of\ncourse, it cannot be verified by direct experiment (since experiment\nimplies artificial arrangement), and the process is too slow for\nobservation, is, nevertheless, to some extent confirmed by the practice\nof gardeners and breeders of animals: since, by taking advantage of\naccidental variations of form and colour in the plants or animals under\ntheir care, and relying on the inheritability of these variations they\nobtain extensive modifications of the original stocks, and adapt them to\nthe various purposes for which flowers and cereals, poultry, dogs and\ncattle are domesticated. This shows, at least, that living forms are\nplastic, and extensively modifiable in a comparatively short time.\n\n\u00a7 4. Suppose, however, that, in verifying a deductive argument, the\neffect as computed from the laws of the causes assigned, does not\ncorrespond with the facts observed: there must then be an error\nsomewhere. If the fact has been accurately observed, the error must lie\neither in the process of deduction and computation, or else in the\npremises. As to the process of deduction, it may be very simple and\neasily revised, as in the above explanation of the common pump; or it\nmay be very involved and comprise long trains of mathematical\ncalculation. If, however, on re-examining the computations, we find them\ncorrect, it remains to look for some mistake in the premises.\n\n(1) We may not have accurately ascertained the laws, or the modes of\noperation, or the amounts of the forces present. Thus, the rate at which\nbodies fall was formerly believed to vary in proportion to their\nrelative weights; and any estimate based upon this belief cannot agree\nwith the facts. Again, the corpuscular theory of light, namely, that\nthe physical cause of light is a stream of fine particles projected in\nstraight lines from the luminous object, though it seemed adequate to\nthe explanation of many optical phenomena, could not be made to agree\nwith the facts of interference and double refraction.\n\n(2) The circumstances in which the agents are combined may not have been\ncorrectly conceived. When Newton began to inquire whether the attraction\nof the earth determined the orbit of the moon, he was at first\ndisappointed. \"According to Newton's calculations, made at this time,\"\nsays Whewell, \"the moon, by her motion in her orbit, was deflected from\nthe tangent every minute through a space of thirteen feet. But by\nnoticing the space which bodies would fall in one minute at the earth's\nsurface, and supposing this to be diminished in the ratio of the inverse\nsquare, it appeared that gravity would, at the moon's orbit, draw a body\nthrough more than fifteen feet.\" In view of this discrepancy he gave up\nthe inquiry for sixteen years, until in 1682, having obtained better\ndata, he successfully renewed it. \"He had been mistaken in the magnitude\nof the earth, and consequently in the distance of the moon, which is\ndetermined by measurements of which the earth's radius is the base.\" It\nwas not, therefore, a mistake as to the law or as to the nature of the\nforces concerned (namely, the law of the inverse square and the identity\nof celestial with terrestrial gravity), but as to the circumstances in\nwhich the agents (earth and moon) were combined, that prevented his\ncalculations being verified. (_Hist. Ind. Sc._: VII. ii. 3.)\n\n(3) One or more of the agents affecting the result may have been\noverlooked and omitted from the estimate. Thus, an attempt to explain\nthe tides by taking account only of the earth and the moon, will not\nentirely agree with the facts, since the sun also influences the tides.\nThis illustration, however, shows that when the conclusion of a\ndeductive explanation does not entirely agree with the facts, it is not\nalways to be inferred that the reasoning is, properly speaking, wrong;\nit may be right as far as it goes, and merely inadequate. Hence (a) in\nsuch cases an opportunity occurs of applying the Method of Residues, by\ndiscovering the agent that must be allowed for in order to complete the\nexplanation. And (b) the investigation of a phenomenon is often\ndesignedly begun upon an imperfect basis for the sake of simplicity; the\nresult being regarded as a first approximation, to be afterwards\ncorrected by including, one by one, the remaining agents or\ncircumstances affecting the phenomenon, until the theory is complete;\nthat is, until its agreement with the facts is satisfactory.\n\n(4) We may have included among the data of our reasonings agents or\ncircumstances that do not exist or do not affect the phenomenon in\nquestion. In the early days of science purely fanciful powers were much\nrelied upon: such as the solid spheres that carried the planets and\nstars; the influence of the planets upon human destiny; the tendency of\neverything to seek \"its own place,\" so that fire rises to heaven, and\nsolids fall to the earth; the \"plastic virtue\" of the soil, which was\nonce thought to have produced fossils. When, however, such conceptions\nhindered the progress of explanation, it was not so much by vitiating\nthe deductive method as by putting men off from exact inquiries. More to\nour present purpose were the supposed cataclysms, or extraordinary\nconvulsions of the earth, a belief in which long hindered the progress\nof Geology. Again, in Biology, Psychology, and Sociology many\nexplanations have depended upon the doctrine that any improvement of\nstructure or faculty acquired by an individual may be inherited by his\ndescendants: as that, if an animal learns to climb trees, his offspring\nhave a greater aptitude for that mode of life; that if a man tries to be\ngood, his children find it easier to be virtuous; that if the\ninhabitants of a district carry on cloth-work, it becomes easier for\neach successive generation to acquire dexterity in that art. But now the\ninheritability of powers acquired by the individual through his own\nefforts, is disputed; and, if the denial be made good, all such\nexplanations as the above must be revised.\n\nIf, then, the premises of a deductive argument be vitiated in any of\nthese four ways, its conclusion will fail to agree with the results of\nobservation and experiment, unless, of course, one kind of error happen\nto be cancelled by another that is 'equal and opposite.' We now come to\na variation of the method of combining Induction with Deduction, so\nimportant as to require separate treatment.\n\n\u00a7 5. The Inverse or Historical Method has of late years become\nremarkably fruitful. When the forces determining a phenomenon are too\nnumerous, or too indefinite, to be combined in a direct deduction, we\nmay begin by collecting an empirical law of the phenomenon (as that 'the\ndemocracies of City-States are arbitrary and fickle'), and then\nendeavour to show by deductions from \"the nature of the case,\" that is,\nfrom a consideration of the circumstances and forces known to be\noperative (of which, in the above instance, the most important is\nsympathetic contagion), that such a law was to be expected. Deduction is\nthus called in to verify a previous induction; whereas in the 'Physical\nMethod' a deduction was verified by comparing it with an induction or an\nexperiment; hence the method now to be discussed has been named the\nInverse Deductive Method.\n\nBut although it is true that, in such inquiries as we are now dealing\nwith, induction generally takes the lead; yet I cannot think that the\nmere order in which the two logical processes occur is the essential\ndistinction between the two ways of combining them. For, in the first\nplace, in investigations of any complexity both induction and deduction\nrecur again and again in whatever order may be most convenient; and, in\nthe second place, the so-called 'inverse order' is sometimes resorted to\nin Astronomy and Physics. For example, Kepler's Laws were first\ncollected empirically from observations of the planetary motions, and\nafterwards deduced by Newton from the Law of Gravitation; this, then,\nwas the Inverse Method; but the result is something very different from\nany that can be obtained by the Historical Method. The essential\ndifference between the Physical and Historical Methods is that, in the\nformer, whether Direct or Inverse, the deductive process, when complete,\namounts to exact demonstration; whereas, in the latter, the deductions\nmay consist of qualitative reasonings, and the results are indefinite.\nThey establish--(1) a merely probable connection between the phenomena\naccording to an empirical law (say, between City-democracy and fickle\npolitics); (2) connect this with other historical or social\ngeneralisations, by showing that they all alike flow from the same\ncauses, namely, from the nature of races of men under certain social and\ngeographical conditions; and (3) explain why such empirical laws may\nfail, according to the differences that prevail among races of men and\namong the conditions under which they live. Thus, seeing how rapidly\nexcitement is propagated by the chatter, grimacing, and gesticulation of\ntownsmen, it is probable enough that the democracy of a City-state\nshould be fickle (and arbitrary, because irresponsible). A similar\nphenomenon of panic, sympathetic hope and despair, is exhibited by every\nstock-exchange, and is not peculiar to political life. And when\npolitical opinion is not manufactured solely in the reverberating\nfurnace of a city, fickleness ceases to characterise democracy; and, in\nfact, is not found in Switzerland, or the United States, nor in France\nso far as politics, depend upon the peasantry.\n\nThis is called the Historical Method, then, because it is especially\nuseful in explaining the movements of history, and in verifying the\ngeneralisations of political and social science. We must not, however,\nsuppose that its use is confined to such studies. Only a ridiculous\npedantry would allot to each subject its own method and forbid the use\nof any other; as if it were not our capital object to establish truth by\nany means. Wherever the forces determining a phenomenon are too numerous\nor too indefinite to be combined in a deductive demonstration, there the\nHistorical Method is likely to be useful; and this seems often to be the\ncase in Geology and Biology, as well as in the Science of History, or\nSociology, and its various subsidiary studies.\n\nConsider upon what causes historical events depend: the customs,\ncharacter, and opinions of all the people concerned; the organisation of\ntheir government, and the character of their religious institutions; the\ndevelopment of industry among them, of the military art, of fine art,\nliterature and science; their relations, commercial, political and\nsocial, with other nations; the physical conditions of climate and\ngeographical position amidst which they live. Hardly an event of\nimportance occurs in any nation that is not, directly or indirectly,\ninfluenced by every one of these circumstances, and that does not react\nupon them. Now, from the nature of the Canons of direct Induction, a\nsatisfactory employment of them in such a complex and tangled situation\nas history presents, is rarely possible; for they all require the actual\nor virtual isolation of the phenomenon under investigation. They also\nrequire the greatest attainable immediacy of connection between cause\nand effect; whereas the causes of social events may accumulate during\nhundreds of years. In collecting empirical laws from history, therefore,\nonly very rough inductions can be hoped for, and we may have to be\ncontent with simple enumeration. Hence the importance of supporting such\nlaws by deduction from the nature of the case, however faint a\nprobability of the asserted connection is thereby raised; and this even\nif each law is valued merely for its own sake. Still more, if anything\nworth the name of Historical Science is to be constructed, must a mere\ncollection of such empiricisms fail to content us; and the only way to\ngive them a scientific character is to show deductively their common\ndependence upon various combinations of the same causes. Yet even those\nwho profess to employ the Historical Method often omit the deductive\nhalf of it; and of course 'practical politicians' boast of their entire\ncontentment with what they call 'the facts.'\n\nSometimes, however, politicians, venturing upon deductive reasoning,\nhave fallen into the opposite error of omitting to test their results by\nany comparison with the facts: arguing from certain 'Rights of Man,' or\n'Interests of Classes,' or 'Laws of Supply and Demand,' that this or\nthat event will happen, or ought to happen, without troubling themselves\nto observe whether it does happen or ever has happened. This method of\nDeduction without any empirical verification, is called by Mill the\nGeometrical; and, plainly, it can be trustworthy only where there is no\nactual conflict of forces to be considered. In pure mathematical\nreasoning about space, time, and number, provided the premises and the\nreasoning be correct, verification by a comparison with the facts may be\nneedless, because there is no possibility of counteraction. But when we\ndeal with actual causes, no computation of their effects can be relied\nupon without comparing our conclusions with the facts: not even in\nAstronomy and Physics, least of all in Politics.\n\nBurke, then, has well said that \"without the guide and light of sound,\nwell-understood principles all our reasoning in politics, as in\neverything else, would be only a confused jumble of particular facts and\ndetails without the means of drawing any sort of theoretical or\npractical conclusion\"; but that, on the other hand, the statesman, who\ndoes not take account of circumstances, infinite and infinitely\ncombined, \"is not erroneous, but stark mad--he is metaphysically mad\"\n(_On the Petition of the Unitarians_). There is, or ought to be, no\nlogical difference between the evidence required by a statesman and that\nappealed to by a philosopher; and since, as we have seen, the\ncombination of principles with circumstances cannot, in solving problems\nof social science, be made with the demonstrative precision that belongs\nto astronomical and physical investigations, there remains the\nHistorical Method as above described.\n\nExamples of the empirical laws from which this method begins abound in\nhistories, newspapers, and political discussions, and are of all shades\nof truth or half-truth: as that 'History consists in the biographies of\ngreat men'; in other words, that the movements of society are due to\nexceptional personal powers, not to general causes; That at certain\nepochs great men occur in groups; That every Fine Art passes through\nperiods of development, culmination and decline; That Democracies tend\nto change into Despotisms; That the possession of power, whether by\nclasses or despots, corrupts the possessor: That 'the governments most\ndistinguished for sustained vigour and abilities have generally been\naristocracies'; That 'revolutions always begin in hunger'; That\ncivilisation is inimical to individuality; That the civilisation of the\ncountry proceeds from the town; That 'the movement of progressive\nsocieties has hitherto been a movement from _Status_ to _Contract_\n(i.e., from a condition in which the individual's rights and duties\ndepend on his caste, or position in his family as slave, child, or\npatriarch, to a condition in which his rights and duties are largely\ndetermined by the voluntary agreements he enters into)'; and this last\nis treated by H. Spencer as one aspect of the law first stated by Comte,\nthat the progress of societies is from the military to the industrial\nstate.\n\nThe deductive process we may illustrate by Spencer's explanation of the\nco-existence in the military state of those specific characters, the\ninductive proof of which furnished an illustration of the method of\nAgreement (ch. xvi. \u00a7 1). The type of the military State involves the\ngrowth of the warrior class, and the treatment of labourers as existing\nsolely to support the warriors; the complete subordination of all\nindividuals to the will of the despotic soldier-king, their property,\nliberty and life being at the service of the State; the regimentation of\nsociety, not only for military, but also for civil purposes; the\nsuppression of all private associations, etc. Now all these\ncharacteristics arise from their utility for the purpose of war, a\nutility amounting to necessity if war is the State's chief purpose. For\nevery purpose is best served when the whole available force co-operates\ntoward it: other things equal, the bigger the army the better; and to\nincrease it, men must be taken from industry, until only just enough\nremain to feed and equip the soldiers. As this arrangement is not to\neverybody's taste, there must be despotic control; and this control is\nmost effective through regimentation by grades of command. Private\nassociations, of course, cannot live openly in such a State, because\nthey may have wills of their own and are convenient for conspiracy. Thus\nthe induction of characteristics is verified by a deduction of them from\nthe nature of the case.\n\n\u00a7 6. The greater indefiniteness of the Historical compared with the\nPhysical Method, both in its inductions and in its deductions, makes it\neven more difficult to work with. It wants much sagacity and more\nimpartiality; for the demon of Party is too much with us. Our first care\nshould be to make the empirical law as nearly true as possible,\ncollecting as many as we can of the facts which the law is supposed to\ngeneralise, and examining them according to the canons of Induction,\nwith due allowance for the imperfect applicability of those canons to\nsuch complex, unwieldy, and indefinite instances. In the examples of\nsuch laws given above, it is clear that in some cases no pains have been\ntaken to examine the facts. What is the inductive evidence that\nDemocracies change into Despotisms; that revolutions always begin in\nhunger; or that civilisation is inimical to individuality? Even Mill's\noften quoted saying, \"that the governments remarkable in history for\nsustained vigour and ability have generally been aristocracies,\" is\noddly over-stated. For if you turn to the passage (_Rep. Gov._ chap.\nvi.), the next sentence tells you that such governments have always been\naristocracies of public functionaries; and the next sentence but one\nrestricts, apparently, the list of such remarkable governments to\ntwo--Rome and Venice. Whence, then, comes the word \"generally\" into\nMill's law?\n\nAs to deducing our empirical law from a consideration of the nature of\nthe case, it is obvious that we ought--(a) to take account of all the\nimportant conditions; (b) to allow weight to them severally in\nproportion to their importance; and (c) not to include in our estimates\nany condition which we cannot show to be probably present and operative.\nThus the Great-Man-Theory of history must surely be admitted to assign a\nreal condition of national success. The great man organises, directs,\ninspires: is that nothing? On the other hand, to recognise no other\ncondition of national success is the manifest frenzy of a mind in the\nmythopoeic age. We must allow the great man his due weight, and then\ninquire into the general conditions that (a) bring him to birth in one\nnation rather than another, and (b) give him his opportunity.\n\nMill's explanation of the success of the aristocratic governments of\nRome and Venice is, that they were, in fact, bureaucracies; that is to\nsay, their members were trained in the science and art of\nadministration and command. Here, again, we have, no doubt, a real\ncondition; but is it the only one? The popular mind, which little\nrelishes the scaling down of Mill's original law to those two remote\ncases, is persuaded that an aristocracy is the depository of hereditary\nvirtue, especially with reference to government, and would at once\nascribe to this circumstance the greater part of the success of any\naristocratic constitution. Now, if the effects of training are\ninherited, they must, in an hereditary aristocracy, increase the energy\nof the cause assigned by Mill; but, if not, such heredity is a condition\n\"not present or not operative.\" Still, if families are ennobled for\ntheir extraordinary natural powers of administration or command (as\nsometimes happens), it is agreed on all hands that innate qualities are\ninheritable; at least, if care be taken to intermarry with families\nsimilarly distinguished, and if by natural or artificial selection all\nthe failures among the offspring be eliminated. The Spartans had some\ncrude notion of both these precautions; and if such measures had been\nwidely adopted, we might deduce from the doctrine of heredity a\nprobability in favour of Mill's original proposition, and thereby verify\nit in its generality, if it could be collected from the facts.\n\nThe Historical Method may be further illustrated by the course adopted\nin that branch of Social Science which has been found susceptible of the\nmost extensive independent development, namely, Economics. First, by way\nof contrast, I should say that the abstract, or theoretical treatment of\nEconomics follows the Physical Method; because, as Mill explains,\nalthough the phenomena of industry are no doubt influenced, like other\nsocial affairs, by all the other circumstances of Society, government,\nreligion, war, art, etc.; yet, where industry is most developed, as in\nEngland and the United States, certain special conditions affecting it\nare so much the most important that, for the purpose at least of a\nfirst outline of the science, they may conveniently be considered as the\nonly ones. These conditions are: (1) the general disposition of men to\nobtain wealth with as little trouble as possible, and (2) to spend it so\nas to obtain the greatest satisfaction of their various desires; (3) the\nfacts that determine population; and (4) the tendency of extractive\nindustry, when pushed beyond a certain limit without any improvement in\nthe industrial arts, to yield \"diminishing returns.\" From these premises\nit is easy to infer the general laws of prices, of wages and interest\n(which are the prices of labour and of the use of capital), and of rent;\nand it remains to verify these laws by comparing them with the facts in\neach case; and (if they fail to agree with the facts) to amend them,\naccording to the Method of Residues, by taking account of those\ninfluential conditions which were omitted from the first draft of the\ntheory.\n\nWhilst, however, this is usually the procedure of those inquirers who\nhave done most to give Economics its scientific character, to insist\nthat no other plan shall be adopted would be sheer pedantry; and Dr.\nKeynes has shown, in his _Scope and Method of Political Economy_, that\nMill has himself sometimes solved economic problems by the Historical\nMethod. With an analysis of his treatment of Peasant Proprietorship\n(_Political Economy_, B. II., cc. 7 and 8) we may close this section.\nMill first shows inductively, by collecting evidence from Switzerland,\nGermany, Norway, Belgium, and France (countries differing in race,\ngovernment, climate and situation), that peasant proprietors are\nsuperhumanly industrious; intelligent cultivators, and generally\nintelligent men; prudent, temperate, and independent, and that they\nexercise self-control in avoiding improvident marriages. This group of\nempirical generalisations as to the character of peasant proprietors he\nthen deduces from the nature of the case: their industry, he says, is a\nnatural consequence of the fact that, however much they produce, it is\nall their own; they cultivate intelligently, because for generations\nthey have given their whole mind to it; they are generally intelligent\nmen, because the variety of work involved in small farming, requiring\nforesight and calculation, necessarily promotes intelligence; they are\nprudent, because they have something to save, and by saving can improve\ntheir station and perhaps buy more land; they are temperate, because\nintemperance is incompatible with industry and prudence; they are\nindependent, because secure of the necessaries of life, and from having\nproperty to fall back upon; and they avoid improvidence in marriage,\nbecause the extent and fertility of their fields is always plainly\nbefore them, and therefore how many children they can maintain is easily\ncalculated. The worst of them is that they work too hard and deny\nthemselves too much: but, over the greater part of the world, other\npeasantry work too hard; though they can scarcely be said to deny\nthemselves too much; since all their labour for others brings them no\nsurplus to squander upon self-indulgence.\n\n\u00a7 7. The foregoing account of the Historical Method is based upon Mill's\ndiscussions in B. VI. of his _Logic_, especially cc. 6 to 11. Mill\nascribes to Comte the first clear statement of the method; and it is\nhighly scientific, and important in generalising the connections of\nhistorical events. But perhaps the expression, 'Historical Method,' is\nmore frequently applied to the Comparative Method, as used in\ninvestigating the history of institutions or the true sense of legends.\n\n(1) Suppose we are trying to explain the institution of capital\npunishment as it now exists in England. (1) We must try to trace the\nhistory of it back to the earliest times; for _social custom and\ntradition is one line of causation_. At present the punishment of death\nis legally incident only to murder and high treason. But early in the\nlast century malefactors were hung for forgery, sheep-stealing, arson\nand a long list of other offences down to pocket-picking: earlier still\nthe list included witchcraft and heresy. At present hanging is the only\nmode of putting a malefactor to death; but formerly the ways of putting\nto death included also burning, boiling, pressing, beheading, and mixed\nmodes. Before the Restoration, however, the offences punishable with\ndeath were far fewer than they afterwards became; and until the twelfth\ncentury, the penalty of death might be avoided by paying compensation,\nthe wer-geld.\n\n(2) Every change in the history of an institution must be explained by\npointing to _the special causes_ in operation during the time when the\nchange was in progress. Thus the restriction of the death penalty, in\nthe nineteenth century, to so few offences was due partly to the growth\nof humane feelings, partly to the belief that the infliction, or threat,\nof the extreme penalty had failed to enforce the law and had demoralised\nthe administration of Justice. The continual extension of the death\npenalty throughout the eighteenth century may be attributed to a belief\nthat it was the most effectual means of deterring evil-doers when the\nmeans of detecting and apprehending criminals were feeble and\nill-organised. The various old brutal ways of execution were adopted\nsometimes to strike terror, sometimes for vengeance, sometimes from\nhorror of the crime, or even from 'conscientious scruples';--which last\nwere the excuse for preferring the burning of heretics to any sort of\nbloodshed.\n\n(3) The causes of any change in the history of an institution in any\ncountry may not be directly discoverable: they must then be investigated\nby the Comparative Method. Again, the recorded history of a nation, and\nof all its institutions, followed backwards, comes at last to an end:\nthen the antecedent history must also be supplied by the Comparative\nMethod; whose special use is to indicate the existence of facts for\nwhich there is no direct evidence.\n\nThis method rests upon the principle that where the causes are alike the\neffects will be alike, and that similar effects are traceable to similar\ncauses. Every department of study--Astronomy, Chemistry, Zoology,\nSociology--is determined by the fact that the phenomena it investigates\nhave certain common characteristics; and we are apt to infer that any\nprocess observed in some of these phenomena, if depending on those\ncommon characteristics, will be found in others. For example, the\ndecomposition, or radio-activity, of certain elements prepares one to\nbelieve that all elements may exhibit it. Where the properties of an\nobject are known to be closely interdependent, as in the organisation of\nplants, animals and societies, we are especially justified in inferring\nfrom one case to another. The whole animal Kingdom has certain common\ncharacters--the metabolic process, dependence upon oxygen, upon\nvegetable food (ultimately), heredity, etc., and, upon this ground, any\nprocess (say, the differentiation of species by Natural Selection) that\nhas been established for some kinds of animal is readily extended to\nothers. If instead of the whole animal Kingdom we take some district of\nit--Class, Order, Family--our confidence in such inferences increases;\nbecause the common characters are more numerous and the conditions of\nlife are more alike; or, in other words, the common causes are more\nnumerous that initiate and control the development of nearly allied\nanimals. For such reasons a few fragmentary remains of an extinct animal\nenable the pal\u00e6ontologist to reconstruct with some probability an\noutline of its appearance, organisation, food, habitat and habits.\n\nApplied to History, the Comparative Method rests upon an assumption\n(which the known facts of (say) 6,000 years amply justify) that human\nnature, after attaining a recognisable type as _homo sapiens_, is\napproximately uniform in all countries and in all ages, though more\nespecially where states of culture are similar. Men living in society\nare actuated by similar motives and reasons in similar ways; they are\nall dependent upon the supply of food and therefore on the sun and the\nseasons and the weather and upon means of making fire, and so on.\nAccordingly, they entertain similar beliefs, and develop similar\ninstitutions through similar series of changes. Hence, if in one nation\nsome institution has been altered for reasons that we cannot directly\ndiscover, whereas we know the reasons why a similar change was adopted\nelsewhere, we may conjecture with more or less probability, after making\nallowance for differences in other circumstances, that the motives or\ncauses in the former case were similar to those in the latter, or in any\ncases that are better known. Or, again, if in one nation we cannot trace\nan institution beyond a certain point, but can show that elsewhere a\nsimilar institution has had such or such an antecedent history, we may\nventure to reconstruct with more or less probability the earlier history\nof that institution in the nation we are studying.\n\nAmongst the English and Saxon tribes that settled in Britain, death was\nthe penalty for murder, and the criminal was delivered to the\nnext-of-kin of his victim for execution; he might, however, compound for\nhis crime by paying a certain compensation. Studying the history of\nother tribes in various parts of the world, we are able, with much\nprobability, to reconstruct the antecedents of this death-penalty in our\nown prehistoric ages, and to trace it to the blood-feud; that is, to a\ntribal condition in which the next-of-kin of a murdered man was socially\nand religiously bound to avenge him by slaying the murderer or one of\nhis kindred. This duty of revenge is sometimes (and perhaps was at first\neverywhere) regarded as necessary to appease the ghost of the victim;\nsometimes as necessary to compensate the surviving members of his\nfamily. In the latter case, it is open to them to accept compensation in\nmoney or cattle, etc. Whether the kin will be ready to accept\ncompensation must depend upon the value they set upon wealth in\ncomparison with revenge; but for the sake of order and tribal strength,\nit is the interest of the tribe, or its elders, or chieftain, to\nencourage or even to enforce such acceptance. It is also their interest\nto take the questions--whether a crime has been committed, by whom, and\nwhat compensation is due--out of the hands of the injured party, and to\nsubmit them to some sort of court or judicial authority. At first,\nfollowing ancient custom as much as possible, the act of requital, or\nthe choice of accepting compensation, is left to the next-of-kin; but\nwith the growth of central power these things are entrusted to ministers\nof the Government. Then revenge has undergone its full transformation\ninto punishment. Very likely the wrong itself will come to be treated as\nhaving been done not to the kindred of the murdered man, but to the\nState or the King, as in fact a \"breach of the King's peace.\" This\nhappened in our own history.\n\n(4) The Comparative Method assumes that human nature is approximately\nthe same in different countries and ages; but, of course,\n'approximately' is an important word. Although there is often a striking\nand significant resemblance between the beliefs and institutions of\nwidely separated peoples, we expect to draw the most instructive\nparallels between those who are nearly related by descent, or\nneighbourhood, or culture. To shed light upon our own manners, we turn\nfirst to other Teutons, then to Slavonians and Kelts, or other Aryans,\nand so on; and we prefer evidence from Europe to examples from Africa.\n\n(5) As to national culture, that it exhibits certain 'stages' of\ndevelopment is popularly recognised in the distinction drawn between\nsavages, barbarians and civilised folk. But the idea remains rather\nvague; and there is not space here to define it. I refer, therefore, to\nthe classifications of stages of culture given by A. Sutherland,\n(_Origin and Growth of Moral Instinct_, Vol. I, p. 103), and L.T.\nHobhouse (_Morals in Evolution_, c. 2). That in any 'state of Society,'\nits factors--religion, government, science, etc.--are mutually\ndependent, was a leading doctrine with Comte, adopted by Mill. There\nmust be some truth in it; but in some cases we do not understand social\ninfluences sufficiently well to trace the connection of factors; and\nwhilst preferring to look for historical parallels between nations of\nsimilar culture, we find many cases in which barbarous or savage customs\nlinger in a civilised country.\n\n(6) It was another favourite doctrine with Comte, also adopted by\nMill--that the general state of culture is chiefly determined by the\nprevailing intellectual condition of a people, especially by the\naccepted ground of explanation--whether the will of supernatural beings,\nor occult powers, or physical antecedents: the \"law of three stages,\"\nFetichism, Metaphysics, Positivism. And this also is, at least, so far\ntrue, that it is useless to try to interpret the manners and\ninstitutions of any nation until we know its predominant beliefs. Magic\nand animism are beliefs everywhere held by mankind in early stages of\nculture, and they influence every action of life. But that is not all:\nthese beliefs retain their hold upon great multitudes of civilised men\nand affect the thoughts of the most enlightened. Whilst the saying 'that\nhuman nature is the same in all ages' seems to make no allowance for the\nfact that, in some nations, a considerable number of individuals has\nattained to powers of deliberation, self-control, and exact reasoning,\nfar above the barbarous level, it is yet so far true that, even in\ncivilised countries, masses of people, were it not for the example and\ninstruction of those individuals, would fall back upon magic and animism\nand the manners that go with those beliefs. The different degrees of\nenlightenment enjoyed by different classes of the population often\nenable the less educated to preserve a barbarous custom amidst many\ncivilised characteristics of the national life.\n\n\u00a7 8. Historical reasoning must start from, or be verified by,\nobservations. If we are writing the history of ourselves: if of another\ntime or country, we can observe some of the present conditions of the\ncountry, its inhabitants, language, manners, institutions, which are\neffects of the past and must be traceable to it; we may also be able to\nobserve ancient buildings or their ruins, funerary remains, coins,\ndating from the very times we are to treat of. Our own observations, of\ncourse, are by no means free from error.\n\nBut even in treating of our own age and country, most of our information\nmust be derived from the testimony of others, who may have made mistakes\nof observation and further mistakes in reporting their observations, or\nmay have intentionally falsified them. Testimony is of two kinds: Oral;\nand Written, inscribed or printed. In investigating the events of a\nremote age, nearly all our direct evidence must be some sort of\ntestimony.\n\n(1) Oral testimony depends upon the character of the witness; and the\nbest witness is not perfectly trustworthy; for he may not have observed\naccurately, or he may not have reported correctly; especially if some\ntime elapsed between the event and his account of it; for no man's\nmemory is perfect. Since witnesses vary widely in capacity and\nintegrity, we must ask concerning any one of them--was he a good judge\nof what he saw, and of what was really important in the event? Had he\ngood opportunities of knowing the circumstances? Had he any interest in\nthe event--personal, or partisan, or patriotic? Such interests would\ncolour his report; and so would the love of telling a dramatic story, if\nthat was a weakness of his. Nay, a love of truth might lead him to\nmodify the report of what he remembered if--as he remembered it--the\nmatter seemed not quite credible. We must also bear in mind that, for\nwant of training, precision in speaking the truth is not understood or\nappreciated by many honest people even now, still less in unscientific\nages.\n\nOral tradition is formed by passing a report from one to another,\ngeneration by generation; and it is generally true that such a tradition\nloses credit at every step, because every narrator has some weakness.\nHowever, the value of tradition depends upon the motives people have to\nreport correctly, and on the form of the communication, and on whether\nmonuments survive in connection with the story. Amongst the things best\nremembered are religious and magic formul\u00e6, heroic poems, lists of\nancestors, popular legends about deeply impressive events, such as\nmigrations, conquests, famines, plagues. We are apt now to underrate the\nvalue of tradition, because the use of writing has made tradition less\nimportant, and therefore less pains are taken to preserve it. In the\nmiddle of last century, it was usual (and then quite justifiable) to\ndepreciate oral tradition as nearly worthless; but the spread of\narch\u00e6ological and anthropological research, and the growth of the\nComparative Method, have given new significance to legends and\ntraditions which, merely by themselves, could not deserve the slightest\nconfidence.\n\n(2) As to written evidence, contemporary inscriptions--such as are found\non rocks and stones and bricks in various parts of the world, and most\nabundantly in Egypt and Western Asia--are of the highest value, because\nleast liable to fraudulent abuse; but must be considered with reference\nto the motives of those who set them forth. Manuscripts and books give\nrise to many difficulties. We have to consider whether they were\noriginally written by some one contemporary with the events recorded: if\nso they have the same value as immediate oral testimony, provided they\nhave not been tampered with since. But if not contemporary records, they\nmay have been derived from other records that were contemporary, or only\nfrom oral tradition. In the latter case they are vitiated by the\nweakness of oral tradition. In the former case, we have to ask what was\nthe trustworthiness of the original records, and how far do the extant\nwritings fairly represent those records?\n\nOur answers to these questions will partly depend upon what we know or\ncan discover of the authors of the MSS. or books. Who was the author? If\na work bears some man's name, did he really write it? The evidence\nbearing upon this question is usually divided into internal, external\nand mixed; but perhaps no evidence is purely internal, if we define it\nas that which is derived entirely from the work itself. Under the name\nof internal evidence it is usual to put the language, the style,\nconsistency of ideas; but if we had no grounds of judgment but the book\nitself, we could not possibly say whether the style was the author's:\nthis requires us to know his other works. Nor could we say whether the\nlanguage was that of his age, unless we knew other literature of the\nsame age; nor even that different passages seem to be written in the\nmanner of different ages, but for our knowledge of change in other\nliteratures. There must in every case be some external reference. Thus\nwe judge that a work is not by the alleged author, nor contemporary with\nhim, if words are used that only became current at a later date, or are\nused in a sense that they only later acquired, or if later writers are\nimitated, or if events are mentioned that happened later\n('anachronism'). Books are sometimes forged outright, that is, are\nwritten by one man and deliberately fathered upon another; but sometimes\nbooks come to be ascribed to a well-known name, which were written by\nsome one else without fraudulent intent, dramatically or as a\nrhetorical exercise.\n\nAs to external evidence, if from other sources we have some knowledge of\nthe facts described in a given book, and if it presents no serious\ndiscrepancies with those facts, this is some confirmation of a claim to\ncontemporaneity. But the chief source of external evidence is other\nliterature, where we may find the book in question referred to or\nquoted. Such other literature may be by another author, as when\nAristotle refers to a dialogue of Plato's, or Shakespeare quotes\nMarlowe; or may be other work of the author himself, as when Aristotle\nin the _Ethics_ refers to his own _Physics_, or Chaucer in _The\nCanterbury Tales_ mentions as his own _The Legend of Good Women_, and in\n_The Legend_ gives a list of other works of his. This kind of argument\nassumes that the authorship of the work we start from is undisputed;\nwhich is practically the case with the _Ethics_ and _The Canterbury\nTales_.\n\nBut, now, granting that a work is by a good author, or contemporary with\nthe events recorded, or healthily related to others that were\ncontemporary, it remains to consider whether it has been well preserved\nand is likely to retain its original sense. It is, therefore, desirable\nto know the history of a book or MS., and through whose hands it has\npassed. Have there been opportunities of tampering with it; and have\nthere been motives to do so? In reprinting books, but still more in\ncopying MSS., there are opportunities of omitting or interpolating\npassages, or of otherwise altering the sense. In fact, slight changes\nare almost sure to be made even without meaning to make them, especially\nin copying MSS., through the carelessness or ignorance of transcribers.\nHence the oldest MS. is reckoned the best.\n\nIf a work contains stories that are physically impossible, it shows a\ndefect of judgment in the author, and decreases our confidence in his\nother statements; but it does not follow that these others are to be\nrejected. We must try to compare them with other evidence. Even\nincredible stories are significant: they show what people were capable\nof believing, and, therefore, under what conditions they reasoned and\nacted. One cause of the incredibility of popular stories is the fusion\nof legend with myth. A legend is a traditionary story about something\nthat really happened: it may have been greatly distorted by stupidity,\nor exaggeration, or dramatisation, or rationalisation, but may still\nretain a good deal of the original fact. A myth, however, has not\nnecessarily any basis of fact: it may be a sort of primitive philosophy,\nan hypothesis freely invented to explain some fact in nature, such as\neclipses, or to explain some social custom whose origin is forgotten,\nsuch as the sacrificing of a ram.\n\nAll historical conclusions, then, depend on a sum of convergent and\nconflicting probabilities in the nature of circumstantial evidence. The\nbest testimony is only highly probable, and it is always incomplete. To\ncomplete the picture of any past age there is no resource but the\nComparative Method. We use this method without being aware of it,\nwhenever we make the records of the last generation intelligible to\nourselves by our own experience. Without it nothing would be\nintelligible: an ancient coin or weapon would have no meaning, were we\nnot acquainted with the origins and uses of other coins and weapons.\nGenerally, the further we go back in history, the more the evidence\nneeds interpretation and reconstruction, and the more prominent becomes\nthe appeal to the Comparative Method. Our aim is to construct a history\nof the world, and of the planet as part of the world, and of mankind as\npart of the life of the planet, in such a way that every event shall be\nconsistent with, and even required by, the rest according to the\nprinciple of Causation.\n\n\n\n\nCHAPTER XVIII\n\nHYPOTHESES\n\n\n\u00a7 1. An Hypothesis, sometimes employed instead of a known law, as a\npremise in the deductive investigation of nature, is defined by Mill as\n\"any supposition which we make (either without actual evidence, or on\nevidence avowedly insufficient) in order to endeavour to deduce from it\nconclusions in accordance with facts which are known to be real; under\nthe idea that if the conclusions to which the hypothesis leads are known\ntruths, the hypothesis itself either must be, or at least is likely to\nbe, true.\" The deduction of known truths from an hypothesis is its\nVerification; and when this has been accomplished in a good many cases,\nand there are no manifest failures, the hypothesis is often called a\nTheory; though this term is also used for the whole system of laws of a\ncertain class of phenomena, as when Astronomy is called the 'theory of\nthe heavens.' Between hypothesis and theory in the former sense no\ndistinct line can be drawn; for the complete proof of any speculation\nmay take a long time, and meanwhile the gradually accumulating evidence\nproduces in different minds very different degrees of satisfaction; so\nthat the sanguine begin to talk of 'the theory,' whilst the circumspect\ncontinue to call it 'the hypothesis.'\n\nAn Hypothesis may be made concerning (1) an Agent, such as the ether; or\n(2) a Collocation, such as the plan of our solar system--whether\ngeocentric or heliocentric; or (3) a Law of an agent's operation, as\nthat light is transmitted by a wave motion of such lengths or of such\nrates of vibration.\n\nThe received explanation of light involves both an agent, the ether, as\nan all-pervading elastic fluid, and also the law of its operation, as\ntransmitting light in waves of definite form and length, with definite\nvelocity. The agreement between the calculated results of this complex\nhypothesis and the observed phenomena of light is the chief part of the\nverification; which has now been so successfully accomplished that we\ngenerally hear of the 'Undulatory Theory.' Sometimes a new agent only is\nproposed; as the planet Neptune was at first assumed to exist in order\nto account for perturbations in the movements of Uranus, influencing it\naccording to the already established law of gravitation. Sometimes the\nagents are known, and only the law of their operation is hypothetical,\nas was at first the case with the law of gravitation itself. For the\nagents, namely, Earth, falling bodies on the Earth, Moon, Sun, and\nplanets were manifest; and the hypothesis was that their motions might\nbe due to their attracting one another with a force inversely\nproportional to the squares of the distances between them. In the\nPtolemaic Astronomy, again, there was an hypothesis as to the\ncollocation of the heavenly bodies (namely, that our Earth was the\ncentre of the universe, and that Moon, Sun, planets and stars revolved\naround her): in the early form of the system there was also an\nhypothesis concerning agents upon which this arrangement depended\n(namely, the crystalline spheres in which the heavenly bodies were\nfixed, though these were afterwards declared to be imaginary); and an\nhypothesis concerning the law of operation (namely, that circular motion\nis the most perfect and eternal, and therefore proper to celestial\nthings).\n\nHypotheses are by no means confined to the physical sciences: we all\nmake them freely in private life. In searching for anything, we guess\nwhere it may be before going to look for it: the search for the North\nPole was likewise guided by hypotheses how best to get there. In\nestimating the characters or explaining the conduct of acquaintances or\nof public men, we frame hypotheses as to their dispositions and\nprinciples. 'That we should not impute motives' is a peculiarly absurd\nmaxim, as there is no other way of understanding human life. To impute\nbad motives, indeed, when good are just as probable, is to be wanting in\nthe scientific spirit, which views every subject in 'a dry light.' Nor\ncan we help 'judging others by ourselves'; for self-knowledge is the\nonly possible starting-point when we set out to interpret the lives of\nothers. But to understand the manifold combinations of which the\nelements of character are susceptible, and how these are determined by\nthe breeding of race or family under various conditions, and again by\nthe circumstances of each man's life, demands an extraordinary union of\nsympathetic imagination with scientific habits of thought. Such should\nbe the equipment of the historian, who pursues the same method of\nhypothesis when he attempts to explain (say) the state of parties upon\nthe Exclusion Bill, or the policy of Louis XI. Problems such as the\nformer of these are the easier; because, amidst the compromises of a\nparty, personal peculiarities obliterate one another, and expose a\nsimpler scheme of human nature with fewer fig-leaves. Much more\nhazardous hypotheses are necessary in interpreting the customs of\nsavages, and the feelings of all sorts of animals. Literary criticisms,\nagain, abound with hypotheses: e.g., as to the composition of the\nHomeric poems, the order of the Platonic dialogues, the authorship of\nthe C\u00e6dmonic poems, or the Ossianic, or of the letters of Junius. Thus\nthe method of our everyday thoughts is identical with that of our most\nrefined speculations; and in every case we have to find whether the\nhypothesis accounts for the facts.\n\n\u00a7 2. It follows from the definition of an hypothesis that none is of\nany use that does not admit of verification (proof or disproof), by\ncomparing the results that may be deduced from it with facts or laws. If\nso framed as to elude every attempt to test it by facts, it can never be\nproved by them nor add anything to our understanding of them.\n\nSuppose that a conjurer asserts that his table is controlled by the\nspirit of your deceased relative, and makes it rap out an account of\nsome adventure that could not easily have been within a stranger's\nknowledge. So far good. Then, trying again, the table raps out some\nblunder about your family which the deceased relative could not have\ncommitted; but the conjurer explains that 'a lying spirit' sometimes\npossesses the table. This amendment of the hypothesis makes it equally\ncompatible with success and with failure. To pass from small things to\ngreat, not dissimilar was the case of the Ptolemaic Astronomy: by\nsuccessive modifications, its hypothesis was made to correspond with\naccumulating observations of the celestial motions so ingeniously that,\nuntil the telescope was invented, it may be said to have been\nunverifiable. Consider, again, the sociological hypothesis, that civil\norder was at first founded on a Contract which remains binding upon all\nmankind: this is reconcilable with the most opposite institutions. For\nwe have no record of such an event: and if the institutions of one State\n(say the British) include ceremonies, such as the coronation oath and\noath of allegiance, which may be remnants of an original contract, they\nmay nevertheless be of comparatively recent origin; whereas if the\ninstitutions of another State (say the Russian) contain nothing that\nadmits of similar interpretation, yet traces of the contract once\nexisting may long since have been obliterated. Moreover, the actual\ncontents of the contract not having been preserved, every adherent of\nthis hypothesis supplies them at his own discretion, 'according to the\ndictates of Reason'; and so one derives from it the duty of passive\nobedience, and another with equal cogency establishes the right of\nrebellion.\n\nTo be verifiable, then, an hypothesis must be definite; if somewhat\nvague in its first conception (which is reasonably to be expected), it\nmust be made definite in order to be put to the proof. But, except this\ncondition of verifiability, and definiteness for the sake of\nverifiability, without which a proposition does not deserve the name of\nan hypothesis, it seems inadvisable to lay down rules for a 'legitimate'\nhypothesis. The epithet is misleading. It suggests that the Logician\nmakes rules for scientific inquirers; whereas his business is to\ndiscover the principles which they, in fact, employ in what are\nacknowledged to be their most successful investigations. If he did make\nrules for them, and they treated him seriously, they might be\ndiscouraged in the exercise of that liberty of hypothesising which is\nthe condition of all originality; whilst if they paid no attention to\nhim, he must suffer some loss of dignity. Again, to say that a\n'legitimate hypothesis' must explain all the facts, at least in the\ndepartment for which it is invented, is decidedly discouraging. No doubt\nit may be expected to do this in the long run when (if ever) it is\ncompletely established; but this may take a long time: is it meanwhile\nillegitimate? Or can this adjective be applied to Newton's corpuscular\ntheory of light, even though it has failed to explain all the facts?\n\n\u00a7 3. Given a verifiable hypothesis, however, what constitutes proof or\ndisproof?\n\n(1) _If a new agent be proposed, it is desirable that we should be able\ndirectly to observe it, or at least to obtain some evidence of its\nexistence of a different kind from the very facts which it has been\ninvented to explain._ Thus, in the discovery of Neptune, after the\nexistence of such a planet outside the orbit of Uranus had been\nconjectured (to account for the movements of the latter), the place in\nthe heavens which such a body should occupy at a certain time was\ncalculated, and there by means of the telescope it was actually seen.\n\nAgents, however, are assumed and reasoned upon very successfully which,\nby their nature, never can be objects of perception: such are the atoms\nof Chemistry and the ether of Optics. But the severer methodologists\nregard them with suspicion: Mill was never completely convinced about\nthe ether; the defining of which has been found very difficult. He was\nwilling, however, to make the most of the evidence that has been adduced\nas indicating a certain property of it distinct from those by which it\ntransmits radiation, namely, mechanical inertia, whereby it has been\nsupposed to retard the career of the heavenly bodies, as shown\nespecially by the history of Encke's comet. This comet returned sooner\nthan it should, as calculated from the usual data; the difference was\nascribed to the influence of a resisting medium in reducing the extent\nof its orbit; and such a medium may be the ether. If this conjecture\n(now of less credit) should gain acceptance, the ether might be regarded\nas a _vera causa_ (that is, a condition whose existence may be proved\nindependently of the phenomena it was intended to explain), in spite of\nits being excluded by its nature from the sphere of direct perception.\nHowever, science is not a way of perceiving things, but essentially a\nway of thinking about them. It starts, indeed, from perception and\nreturns to it, and its thinking is controlled by the analogies of\nperception. Atoms and ether are thought about as if they could be seen\nor felt, not as noumena; and if still successful in connecting and\nexplaining perceptions, and free from contradiction, they will stand as\nhypotheses on that ground.\n\nOn the other hand, a great many agents, once assumed in order to explain\nphenomena, have since been explained away. Of course, a _fact_ can never\nbe 'explained away': the phrase is properly applicable to the fate of\nerroneous hypotheses, when, not only are they disproved, but others are\nestablished in their places. Of the Aristotelian spheres, which were\nsupposed to support and translate sun, moon and planets, no trace has\never been found: they would have been very much in the way of the\ncomets. Phlogiston, again, an agent much in favour with the earlier\nChemists, was found, Whewell tells us, when their theories were tested\nby exact weighing, to be not merely non-existent but a minus quantity;\nthat is to say, it required the assumption of its absolute lightness \"so\nthat it diminished the weight of the compounds into which it entered.\"\nThese agents, then, the spheres and phlogiston, have been explained\naway, and instead of them we have the laws of motion and oxygen.\n\n(2) _Whether the hypothetical agent be perceptible or not, it cannot be\nestablished as a cause, nor can a supposed law of such an agent be\naccepted as sufficient to the given inquiry, unless it is adequate to\naccount for the effects which it is called upon to explain, at least so\nfar as it pretends to explain them._ The general truth of this is\nsufficiently obvious, since to explain the facts is the purpose of an\nhypothesis; and we have seen that Newton gave up his hypothesis that the\nmoon was a falling body, as long as he was unable to show that the\namount of its deflection from a tangent (or fall) in a given time, was\nexactly what it should be, if the Moon was controlled by the same force\nas falling bodies on the Earth.\n\nIt is important to observe the limitations to this canon. In the first\nplace, it says that, unless adequate to explain the facts in question,\nan hypothesis cannot be '_established_'; but, for all that, such an\nhypothesis may be a very promising one, not to be hastily rejected,\nsince it may take a very long time fully to verify an hypothesis. Some\nfacts may not be obtainable that are necessary to show the connection of\nothers: as, for example, the hypothesis that all species of animals\nhave arisen from earlier ones by some process of gradual change, can be\nonly imperfectly verified by collecting the fossil remains of extinct\nspecies, because immense depths and expanses of fossiliferous strata\nhave been destroyed. Or, again, the general state of culture may be such\nas to prevent men from tracing the consequences of an hypothesis; for\nwhich reason, apparently, the doctrine that the Sun is the centre of our\nplanetary system remained a discredited hypothesis for 2000 years. This\nshould instruct us not to regard an hypothesis as necessarily erroneous\nor illegitimate merely because we cannot yet see how it works out: but\nneither can we in such a case regard it as established, unless we take\nsomebody's word for it.\n\nSecondly, the canon says that an hypothesis is not established, unless\nit accounts for the phenomena _so far as it professes to_. But it\nimplies a complete misunderstanding to assail a doctrine for not\nexplaining what lies beyond its scope. Thus, it is no objection to a\ntheory of the origin of species, that it does not explain the origin of\nlife: it does not profess to. For the same reason, it is no objection to\nthe theory of Natural Selection, that it does not account for the\nvariations which selection presupposes. But such objections might be\nperfectly fair against a general doctrine of Evolution.\n\nAn interesting case in Wallace's _Darwinism_ (chap. x.) will illustrate\nthe importance of attending to the exact conditions of an hypothesis. He\nsays that in those groups of \"birds that need protection from enemies,\"\n\"when the male is brightly coloured and the female sits exposed on the\nnest, she is always less brilliant and generally of quite sober and\nprotective hues\"; and his hypothesis is, that these sober hues have been\nacquired or preserved by Natural Selection, because it is important to\nthe family that the sitting bird should be inconspicuous. Now to this it\nmight be objected that in some birds both sexes are brilliant or\nconspicuous; but the answer is that the female of such species _does not\nsit exposed on the nest_; for the nests are either domed over, or made\nin a hole; so that the sitting bird does not need protective colouring.\nIf it be objected, again, that some sober-coloured birds build domed\nnests, it may be replied that the proposition 'All conspicuously\ncoloured birds are concealed in the nest,' is not to be converted simply\ninto 'All birds that sit concealed in the nest are conspicuously\ncoloured.' In the cases alleged the domed nests are a protection against\nthe weather, and the sober colouring is a general protection to the\nbird, which inhabits an open country. It may be urged, however, that\njays, crows, and magpies are conspicuous birds, and yet build open\nnests: but these are aggressive birds, _not needing protection from\nenemies_. Finally, there are cases, it must be confessed, in which the\nfemale is more brilliant than the male, and which yet have open nests.\nYes: but _then the male sits upon the eggs_, and the female is stronger\nand more pugnacious!\n\nThus every objection is shown to imply some inattention to the\nconditions of the hypothesis; and in each case it may be said, _exceptio\nprobat regulam_--the exception _tests_ the rule. (Of course, the usual\ntranslation \"proves the rule,\" in the restricted modern sense of\n\"prove,\" is absurd.) That is to say, it appears on examination: (1) that\nthe alleged exception is not really one, and (2) that it stands in such\nrelation to the rule as to confirm it. For to all the above objections\nit is replied that, granting the phenomenon in question (special\nprotective colouring for the female) to be absent, the alleged cause\n(need of protection) is also absent; so that the proof is, by means of\nthe objections, extended, from being one by the method of Agreement,\ninto one by the Double Method.\n\nThirdly, an hypothesis originally intended to account for the whole of a\nphenomenon and failing to do so, though it cannot be established in that\nsense, may nevertheless contain an essential part of the explanation.\nThe Neptunian Hypothesis in Geology, was an attempt to explain the\nformation of the Earth's outer crust, as having been deposited from an\nuniversal ocean of mud. In the progress of the science other causes,\nseismic, fluvial and atmospheric, have been found necessary in order to\ncomplete the theory of the history of the Earth's crust; but it remains\ntrue that the stratified rocks, and some that have lost their stratified\ncharacter, were originally deposited under water. Inadequacy, therefore,\nis not a reason for entirely rejecting an hypothesis or treating it as\nillegitimate.\n\n(3) Granting that the hypothetical cause is real and adequate, the\ninvestigation is not complete. Agreement with the facts is a very\npersuasive circumstance, the more so the more extensive the agreement,\nespecially if no exceptions are known. Still, if this is all that can be\nsaid in favour of an hypothesis, it amounts to proof at most by the\nmethod of Agreement; it does not exclude the possibility of vicarious\ncauses; and if the hypothesis proposes a new agent that cannot be\ndirectly observed, an equally plausible hypothesis about another\nimagined agent may perhaps be invented.\n\nAccording to Whewell, it is a strong mark of the truth of an hypothesis\nwhen it agrees with distinct inductions concerning different classes of\nfacts, and he calls this the 'Consilience of Inductions,' because they\njump together in the unity of the hypothesis. It is particularly\nconvincing when this consilience takes place easily and naturally\nwithout necessitating the mending and tinkering of the hypothesis; and\nhe cites the Theory of Gravitation and the Undulatory Theory of Light as\nthe most conspicuous examples of such ever-victorious hypotheses. Thus,\ngravitation explains the fall of bodies on the Earth, and the orbits of\nthe planets and their satellites; it applies to the tides, the comets,\nthe double stars, and gives consistency to the Nebular Hypothesis,\nwhence flow important geological inferences; and all this without any\nneed of amendment. Nevertheless, Mill, with his rigorous sense of duty,\npoints out, that an induction is merely a proposition concerning many\nfacts, and that a consilience of inductions is merely a multiplication\nof the facts explained; and that, therefore, if the proof is merely\nAgreement in each case, there can be no more in the totality; the\npossibility of vicarious causes is not precluded; and the hypothesis\nmay, after all, describe an accidental circumstance.\n\nWhewell also laid great stress upon prediction as a mark of a true\nhypothesis. Thus, Astronomers predict eclipses, occultations, transits,\nlong beforehand with the greatest precision; and the prediction of the\nplace of Neptune by sheer force of deduction is one of the most\nastonishing things in the history of science. Yet Mill persisted in\nshowing that a predicted fact is only another fact, and that it is\nreally not very extraordinary that an hypothesis, that happens to agree\nwith many known facts, should also agree with some still undiscovered.\nCertainly, there seems to be some illusion in the common belief in the\nprobative force of prediction. Prediction surprises us, puts us off our\nguard, and renders persuasion easy; in this it resembles the force of an\nepigram in rhetoric. But cases can be produced in which erroneous\nhypotheses have led to prediction; and Whewell himself produces them.\nThus, he says that the Ptolemaic theory was confirmed by its predicting\neclipses and other celestial phenomena, and by leading to the\nconstruction of Tables in which the places of the heavenly bodies were\ngiven at every moment of time. Similarly, both Newton's theory of light\nand the chemical doctrine of phlogiston led to predictions which came\ntrue.\n\nWhat sound method demands in the proof of an hypothesis, then, is _not\nmerely that it be shown to agree with the facts, but that every other\nhypothesis be excluded._ This, to be sure, may be beyond our power;\nthere may in some cases be no such negative proof except the exhaustion\nof human ingenuity in the course of time. The present theory of colour\nhas in its favour the failure of Newton's corpuscular hypothesis and of\nGoethe's anti-mathematical hypothesis; but the field of conjecture\nremains open. On the other hand, Newton's proof that the solar system is\ncontrolled by a central force, was supported by the demonstration that a\nforce having any other direction could not have results agreeing with\nKepler's second law of the planetary motions, namely, that, as a planet\nmoves in its orbit, the areas described by a line drawn from the sun to\nthe planet are proportional to the times occupied in the planet's\nmotion. When a planet is nearest to the sun, the area described by such\na line is least for any given distance traversed by the planet; and then\nthe planet moves fastest: when the planet is furthest from the sun, the\narea described by such a line is greatest for an equal distance\ntraversed; and then the planet moves slowest. This law may be deduced\nfrom the hypothesis of a central force, but not from any other; the\nproof, therefore, as Mill says, satisfies the method of Difference.\n\nApparently, to such completeness of demonstration certain conditions are\nnecessary: the possibilities must lie between alternatives, such as A or\nnot-A, or amongst some definite list of cases that may be exhausted,\nsuch as equal, greater or less. He whose hypothesis cannot be brought to\nsuch a definite issue, must try to refute whatever other hypotheses are\noffered, and naturally he will attack first the strongest rivals. With\nthis object in view he looks about for a \"crucial instance,\" that is, an\nobservation or experiment that stands like a cross (sign-post) at the\nparting of the ways to guide us into the right way, or, in plain words,\nan instance that can be explained by one hypothesis but not by another.\nThus the phases of Venus, similar to those of the Moon, but concurring\nwith great changes of apparent size, presented, when discovered by\nGalileo, a crucial instance in favour of the Copernican hypothesis, as\nagainst the Ptolemaic, so far at least as to prove that Venus revolved\naround the Sun inside the orbit of the Earth. Foucault's experiment\ndetermining the velocity of Light (cited in the last chapter) was at\nfirst intended as an _experimentum crucis_ to decide between the\ncorpuscular and undulatory theories; and answered this purpose, by\nshowing that the velocity of a beam passed through water was less than\nit should be by the former, but in agreement with the latter doctrine\n(Deschanel: \u00a7 813).\n\nPerhaps experiments of this decisive character are commonest in\nChemistry: chemical tests, says Herschel, \"are almost universally\ncrucial experiments.\" The following is abridged from Playfair (_Encycl.\nMet., Diss._ III.): The Chemists of the eighteenth century observed that\nmetals were rendered heavier by calcination; and there were two ways of\naccounting for this: either something had been added in the process,\nthough what, they could not imagine; or, something had been driven off\nthat was in its nature light, namely, phlogiston. To decide between\nthese hypotheses, Lavoisier hermetically sealed some tin in a glass\nretort, and weighed the whole. He then heated it; and, when the tin was\ncalcined, weighed the whole again, and found it the same as before. No\nsubstance, therefore, either light or heavy, had escaped. Further, when\nthe retort was cooled and opened, the air rushed in, showing that some\nof the air formerly within had disappeared or lost its elasticity. On\nweighing the whole again, its weight was now found to have increased by\nten grains; so that ten grains of air had entered when it was opened.\nThe calcined tin was then weighed separately, and proved to be exactly\nten grains heavier than when it was placed in the retort; showing that\nthe ten grains of air that had disappeared had combined with the metal\nduring calcination. This experiment, then, decided against phlogiston,\nand led to an analysis of common air confirming Priestley's discovery of\noxygen.\n\n(4) _An hypothesis must agree with the rest of the laws of Nature; and,\nif not itself of the highest generality, must be derivable from primary\nlaws_ (chap. xix. \u00a7 1). Gravitation and the diffusion of heat, light and\nsound from a centre, all follow the 'law of the inverse square,' and\nagree with the relation of the radius of a sphere to its surface. Any\none who should think that he had discovered a new central force would\nnaturally begin to investigate it on the hypothesis that it conformed to\nthe same law as gravitation or light. A Chemist again, who should\nbelieve himself to have discovered a new element, would expect it to\nfill one of the vacant places in the Periodic Table. Conformity, in such\ncases, is strong confirmation, and disagreement is an occasion of\nmisgivings.\n\nA narrower hypothesis, as 'that the toad's ugliness is protective',\nwould be supported by the general theory of protective colouring and\nfigure, and by the still more general theory of Natural Selection, if\nfacts could be adduced to show that the toad's appearance does really\ndeter its enemies. Such an hypothesis resembles an Empirical Law in its\nneed of derivation (chap. xix. \u00a7\u00a7 1, 2). If underivable from, or\nirreconcilable with, known laws, it is a mere conjecture or prejudice.\nThe absolute leviation of phlogiston, in contrast with the gravitation\nof all other forms of matter, discredited that supposed agent. That\nMacpherson should have found the Ossianic poems extant in the Gaelic\nmemory, was contrary to the nature of oral tradition; except where\ntradition is organised, as it was for ages among the Brahmins. The\nsuggestion that xanthochroid Aryans were \"bleached\" by exposure during\nthe glacial period, does not agree with Wallace's doctrine concerning\nthe coloration of Arctic animals. That our forefathers being predatory,\nlike bears, white variations amongst them were then selected by the\nadvantage of concealment, is a more plausible hypothesis.\n\nAlthough, then, the consilience of Inductions or Hypotheses is not a\nsufficient proof of their truth, it is still a condition of it;\nnonconsilience is a suspicious circumstance, and resilience (so to\nspeak), or mutual repugnance, is fatal to one or all.\n\n\u00a7 4. We have now seen that a scientific hypothesis, to deserve the name,\nmust be verifiable and therefore definite; and that to establish itself\nas a true theory, it must present some symptom of reality, and be\nadequate and exclusive and in harmony with the system of experience.\nThus guarded, hypotheses seem harmless enough; but some people have a\nstrong prejudice against them, as against a tribe of savages without\ngovernment, or laws, or any decent regard for vested interests. It is\nwell known, too, that Bacon and Newton disparaged them. But Bacon, in\nhis examples of an investigation according to his own method, is\nobliged, after a preliminary classification of facts, to resort to an\nhypothesis, calling it _permissio intellectus_, _interpretatio inchoata_\nor _vindemiatio prima_. And Newton when he said _hypotheses non fingo_,\nmeant that he did not deal in fictions, or lay stress upon supposed\nforces (such as 'attraction'), that add nothing to the law of the facts.\nHypotheses are essential aids to discovery: speaking generally,\ndeliberate investigation depends wholly upon the use of them.\n\nIt is true that we may sometimes observe a train of events that chances\nto pass before us, when either we are idle or engaged with some other\ninquiry, and so obtain a new glimpse of the course of nature; or we may\ntry experiments haphazard, and watch the results. But, even in these\ncases, before our new notions can be considered knowledge, they must be\ndefinitely framed in hypotheses and reobserved or experimented upon,\nwith whatever calculations or precautions may be necessary to ensure\naccuracy or isolation. As a rule, when inquiring deliberately into the\ncause of an event, whether in nature or in history, we first reflect\nupon the circumstances of the case and compare it with similar ones\npreviously investigated, and so are guided by a preconception more or\nless definite of 'what to look for,' what the cause is likely to be,\nthat is, by an hypothesis. Then, if our preconception is justified, or\nsomething which we observe leads to a new hypothesis, either we look for\nother instances to satisfy the canons of Agreement; or (if the matter\nadmits of experiment) we endeavour, under known conditions according to\nthe canon of Difference, to reproduce the event by means of that which\nour hypothesis assigns as the cause; or we draw remote inferences from\nour hypothesis, and try to test these by the Inductive Canons.\n\nIf we argue from an hypothesis and express ourselves formally, it will\nusually appear as the major premise; but this is not always the case. In\nextending ascertained laws to fresh cases, the minor premise may be an\nhypothesis, as in testing the chemical constitution of any doubtful\nsubstance, such as a piece of ore. Some solution or preparation, A, is\ngenerally made which (it is known) will, on the introduction of a\ncertain agent, B, give a reaction, C, if the preparation contains a\ngiven substance, X. The major premise is the law of reaction--\n\n Whenever A is X, if treated with B it is C.\n\nThe minor premise is an hypothesis that the preparation contains X. An\nexperiment then treats A with B. If C result, a probability is raised in\nfavour of the hypothesis that A is X; or a certainty, if we know that C\nresults on that condition only.\n\nSo important are hypotheses to science, that Whewell insists that they\nhave often been extremely valuable even though erroneous. Of the\nPtolemaic system he says, \"We can hardly imagine that Astronomy could,\nin its outset, have made so great a progress under any other form.\" It\nserved to connect men's thoughts on the subject and to sustain their\ninterest in working it out; by successive corrections \"to save\nappearances,\" it attained at last to a descriptive sort of truth, which\nwas of great practical utility; it also occasioned the invention of\ntechnical terms, and, in general digested the whole body of observations\nand prepared them for assimilation by a better hypothesis in the fulness\nof time. Whewell even defends the maxim that \"Nature abhors a vacuum,\"\nas having formerly served to connect many facts that differ widely in\ntheir first aspect. \"And in reality is it not true,\" he asks, \"that\nnature _does_ abhor a vacuum, and does all she can to avoid it?\" Let no\nforlorn cause despair of a champion! Yet no one has accused Whewell of\nQuixotry; and the sense of his position is that the human mind is a\nrather feeble affair, that can hardly begin to think except with\nblunders.\n\nThe progress of science may be plausibly attributed to a process of\nNatural Selection; hypotheses are produced in abundance and variety, and\nthose unfit to bear verification are destroyed, until only the fittest\nsurvive. Wallace, a practical naturalist, if there ever was one, as well\nas an eminent theorist, takes the same view as Whewell of such\ninadequate conjectures. Of 'Lemuria,' an hypothetical continent in the\nIndian Ocean, once supposed to be traceable in the islands of\nMadagascar, Seychelles, and Mauritius, its surviving fragments, and\nnamed from the Lemurs, its characteristic denizens, he says (_Island\nLife_, chap. xix.) that it was \"essentially a provisional hypothesis,\nvery useful in calling attention to a remarkable series of problems in\ngeographical distribution [of plants and animals], but not affording the\ntrue solution of those problems.\" We see, then, that 'provisional\nhypotheses,' or working hypotheses,' though erroneous, may be very\nuseful or (as Whewell says) necessary.\n\nHence, to be prolific of hypotheses is the first attribute of scientific\ngenius; the first, because without it no progress whatever can be made.\nAnd some men seem to have a marked felicity, a sort of instinctive\njudgment even in their guesses, as if their heads were made according to\nNature. But others among the greatest, like Kepler, guess often and are\noften wrong before they hit upon the truth, and themselves, like Nature,\ndestroy many vain shoots and seedlings of science for one that they find\nfit to live. If this is how the mind works in scientific inquiry (as it\ncertainly is, with most men, in poetry, in fine art, and in the scheming\nof business), it is useless to complain. We should rather recognise a\nplace for fools' hypotheses, as Darwin did for \"fools' experiments.\" But\nto complete the scientific character, there must be great patience,\naccuracy, and impartiality in examining and testing these conjectures,\nas well as great ingenuity in devising experiments to that end. The want\nof these qualities leads to crude work and public failure and brings\nhypotheses into derision. Not partially and hastily to believe in one's\nown guesses, nor petulantly or timidly to reject them, but to consider\nthe matter, to suspend judgment, is the moral lesson of science:\ndifficult, distasteful, and rarely mastered.\n\n\u00a7 5. The word 'hypothesis' is often used also for the scientific device\nof treating an Abstraction as, for the purposes of argument, equivalent\nto the concrete facts. Thus, in Geometry, a line is treated as having no\nbreadth; in Mechanics, a bar may be supposed absolutely rigid, or a\nmachine to work without friction; in Economics, man is sometimes\nregarded as actuated solely by love of gain and dislike of exertion. The\nresults reached by such reasoning may be made applicable to the concrete\nfacts, if allowance be made for the omitted circumstances or properties,\nin the several cases of lines, bars, and men; but otherwise all\nconclusions from abstract terms are limited by their definitions.\nAbstract reasoning, then (that is, reasoning limited by definitions),\nis often said to imply 'the hypothesis' that things exist as their names\nare defined, having no properties but those enumerated in their\ndefinitions. This seems, however, a needless and confusing extension of\nthe term; for an hypothesis proposes an agent, collocation, or law\nhitherto unknown; whereas abstract reasoning proposes to exclude from\nconsideration a good deal that is well known. There seems no reason why\nthe latter device should not be plainly called an Abstraction.\n\nSuch abstractions are necessary to science; for no object is\ncomprehensible by us in all its properties at once. But if we forget the\nlimitations of our abstract data, we are liable to make strange blunders\nby mistaking the character of the results: treating the results as\nsimply true of actual things, instead of as true of actual things only\nso far as they are represented by the abstractions. In addressing\nabstract reasoning, therefore, to those who are unfamiliar with\nscientific methods, pains should be taken to make it clear what the\nabstractions are, what are the consequent limitations upon the argument\nand its conclusions, and what corrections and allowances are necessary\nin order to turn the conclusions into an adequate account of the\nconcrete facts. The greater the number, variety, and subtlety of the\nproperties possessed by any object (such as human nature), the greater\nare the qualifications required in the conclusions of abstract\nreasoning, before they can hold true of such an object in practical\naffairs.\n\nClosely allied to this method of Abstraction is the Mathematical Method\nof Limits. In his _History of Scientific Ideas_ (B. II. c. 12), Whewell\nsays: \"The _Idea of a Limit_ supplies a new mode of establishing\nmathematical truths. Thus with regard to the length of any portion of a\ncurve, a problem which we have just mentioned; a curve is not made up of\nstraight lines, and therefore we cannot by means of any of the\ndoctrines of elementary geometry measure the length of any curve. But we\nmay make up a figure nearly resembling any curve by putting together\nmany short straight lines, just as a polygonal building of very many\nsides may nearly resemble a circular room. And in order to approach\nnearer and nearer to a curve, we may make the sides more and more small,\nmore and more numerous. We may then possibly find some mode of\nmeasurement, some relation of these small lines to other lines, which is\nnot disturbed by the multiplication of the sides, however far it be\ncarried. And thus we may do what is equivalent to measuring the curve\nitself; for by multiplying the sides we may approach more and more\nclosely to the curve till no appreciable difference remains. The curve\nline is the _Limit_ of the polygon; and in this process we proceed on\nthe _Axiom_ that 'What is true up to the Limit is true at the Limit.'\"\n\nWhat Whewell calls the Axiom here, others might call an Hypothesis; but\nperhaps it is properly a Postulate. And it is just the obverse of the\nPostulate implied in the Method of Abstractions, namely, that 'What is\ntrue of the Abstraction is true of concrete cases the more nearly they\napproach the Abstraction.' What is true of the 'Economic Man' is truer\nof a broker than of a farmer, of a farmer than of a labourer, of a\nlabourer than of the artist of romance. Hence the Abstraction may be\ncalled a Limit or limiting case, in the sense that it stands to concrete\nindividuals, as a curve does to the figures made up \"by putting together\nmany short straight lines.\" Correspondingly, the Proper Name may be\ncalled the Limit of the class-name; since its attributes are infinite,\nwhereas any name whose attributes are less than infinite stands for a\npossible class. In short, for logical purposes, a Limit may be defined\nas any extreme case to which actual examples may approach without ever\nreaching it. And in this sense 'Method of Limits' might be used as a\nterm including the Method of Abstractions; though it would be better to\nspeak of them generically as 'Methods of Approximation.'\n\nWe may also notice the Assumptions (as they may be called) that are\nsometimes employed to facilitate an investigation, because some definite\nground must be taken and nothing better can be thought of: as in\nestimating national wealth, that furniture is half the value of the\nhouses.\n\nIt is easy to conceive of an objector urging that such devices as the\nabove are merely ways of avoiding the actual problems, and that they\ndisplay more cunning than skill. But science, like good sense, puts up\nwith the best that can be had; and, like prudence, does not reject the\nhalf-loaf. The position, that a conceivable case that can be dealt with\nmay, under certain conditions, be substituted for one that is\nunworkable, is a touchstone of intelligence. To stand out for ideals\nthat are known to be impossible, is only an excuse for doing nothing at\nall.\n\nIn another sense, again, the whole of science is sometimes said to be\nhypothetical, because it takes for granted the Uniformity of Nature; for\nthis, in its various aspects, can only be directly ascertained by us as\nfar as our experience extends; whereas the whole value of the principle\nof Uniformity consists in its furnishing a formula for the extension of\nour other beliefs beyond our actual experience. Transcendentalists,\nindeed, call it a form of Reason, just because it is presupposed in all\nknowledge; and they and the Empiricists agree that to adduce material\nevidence for it, in its full extent, is impossible. If, then, material\nevidence is demanded by any one, he cannot regard the conclusions of\nMathematics and Physical Science as depending on what is itself\nunproved; he must, with Mill, regard these conclusions as drawn \"not\nfrom but according to\" the axioms of Equality and Causation. That is to\nsay, if the axioms are true, the conclusions are; the material evidence\nfor both the axioms and the conclusions being the same, namely,\nuncontradicted experience. Now when we say, 'If Nature is uniform,\nscience is true,' the hypothetical character of science appears in the\nform of the statement. Nevertheless, it seems undesirable to call our\nconfidence in Nature's uniformity an 'hypothesis': it is incongruous to\nuse the same term for our tentative conjectures and for our most\nindispensable beliefs. 'The Universal Postulate' is a better term for\nthe principle which, in some form or other, every generalisation takes\nfor granted.\n\nWe are now sometimes told that, instead of the determinism and\ncontinuity of phenomena hitherto assumed by science, we should recognise\nindeterminism and discontinuity. But it will be time enough to fall in\nwith this doctrine when its advocates produce a new Logic of Induction,\nand explain the use of the method of Difference and of control\nexperiments according to the new postulates.\n\n\n\n\nCHAPTER XIX\n\nLAWS CLASSIFIED; EXPLANATION; CO-EXISTENCE; ANALOGY\n\n\n\u00a7 1. Laws are classified, according to their degrees of generality, as\nhigher and lower, though the grades may not be decisively\ndistinguishable.\n\nFirst, there are Axioms or Principles, that is real, universal,\nself-evident propositions. They are--(1) real propositions; not, like\n'The whole is greater than any of its parts,' merely definitions, or\nimplied in definitions. (2) They are regarded as universally true of\nphenomena, as far as the form of their expression extends; that is, for\nexample, Axioms concerning quantity are true of everything that is\nconsidered in its quantitative aspect, though not (of course) in its\nqualitative aspect. (3) They are self-evident; that is, each rests upon\nits own evidence (whatever that may be); they cannot be derived from one\nanother, nor from any more general law. Some, indeed, are more general\nthan others: the Logical Principle of Contradiction, 'if A is B, it is\nnot not-B', is true of qualities as well as of quantities; whereas the\nAxioms of Mathematics apply only to quantities. The Mathematical Axioms,\nagain, apply to time, space, mental phenomena, and matter and energy;\nwhereas the Law of Causation is only true of concrete events in the\nredistribution of matter and energy: such, at least, is the strict limit\nof Causation, if we identify it with the Conservation of Energy;\nalthough our imperfect knowledge of life and mind often drives us to\nspeak of feelings, ideas, volitions, as causes. Still, the Law of\nCausation cannot be derived from the Mathematical Axioms, nor these from\nthe Logical. The kind of evidence upon which Axioms rest, or whether any\nevidence can be given for them, is (as before observed) a question for\nMetaphysics, not for Logic. Axioms are the upward limit of Logic, which,\nlike all the special sciences, necessarily takes them for granted, as\nthe starting point of all deduction and the goal of all generalisation.\n\nNext to Axioms, come Primary Laws of Nature: these are of less\ngenerality than the Axioms, and are subject to the conditions of\nmethodical proof; being universally true only of certain forces or\nproperties of matter, or of nature under certain conditions; so that\nproof of them by logical or mathematical reasoning is expected, because\nthey depend upon the Axioms for their formal evidence. Such are the law\nof gravitation, in Astronomy; the law of definite proportions, in\nChemistry; the law of heredity, in Biology; and in Psychology, the law\nof relativity.\n\nThen, there are Secondary Laws, of still less generality, resulting from\na combination of conditions or forces in given circumstances, and\ntherefore conceivably derivable from the laws of those conditions or\nforces, if we can discover them and compute their united effects.\nAccordingly, Secondary Laws are either--(1) Derivative, having been\nanalysed into, and deduced from, Primary Laws; or (2) Empirical, those\nthat have not yet been deduced (though from their comparatively special\nand complex character, it seems probable they may be, given sufficient\ntime and ingenuity), and that meanwhile rest upon some unsatisfactory\nsort of induction by Agreement or Simple Enumeration.\n\nWhether laws proved only by the canon of Difference are to be considered\nEmpirical, is perhaps a question: their proof derives them from the\nprinciple of Causation; but, being of narrow scope, some more special\naccount of them seems requisite in relation to the Primary Laws before\nwe can call them Derivative in the technical sense.\n\nMany Secondary Laws, again, are partially or imperfectly Derivative; we\ncan give general reasons for them, without being able to determine\ntheoretically the precise relations of the phenomena they describe.\nMeteorologists can explain the general conditions of all sorts of\nweather, but have made little progress toward predicting the actual\ncourse of it (at least, for our island): Geologists know the general\ncauses of mountain ranges, but not why they rise just where we find\nthem: Economists explain the general course of a commercial crisis, but\nnot why the great crises recurred at intervals of about ten years.\n\nDerivative Laws make up the body of the exact sciences, having been\nassimilated and organised; whilst Empirical Laws are the undigested\nmaterials of science. The theorems of Euclid are good examples of\nderivative laws in Mathematics; in Astronomy, Kepler's laws and the laws\nof the tides; in Physics, the laws of shadows, of perspective, of\nharmony; in Biology, the law of protective coloration; in Economics, the\nlaws of prices, wages, interest, and rent.\n\nEmpirical Laws are such as Bode's law of the planetary distances; the\nlaws of the expansion of different bodies by heat, and formul\u00e6\nexpressing the electrical conductivity of each substance as a function\nof the temperature. Strictly speaking, I suppose, all the laws of\nchemical combination are empirical: the law of definite proportions is\nverifiable in all cases that have been examined, except for variations\nthat may be ascribed to errors of experiment. Much the same is true in\nBiology; most of the secondary laws are empirical, except so far as\nstructures or functions may be regarded as specialised cases in Physics\nor Chemistry and deducible from these sciences. The theory of Natural\nSelection, however, has been the means of rendering many laws, that were\nonce wholly empirical, at least partially derivative; namely, the laws\nof the geographical distribution of plants and animals, and of their\nadaptation in organisation, form and colour, habits and instincts, to\ntheir various conditions of life. The laws that remain empirical in\nBiology are of all degrees of generality from that of the tendency to\nvariation in size and in every other character shown by every species\n(though as to the reason of this there are promising hypotheses), down\nto such curious cases as that the colour of roses and carnations never\nvaries into blue, that scarlet flowers are never sweet-scented, that\nbullfinches fed on hemp-seed turn black, that the young of white, yellow\nand dun pigeons are born almost naked (whilst others have plenty of\ndown); and so on. The derivation of empirical laws is the greater part\nof the explanation of Nature (\u00a7\u00a7 5, 6).\n\nA 'Fact,' in the common use of the word, is a particular observation: it\nis the material of science in its rawest state. As perceived by a mind,\nit is, of course, never absolutely particular: for we cannot perceive\nanything without classing it, more or less definitely, with things\nalready known to us; nor describe it without using connotative terms\nwhich imply a classification of the things denoted. Still, we may\nconsider an observation as particular, in comparison with a law that\nincludes it with numerous others in one general proposition. To turn an\nobservation into an experiment, or (where experiment is impracticable)\nto repeat it with all possible precautions and exactness, and to\ndescribe it as to the duration, quantity, quality and order of\noccurrence of its phenomena, is the first stage of scientific\nmanufacture. Then comes the formulation of an empirical law; and lastly,\nif possible, deduction or derivation, either from higher laws previously\nascertained, or from an hypothesis. However, as a word is used in\nvarious senses, we often speak of laws as 'facts': we say the law of\ngravitation is a fact, meaning that it is real, or verifiable by\nobservations or experiments.\n\n\u00a7 2. Secondary Laws may also be classified according to their constancy\ninto--(1) the Invariable (as far as experience reaches), and (2)\nApproximate Generalisations in the form--Most X's are Y. Of the\ninvariable we have given examples above. The following are approximate\ngeneralisations: Most comets go round the Sun from East to West; Most\nmetals are solid at ordinary temperatures; Most marsupials are\nAustralasian; Most arctic animals are white in winter; Most cases of\nplague are fatal; Most men think first of their own interests. Some of\nthese laws are empirical, as that 'Most metals are solid at ordinary\ntemperatures': at present no reason can be given for this; nor do we\nknow why most cases of plague are fatal. Others, however, are at least\npartially derivative, as that 'Most arctic animals are white'; for this\nseems to be due to the advantage of concealment in the snow; whether, as\nwith the bear, the better to surprise its prey, or, with the hare, to\nescape the notice of its enemies.\n\nBut the scientific treatment of such a proposition requires that we\nshould also explain the exceptions: if 'Most are,' this implies that\n'Some are not'; why not, then? Now, if we can give reasons for all the\nexceptions, the approximate generalisation may be converted into an\nuniversal one, thus: 'All arctic animals are white, unless (like the\nraven) they need no concealment either to prey or to escape; or unless\nmutual recognition is more important to them than concealment (as with\nthe musk-sheep)'. The same end of universal statement may be gained by\nincluding the conditions on which the phenomenon depends, thus: 'All\narctic animals to whom concealment is of the utmost utility are white.'\n\nWhen statistics are obtainable, it is proper to convert an approximate\ngeneralisation into a proportional statement of the fact, thus: instead\nof 'Most attacks of plague are fatal', we might find that in a certain\ncountry 70 per cent. were so. Then, if we found that in another country\nthe percentage of deaths was 60, in another 40, we might discover, in\nthe different conditions of these countries, a clue to the high rate of\nmortality from this disease. Even if the proportion of cases in which\ntwo facts are connected does not amount to 'Most,' yet, if any definite\npercentage is obtainable, the proposition has a higher scientific value\nthan a vague 'Some': as if we know that 2 per cent. of the deaths in\nEngland are due to suicide, this may be compared with the rates of\nsuicide in other countries; from which perhaps inferences may be drawn\nas to the causes of suicide.\n\nIn one department of life, namely, Politics, there is a special\nadvantage in true approximate generalisations amounting to 'Most cases.'\nThe citizens of any State are so various in character, enlightenment,\nand conditions of life, that we can expect to find few propositions\nuniversally true of them: so that propositions true of the majority must\nbe trusted as the bases of legislation. If most men are deterred from\ncrime by fear of punishment; if most men will idle if they can obtain\nsupport without industry; if most jurymen will refuse to convict of a\ncrime for which the prescribed penalties seem to them too severe; these\nare most useful truths, though there should be numerous exceptions to\nthem all.\n\n\u00a7 3. Secondary Laws can only be trusted in 'Adjacent Cases'; that is,\nwhere the circumstances are similar to those in which the laws are known\nto be true.\n\nA Derivative Law will be true wherever the forces concerned exist in the\ncombinations upon which the law depends, if there are no counteracting\nconditions. That water can be pumped to about 33 feet at the sea-level,\nis a derivative law on this planet: is it true in Mars? That depends on\nwhether there are in Mars bodies of a liquid similar to our water;\nwhether there is an atmosphere there, and how great its pressure is;\nwhich will vary with its height and density. If there is no atmosphere\nthere can be no pumping; or if there is an atmosphere of less pressure\nthan ours, water such as ours can only be pumped to a less height than\n33 feet. Again, we know that there are arctic regions in Mars; if there\nare also arctic animals, are they white? That may depend upon whether\nthere are any beasts of prey. If not, concealment seems to be of no use.\n\nAn Empirical Law, being one whose conditions we do not know, the extent\nof its prevalence is still less ascertainable. Where it has not been\nactually observed to be true, we cannot trust it unless the\ncircumstances, on the whole, resemble so closely those amongst which it\nhas been observed, that the unknown causes, whatever they may be, are\nlikely to prevail there. And, even then, we cannot have much confidence\nin it; for there may be unknown circumstances which entirely frustrate\nthe effect. The first naturalist who travelled (say) from Singapore\neastward by Sumatra and Java, or Borneo, and found the mammalia there\nsimilar to those of Asia, may naturally have expected the same thing in\nCelebes and Papua; but, if so, he was entirely disappointed; for in\nPapua the mammalia are marsupials like those of Australia. Thus his\nempirical law, 'The mammalia of the Eastern Archipelago are Asiatic,'\nwould have failed for no apparent reason. According to Mr. Wallace,\nthere is a reason for it, though such as could only be discovered by\nextensive researches; namely, that the sea is deep between Borneo and\nCelebes, so that they must have been separated for many ages; whereas it\nis shallow from Borneo westward to Asia, and also southward from Celebes\nto Australia; so that these regions, respectively, may have been\nrecently united: and the true law is that similar mammalia belong to\nthose tracts which at comparatively recent dates have formed parts of\nthe same continents (unless they are the remains of a former much wider\ndistribution).\n\nA considerable lapse of time may make an empirical law no longer\ntrustworthy; for the forces from whose combination it resulted may have\nceased to operate, or to operate in the same combination; and since we\ndo not know what those forces were, even the knowledge that great\nchanges have taken place in the meantime cannot enable us, after an\ninterval, to judge whether or not the law still holds true. New stars\nshine in the sky and go out; species of plants and animals become\nextinct; diseases die out and fresh ones afflict mankind: all these\nthings doubtless have their causes, but if we do not know what they are,\nwe have no measure of the effects, and cannot tell when or where they\nwill happen.\n\nLaws of Concomitant Variations may hold good only within certain limits.\nThat bodies contract as the temperature falls, is not true of water\nbelow 39\u00b0 F. In Psychology, Weber's Law is only true within the median\nrange of sensation-intensities, not for very faint, nor for very strong,\nstimuli. In such cases the failure of the laws may depend upon something\nimperfectly understood in the collocation: as to water, on its molecular\nconstitution; as to sensation, upon the structure of the nervous system.\n\n\u00a7 4. Secondary Laws, again, are either of Succession or of Co-existence.\n\nThose of Succession are either--(1) of direct causation, as that 'Water\nquenches fire,' or (more strictly) that 'Evaporation reduces\ntemperature'; or (2) of the effect of a remote cause, as 'Bad harvests\ntend to raise the price of bread'; or (3) of the joint effects of the\nsame cause, as that 'Night follows day' (from the revolution of the\nearth), or the course of the seasons (from the inclination of the\nearth's axis).\n\nLaws of Co-existence are of several classes. (1) One has the generality\nof a primary law, though it is proved only by Agreement, namely, 'All\ngravitating bodies are inert'. Others, though less general than this,\nare of very extensive range, as that 'All gases that are not decomposed\nby rise of temperature have the same rate of expansion'; and, in Botany\nthat 'All monocotyledonous plants are endogenous'. These laws of\nCo-existence are concerned with fundamental properties of bodies.\n\n(2) Next come laws of the Co-existence of those properties which are\ncomprised in the definitions of Natural Kinds. Mill distinguished\nbetween ([alpha]) classes of things that agree among themselves and differ\nfrom others only in one or a few attributes (such as 'red things,'\n'musical notes', 'carnivorous animals', 'soldiers'), and ([beta]) classes of\nthings that agree among themselves and differ from others in a multitude\nof characters: and the latter he calls Natural Kinds. These comprise the\nchemical elements and their pure compounds (such as water, alcohol,\nrock-salt), and the species of plants and animals. Clearly, each of\nthese is constituted by the co-existence or co-inherence of a multitude\nof properties, some of which are selected as the basis of their\ndefinitions. Thus, Gold is a metal of high specific gravity, atomic\nweight 197.2, high melting point, low chemical affinities, great\nductility, yellow colour, etc.: a Horse has 'a vertebral column,\nmamm\u00e6, a placental embryo, four legs, a single well-developed toe in\neach foot provided with a hoof, a bushy tail, and callosities on the\ninner sides of both the fore and the hind legs' (Huxley).\n\nSince Darwinism has obtained general acceptance, some Logicians have\ndoubted the propriety of calling the organic species 'Kinds,' on the\nground that they are not, as to definiteness and permanence, on a par\nwith the chemical elements or such compounds as water and rock-salt;\nthat they vary extensively, and that it is only by the loss of former\ngenerations of animals that we are able to distinguish species at all.\nBut to this it may be replied that species are often approximately\nconstant for immense periods of time, and may be called permanent in\ncomparison with human generations; and that, although the leading\nprinciples of Logic are perhaps eternal truths, yet upon a detail such\nas this, the science may condescend to recognise a distinction if it is\ngood for (say) only 100,000 years. That if former generations of plants\nand animals were not lost, all distinctions of species would disappear,\nmay be true; but they are lost--for the most part beyond hope of\nrecovery; and accordingly the distinction of species is still\nrecognised; although there are cases, chiefly at the lower stages of\norganisation, in which so many varieties occur as to make adjacent\nspecies almost or quite indistinguishable. So far as species are\nrecognised, then, they present a complex co-inherence of qualities,\nwhich is, in one aspect, a logical problem; and, in another, a logical\ndatum; and, coming more naturally under the head of Natural Kinds than\nany other, they must be mentioned in this place.\n\n(3) There are, again, certain coincidences of qualities not essential to\nany kind, and sometimes prevailing amongst many different kinds: such as\n'Insects of nauseous taste have vivid (warning) colours'; 'White\ntom-cats with blue eyes are deaf'; 'White spots and patches, when they\nappear in domestic animals, are most frequent on the left side.'\n\n(4) Finally, there may be constancy of relative position, as of sides\nand angles in Geometry; and also among concrete things (at least for\nlong periods of time), as of the planetary orbits, the apparent\npositions of fixed stars in the sky, the distribution of land and water\non the globe, opposite seasons in opposite hemispheres.\n\nAll these cases of Co-existence (except the geometrical) present the\nproblem of deriving them from Causation; for there is no general Law of\nCo-existence from which they can be derived; and, indeed, if we conceive\nof the external world as a perpetual redistribution of matter and\nenergy, it follows that the whole state of Nature at any instant, and\ntherefore every co-existence included in it, is due to causation issuing\nfrom some earlier distribution of matter and energy. Hence, indeed, it\nis not likely that the problems of co-existence as a whole will ever be\nsolved, since the original distribution of matter is, of course,\nunknown. Still, starting with any given state of Nature, we may hope to\nexplain some of the co-existences in any subsequent state. We do not,\nindeed, know why heavy bodies are always inert, nor why the chemical\nelements are what they are; but it is known that \"the properties of the\nelements are functions of their atomic weight,\" which (though, at\npresent, only an empirical law) may be a clue to some deeper\nexplanation. As to plants and animals, we know the conditions of their\ngeneration, and can trace a connection between most of their\ncharacteristics and the conditions of their life: as that the teeth and\nstomach of animals vary with their food, and that their colour generally\nvaries with their habitat.\n\nGeometrical Co-existence, when it is not a matter of definition (as 'a\nsquare is a rectangle with four equal sides'), is deduced from the\ndefinitions and axioms: as when it is shown that in triangles the\ngreater side is opposite the greater angle. The deductions of theorems\nor secondary laws, in Geometry is a type of what is desirable in the\nPhysical Sciences: the demonstration, namely, that all the connections\nof phenomena, whether successive or co-existent, are consequences of the\nredistribution of matter and energy according to the principle of\nCausation.\n\nCoincidences of Co-existence (Group (3)) may sometimes be deduced and\nsometimes not. That 'nauseous insects have vivid coloration' comes under\nthe general law of 'protective coloration'; as they are easily\nrecognised and therefore avoided by insectivorous birds and other\nanimals. But why white tom-cats with blue-eyes should be deaf, is (I\nbelieve) unknown. When co-existences cannot be derived from causation,\nthey can only be proved by collecting examples and trusting vaguely to\nthe Uniformity of Nature. If no exceptions are found, we have an\nempirical law of considerable probability within the range of our\nexploration. If exceptions occur, we have at most an approximate\ngeneralisation, as that 'Most metals are whitish,' or 'Most domestic\ncats are tabbies' (but this probably is the ancestral colouring). We may\nthen resort to statistics for greater definiteness, and find that in\nHampshire (say) 90 _per cent._ of the domestic cats are tabby.\n\n\u00a7 5. Scientific Explanation consists in discovering, deducing, and\nassimilating the laws of phenomena; it is the analysis of that\nHeracleitan 'flux' which so many philosophers have regarded as\nintractable to human inquiry. In the ordinary use of the word,\n'explanation' means the satisfying a man's understanding; and what may\nserve this purpose depends partly upon the natural soundness of his\nunderstanding, and partly on his education; but it is always at last an\nappeal to the primary functions of cognition, discrimination and\nassimilation.\n\nGenerally, what we are accustomed to seems to need no explanation,\nunless our curiosity is particularly directed to it. That boys climb\ntrees and throw stones, and that men go fox-hunting, may easily pass for\nmatters of course. If any one is so exacting as to ask the reason, there\nis a ready answer in the 'need of exercise.' But this will not explain\nthe peculiar zest of those exercises, which is something quite different\nfrom our feelings whilst swinging dumb-bells or tramping the highway.\nOthers, more sophisticated, tell us that the civilised individual\nretains in his nature the instincts of his remote ancestors, and that\nthese assert themselves at stages of his growth corresponding with\nancestral periods of culture or savagery: so that if we delight to climb\ntrees, throw stones, and hunt, it is because our forefathers once lived\nin trees, had no missiles but stones, and depended for a livelihood\nupon killing something. To some of us, again, this seems an\nexplanation; to others it merely gives annoyance, as a superfluous\nhypothesis, the fruit of a wanton imagination and too much leisure.\n\nHowever, what we are not accustomed to immediately excites curiosity. If\nit were exceptional to climb trees, throw stones, ride after foxes,\nwhoever did such things would be viewed with suspicion. An eclipse, a\nshooting star, a solitary boulder on the heath, a strange animal, or a\nChinaman in the street, calls for explanation; and among some nations,\neclipses have been explained by supposing a dragon to devour the sun or\nmoon; solitary boulders, as the missiles of a giant; and so on. Such\nexplanations, plainly, are attempts to regard rare phenomena as similar\nto others that are better known; a snake having been seen to swallow a\nrabbit, a bigger one may swallow the sun: a giant is supposed to bear\nmuch the same relation to a boulder as a boy does to half a brick. When\nany very common thing seems to need no explanation, it is because the\nseveral instances of its occurrence are a sufficient basis of\nassimilation to satisfy most of us. Still, if a reason for such a thing\nbe demanded, the commonest answer has the same implication, namely, that\nassimilation or classification is a sufficient reason for it. Thus, if\nclimbing trees is referred to the need of exercise, it is assimilated to\nrunning, rowing, etc.; if the customs of a savage tribe are referred\nto the command of its gods, they are assimilated to those things that\nare done at the command of chieftains.\n\nExplanation, then, is a kind of classification; it is the finding of\nresemblance between the phenomenon in question and other phenomena. In\nMathematics, the explanation of a theorem is the same as its proof, and\nconsists in showing that it repeats, under different conditions, the\ndefinitions and axioms already assumed and the theorems already\ndemonstrated. In Logic, the major premise of every syllogism is an\nexplanation of the conclusion; for the minor premise asserts that the\nconclusion is an example of the major premise.\n\nIn Concrete Sciences, to discover the cause of a phenomenon, or to\nderive an empirical law from laws of causation, is to explain it;\nbecause a cause is an invariable antecedent, and therefore reminds us\nof, or enables us to conceive, an indefinite number of cases similar to\nthe present one wherever the cause exists. It classifies the present\ncase with other instances of causation, or brings it under the universal\nlaw; and, as we have seen that the discovery of the laws of nature is\nessentially the discovery of causes, the discovery and derivation of\nlaws is scientific explanation.\n\nThe discovery of quantitative laws is especially satisfactory, because\nit not only explains why an event happens at all, but why it happens\njust in this direction, degree, or amount; and not only is the given\nrelation of cause and effect definitely assimilated to other causal\ninstances, but the effect is identified with the cause as the same\nmatter and energy redistributed; wherefore, whether the conservation of\nmatter and energy be universally true or not, it must still be an\nuniversal postulate of scientific explanation.\n\nThe mere discovery of an empirical law of co-existence, as that 'white\ntom-cats with blue eyes are deaf', is indeed something better than an\nisolated fact: every general proposition relieves the mind of a load of\nfacts; and, for many people, to be able to say--'It is always so'--may\nbe enough; but for scientific explanation we require to know the reason\nof it, that is, the cause. Still, if asked to explain an axiom, we can\nonly say, 'It is always so:' though it is some relief to point out\nparticular instances of its realisation, or to exhibit the similarity of\nits form to that of other axioms--as of the _Dictum_ to the axiom of\nequality.\n\n\u00a7 6. There are three modes of scientific Explanation; First, the\nanalysis of a phenomenon into the laws of its causes and the concurrence\nof those causes.\n\nThe pumping of water implies (1) pressure of the air, (2) distribution\nof pressure in a liquid, (3) that motion takes the direction of least\nresistance. Similarly, that thunder follows forked lightning, and that\nthe report of a gun follows the flash, are resolvable into (1) the\ndischarge of electricity, or the explosion of gunpowder; (2) distance of\nthe observer from the event; (3) that light travels faster than sound.\nThe planetary orbits are analysable into the tendency of planets to fall\ninto the sun, and their tendency to travel in a straight line. When this\nconception is helped out by swinging a ball round by a string, and then\nletting it go, to show what would happen to the earth if gravitation\nceased, we see how the recognition of resemblance lies at the bottom of\nexplanation.\n\nSecondly, the discovery of steps of causation between a cause and its\nremote effects; the interpolation and concatenation of causes.\n\nThe maxim 'No cats no clover' is explained by assigning the intermediate\nsteps in the following series; that the fructification of red clover\ndepends on the visits of humble-bees, who distribute the pollen in\nseeking honey; that if field-mice are numerous they destroy the\nhumble-bees' nests; and that (owls and weasels being exterminated by\ngamekeepers) the destruction of field-mice depends upon the supply of\ncats; which, therefore, are a remote condition of the clover crop.\nAgain, the communication of thought by speech is an example of something\nso common that it seems to need no explanation; yet to explain it is a\nlong story. A thought in one man's mind is the remote cause of a similar\nthought in another's: here we have (1) a thought associated with mental\nwords; (2) a connection between these thoughts and some tracts of the\nbrain; (3) a connection between these tracts of the brain and the\nmuscles of the larynx, the tongue and the lips; (4) movements of the\nchest, larynx and mouth, propelling and modifying waves of air; (5) the\nimpinging of these air-waves upon another man's ear, and by a complex\nmechanism exciting the aural nerve; (6) the transfer of this excitation\nto certain tracts of his brain; (7) a connection there with sounds of\nwords and their associated thoughts. If one of these links fail, there\nis no communication.\n\nThirdly, the subsumption of several laws under one more general\nexpression.\n\nThe tendency of bodies to fall to the earth and the tendency of the\nearth itself (with the other planets) to fall into the sun, are subsumed\nunder the general law that 'All matter gravitates.' The same law\nsubsumes the movements of the tide. By means of the notion of specific\ngravity, it includes 'levitation,' or the actual rising of some bodies,\nas of corks in water, of balloons, or flames in the air: the fact being\nthat these things do not tend to rise, but to fall like everything else;\nonly as the water or air weighs more in proportion to its volume than\ncorks or balloons, the latter are pushed up.\n\nThis process of subsumption bears the same relation to secondary laws,\nthat these do to particular facts. The generalisation of many particular\nfacts (that is, a statement of that in which they agree) is a law; and\nthe generalisation of these laws (that is, again, a statement of that in\nwhich they agree) is a higher law; and this process, upwards or\ndownwards, is characteristic of scientific progress. The perfecting of\nany science consists in comprehending more and more of the facts within\nits province, and in showing that they all exemplify a smaller and\nsmaller number of principles, which express their most profound\nresemblances.\n\nThese three modes of explanation (analysis, interpolation, subsumption)\nall consist in generalising or assimilating the phenomena. The pressure\nof the air, of a liquid, and motion in the direction of least\nresistance, are all commoner facts than pumping; that light travels\nfaster than sound is a commoner fact than a thunderstorm or gun-firing.\nEach of the laws--'Cats kill mice,' 'Mice destroy humble-bees' nests,'\n'Humble-bees fructify red clover'--is wider and expresses the\nresemblance of more numerous cases than the law that 'Clover depends on\ncats'; because each of them is less subject to further conditions.\nSimilarly, every step in the communication of thought by language is\nless conditional, and therefore more general, than the completion of the\nprocess.\n\nIn all the above cases, again, each law into which the phenomenon\n(whether pumping or conversation) is resolved, suggests a host of\nparallel cases: as the modifying of air-waves by the larynx and lips\nsuggests the various devices by which the strings and orifices of\nmusical instruments modify the character of notes.\n\nSubsumption consists entirely in proving the existence of an essential\nsimilarity between things where it was formerly not observed: as that\nthe gyrations of the moon, the fall of apples, and the flotation of\nbubbles are all examples of gravitation: or that the purifying of the\nblood by breathing, the burning of a candle, and the rusting of iron are\nall cases of oxidation: or that the colouring of the underside of a\nred-admiral's wings, the spots of the giraffe, the shape and attitude of\na stick-caterpillar, the immobility of a bird on its nest, and countless\nother cases, though superficially so different, agree in this, that they\nconceal and thereby protect the organism.\n\nNot any sort of likeness, however, suffices for scientific explanation:\nthe only satisfactory explanation of concrete things or events, is to\ndiscover their likeness to others in respect of Causation. Hence\nattempts to help the understanding by familiar comparisons are often\nworse than useless. Any of the above examples will show that the first\nresult of explanation is not to make a phenomenon seem familiar, but to\nput (as the saying is) 'quite a new face upon it.' When, indeed, we have\nthought it over in all its newly discovered relations, we feel more at\nhome with it than ever; and this is one source of our satisfaction in\nexplaining things; and hence to substitute immediate familiarisation for\nradical explanation, is the easily besetting sin of human understanding:\nthe most plausible of fallacies, the most attractive, the most difficult\nto avoid even when we are on our guard against it.\n\n\u00a7 7. The explanation of Nature (if it be admitted to consist in\ngeneralisation, or the discovery of resemblance amidst differences) can\nnever be completed. For--(1) there are (as Mill says) facts, namely,\nfundamental states or processes of consciousness, which are distinct; in\nother words, they do not resemble one another, and therefore cannot be\ngeneralised or subsumed under one explanation. Colour, heat, smell,\nsound, touch, pleasure and pain, are so different that there is one\ngroup of conditions to be sought for each; and the laws of these\nconditions cannot be subsumed under a more general one without leaving\nout the very facts to be explained. A general condition of sensation,\nsuch as the stimulating of the sensory organs of a living animal, gives\nno account of the _special_ characters of colour, smell, etc.; which\nare, however, the phenomena in question; and each of them has its own\nlaw. Nay, each distinct sensation-quality, or degree, must have its own\nlaw; for in each ultimate difference there is something that cannot be\nassimilated. Such differences amount, according to experimental\nPsychologists, to more than 50,000. Moreover, a neural process can never\nexplain a conscious process in the way of cause and effect; for there is\nno equivalence between them, and one can never absorb the other.\n\n(2) When physical science is treated objectively (that is, with as\nlittle reference as possible to the fact that all phenomena are only\nknown in relation to the human mind), colour, heat, smell, sound\n(considered as sensations) are neglected, and attention is fixed upon\ncertain of their conditions: extension, figure, resistance, weight,\nmotion, with their derivatives, density, elasticity, etc. These are\ncalled the Primary Qualities of Matter; and it is assumed that they\nbelong to matter by itself, whether we look on or not: whilst colour,\nheat, sound, etc., are called Secondary Qualities, as depending\nentirely upon the reaction of some conscious animal. By physical science\nthe world is considered in the abstract, as a perpetual redistribution\nof matter and energy, and the distracting multiplicity of sensations\nseems to be got rid of.\n\nBut, not to dwell upon the difficulty of reducing the activities of life\nand chemistry to mechanical principles--even if this were done, complete\nexplanation could not be attained. For--(a) as explanation is the\ndiscovery of causes, we no sooner succeed in assigning the causes of the\npresent state of the world than we have to inquire into the causes of\nthose causes, and again the still earlier causes, and so on to infinity.\nBut, this being impossible, we must be content, wherever we stop, to\ncontemplate the uncaused, that is, the unexplained; and then all that\nfollows is only relatively explained.\n\nBesides this difficulty, however, there is another that prevents the\nperfecting of any theory of the abstract material world, namely (b),\nthat it involves more than one first principle. For we have seen that\nthe Uniformity of Nature is not really a principle, but a merely nominal\ngeneralisation, since it cannot be definitely stated; and, therefore,\nthe principles of Contradiction, Mediate Equality, and Causation remain\nincapable of subsumption; nor can any one of them be reduced to another:\nso that they remain unexplained.\n\n(3) Another limit to explanation lies in the infinite character of every\nparticular fact; so that we may know the laws of many of its properties\nand yet come far short of understanding it as a whole. A lump of\nsandstone in the road: we may know a good deal about its specific\ngravity, temperature, chemical composition, geological conditions; but\nif we inquire the causes of the particular modifications it exhibits of\nthese properties, and further why it is just so big, containing so many\nmolecules, neither more nor less, disposed in just such relations to one\nanother as to give it this particular figure, why it lies exactly there\nrather than a yard off, and so forth, we shall get no explanation of all\nthis. The causes determining each particular phenomenon are infinite,\nand can never be computed; and, therefore, it can never be fully\nexplained.\n\n\u00a7 8. Analogy is used in two senses: (1) for the resemblance of relations\nbetween terms that have little or no resemblance--as _The wind drives\nthe clouds as a shepherd drives his sheep_--where wind and shepherd,\nclouds and sheep are totally unlike. Such analogies are a favourite\nfigure in poetry and rhetoric, but cannot prove anything. For valid\nreasoning there must be parallel cases, according to substance and\nattribute, or cause and effect, or proportion: e.g. _As cattle and deer\nare to herbivorousness, so are camels; As bodies near the earth fall\ntoward it, so does the moon; As 2 is to 3 so is 4 to 6._\n\n(2) Analogy is discussed in Logic as a kind of probable proof based upon\nimperfect similarity (as the best that can be discovered) between the\n_data_ of comparison and the subject of our inference. Like Deduction\nand Induction, it assumes that things which are alike in some respects\nare also alike in others; but it differs from them in not appealing to a\ndefinite general law assigning the essential points of resemblance upon\nwhich the argument relies. In Deductive proof, this is done by the major\npremise of every syllogism: if the major says that 'All fat men are\nhumorists,' and we can establish the minor, 'X is a fat man,' we have\nsecured the essential resemblance that carries the conclusion. In\ninduction, the Law of Causation and its representatives, the Canons,\nserve the same purpose, specifying the essential marks of a cause. But,\nin Analogy, the resemblance relied on cannot be stated categorically.\n\nIf we argue that Mars is inhabited because it resembles the datum, our\nEarth, (1) in being a planet, (2) neither too hot nor too cold for life,\n(3) having an atmosphere, (4) land and water, etc., we are not\nprepared to say that 'All planets having these characteristics are\ninhabited.' It is, therefore, not a deduction; and since we do not know\nthe original causes of life on the Earth, we certainly cannot show by\ninduction that adequate causes exist in Mars. We rely, then, upon some\nsuch vague notion of Uniformity as that 'Things alike in some points are\nalike in others'; which, plainly, is either false or nugatory. But if\nthe linear markings upon the surface of Mars indicate a system of\ncanals, the inference that he has intelligent inhabitants is no longer\nanalogical, since canals can have no other cause.\n\nThe cogency of any proof depends upon the _character_ and _definiteness_\nof the likeness which one phenomenon bears to another; but Analogy\ntrusts to the general _quantity_ of likeness between them, in ignorance\nof what may be the really important likeness. If, having tried with a\nstone, an apple, a bullet, etc., we find that they all break an\nordinary window, and thence infer that a cricket ball will do so, we do\nnot reason by analogy, but make instinctively a deductive extension of\nan induction, merely omitting the explicit generalisation, 'All missiles\nof a certain weight, size and solidity break windows.' But if, knowing\nnothing of snakes except that the viper is venomous, a child runs away\nfrom a grass-snake, he argues by analogy; and, though his conduct is\nprudentially justifiable, his inference is wrong: for there is no law\nthat 'All snakes are venomous,' but only that those are venomous that\nhave a certain structure of fang; a point which he did not stay to\nexamine.\n\nThe discovery of an analogy, then, may suggest hypotheses; it states a\nproblem--to find the causes of the analogy; and thus it may lead to\nscientific proof; but merely analogical argument is only probable in\nvarious degrees. (1) The greater the number and importance of the points\nof agreement, the more probable is the inference. (2) The greater the\nnumber and importance of the points of difference, the less probable is\nthe inference. (3) The greater the number of unknown properties in the\nsubject of our argument, the less the value of any inference from those\nthat we do know. Of course the number of unknown properties can itself\nbe estimated only by analogy. In the case of Mars, they are probably\nvery numerous; and, apart from the evidence of canals, the prevalent\nassumption that there are intelligent beings in that planet, seems to\nrest less upon probability than on a curiously imaginative extension of\nthe gregarious sentiment, the chilly discomfort of mankind at the\nthought of being alone in the universe, and a hope that there may be\nconversable and 'clubable' souls nearer than the Dog-star.\n\n\n\n\nCHAPTER XX\n\nPROBABILITY\n\n\n\u00a7 1. Chance was once believed to be a distinct power in the world,\ndisturbing the regularity of Nature; though, according to Aristotle, it\nwas only operative in occurrences below the sphere of the moon. As,\nhowever, it is now admitted that every event in the world is due to some\ncause, if we can only trace the connection, whilst nevertheless the\nnotion of Chance is still useful when rightly conceived, we have to find\nsome other ground for it than that of a spontaneous capricious force\ninherent in things. For such a conception can have no place in any\nlogical interpretation of Nature: it can never be inferred from a\nprinciple, seeing that every principle expresses an uniformity; nor,\nagain, if the existence of a capricious power be granted, can any\ninference be drawn from it. Impossible alike as premise and as\nconclusion, for Reason it is nothing at all.\n\nEvery event is a result of causes: but the multitude of forces and the\nvariety of collocations being immeasurably great, the overwhelming\nmajority of events occurring about the same time are only related by\nCausation so remotely that the connection cannot be followed. Whilst my\npen moves along the paper, a cab rattles down the street, bells in the\nneighbouring steeple chime the quarter, a girl in the next house is\npractising her scales, and throughout the world innumerable events are\nhappening which may never happen together again; so that should one of\nthem recur, we have no reason to expect any of the others. This is\nChance, or chance coincidence. The word Coincidence is vulgarly used\nonly for the inexplicable concurrence of _interesting_ events--\"quite a\ncoincidence!\"\n\nOn the other hand, many things are now happening together or coinciding,\nthat will do so, for assignable reasons, again and again; thousands of\nmen are leaving the City, who leave at the same hour five days a week.\nBut this is not chance; it is causal coincidence due to the custom of\nbusiness in this country, as determined by our latitude and longitude\nand other circumstances. No doubt the above chance\ncoincidences--writing, cab-rattling, chimes, scales, etc.--are\ncausally connected at some point of past time. They were predetermined\nby the condition of the world ten minutes ago; and that was due to\nearlier conditions, one behind the other, even to the formation of the\nplanet. But whatever connection there may have been, we have no such\nknowledge of it as to be able to deduce the coincidence, or calculate\nits recurrence. Hence Chance is defined by Mill to be: Coincidence\ngiving no ground to infer uniformity.\n\nStill, some chance coincidences do recur according to laws of their own:\nI say _some_, but it may be all. If the world is finite, the possible\ncombinations of its elements are exhaustible; and, in time, whatever\nconditions of the world have concurred will concur again, and in the\nsame relation to former conditions. This writing, that cab, those\nchimes, those scales will coincide again; the Argonautic expedition, and\nthe Trojan war, and all our other troubles will be renewed. But let us\nconsider some more manageable instance, such as the throwing of dice.\nEvery one who has played much with dice knows that double sixes are\nsometimes thrown, and sometimes double aces. Such coincidences do not\nhappen once and only once; they occur again and again, and a great\nnumber of trials will show that, though their recurrence has not the\nregularity of cause and effect, it yet has a law of its own, namely--a\ntendency to average regularity. In 10,000 throws there will be some\nnumber of double sixes; and the greater the number of throws the more\nclosely will the average recurrence of double sixes, or double aces,\napproximate to one in thirty-six. Such a law of average recurrence is\nthe basis of Probability. Chance being the fact of coincidence without\nassignable cause, Probability is expectation based on the average\nfrequency of its happening.\n\n\u00a7 2. Probability is an ambiguous term. Usually, when we say that an\nevent is 'probable,' we mean that it is more likely than not to happen.\nBut, scientifically, an event is probable if our expectation of its\noccurrence is less than certainty, as long as the event is not\nimpossible. Probability, thus conceived, is represented by a fraction.\nTaking 1 to stand for certainty, and 0 for impossibility, probability\nmay be 999/1000, or 1/1000, or (generally) 1/_m_. The denominator\nrepresents the number of times that an event happens, and the numerator\nthe number of times that it coincides with another event. In throwing a\ndie, the probability of ace turning up is expressed by putting the\nnumber of throws for the denominator and the number of times that ace is\nthrown for the numerator; and we may assume that the more trials we make\nthe nearer will the resulting fraction approximate to 1/6.\n\nInstead of speaking of the 'throwing of the die' and its 'turning up\nace' as two events, the former is called 'the event' and the latter 'the\nway of its happening.' And these expressions may easily be extended to\ncover relations of distinct events; as when two men shoot at a mark and\nwe desire to represent the probability of both hitting the bull's eye\ntogether, each shot may count as an event (denominator) and the\ncoincidence of 'bull's-eyes' as the way of its happening (numerator).\n\nIt is also common to speak of probability as a proportion. If the\nfraction expressing the probability of ace being cast is 1/6, the\nproportion of cases in which it happens is 1 to 5; or (as it is,\nperhaps, still more commonly put) 'the chances are 5 to 1 against it.'\n\n\u00a7 3. As to the grounds of probability opinions differ. According to one\nview the ground is subjective: probability depends, it is said, upon the\nquantity of our Belief in the happening of a certain event, or in its\nhappening in a particular way. According to the other view the ground is\nobjective, and, in fact, is nothing else than experience, which is most\ntrustworthy when carefully expressed in statistics.\n\nTo the subjective view it may be objected, (a) that belief cannot by\nitself be satisfactorily measured. No one will maintain that belief,\nmerely as a state of mind, always has a definite numerical value of\nwhich one is conscious, as 1/100 or 1/10. Let anybody mix a number of\nletters in a bag, knowing nothing of them except that one of them is X,\nand then draw them one by one, endeavouring each time to estimate the\nvalue of his belief that the next will be X; can he say that his belief\nin the drawing of X next time regularly increases as the number of\nletters left decreases?\n\nIf not, we see that (b) belief does not uniformly correspond with the\nstate of the facts. If in such a trial as proposed above, we really wish\nto draw X, as when looking for something in a number of boxes, how\ncommon it is, after a few failures, to feel quite hopeless and to say:\n\"Oh, of course it will be in the last.\" For belief is subject to hope\nand fear, temperament, passion, and prejudice, and not merely to\nrational considerations. And it is useless to appeal to 'the Wise Man,'\nthe purely rational judge of probability, unless he is producible. Or,\nif it be said that belief is a short cut to the evaluation of\nexperience, because it is the resultant of all past experience, we may\nreply that this is not true. For one striking experience, or two or\nthree recent ones, will immensely outweigh a great number of faint or\nremote experiences. Moreover, the experience of two men may be\npractically equal, whilst their beliefs upon any question greatly\ndiffer. Any two Englishmen have about the same experience, personal and\nancestral, of the weather; yet their beliefs in the saw that 'if it rain\non St. Swithin's Day it will rain for forty days after,' may differ as\nconfident expectation and sheer scepticism. Upon which of these beliefs\nshall we ground the probability of forty days' rain?\n\nBut (c) at any rate, if Probability is to be connected with Inductive\nLogic, it must rest upon the same ground, namely--observation.\nInduction, in any particular case, is not content with beliefs or\nopinions, but aims at testing, verifying or correcting them by appealing\nto the facts; and Probability has the same object and the same basis.\n\nIn some cases, indeed, the conditions of an event are supposed to be\nmathematically predetermined, as in tossing a penny, throwing dice,\ndealing cards. In throwing a die, the ways of happening are six; in\ntossing a penny only two, head and tail: and we usually assume that the\nodds with a die are fairly 5 to 1 against ace, whilst with a penny 'the\nbetting is even' on head or tail. Still, this assumption rests upon\nanother, that the die is perfectly fair, or that the head and tail of a\npenny are exactly alike; and this is not true. With an ordinary die or\npenny, a very great number of trials would, no doubt, give an average\napproximating to 1/6 or 1/2; yet might always leave a certain excess one\nway or the other, which would also become more definite as the trials\nwent on; thus showing that the die or penny did not satisfy the\nmathematical hypothesis. Buffon is said to have tossed a coin 4040\ntimes, obtaining 1992 heads and 2048 tails; a pupil of De Morgan tossed\n4092 times, obtaining 2048 heads and 2044 tails.\n\nThere are other important cases in which probability is estimated and\nnumerically expressed, although statistical evidence directly bearing\nupon the point in question cannot be obtained; as in betting upon a\nrace; or in the prices of stocks and shares, which are supposed to\nrepresent the probability of their paying, or continuing to pay, a\ncertain rate of interest. But the judgment of experts in such matters is\ncertainly based upon experience; and great pains are taken to make the\nevidence as definite as possible by comparing records of speed, or by\nfinancial estimates; though something must still be allowed for reports\nof the condition of horses, or of the prospects of war, harvests, etc.\n\nHowever, where statistical evidence is obtainable, no one dreams of\nestimating probability by the quantity of his belief. Insurance offices,\ndealing with fire, shipwreck, death, accident, etc., prepare elaborate\nstatistics of these events, and regulate their rates accordingly. Apart\nfrom statistics, at what rate ought the lives of men aged 40 to be\ninsured, in order to leave a profit of 5 per cent. upon \u00a31000 payable at\neach man's death? Is 'quantity of belief' a sufficient basis for doing\nthis sum?\n\n\u00a7 4. The ground of probability is experience, then, and, whenever\npossible, statistics; which are a kind of induction. It has indeed been\nurged that induction is itself based upon probability; that the\nsubtlety, complexity and secrecy of nature are such, that we are never\nquite sure that we fully know even what we have observed; and that, as\nfor laws, the conditions of the universe at large may at any moment be\ncompletely changed; so that all imperfect inductions, including the law\nof causation itself, are only probable. But, clearly, this doctrine\nturns upon another ambiguity in the word 'probable.' It may be used in\nthe sense of 'less than absolutely certain'; and such doubtless is the\ncondition of all human knowledge, in comparison with the comprehensive\nintuition of arch-angels: or it may mean 'less than certain according\nto _our_ standard of certainty,' that is, in comparison with the law of\ncausation and its derivatives.\n\nWe may suppose some one to object that \"by this relative standard even\nempirical laws cannot be called 'only probable' as long as we 'know no\nexception to them'; for that is all that can be said for the boasted law\nof causation; and that, accordingly, we can frame no fraction to\nrepresent their probability. That 'all swans are white' was at one time,\nfrom this point of view, not probable but certain; though we now know it\nto be false. It would have been an indecorum to call it only probable as\nlong as no other-coloured swan had been discovered; not merely because\nthe quantity of belief amounted to certainty, but because the number of\nevents (seeing a swan) and the number of their happenings in a certain\nway (being white) were equal, and therefore the evidence amounted to 1\nor certainty.\" But, in fact, such an empirical law is only probable; and\nthe estimate of its probability must be based on the number of times\nthat similar laws have been found liable to exceptions. Albinism is of\nfrequent occurrence; and it is common to find closely allied varieties\nof animals differing in colour. Had the evidence been duly weighed, it\ncould never have seemed more than probable that 'all swans are white.'\nBut what law, approaching the comprehensiveness of the law of causation,\npresents any exceptions?\n\nSupposing evidence to be ultimately nothing but accumulated experience,\nthe amount of it in favour of causation is incomparably greater than the\nmost that has ever been advanced to show the probability of any other\nkind of event; and every relation of events which is shown to have the\nmarks of causation obtains the support of that incomparably greater body\nof evidence. Hence the only way in which causation can be called\nprobable, for us, is by considering it as the upward limit (1) to which\nthe series of probabilities tends; as impossibility is the downward\nlimit (0). Induction, 'humanly speaking,' does not rest on probability;\nbut the probability of concrete events (not of mere mathematical\nabstractions like the falling of absolutely true dice) rests on\ninduction and, therefore, on causation. The inductive evidence\nunderlying an estimate of probability may be of three kinds: (a) direct\nstatistics of the events in question; as when we find that, at the age\nof 20, the average expectation of life is 39-40 years. This is an\nempirical law, and, if we do not know the causes of any event, we must\nbe content with an empirical law. But (b) if we do know the causes of an\nevent, and the causes which may prevent its happening, and can estimate\nthe comparative frequency of their occurring, we may deduce the\nprobability that the effect (that is, the event in question) will occur.\nOr (c) we may combine these two methods, verifying each by means of the\nother. Now either the method (b) or (_a fortiori_) the method (c) (both\ndepending on causation) is more trustworthy than the method (a) by\nitself.\n\nBut, further, a merely empirical statistical law will only be true as\nlong as the causes influencing the event remain the same. A die may be\nfound to turn ace once in six throws, on the average, in close\naccordance with mathematical theory; but if we load it on that facet the\nresults will be very different. So it is with the expectation of life,\nor fire, or shipwreck. The increased virulence of some epidemic such as\ninfluenza, an outbreak of anarchic incendiarism, a moral epidemic of\nover-loading ships, may deceive the hopes of insurance offices. Hence we\nsee, again, that probability depends upon causation, not causation upon\nprobability.\n\nThat uncertainty of an event which arises not from ignorance of the law\nof its cause, but from our not knowing whether the cause itself does or\ndoes not occur at any particular time, is Contingency.\n\n\u00a7 5. The nature of an average supposes deviations from it. Deviations\nfrom an average, or \"errors,\" are assumed to conform to the law (1) that\nthe greater errors are less frequent than the smaller, so that most\nevents approximate to the average; and (2) that errors have no \"bias,\"\nbut are equally frequent and equally great in both directions from the\nmean, so that they are scattered symmetrically. Hence their distribution\nmay be expressed by some such figure as the following:\n\n[Illustration: FIG. 11.]\n\nHere _o_ is the average event, and _oy_ represents the number of average\nevents. Along _ox_, in either direction, deviations are measured. At _p_\nthe amount of error or deviation is _op_; and the number of such\ndeviations is represented by the line or ordinate _pa_. At _s_ the\ndeviation is _os_; and the number of such deviations is expressed by\n_sb_. As the deviations grow greater, the number of them grows less. On\nthe other side of _o_, toward _-x_, at distances, _op'_, _os'_ (equal to\n_op_, _os_) the lines _p'a'_, _s'b'_ represent the numbers of those\nerrors (equal to _pa_, _sb_).\n\nIf _o_ is the average height of the adult men of a nation, (say) 5 ft. 6\nin., _s'_ and _s_ may stand for 5 ft. and 6 ft.; men of 4 ft. 6 in. lie\nfurther toward _-x_, and men of 6 ft. 6 in. further toward _x_. There\nare limits to the stature of human beings (or to any kind of animal or\nplant) in both directions, because of the physical conditions of\ngeneration and birth. With such events the curve _b'yb_ meets the\nabscissa at some point in each direction; though where this occurs can\nonly be known by continually measuring dwarfs and giants. But in\nthrowing dice or tossing coins, whilst the average occurrence of ace is\nonce in six throws, and the average occurrence of 'tail' is once in two\ntosses, there is no necessary limit to the sequences of ace or of 'tail'\nthat may occur in an infinite number of trials. To provide for such\ncases the curve is drawn as if it never touched the abscissa.\n\nThat some such figure as that given above describes a frequent\ncharacteristic of an average with the deviations from it, may be shown\nin two ways: (1) By arranging the statistical results of any homogeneous\nclass of measurements; when it is often found that they do, in fact,\napproximately conform to the figure; that very many events are near the\naverage; that errors are symmetrically distributed on either side, and\nthat the greater errors are the rarer. (2) By mathematical demonstration\nbased upon the supposition that each of the events in question is\ninfluenced, more or less, by a number of unknown conditions common to\nthem all, and that these conditions are independent of one another. For\nthen, in rare cases, all the conditions will operate favourably in one\nway, and the men will be tall; or in the opposite way, and the men will\nbe short; in more numerous cases, many of the conditions will operate in\none direction, and will be partially cancelled by a few opposing them;\nwhilst in still more cases opposed conditions will approximately balance\none another and produce the average event or something near it. The\nresults will then conform to the above figure.\n\nFrom the above assumption it follows that the symmetrical curve\ndescribes only a 'homogeneous class' of measurements; that is, a class\nno portion of which is much influenced by conditions peculiar to itself.\nIf the class is not homogeneous, because some portion of it is subject\nto _peculiar_ conditions, the curve will show a hump on one side or the\nother. Suppose we are tabulating the ages at which Englishmen die who\nhave reached the age of 20, we may find that the greatest number die at\n39 (19 years being the average expectation of life at 20) and that as\nfar as that age the curve upwards is regular, and that beyond the age of\n39 it begins to descend regularly, but that on approaching 45 it bulges\nout some way before resuming its regular descent--thus:\n\n[Illustration: FIG. 12.]\n\nSuch a hump in the curve might be due to the presence of a considerable\nbody of teetotalers, whose longevity was increased by the peculiar\ncondition of abstaining from alcohol, and whose average age was 45, 6\nyears more than the average for common men.\n\nAgain, if the group we are measuring be subject to selection (such as\nBritish soldiers, for which profession all volunteers below a certain\nheight--say, 5 ft. 5 in.--are rejected), the curve will fall steeply on\none side, thus:\n\n[Illustration: FIG. 13.]\n\nIf, above a certain height, volunteers are also rejected, the curve will\nfall abruptly on both sides. The average is supposed to be 5 ft. 8 in.\n\nThe distribution of events is described by 'some such curve' as that\ngiven in Fig. 11; but different groups of events may present figures or\nsurfaces in which the slopes of the curves are very different, namely,\nmore or less steep; and if the curve is very steep, the figure runs into\na peak; whereas, if the curve is gradual, the figure is comparatively\nflat. In the latter case, where the figure is flat, fewer events will\nclosely cluster about the average, and the deviations will be greater.\n\nSuppose that we know nothing of a given event except that it belongs to\na certain class or series, what can we venture to infer of it from our\nknowledge of the series? Let the event be the cephalic index of an\nEnglishman. The cephalic index is the breadth of a skull \u00d7 100 and\ndivided by the length of it; e.g. if a skull is 8 in. long and 6 in.\nbroad, (6\u00d7100)/8=75. We know that the average English skull has an index\nof 78. The skull of the given individual, therefore, is more likely to\nhave that index than any other. Still, many skulls deviate from the\naverage, and we should like to know what is the probable error in this\ncase. The probable error is the measurement that divides the deviations\nfrom the average in either direction into halves, so that there are as\nmany events having a greater deviation as there are events having a less\ndeviation. If, in Fig. 11 above, we have arranged the measurements of\nthe cephalic index of English adult males, and if at _o_ (the average or\nmean) the index is 78, and if the line _pa_ divides the right side of\nthe fig. into halves, then _op_ is the probable error. If the\nmeasurement at _p_ is 80, the probable error is 2. Similarly, on the\nleft hand, the probable error is _op'_, and the measurement at _p'_ is\n76. We may infer, then, that the skull of the man before us is more\nlikely to have an index of 78 than any other; if any other, it is\nequally likely to lie between 80 and 76, or to lie outside them; but as\nthe numbers rise above 80 to the right, or fall below 76 to the left, it\nrapidly becomes less and less likely that they describe this skull.\n\nIn such cases as heights of men or skull measurements, where great\nnumbers of specimens exist, the average will be actually presented by\nmany of them; but if we take a small group, such as the measurements of\na college class, it may happen that the average height (say, 5 ft. 8\nin.) is not the actual height of any one man. Even then there will\ngenerally be a closer cluster of the actual heights about that number\nthan about any other. Still, with very few cases before us, it may be\nbetter to take the median than the average. The median is that event on\neither side of which there are equal numbers of deviations. One\nadvantage of this procedure is that it may save time and trouble. To\nfind approximately the average height of a class, arrange the men in\norder of height, take the middle one and measure him. A further\nadvantage of this method is that it excludes the influence of\nextraordinary deviations. Suppose we have seven cephalic indices, from\nskeletons found in the same barrow, 75-1/2, 76, 78, 78, 79, 80-1/2, 86.\nThe average is 79; but this number is swollen unduly by the last\nmeasurement; and the median, 78, is more fairly representative of the\nseries; that is to say, with a greater number of skulls the average\nwould probably have been nearer 78.\n\nTo make a single measurement of a phenomenon does not give one much\nconfidence. Another measurement is made; and then, if there is no\nopportunity for more, one takes the mean or average of the two. But why?\nFor the result may certainly be worse than the first measurement.\nSuppose that the events I am measuring are in fact fairly described by\nFig. II, although (at the outset) I know nothing about them; and that my\nfirst measurement gives _p_, and my second _s_; the average of them is\nworse than _p_. Still, being yet ignorant of the distribution of these\nevents, I do rightly in taking the average. For, as it happens, 3/4 of\nthe events lie to the left of _p_; so that if the first trial gives _p_,\nthen the average of _p_ and any subsequent trial that fell nearer than\n(say) _s'_ on the opposite side, would be better than _p_; and since\ndeviations greater than _s'_ are rare, the chances are nearly 3 to 1\nthat the taking of an average will improve the observation. Only if the\nfirst trial give _o_, or fall within a little more than 1/2 _p_ on\neither side of _o_, will the chances be against any improvement by\ntrying again and taking an average. Since, therefore, we cannot know the\nposition of our first trial in relation to _o_, it is always prudent to\ntry again and take the average; and the more trials we can make and\naverage, the better is the result. The average of a number of\nobservations is called a \"Reduced Observation.\"\n\nWe may have reason to believe that some of our measurements are better\nthan others because they have been taken by a better trained observer,\nor by the same observer in a more deliberate way, or with better\ninstruments, and so forth. If so, such observations should be\n'weighted,' or given more importance in our calculations; and a simple\nway of doing this is to count them twice or oftener in taking the\naverage.\n\n\u00a7 6. These considerations have an important bearing upon the\ninterpretation of probabilities. The average probability for any\n_general class_ or series of events cannot be confidently applied to any\n_one instance_ or to any _special class_ of instances, since this one,\nor this special class, may exhibit a striking error or deviation; it\nmay, in fact, be subject to special causes. Within the class whose\naverage is first taken, and which is described by general characters as\n'a man,' or 'a die,' or 'a rifle shot,' there may be classes marked by\nspecial characters and determined by special influences. Statistics\ngiving the average for 'mankind' may not be true of 'civilised men,' or\nof any still smaller class such as 'Frenchmen.' Hence life-insurance\noffices rely not merely on statistics of life and death in general, but\ncollect special evidence in respect of different ages and sexes, and\nmake further allowance for teetotalism, inherited disease, etc.\nSimilarly with individual cases: the average expectation for a class,\nwhether general or special, is only applicable to any particular case if\nthat case is adequately described by the class characters. In England,\nfor example, the average expectation of life for males at 20 years of\nage is 39.40; but at 60 it is still 13.14, and at 73 it is 7.07; at 100\nit's 1.61. Of men 20 years old those who live more or less than 39.40\nyears are deviations or errors; but there are a great many of them. To\ninsure the life of a single man at 20, in the expectation of his dying\nat 60, would be a mere bet, if we had no special knowledge of him; the\nsafety of an insurance office lies in having so many clients that\nopposite deviations cancel one another: the more clients the safer the\nbusiness. It is quite possible that a hundred men aged 20 should be\ninsured in one week and all of them die before 25; this would be\nruinous, if others did not live to be 80 or 90.\n\nNot only in such a practical affair as insurance, but in matters purely\nscientific, the minute and subtle peculiarities of individuals have\nimportant consequences. Each man has a certain cast of mind, character,\nphysique, giving a distinctive turn to all his actions even when he\ntries to be normal. In every employment this determines his Personal\nEquation, or average deviation from the normal. The term Personal\nEquation is used chiefly in connection with scientific observation, as\nin Astronomy. Each observer is liable to be a little wrong, and this\nerror has to be allowed for and his observations corrected accordingly.\n\nThe use of the term 'expectation,' and of examples drawn from insurance\nand gambling, may convey the notion that probability relates entirely to\nfuture events; but if based on laws and causes, it can have no reference\nto point of time. As long as conditions are the same, events will be the\nsame, whether we consider uniformities or averages. We may therefore\ndraw probable inferences concerning the past as well as the future,\nsubject to the same hypothesis, that the causes affecting the events in\nquestion were the same and similarly combined. On the other hand, if we\nknow that conditions bearing on the subject of investigation, have\nchanged since statistics were collected, or were different at some time\nprevious to the collection of evidence, every probable inference based\non those statistics must be corrected by allowing for the altered\nconditions, whether we desire to reason forwards or backwards in time.\n\n\u00a7 7. The rules for the combination of probabilities are as follows:\n\n(1) If two events or causes do not concur, the probability of one or the\nother occurring is the sum of the separate probabilities. A die cannot\nturn up both ace and six; but the probability in favour of each is 1/6:\ntherefore, the probability in favour of one or the other is 1/3. Death\ncan hardly occur from both burning and drowning: if 1 in 1000 is burned\nand 2 in 1000 are drowned, the probability of being burned or drowned is\n3/1000.\n\n(2) If two events are independent, having neither connection nor\nrepugnance, the probability of their concurring is found by multiplying\ntogether the separate probabilities of each occurring. If in walking\ndown a certain street I meet A once in four times, and B once in three\ntimes, I ought (by mere chance) to meet both once in twelve times: for\nin twelve occasions I meet B four times; but once in four I meet A.\n\nThis is a very important rule in scientific investigation, since it\nenables us to detect the presence of causation. For if the coincidence\nof two events is more or less frequent than it would be if they were\nentirely independent, there is either connection or repugnance between\nthem. If, e.g., in walking down the street I meet both A and B oftener\nthan once in twelve times, they may be engaged in similar business,\ncalling them from their offices at about the same hour. If I meet them\nboth less often than once in twelve times, they may belong to the same\noffice, where one acts as a substitute for the other. Similarly, if in a\nmultitude of throws a die turns six oftener than once in six times, it\nis not a fair one: that is, there is a cause favouring the turning of\nsix. If of 20,000 people 500 see apparitions and 100 have friends\nmurdered, the chance of any man having both experiences is 1/8000; but\nif each lives on the average 300,000 hours, the chance of both events\noccurring in the same hour is 1/2400000000. If the two events occur in\nthe same hour oftener than this, there is more than a chance\ncoincidence.\n\nThe more minute a cause of connection or repugnance between events, the\nlonger the series of trials or instances necessary to bring out its\ninfluence: the less a die is loaded, the more casts must be made before\nit can be shown that a certain side tends to recur oftener than once in\nsix.\n\n(3) The rule for calculating the probability of a dependent event is the\nsame as the above; for the concurrence of two independent events is\nitself dependent upon each of them occurring. My meeting with both A and\nB in the street is dependent on my walking there and on my meeting one\nof them. Similarly, if A is sometimes a cause of B (though liable to be\nfrustrated), and B sometimes of C (C and B having no causes independent\nof B and A respectively), the occurrence of C is dependent on that of B,\nand that again on the occurrence of A. Hence we may state the rule: If\ntwo events are dependent each on another, so that if one occur the\nsecond may (or may not), and if the second a third; whilst the third\nnever occurs without the second, nor the second without the first; the\nprobability that if the first occur the third will, is found by\nmultiplying together the fractions expressing the probability that the\nfirst is a mark of the second and the second of the third.\n\nUpon this principle the value of hearsay evidence or tradition\ndeteriorates, and generally the cogency of any argument based upon the\ncombination of approximate generalisations dependent on one another or\n\"self-infirmative.\" If there are two witnesses, A and B, of whom A saw\nan event, whilst B only heard A relate it (and is therefore dependent on\nA), what credit is due to B's recital? Suppose the probability of each\nman's being correct as to what he says he saw, or heard, is 3/4: then\n(3/4 \u00d7 3/4 = 9/16) the probability that B's story is true is a little\nmore than 1/2. For if in 16 attestations A is wrong 4 times, B can only\nbe right in 3/4 of the remainder, or 9 times in 16. Again, if we have\nthe Approximate Generalisations, 'Most attempts to reduce wages are met\nby strikes,' and 'Most strikes are successful,' and learn, on\nstatistical inquiry, that in every hundred attempts to reduce wages\nthere are 80 strikes, and that 70 p.c. of the strikes are successful,\nthen 56 p.c. of attempts to reduce wages are unsuccessful.\n\nOf course this method of calculation cannot be quantitatively applied if\nno statistics are obtainable, as in the testimony of witnesses; and even\nif an average numerical value could be attached to the evidence of a\ncertain class of witnesses, it would be absurd to apply it to the\nevidence of any particular member of the class without taking account of\nhis education, interest in the case, prejudice, or general capacity.\nStill, the numerical illustration of the rapid deterioration of hearsay\nevidence, when less than quite veracious, puts us on our guard against\nrumour. To retail rumour may be as bad as to invent an original lie.\n\n(4) If an event may coincide with two or more other independent events,\nthe probability that they will together be a sign of it, is found by\nmultiplying together the fractions representing the improbability that\neach is a sign of it, and subtracting the product from unity.\n\nThis is the rule for estimating the cogency of circumstantial evidence\nand analogical evidence; or, generally, for combining approximate\ngeneralisations \"self-corroboratively.\" If, for example, each of two\nindependent circumstances, A and B, indicates a probability of 6 to 1 in\nfavour of a certain event; taking 1 to represent certainty, 1-6/7 is the\nimprobability of the event, notwithstanding each circumstance. Then 1/7\n\u00d7 1/7 = 1/49, the improbability of both proving it. Therefore the\nprobability of the event is 48 to 1. The matter may be plainer if put\nthus: A's indication is right 6 times in 7, or 42 in 49; in the\nremaining 7 times in 49, B's indication will be right 6 times.\nTherefore, together they will be right 48 times in 49. If each of two\nwitnesses is truthful 6 times in 7, one or the other will be truthful 48\ntimes in 49. But they will not be believed unless they agree; and in\nthe 42 cases of A being right, B will contradict him 6 times; so that\nthey only concur in being right 36 times. In the remaining 7 times in\nwhich A is wrong, B will contradict him 6 times, and once they will both\nbe wrong. It does not follow that when both are wrong they will concur;\nfor they may tell very different stories and still contradict one\nanother.\n\nIf in an analogical argument there were 8 points of comparison, 5 for\nand 3 against a certain inference, and the probability raised by each\npoint could be quantified, the total value of the evidence might be\nestimated by doing similar sums for and against, and subtracting the\nunfavourable from the favourable total.\n\nWhen approximate generalisations that have not been precisely quantified\ncombine their evidence, the cogency of the argument increases in the\nsame way, though it cannot be made so definite. If it be true that most\npoets are irritable, and also that most invalids are irritable, a still\ngreater proportion will be irritable of those who are both invalids and\npoets.\n\nOn the whole, from the discussion of probabilities there emerge four\nprincipal cautions as to their use: Not to make a pedantic parade of\nnumerical probability, where the numbers have not been ascertained; Not\nto trust to our feeling of what is likely, if statistics can be\nobtained; Not to apply an average probability to special classes or\nindividuals without inquiring whether they correspond to the average\ntype; and Not to trust to the empirical probability of events, if their\ncauses can be discovered and made the basis of reasoning which the\nempirical probability may be used to verify.\n\nThe reader who wishes to pursue this subject further should read a work\nto which the foregoing chapter is greatly indebted, Dr. Venn's _Logic of\nChance_.\n\n\n\n\nCHAPTER XXI\n\nDIVISION AND CLASSIFICATION\n\n\n\u00a7 1. Classification, in its widest sense, is a mental grouping of facts\nor phenomena according to their resemblances and differences, so as best\nto serve some purpose. A \"mental grouping\": for although in museums we\noften see the things themselves arranged in classes, yet such an\narrangement only contains specimens representing a classification. The\nclassification itself may extend to innumerable objects most of which\nhave never been seen at all. Extinct animals, for example, are\nclassified from what we know of their fossils; and some of the fossils\nmay be seen arranged in a museum; but the animals themselves have\ndisappeared for many ages.\n\nAgain, things are classed according to their resemblances and\ndifferences: that is to say, those that most closely resemble one\nanother are classed together on that ground; and those that differ from\none another in important ways, are distributed into other classes. The\nmore the things differ, the wider apart are their classes both in\nthought and in the arrangements of a museum. If their differences are\nvery great, as with animals, vegetables and minerals, the classing of\nthem falls to different departments of thought or science, and is often\nrepresented in different museums, zoological, botanical, mineralogical.\n\nWe must not, however, suppose that there is only one way of classifying\nthings. The same objects may be classed in various ways according to\nthe purpose in view. For gardening, we are usually content to classify\nplants into trees, shrubs, flowers, grasses and weeds; the ordinary\ncrops of English agriculture are distinguished, in settling their\nrotation, into white and green; the botanist divides the higher plants\ninto gymnosperms and angiosperms, and the latter into monocotyledons and\ndicotyledons. The principle of resemblance and difference is recognised\nin all these cases; but what resemblances or differences are important\ndepends upon the purpose to be served.\n\nPurposes are either ([alpha]) special or practical, as in gardening or\nhunting, or ([beta]) general or scientific, as in Botany or Zoology. The\nscientific purpose is merely knowledge; it may indeed subserve all\nparticular or practical ends, but has no other end than knowledge\ndirectly in view. And whilst, even for knowledge, different\nclassifications may be suitable for different lines of inquiry, in\nBotany and Zoology the Morphological Classification is that which gives\nthe most general and comprehensive knowledge (see Huxley, _On the\nClassification of Animals_, ch. 1). Most of what a logician says about\nclassification is applicable to the practical kind; but the scientific\n(often called 'Natural Classification'), as the most thorough and\ncomprehensive, is what he keeps most constantly before him.\n\nScientific classification comes late in human history, and at first\nworks over earlier classifications which have been made by the growth of\nintelligence, of language, and of the practical arts. Even in the\ndistinctions recognised by animals, may be traced the grounds of\nclassification: a cat does not confound a dog with one of its own\nspecies, nor water with milk, nor cabbage with fish. But it is in the\ndevelopment of language that the progress of instinctive classification\nmay best be seen. The use of general names implies the recognition of\nclasses of things corresponding to them, which form their denotation,\nand whose resembling qualities, so far as recognised, form their\nconnotation; and such names are of many degrees of generality. The use\nof abstract names shows that the objects classed have also been\nanalysed, and that their resembling qualities have been recognised\namidst diverse groups of qualities.\n\nOf the classes marked by popular language it is worth while to\ndistinguish two sorts (_cf._ chap. xix. \u00a7 4): Kinds, and those having\nbut few points of agreement.\n\nBut the popular classifications, made by language and the primitive\narts, are very imperfect. They omit innumerable things which have not\nbeen found useful or noxious, or have been inconspicuous, or have not\nhappened to occur in the region inhabited by those who speak a\nparticular language; and even things recognised and named may have been\nvery superficially examined, and therefore wrongly classed, as when a\nwhale or porpoise is called a fish, or a slowworm is confounded with\nsnakes. A scientific classification, on the other hand, aims at the\nutmost comprehensiveness, ransacking the whole world from the depths of\nthe earth to the remotest star for new objects, and scrutinising\neverything with the aid of crucible and dissecting knife, microscope and\nspectroscope, to find the qualities and constitution of everything, in\norder that it may be classed among those things with which it has most\nin common and distinguished from those other things from which it\ndiffers. A scientific classification continually grows more\ncomprehensive, more discriminative, more definitely and systematically\ncoherent. Hence the uses of classification may be easily perceived.\n\n\u00a7 2. The first use of classification is the better understanding of the\nfacts of Nature (or of any sphere of practice); for understanding\nconsists in perceiving and comprehending the likeness and difference of\nthings, in assimilating and distinguishing them; and, in carrying out\nthis process systematically, new correlations of properties are\ncontinually disclosed. Thus classification is closely analogous to\nexplanation. Explanation has been shown (chap. xix. \u00a7 5) to consist in\nthe discovery of the laws or causes of changes in Nature; and laws and\ncauses imply similarity, or like changes under like conditions: in the\nsame way classification consists in the discovery of resemblances in the\nthings that undergo change. We may say (subject to subsequent\nqualifications) that Explanation deals with Nature in its dynamic,\nClassification in its static aspect. In both cases we have a feeling of\nrelief. When the cause of any event is pointed out, or an object is\nassigned its place in a system of classes, the gaping wonder, or\nconfusion, or perplexity, occasioned by an unintelligible thing, or by a\nmultitude of such things, is dissipated. Some people are more than\nothers susceptible of this pleasure and fastidious about its purity.\n\nA second use of classification is to aid the memory. It strengthens\nmemory, because one of the conditions of our recollecting things is,\nthat they resemble what we last thought of; so that to be accustomed to\nstudy and think of things in classes must greatly facilitate\nrecollection. But, besides this, a classification enables us easily to\nrun over all the contrasted and related things that we want to think of.\nExplanation and classification both tend to rationalise the memory, and\nto organise the mind in correspondence with Nature.\n\nEvery one knows how a poor mind is always repeating itself, going by\nrote through the same train of words, ideas, actions; and that such a\nmind is neither interesting nor practical. It is not practical, because\nthe circumstances of life are rarely exactly repeated, so that for a\npresent purpose it is rarely enough to remember only one former case; we\nneed several, that by comparing (perhaps automatically) their\nresemblances and differences with the one before us, we may select a\ncourse of action, or a principle, or a parallel, suited to our\nimmediate needs. Greater fertility and flexibility of thought seem\nnaturally to result from the practice of explanation and classification.\nBut it must be honestly added, that the result depends upon the spirit\nin which such study is carried on; for if we are too fond of finality,\ntoo eager to believe that we have already attained a greater precision\nand comprehension than are in fact attainable, nothing can be more\npetrific than 'science,' and our last state may be worse than the first.\nOf this, students of Logic have often furnished examples.\n\n\u00a7 3. Classification may be either Deductive or Inductive; that is to\nsay, in the formation of classes, as in the proof of propositions, we\nmay, on the whole, proceed from the more to the less, or from the less\nto the more general; not that these two processes are entirely\nindependent.\n\nIf we begin with some large class, such as 'Animal,' and subdivide it\ndeductively into Vertebrate and Invertebrate, yet the principle of\ndivision (namely, central structure) has first been reached by a\ncomparison of examples and by generalisation; if, on the other hand,\nbeginning with individuals, we group them inductively into classes, and\nthese again into wider ones (as dogs, rats, horses, whales and monkeys\ninto mammalia) we are guided both in special cases by hypotheses as to\nthe best grounds of resemblance, and throughout by the general principle\nof classification--to associate things that are alike and to separate\nthings that are unlike. This principle holds implicitly a place in\nclassification similar to that of causation in explanation; both are\nprinciples of intelligence. Here, then, as in proof, induction is\nimplied in deduction, and deduction in induction. Still, the two modes\nof procedure may be usefully distinguished: in deduction, we proceed\nfrom the idea of a whole to its parts, from general to special; in\ninduction, from special (or particular) to general, from parts to the\nidea of a whole.\n\n\u00a7 4. The process of Deductive Classification, or Formal Division, may be\nrepresented thus:\n\n A\n |\n -------------------\n | |\n A B A b\n | |\n ---------- ----------\n | | | |\n A B C A B c A b C A b c\n\nGiven any class (A) to be divided:\n\n1. Select one important character, attribute, or quality (B), not common\nto all the individuals comprehended in the class, as the basis of\ndivision (_fundamentum divisionis_).\n\n2. Proceed by Dichotomy; that is, cut the given class into two, one\nhaving the selected attribute (say, B), the other not having it (b).\nThis, like all formal processes, assumes the principles of Contradiction\nand Excluded Middle, that 'No A is both B and not-B,' and that 'Every A\nis either B or not-B' (chap. vi. \u00a7 3); and if these principles are not\ntrue, or not applicable, the method fails.\n\nWhen a class is thus subdivided, it may be called, in relation to its\nsubclasses, a Genus; and in relation to it, the subclasses may be called\nSpecies: thus--genus A, species AB and Ab, etc.\n\n3. Proceed gradually in the order of the importance of characters; that\nis, having divided the given class, subdivide on the same principle the\ntwo classes thence arising; and so again and again, step by step, until\nall the characters are exhausted: _Divisio ne fiat per saltum_.\n\nSuppose we were to attempt an exhaustive classification of things by\nthis method, we must begin with 'All Things,' and divide them (say) into\nphenomenal and not-phenomenal, and then subdivide phenomena, and so on,\nthus:\n\n All Things\n |\n ------------------\n | |\n Phenomenal Not-phenomenal\n |\n --------------------\n | |\n Extended Unextended\n | (e.g., Pleasure and Pain)\n |\n ----------------\n | |\n Resistant Not-resistant\n (Matter) (Space)\n |\n -------------------\n | |\n Gravitating Not-gravitating\n |\n -----------\n | |\nSimple Compound\n\nHaving subdivided 'Simple' by all possible characters, we must then go\nback and similarly subdivide Not-phenomenal, Unextended, Not-resistant,\nNot-gravitating, and Compound. Now, if we knew all possible characters,\nand the order of their importance, we might prepare _a priori_ a\nclassification of all possible things; at least, of all things that come\nunder the principles of Contradiction and Excluded Middle. Many of our\ncompartments might contain nothing actual; there may, for example, be\nnothing that is not phenomenal to some mind, or nothing that is extended\nand not-resistant (no vacuum), and so forth. This would imply a breach\nof the rule, that the dividing quality be not common to the whole class;\nbut, in fact, doubts have been, and are, seriously entertained whether\nthese compartments are filled or not. If they are not, we have concepts\nrepresenting nothing, which have been generated by the mere force of\ngrammatical negation, or by the habit of thinking according to the\nprinciple of Excluded Middle; and, on the strength of these empty\nconcepts, we have been misled into dividing by an attribute, which\n(being universal) cannot be a _fundamentum divisionis_. But though in\nsuch a classification places might be empty, there would be a place for\neverything; for whatever did not come into some positive class (such as\nGravitating) must fall under one of the negative classes (the 'Nots')\nthat run down the right-hand side of the Table and of its subdivisions.\n\nThis is the ideal of classification. Unfortunately we have to learn what\ncharacters or attributes are possible, by experience and comparison; we\nare far from knowing them all: and we do not know the order of their\nimportance; nor are we even clear what 'important' means in this\ncontext, whether 'widely prevalent,' or 'ancient,' or 'causally\ninfluential,' or 'indicative of others.' Hence, in classifying actual\nthings, we must follow the inductive method of beginning with\nparticulars, and sorting them according to their likeness and difference\nas discovered by investigation. The exceptional cases, in which\ndeduction is really useful, occur where certain limits to the number and\ncombination of qualities happen to be known, as they may be in human\ninstitutions, or where there are mathematical conditions. Thus, we might\nbe able to classify orders of Architecture, or the classical metres and\nstanzas of English poetry; though, in fact, these things are too free,\nsubtle and complex for deductive treatment: for do not the Arts grow\nlike trees? The only sure cases are mathematical; as we may show that\nthere are possible only three kinds of plane triangles, four conic\nsections, five regular solids.\n\n\u00a7 5. The rules for _testing_ a Division are as follows:\n\n1. Each Sub-class, or Species, should comprise less than the Class, or\nGenus, to be divided. This provides that the division shall be a real\none, and not based upon an attribute common to the whole class; that,\ntherefore, the first rule for making a division shall have been adhered\nto. But, as in \u00a7 4, we are here met by a logical difficulty. Suppose\nthat the class to be divided is A, and that we attempt to divide upon\nthe attribute B, into AB and Ab; is this a true division, if we do not\nknow any A that is not B? As far as our knowledge extends, we have not\ndivided A at all. On the other hand, our knowledge of concrete things is\nnever exhaustive; so that, although we know of no A that is not B, it\nmay yet exist, and we have seen that it is a logical caution not to\nassume what we do not know. In a deductive classification, at least, it\nseems better to regard every attribute as a possible ground of division.\nHence, in the above division of 'All Things,'--'Not-phenomenal,'\n'Extended-Not-resistant,' 'Resistant-Not-gravitating,' appear as\nnegative classes (that is, classes based on the negation of an\nattribute), although their real existence may be doubtful. But, if this\nbe justifiable, we must either rewrite the first test of a division\nthus: 'Each sub-class should _possibly_ comprise less than the class to\nbe divided'; or else we must confine the test to (a) thoroughly\nempirical divisions, as in dividing Colour into Red and Not-red, where\nwe know that both sub-classes are real; and (b) divisions under\ndemonstrable conditions--as in dividing the three kinds of triangles by\nthe quality equilateral, we know that it is only applicable to\nacute-angled triangles, and do not attempt to divide the right-angled or\nobtuse-angled by it.\n\n2. The Sub-classes taken together should be equal to the Class to be\ndivided: the sum of the Species constitutes the Genus. This provides\nthat the division shall be exhaustive; which dichotomy always secures,\naccording to the principle of Excluded Middle; because whatever is not\nin the positive class, must be in the negative: Red and Not-red include\nall colours.\n\n3. The Sub-classes must be opposed or mutually exclusive: Species must\nnot overlap. This again is secured by dichotomy, according to the\nprinciple of Contradiction, provided the division be made upon one\nattribute at a time. But, if we attempt to divide simultaneously upon\ntwo attributes, as 'Musicians' upon 'nationality' and 'method,' we get\nwhat is called a Cross-division, thus 'German Musicians.' 'Not-German,'\n'Classical,' 'Not-Classical;' for these classes may overlap, the same\nmen sometimes appearing in two groups--Bach in 'German' and 'Classical,'\nPergolesi in 'Not-German' and 'Classical.' If, however, we divide\nMusicians upon these attributes successively, cross division will be\navoided, thus:\n\n Musicians\n |\n ------------------------\n | |\n Classical Not-classical\n | |\n ------------ ------------\n | | | |\nGerman Not-German German Not-German\n\nHere no Musician will be found in two classes, _unless_ he has written\nworks in two styles, _or unless_ there are works whose style is\nundecided. This \"unless--or unless\" may suggest caution in using\ndichotomy as a short cut to the classification of realities.\n\n4. No Sub-class must include anything that is not comprised in the class\nto be divided: the Genus comprises all the Species. We must not divide\nDogs into fox-terriers and dog-fish.\n\n\u00a7 6. The process of Inductive Classification may be represented thus:\n\nGiven any multitude of individuals to be classified:\n\n(1) Place together in groups (or in thought) those things that have in\ncommon the most, the most widely diffused and the most important\nqualities.\n\n(2) Connect those groups which have, as groups, the greater resemblance,\nand separate those that have the greater difference.\n\n(3) Demarcate, as forming higher or more general classes, those groups\nof groups that have important characters in common; and, if possible, on\nthe same principle, form these higher classes into classes higher still:\nthat is to say, graduate the classification upwards.\n\nWhilst in Division the terms 'Genus' and 'Species' are entirely relative\nto one another and have no fixed positions in a gradation of classes, it\nhas been usual, in Inductive Classification, to confine the term\n'Species' to classes regarded as lowest in the scale, to give the term\n'Genera' to classes on the step above, and at each higher step to find\nsome new term such as 'Tribe,' 'Order,' 'Sub-kingdom,' 'Kingdom'; as may\nbe seen by turning to any book on Botany or Zoology. If, having fixed\nour Species, we find them subdivisible, it is usual to call the\nSub-species 'Varieties.'\n\nSuppose an attempt to classify by this method the objects in a\nsitting-room. We see at a glance carpets, mats, curtains, grates,\nfire-irons, coal-scuttles, chairs, sofas, tables, books, pictures,\nmusical instruments, etc. These may be called 'Species.' Carpets and\nmats go together; so do chairs and sofas; so do grates, fire-irons, and\ncoal-scuttles and so on. These greater groups, or higher classes, are\n'Genera.' Putting together carpets, mats and curtains as\n'warmth-fabrics'; chairs, sofas and tables as 'supports'; books,\npictures and musical instruments as 'means of culture'; these groups we\nmay call Orders. Sum up the whole as, from the housewife's point of\nview, 'furniture.' If we then subdivide some of the species, as books\ninto poetry, novels, travels, etc., these Sub-species may be\nconsidered 'Varieties.'\n\nA Classification thus made, may be tested by the same rules as those\ngiven for testing a Division; but if it does not stand the test, we must\nnot infer that the classification is a bad one. If the best possible, it\nis good, though formally imperfect: whatever faults are found must then\nbe charged upon the 'matter,' which is traditionally perverse and\nintractable. If, for example, there is a hammock in the room, it must be\nclassed not with the curtains as a warmth-fabric, but with the sofas as\na support; and books and pictures may be classed as, in a peculiar\nsense, means of culture, though all the objects in the room may have\nbeen modified and assorted with a view to gratifying and developing good\ntaste.\n\n\u00a7 7. The difficulty of classifying natural objects is very great. It is\nnot enough to consider their external appearance: exhaustive knowledge\nof their internal structure is necessary, and of the functions of every\npart of their structure. This is a matter of immense research, and has\noccupied many of the greatest minds for very many years. The following\nis a tabular outline of the classification of the\n\n Animal Kingdom\n |\n -------------------\n | |\nSUB-KINGDOM, Vertebrates Invertebrates (10 Sub-kingdom 5)\n or |\n Phylum: |-------------------------------\n | | |\n | Sauropsida Ichthyopsida\n | | |\n | --------- -----------\n | | | | |\nCLASS: Mammalia Birds Reptiles Amphibia Fishes\n |\n -------------------------\n | |\nSUB-CLASS: Placental Implacental\n | |\n | -------------------\n | | |\nDIVISION: Monodelphia Didelphia Ornithodelphia\n |\n ---------------------------------------\n | | | | |\nORDER: Quadrumana Rodentia Carnivora Ungulata C\u00e6tacea, etc.\n |\n ----------------------------------\n | | |\nSECTION: Pinnigrada Plantigrada Digitigrada\n | | |\n (Seals, etc.) (Bears, etc.) |\n |\n --------------------------------------\n | | | | |\nGENUS: Mustelid\u00e6 Viverrid\u00e6 Hya\u00e6nid\u00e6 Canid\u00e6 Felid\u00e6\n | | |\n (Weasels, etc.) (Civets, etc.) |\n |\n ---------------------------------------\n | | | | | |\nSPECIES: Lion Tiger Leopard Puma Lynx Cat, etc.\n |\n ---------------------\n | | |\nVARIETY: African Syrian Cave-lion (extinct)\n\nAs there is not space enough to tabulate such a classification in full,\nI have developed at each step the most interesting groups: Vertebrates,\nMammalia, Monodelphia Carnivora, Digitigrada, Felid\u00e6, Lion. Most of the\nother groups in each grade are also subdivisible, though some of them\ncontain far fewer sub-classes than others.\n\nTo see the true character of this classification, we must consider that\nit is based chiefly upon knowledge of existing animals. Some extinct\nanimals, known by their fossils, find places in it; for others new\nplaces have been made. But it represents, on the whole, a cross-section,\nor cross-sections of Nature as developing in time; and, in order to give\na just view of the relations of animals, it must be seen in the light of\nother considerations. The older systems of classification, and the rules\nfor making them, seem to have assumed that an actual system of classes,\nor of what Mill calls 'Kinds,' exists in nature, and that the relations\nof Kinds in this system are determined by quantity of resemblance in\nco-inherent qualities, as the ground of their affinity.\n\n\u00a7 8. Darwin's doctrine of the origin of species affects the conception\nof natural classification in several ways, (1) If all living things are\nblood-relations, modified in the course of ages according to their\nvarious conditions of life, 'affinity' must mean 'nearness of common\ndescent'; and it seems irrational to propose a classification upon any\nother basis. We have to consider the Animal (or the Vegetable) Kingdom\nas a family tree, exhibiting a long line of ancestors, and (descended\nfrom them) all sorts of cousins, first, second, third, etc., perhaps\nonce, twice, or oftener 'removed.' Animals in the relation of first\ncousins must be classed as nearer than second cousins, and so on.\n\nBut, if we accept this principle, and are able to trace relationship, it\nmay not lead to the same results as would be reached by simply relying\nupon the present 'quantity of resemblance,' unless we understand this\nin a very particular way. For the most obvious features of an animal may\nhave been recently acquired; which often happens with those characters\nthat adapt an animal to its habits of life, as the wings of a bat, or\nthe fish-like shape of a dolphin; or as in cases of 'mimicry.' Some\nbutterflies, snakes, etc., have grown to resemble closely, in a\nsuperficial way, other butterflies and snakes, from which a stricter\ninvestigation widely separates them; and this superficial resemblance is\nprobably a recent acquisition, for the sake of protection; the imitated\nbutterflies being nauseous, and the imitated snakes poisonous. On the\nother hand, ancient and important traits of structure may, in some\nspecies, have dwindled into inconspicuous survivals or be still found\nonly in the embryo; so that only great knowledge and sagacity can\nidentify them; yet upon ancient traits, though hidden, classification\ndepends. The seal seems nearer allied to the porpoise than to the tiger,\nthe shrew nearer to the mouse than to the hedgehog; and the Tasmanian\nwolf looks more like a true wolf, the Tasmanian devil more like a\nbadger, than like a kangaroo: yet the seal is nearer akin to the tiger,\nthe shrew to the hedgehog, and the Tasmanian flesh-eaters are marsupial,\nlike the kangaroo. To overcome this difficulty we must understand the\nresemblance upon which classification is based to include resemblance of\nCausation, that is, the fact itself of descent from common ancestors.\nFor organic beings, all other rules of classification are subordinate to\none: trace the genealogy of every form.\n\nBy this rule we get a definite meaning for the phrase 'important or\nfundamental attribute' as determining organic classes; namely, most\nancient, or 'best serving to indicate community of origin.' Grades of\nclassification will be determined by such fundamental characters, and\nmay correspond approximately to the more general types (now extinct)\nfrom which existing animals have descended.\n\n(2) By the hypothesis of development the fixity of species is\ndiscredited. The lowest grade of a classification is made up not of\nwell-defined types unchanging from age to age, but of temporary species,\noften connected by uncertain and indistinct varieties: some of which\nmay, in turn, if the conditions of their existence alter, undergo such\nchanges as to produce new species. Hence the notion that Kinds exist in\norganic nature must be greatly modified. During a given period of a few\nthousand years, Kinds may be recognised, because, under such conditions\nas now prevail in the world, that period of time is insufficient to\nbring about great changes. But, if it be true that lions, tigers, and\nleopards have had a common ancestor, from whose type they have gradually\ndiverged, it is plain that their present distinctness results only from\nthe death of intermediate specimens and the destruction of intermediate\nvarieties. Were it possible to restore, by the evidence of fossils, all\nthe ranks of the great processions that have descended from the common\nancestor, there would nowhere occur a greater difference than between\noffspring and parents; and the appearance of Kinds existing in nature,\nwhich is so striking in a museum or zoological garden, would entirely\nvanish.\n\nA classification, then, as formerly observed, represents a cross-section\nof nature as developing in time: could we begin at the beginning and\nfollow this development down the course of time, we should find no\nclasses, but an ever-moving, changing, spreading, branching continuum.\nIt may be represented thus: Suppose an animal (or plant) A, extending\nover a certain geographical area, subject to different influences and\nconditions of climate, food, hill and plain, wood and prairie, enemies\nand rivals, and undergoing modifications here and there in adaptation to\nthe varying conditions of life: then varieties appear. These varieties,\ndiverging more and more, become distinct species (AB, AC, AD, AX). Some\nof these species, the more widely diffused, again produce varieties;\nwhich, in turn become species (ABE, ABF, ADG, ADH). From these, again,\nABE, ABFI, ABFJ, AC, ADHK, ADHL, ADHM, the extant species, descend.\n\n\n A\n /|\\\\_\n / | \\ \\__\n / | \\ \\_____\n ________/ | \\__ \\\n / | \\ \\\n AB AC AD AX\n /\\ | /\\\n / \\ | / \\\n / \\ | / \\\n ABE ABF | ADG ADH\n / / \\ | /|\\\n / / \\ | / | \\\n / / \\ | / | \\\nABE ABFI ABFJ AC ADHK ADHL ADHM\n\n\nIf in this age a classifier appears, he finds seven living species,\nwhich can be grouped into four genera (ABE, ABF, AC, ADH), and these\nagain into three Families (AB, AC, AD), all forming one Order. But the\nanimals which were their ancestors are all extinct. If the fossils of\nany of them--say AB, ADG and AX--can be found, he has three more\nspecies, one more genus (ADG), and one more family (AX). For AC, which\nhas persisted unchanged, and AX, which has become extinct, are both of\nthem Families, each represented by only one species. It seems necessary\nto treat such ancient types as species on a level with extant forms; but\nthe naturalist draws our attention to their archaic characteristics, and\ntries to explain their places in the order of evolution and their\nrelationships.\n\nBut now suppose that he could find a fossil specimen of every generation\n(hundreds of thousands of generations), from ABFI, etc., up to A;\nthen, as each generation would only differ from the preceding as\noffspring from parents, he would be unable at any point to distinguish a\nspecies; at most, he would observe a slightly marked variety. ABFI and\nABFJ would grow more and more alike, until they became indistinguishable\nin ABF; ABF and ABE would merge into AB; AB, AC, AD and AX would merge\ninto A. Hence, the appearance of species is due to our taking\ncross-sections of time, or comparing forms that belong to periods remote\nfrom one another (like AX, ADG, and ADHK, or AD, ADH and ADHK), and this\nappearance of species depends upon the destruction of ancestral\nintermediate forms.\n\n(3) The hypothesis of development modifies the logical character of\nclassification: it no longer consists in a direct induction of\nco-inherent characters, but is largely a deduction of these from the\ncharacters of earlier forms, together with the conditions of variation;\nin other words, the definition of a species must, with the progress of\nscience, cease to be a mere empirical law of co-inherence and become a\nderivative law of Causation. But this was already implied in the\nposition that causation is the fundamental principle of the explanation\nof concrete things; and accordingly, the derivative character of species\nor kinds extends beyond organic nature.\n\n\u00a7 9. The classification of inorganic bodies also depends on causation.\nThere is the physical classification into Solids, Liquids, and Gases.\nBut these states of matter are dependent on temperature; at different\ntemperatures, the same body may exist in all three states. They cannot\ntherefore be defined as solid, liquid, or gaseous absolutely, but only\nwithin certain degrees of temperature, and therefore as dependent upon\ncausation. Similarly, the geological classification of rocks, according\nto relative antiquity (primary, secondary, tertiary, with their\nsubdivisions), and mode of formation (igneous and aqueous), rests upon\ncausation; and so does the chemical classification of compound bodies\naccording to the elements that enter into them in definite proportions.\nHence, only the classification of the elements themselves (amongst\nconcrete things), at present, depends largely upon empirical\nCoinherence. If the elements remain irresolvable into anything simpler,\nthe definitions of the co-inherent characters that distinguish them must\nbe reckoned amongst the ultimate Uniformities of Nature. But if a\ndefinite theory of their origin both generally and severally, whether\nout of ether-vortices, or groups of electric corpuscles, or whatnot,\nshall ever gain acceptance, similarity of genesis or causation will\nnaturally be the leading consideration in classifying the chemical\nelements. To find common principles of causation, therefore, constitutes\nthe verification of every Natural Classification. The ultimate\nexplanation of nature is always causation; the Law of Causation is the\nbackbone of the system of Experience.\n\n\n\n\nCHAPTER XXII\n\nNOMENCLATURE, DEFINITION, PREDICABLES\n\n\n\u00a7 1. Precision of thought needs precision of language for the recording\nof such thought and for communicating it to others. We can often\nremember with great vividness persons, things, landscapes, changes and\nactions of persons or things, without the aid of language (though words\nare often mixed with such trains of imagery), and by this means may form\njudgments and inferences in particular cases; but for general notions,\njudgments and inferences, not merely about this or that man, or thing,\nbut about all men or all kinds of things, we need something besides the\nfew images we can form of them from observation. Even if we possess\ngeneric images, say, of 'horse' or 'cat' (that is, images formed, like\ncomposite photographs, by a coalescence of the images of all the horses\nor cats we have seen, so that their common properties stand out and\ntheir differences frustrate and cancel one another), these are useless\nfor precise thought; for the generic image will not correspond with the\ngeneral appearance of horse or cat, unless we have had proportional\nexperience of all varieties and have been impartially interested in all;\nand, besides, what we want for general thought is not a generic image of\nthe appearance of things, though it were much more definite and fairly\nrepresentative than such images ever are, but a general representation\nof their important characters; which may be connected with internal\norgans, such as none but an anatomist ever sees. We require a symbol\nconnected with the general character of a thing, or quality, or process,\nas scientifically determined, whose representative truth may be trusted\nin ordinary cases, or may be verified whenever doubt arises. Such\nsymbols are for most purposes provided by language; Mathematics and\nChemistry have their own symbols.\n\n\u00a7 2. First there should be \"a name for every important meaning\": (a) A\nNomenclature, or system of the names of all classes of objects, adapted\nto the use of each science. Thus, in Geology there are names for classes\nof rocks and strata, in Chemistry for the elements and their compounds,\nin Zoology and Botany for the varieties and species of animals and\nplants, their genera, families and orders.\n\nTo have such names, however, is not the whole aim in forming a\nscientific language; it is desirable that they should be systematically\nsignificant, and even elegant. Names, like other instruments, ought to\nbe efficient, and the efficiency of names consists in conveying the most\nmeaning with the least effort. In Botany and Zoology this result is\nobtained by giving to each species a composite name which includes that\nof the genus to which it belongs. The species of Felid\u00e6 given in chap.\nxvii. \u00a7 7, are called _Felis leo_ (lion), _Felis tigris_ (tiger), _Felis\nleopardus_ (leopard), _Felis concolor_ (puma), _Felis lyncus_ (European\nlynx), _Felis catus_ (wild cat). In Chemistry, the nomenclature is\nextremely efficient. Names of the simpler compounds are formed by\ncombining the names of the elements that enter into them; as Hydrogen\nChloride, Hydrogen Sulphide, Carbon Dioxide; and these can be given\nstill more briefly and efficiently in symbols, as HCl, H_{2}S, CO_{2}.\nThe symbolic letters are usually initials of the names of the elements:\nas C = Carbon, S = Sulphur; sometimes of the Latin name, when the common\nname is English, as Fe = Iron. Each letter represents a fixed quantity\nof the element for which it stands, viz., the atomic weight. The\nnumber written below a symbol on the right-hand side shows how many\natoms of the element denoted enter into a molecule of the compound.\n\n(b) A Terminology is next required, in order to describe and define the\nthings that constitute the classes designated by the nomenclature, and\nto describe and explain their actions.\n\n(i) A name for every integral part of an object, as head, limb,\nvertebra, heart, nerve, tendon; stalk, leaf, corolla, stamen, pistil;\nplinth, frieze, etc. (ii) A name for every metaphysical part or\nabstract quality of an object, and for its degrees and modes; as\nextension, figure, solidity, weight; rough, smooth, elastic, friable;\nthe various colours, red, blue, yellow, in all their shades and\ncombinations and so with sounds, smells, tastes, temperatures. The terms\nof Geometry are employed to describe the modes of figure, as angular,\ncurved, square, elliptical; and the terms of Arithmetic to express the\ndegrees of weight, elasticity, temperature, pitch of sound. When other\nmeans fail, qualities are suggested by the names of things which exhibit\nthem in a salient way; figures by such terms as amphitheatre, bowl-like,\npear-shaped, egg-shaped; colours by lias-blue, sky-blue, gentian-blue,\npeacock-blue; and similarly with sounds, smells and tastes. It is also\nimportant to express by short terms complex qualities, as harmony,\nfragrance, organisation, sex, symmetry, stratification.\n\n(iii) In the explanation of Nature we further require suitable names for\nprocesses and activities: as deduction, conversion, verification,\naddition, integration, causation, tendency, momentum, gravitation,\naberration, refraction, conduction, affinity, combination, germination,\nrespiration, attention, association, development.\n\nThere may sometimes be a difficulty in distinguishing the terms which\nstand for qualities from those that express activities, since all\nqualities imply activities: weight, for example, implies gravitation;\nand the quality heat is also a kind of motion. The distinction aimed at\nlies between a quality as perceived by means of an effect upon our\nsenses (as weight is resistance to our effort in lifting; heat, a\nsensation when we approach fire), and that property of a body which is\nconceived to account for its energy (as gravitation that brings a body\nto the ground, or physical heat that expands an iron bar or works an\nengine). The former class of words, expressing qualities, are chiefly\nused in description: the latter class, expressing activities, are\nchiefly needed in explanation. They correspond respectively, like\nclassification and explanation, with the static and dynamic aspects of\nNature.\n\nThe terms of ordinary language fall into the same classes as those of\nscience: they stand for things, classes of things, parts, or qualities,\nor activities of things; but they are far less precise in their\nsignification. As long as popular thought is vague its language must be\nvague; nor is it desirable too strictly to correct the language whilst\nthe thought is incorrigible. Much of the effect of poetry and eloquence\ndepends upon the elasticity and indirect suggestiveness of common terms.\nEven in reasoning upon some subjects, it is a mistake to aim at an\nunattainable precision. It is better to be vaguely right than exactly\nwrong. In the criticism of manners, of fine art, or of literature, in\npolitics, religion and moral philosophy, what we are anxious to say is\noften far from clear to ourselves; and it is better to indicate our\nmeaning approximately, or as we feel about it, than to convey a false\nmeaning, or to lose the warmth and colour that are the life of such\nreflections. It is hard to decide whether more harm has been done by\nsophists who take a base advantage of the vagueness of common terms, or\nby honest paralogists (if I may use the word) who begin by deceiving\nthemselves with a plausible definiteness of expression, and go on to\npropagate their delusions amongst followers eager for systematic insight\nbut ignorant of the limits of its possibility.\n\n\u00a7 3. A Definition is necessary (if possible) for every scientific name.\nTo define a name is to give a precise statement of its meaning or\nconnotation. The name to be defined is the subject of a proposition,\nwhose predicate is a list of the fundamental qualities common to the\nthings or processes which the subject denotes, and on account of\npossessing which qualities this name is given to them.\n\nThus, a curve is a line of which no part is straight. The momentum of a\nmoving body is the product of its mass and its velocity (these being\nexpressed in numbers of certain units). Nitrogen is a transparent\ncolourless gas, atomic weight 14, specific gravity .9713, not readily\ncombining, etc. A lion is a monodelphian mammal, predatory, walking on\nits toes, of nocturnal habits, with a short rounded head and muzzle;\ndental formula: Incisors (3-3)/(3-3), canines (1-1)/(1/1), pr\u00e6molars\n(3-3)/(2-2), molars (1-1)/(1-1) = 30; four toes on the hind and five on\nthe fore foot, retractile claws, prickly tongue, light and muscular in\nbuild, about 9-1/2 feet from muzzle to tip of tail, tawny in colour, the\nmales maned, with a tufted tail. If anything answers to this\ndescription, it is called a lion; if not, not: for this is the meaning\nof the name.\n\nFor ordinary purposes, it may suffice to give an Incomplete Definition;\nthat is, a list of qualities not exhaustive, but containing enough to\nidentify the things denoted by the given name; as if we say that a lion\nis 'a large tawny beast of prey with a tufted tail.' Such purposes may\nalso be served by a Description; which is technically, a proposition\nmentioning properties sufficient to distinguish the things denoted, but\nnot the properties that enter into the definition; as if nitrogen be\nindicated as the gas that constitutes 4/5 of the atmosphere.\n\n\u00a7 4. The rules for testing a Definition are: I.--As to its Contents--\n\n(1) It must state the whole connotation of the name to be defined.\n\n(2) It must not include any quality derivative from the connotation.\nSuch a quality is called a Proprium. A breach of this rule can do no\npositive harm, but it is a departure from scientific economy. There is\nno need to state in the definition what can be derived from it; and\nwhatever can be derived by causation, or by mathematical demonstration,\nshould be exhibited in that manner.\n\n(3) It must not mention any circumstance that is not a part of the\nconnotation, even though it be universally found in the things denoted.\nSuch a circumstance, if not derivable from the connotation, is called an\nAccident. That, for example, the lion at present only inhabits the Old\nWorld, is an accident: if a species otherwise like a lion were found in\nBrazil, it would not be refused the name of lion on the score of\nlocality. Whilst, however, the rules of Logic have forbidden the\ninclusion of proprium or accident in a definition, in fact the\ndefinitions of Natural History often mention such attributes when\ncharacteristic. Indeed, definitions of superordinate classes--Families\nand Orders--not infrequently give qualities as generally found in the\nsubordinate classes, and at the same time mention exceptional cases in\nwhich they do not occur.\n\nII.--As to its Expression--\n\n(4) A Definition must not include the very term to be defined, nor any\ncognate. In defining 'lion' we must not repeat 'lion,' nor use\n'leonine'; it would elucidate nothing.\n\n(5) It must not be put in vague language.\n\n(6) It must not be in a negative form, if a positive form be obtainable.\nWe must not be content to say that a lion is 'no vegetarian,' or 'no\nlover of daylight.' To define a curve as a line 'always changing its\ndirection' may be better than as 'in no part straight.'\n\n\u00a7 5. The process of determining a Definition is inseparable from\nclassification. We saw that classification consists in distributing\nthings into groups according to their likenesses and differences,\nregarding as a class those individuals which have most qualities in\ncommon. In doing so we must, of course, recognise the common qualities\nor points of likeness; and to enumerate these is to define the name of\nthe class. If we discover the qualities upon which a class is based by\ndirect observation and induction, by the same method we discover the\ndefinition of its name.\n\nWe saw also that classification is not merely the determination of\nisolated groups of things, but a systematic arrangement of such groups\nin relation to one another. Hence, again, Definitions are not\nindependent, but relative to one another; and, of course, in the same\nway as classes are relative. That is to say, as a class is placed in\nsubordination to higher or more comprehensive groups, so the definition\nof its name is subordinate to that of their names; and as a class stands\nin contrast with co-ordinate classes (those that are in the same degree\nof subordination to the same higher groups), so the definition of its\nname is in contrast or co-ordination with the definitions of their\nnames. Lion is subordinate to _Felis_, to Digitigrade, to Carnivore and\nso on up to Animal; and, beyond the Animal Kingdom, to Phenomenon; it is\nco-ordinate with tiger, puma, etc.; and more remotely it is\nco-ordinate with dog, jackal, wolf, which come under _Canis_--a genus\nco-ordinate with _Felis_. The definition of lion, therefore, is\nsubordinate to that of _Felis_, and to all above it up to Phenomenon;\nand is co-ordinate with that of tiger, and with all species in the same\ngrade. This is the ground of the old method of definition _per genus et\ndifferentiam_.\n\nThe genus being the next class above any species, the _differentia_ or\nDifference consists of the qualities which mark that species in addition\nto those that mark the genus, and which therefore distinguish it from\nall other species of the same genus. In the above definition of lion,\nfor example, all the properties down to \"light and muscular in build\"\nare generic, that is, are possessed by the whole genus, _Felis_; and the\nremaining four (size, colour, tufted tail, and mane in the male) are the\nDifference or specific properties, because in those points the lion\ncontrasts with the other species of that genus. Differences may be\nexhibited thus:\n\n _Lion._ _Tiger._\nSIZE: about 9-1/2 feet from nose | About 10 feet.\n to tip of tail. |\nCOLOUR: tawny. | Warm tawny, striped with black.\nTAIL: tufted. | Tapering.\nMANE: present in the male. | Both sexes maneless.\n\nThere are other differences in the shape of the skull. In defining lion,\nthen, it would have been enough to mention the genus and the properties\nmaking up the Difference; because the properties of the genus may be\nfound by turning to the definition of the genus; and, on the principle\nof economy, whatever it is enough to do it is right to do. To define 'by\ngenus and difference' is a point of elegance, when the genus is known;\nbut the only way of knowing it is to compare the individuals comprised\nin it and in co-ordinate genera, according to the methods of scientific\nclassification. It may be added that, as the genus represents ancestral\nderivation, the predication of genus in a definition indicates the\nremote causes of the phenomena denoted by the name defined. And this way\nof defining corresponds with the method of double naming by genus and\nspecies: _Felis leo_, _Felis tigris_, etc.; _Vanessa Atalanta_,\n_Vanessa Io_, etc.\n\nThe so-called Genetic Definition, chiefly used in Mathematics, is a rule\nfor constructing that which a name denotes, in such a way as to ensure\nits possessing the tributes connoted by the name. Thus, for a circle:\nTake any point and, at any constant distance from it, trace a line\nreturning into itself. In Chemistry a genetic definition of any compound\nmight be given in the form of directions for the requisite synthesis of\nelements.\n\n\u00a7 6. The chief difficulty in the definition of scientific names consists\nin determining exactly the nature of the things denoted by them, as in\nclassifying plants and animals. If organic species are free growths,\ncontinually changing, however gradually, according as circumstances give\nsome advantage to one form over others, we may expect to find such\nspecies branching into varieties, which differ considerably from one\nanother in some respects, though not enough to constitute distinct\nspecies. This is the case; and, consequently, there arises some\nuncertainty in collecting from all the varieties those attributes which\nare common to the species as a whole; and, therefore, of course,\nuncertainty in defining the species. The same difficulty may occur in\ndefining a genus, on account of the extent to which some of its species\ndiffer from others, whilst having enough of the common character to\ndeter the classifier from forming a distinct genus on their account. On\nthe other hand the occurrence of numerous intermediate varieties may\nmake it difficult to distinguish genera or species at all. Even the\nKingdoms of plants and animals are hard to discriminate at the lowest\nlevels of organisation. Now, where there is a difficulty of\nclassification there must be a corresponding difficulty of definition.\n\nIt has been proposed in such cases to substitute a Type for a\nDefinition; to select some variety of a species, or species of a genus,\nas exhibiting its character in an eminent degree, and to regard other\ngroups as belonging to the same species or genus, according as they\nagree more with this type than with other types representing other\nspecies or genera. But the selection of one group as typical implies a\nrecognition of its attributes as prevailing generally (though not\nuniversally) throughout the species or genus; and to recognise these\nattributes and yet refuse to enumerate them in a definition, seems to be\nno great gain. To enumerate the attributes of the type as an Approximate\nDefinition of the species or genus, true of _most_ of the groups\nconstituting the species or genus, answers the same purpose, is more\nexplicit, and can mislead no one who really attends to the exposition.\nAn approximate definition is, indeed, less misleading than the\nindication of a type; for the latter method seems to imply that the\ngroup which is now typical has a greater permanence or reality than its\nco-ordinate groups; whereas, for aught we know, one of the outside\nvarieties or species may even now be superseding and extinguishing it.\nBut the statement of a definition as approximate, is an honest\nconfession that both the definition and the classification are (like a\nprovisional hypothesis) merely the best account we can give of the\nmatter according to our present knowledge.\n\n\u00a7 7. The limits of Definition are twofold: (a) A name whose meaning\ncannot be analysed cannot be defined. This limitation meets us only in\ndealing with the names of the metaphysical parts or simple qualities of\nobjects under the second requisite of a Terminology. Resistance and\nweight, colour and its modes, many names of sounds, tastes, smells, heat\nand cold--in fact, whatever stands for an unanalysable perception,\ncannot be made intelligible to any one who has not had experience of the\nfacts denoted; they cannot be defined, but only exemplified. A sort of\ngenetic definition may perhaps be attempted, as if we say that colour is\nthe special sensation of the cones of the retina, or that blue is the\nsensation produced by a ray of light vibrating about 650,000,000,000,000\ntimes a second; but such expressions can give no notion of our meaning\nto a blind man, or to any one who has never seen a blue object. Nor can\nwe explain what heat is like, or the smell of tobacco, to those who have\nnever experienced them; nor the sound of C 128 to one who knows nothing\nof the musical scale.\n\nIf we distinguish the property of an object from the sensation it\nexcites in us, we may define any simple property as 'the power of\nproducing the sensation'; the colour of a flower as the power of\nexciting the sensation of colour in us. Still, this gives no information\nto the blind nor to the colour-blind. Abstract names may be defined by\ndefining the corresponding concrete: the definition of 'human nature' is\nthe same as of 'man.' But if the corresponding concrete be a simple\nsensation (as blue), this being indefinable, the abstract (blueness) is\nalso indefinable.\n\n(b) The second limit of Definition is the impossibility of exhausting\ninfinity, which would be necessary in order to convey the meaning of the\nname of any individual thing or person. For, as we saw in chap. iv., if\nin attempting to define a proper name we stop short of infinity, our\nlist of qualities or properties may possibly be found in two\nindividuals, and then it becomes the definition of a class-name or\ngeneral name, however small the actual class. Hence we can only give a\nDescription of that which a proper name denotes, enumerating enough of\nits properties to distinguish it from everything else as far as our\nknowledge goes.\n\n\u00a7 8. The five Predicables (Species, Genus, Difference, Proprium,\nAccident) may best be discussed in connection with Classification and\nDefinition; and in giving an account of Classification, most of what has\nto be said about them has been anticipated. Their name, indeed, connects\nthem with the doctrine of Propositions; for Predicables are terms that\nmay be predicated, classified according to their connotative relation to\nthe subject of a proposition (that is, according to the relation in\nwhich their connotation stands to the connotation of the subject):\nnevertheless, the significance of the relations of such predicates to a\nsubject is derivative from the general doctrine of classification.\n\nFor example, in the proposition 'X is Y,' Y must be one of the five\nsorts of predicables in relation to X; but of what sort, depends upon\nwhat X (the subject) is, or means. The subject of the proposition must\nbe either a definition, or a general connotative name, or a singular\nname.\n\nIf X be a definition, Y must be a species; for nothing but a general\nname can be predicated of a definition: and, strictly speaking, it is\nonly in relation to a definition (as subject) that species can be a\npredicable; when it is called _Species predicabilis_ (1).\n\nIf X be a connotative name, it is itself a species (_Species\nsubjicibilis_); and the place of the subject of a proposition is the\nusual one for species. The predicate, Y, may then be related to the\nspecies in three different ways. First, it may be a definition, exactly\nequivalent to the species;--in fact, nothing else than the species in an\nexplicit form, the analysis of its connotation. Secondly, the predicate\nmay be, or connote, some _part only_ of the definition or connotation of\nthe species; and then it is either genus (2), or difference (3).\nThirdly, the predicate may connote _no part_ of the definition, and then\nit is either derivable from it, being a proprium (4), or not derivable\nfrom it, being an accident (5). These points of doctrine will be\nexpanded and illustrated in subsequent pages.\n\nIf X be a singular name, deriving connotation from its constituent terms\n(chap. iv. \u00a7 2), as 'The present Emperor of China,' it may be treated as\na _Species subjicibilis_. Then that he is 'an absolute monarch,'\npredicates a genus; because that is a genus of 'Emperor,' a part of the\nsingular name that gives it connotation. That he wears a yellow robe is\na proprium, derivable from the ceremonial of his court. That he is\nthirty years of age is an accident.\n\nBut if X be a proper name, having no connotation, Y must always be an\naccident; since there can then be no definition of X, and therefore\nneither species, genus, difference, nor proprium. Hence, that 'John Doe\nis a man' is an accidental proposition: 'man' is not here a _Species\npredicabilis_; for the name might have been given to a dog or a\nmountain. That is what enables the proposition to convey information: it\nwould be useless if the proper name implied 'humanity.'\n\n'Species' is most frequently used (as in Zoology) for the _class\ndenoted_ by a general name; but in Logic it is better to treat it as a\ngeneral name used connotatively for the attributes possessed in common\nby the things denoted, and on account of which they are regarded as a\nclass: it is sometimes called the Essence (\u00a7 9). In this connotative\nsense, a species is implicitly what the definition is explicitly; and\ntherefore the two are always simply convertible. Thus, 'A plane\ntriangle' (species) is 'a figure enclosed by three straight lines'\n(definition): clearly we may equally say, 'A figure enclosed by three\nstraight lines is a plane triangle.' It is a simple identity.\n\nA genus is also commonly viewed denotatively, as a class containing\nsmaller classes, its species; but in Logic it is, again, better to treat\nit connotatively, as a name whose definition is part of the definition\nof a given species.\n\nA difference is the remainder of the definition of any species after\nsubtracting a given genus. Hence, the genus and difference together make\nup the species; whence the method of definition _per genus et\ndifferentiam_ (_ante_, \u00a7 5).\n\nWhilst in Botany and Zoology the species is fixed at the lowest step of\nthe classification (varieties not being reckoned as classes), and the\ngenus is also fixed on the step next above it, in Logic these\npredicables are treated as movable up and down the ladder: any lower\nclass being species in relation to any higher; which higher class,\nwherever taken, thus becomes a genus. Lion may logically be regarded as\na species of digitigrade, or mammal, or animal; and then each of these\nis a genus as to lion: or, again, digitigrade may be regarded as a\nspecies of mammal, or mammal as a species of animal. The highest class,\nhowever, is never a species; wherefore it is called a _Summum Genus_:\nand the lowest class is never a genus; wherefore it is called an _Infima\nSpecies_. Between these two any step may be either species or genus,\naccording to the relation in which it is viewed to other classes, and is\nthen called Subaltern. The _summum genus_, again, may be viewed in\nrelation to a _given_ universe or _suppositio_ (that is, any limited\narea of existence now the object of attention), or to the _whole_\nuniverse. If we take the animal kingdom as our _suppositio_, Animal is\nthe _summum genus_; but if we take the whole universe, 'All things' is\nthe _summum genus_.\n\n\"Porphyry's tree\" is used to illustrate this doctrine. It begins with a\n_summum genus_, 'Substance,' and descends by adding differences, step by\nstep, to the _infima species_, 'Man.' It also illustrates Division by\nDichotomy.\n\n SUBSTANCE\n / \\\n CORPOREAL || INCORPOREAL\n ||\n BODY\n / \\\n ANIMATE || INANIMATE\n ||\n LIVING BODY\n / \\\n SENSIBLE || INSENSIBLE\n ||\n ANIMAL\n / \\\n RATIONAL || IRRATIONAL\n ||\n MAN\n //||\\\\\n // || \\\\\n // || \\\\\n // || \\\\\n // || \\\\\n // || \\\\\n // || \\\\\n _Socrates_ _Plato_ _Aristotle_\n\nBeginning with 'Substance,' as _summum genus_, and adding the\ndifference 'Corporeal,' we frame the species 'Body.' Taking 'Body' as\nthe genus and adding the difference 'Animate,' we frame the species\n'Living Body;' and so on till 'Man' is reached; which, being _infima\nspecies_, is only subdivisible into individuals. But the division of Man\ninto individuals involves a change of principle; it is a division of the\ndenotation, not an increase of the connotation as in the earlier steps.\nOnly one side of each dichotomy is followed out in the 'tree': if the\nother side had been taken, Incorporeal Substance would be 'Spirit';\nwhich might be similarly subdivided.\n\nGenus and species, then, have a double relation. In denotation the genus\nincludes the species; in connotation the species includes the genus.\nHence the doctrine that by increasing the connotation of a name we\ndecrease its denotation: if, for example, to the definition of 'lion' we\nadd 'inhabiting Africa,' Asiatic lions are no longer denoted by it. On\nthe other hand, if we use a name to denote objects that it did not\nformerly apply to, some of the connotation must be dropped: if, for\nexample, the name 'lion' be used to include 'pumas,' the tufted tail and\nmane can no longer be part of the meaning of the word; since pumas have\nnot these properties.\n\nThis doctrine is logically or formally true, but it may not always be\ntrue in fact. It is logically true; because wherever we add to the\nconnotation of a name, it is possible that some things to which it\nformerly applied are now excluded from its denotation, though we may not\nknow of any such things. Still, as a matter of fact, an object may be\ndiscovered to have a property previously unknown, and this property may\nbe fundamental and co-extensive with the denotation of its name, or even\nmore widely prevalent. The discovery that the whale is a mammal did not\nlimit the class 'whale'; nor did the discovery that lions, dogs, wolves,\netc., walk upon their toes, affect the application of any of these\nnames.\n\nSimilarly, the extension of a name to things not previously denoted by\nit, may not in fact alter its definition; for the extension may be made\non the very ground that the things now first denoted by it have been\nfound to have the properties enumerated in its definition, as when the\nname 'mammal' was applied to whales, dolphins, etc. If, however,\n'mammal' had formerly been understood to apply only to land animals, so\nthat its definition included (at least, popularly) the quality of\n'living on the land,' this part of the connotation was of course lost\nwhen the denotation came to include certain aquatic animals.\n\nA proprium is an attribute derived from the definition: being either (a)\nimplied in it, or deducible from it, as 'having its three angles equal\nto two right angles' may be proved from the definition of a triangle; or\n(b) causally dependent on it, as being 'dangerous to flocks' results\nfrom the nature of a wolf, and as 'moving in an ellipse' results from\nthe nature of a planet in its relation to the sun.\n\nAn accident is a property accompanying the defining attributes without\nbeing deducible from them. The word suggests that such a property is\nmerely 'accidental,' or there 'by chance'; but it only means that we do\nnot understand the connection.\n\nProprium and Accident bear the same relation to one another as\nDerivative and Empirical Laws: the predication of a proprium is a\nderivative law, and the predication of an accident is an empirical law.\nBoth accidents and empirical laws present problems, the solution of\nwhich consists in reducing them, respectively, to propria and derivative\nlaws. Thus the colour of animals was once regarded as an accident for\nwhich no reason could be given; but now the colour of animals is\nregarded as an effect of their nature and habits, the chief determinants\nof it being the advantage of concealment; whilst in other cases, as\namong brightly coloured insects and snakes, the determinant may be the\nadvantage of advertising their own noxiousness. If such reasoning is\nsound, colour is a proprium (and if so, it cannot _logically_ be\nincluded in a definition; but it is better to be judicious than formal).\n\nIf the colour of animals is a proprium, we must recognise a distinction\nbetween Inseparable and Separable Propria, according as they do, or do\nnot, always accompany the essence: for mankind is regarded as one\nspecies; but each colour, white, black or yellow, is separable from it\nunder different climatic conditions; whilst tigers are everywhere\ncoloured and striped in much the same way; so that we may consider their\ncolouring as inseparable, in spite of exceptional specimens black or\nwhite or clouded.\n\nThe same distinction may be drawn between accidents. 'Inhabiting Asia'\nis an Inseparable Accident of tiger, but a Separable Accident of lion.\nEven the occasional characteristics and occupations of individuals are\nsometimes called separable accidents of the species; as, of man, being\ncolour-blind, carpentering, or running.\n\nA proprium in the original signification of the term [Greek: hidion] was\npeculiar to a species, never found with any other, and was therefore\nconvertible with the subject; but this restriction is no longer insisted on.\n\n\u00a7 9. Any predication of a genus, difference or definition, is a verbal,\nanalytic, or essential proposition: and any predication of a proprium or\naccident, is a real, synthetic, or accidental proposition (chap. v. \u00a7\n6). A proposition is called verbal or analytic when the predicate is a\npart, or the whole, of the meaning of the subject; and the subject being\nspecies, a genus or difference is part, and a definition is the whole,\nof its meaning or connotation. Hence such a proposition has also been\ncalled explicative. Again, a proposition is called real or synthetic\nwhen the predicate is no part of the meaning of the subject; and, the\nsubject being species, a proprium or accident is no part of its meaning\nor connotation. Hence such a proposition has been called ampliative.\n\nAs to Essential and Accidental, these terms are derived from the\ndoctrine of Realism. Realists maintain that the essence of a thing, or\nthat which makes a thing to be what (or of what kind) it is, also makes\neverything else of the same kind to be what it is. The essence, they\nsay, is not proper to each thing or separately inherent in it, but is an\n'Universal' common to all things of that kind. Some hold that the\nuniversal nature of things of any kind is an Idea existing (apart from\nthe things) in the intelligible world, invisible to mortal eye and only\naccessible to thought; whence the Idea is called a noumenon: that only\nthe Idea is truly real, and that the things (say, trees, bedsteads and\ncities) which appear to us in sense-perception, and which therefore are\ncalled phenomena, only exist by participating in, or imitating, the Idea\nof each kind of them. The standard of this school bears the legend\n_Universalia ante rem_.\n\nBut others think that the Universal does not exist apart from particular\nthings, but is their present essence; gives them actuality as individual\nsubstances; \"informs\" them, or is their formal cause, and thus makes\nthem to be what they are of their kind according to the definition: the\nuniversal lion is in all lions, and is not merely similar, but identical\nin all; for thus the Universal Reason thinks and energises in Nature.\nThis school inscribes upon its banners, _Universalia in re_.\n\nTo define anything, then, is to discover its essence, whether\ntranscendent or immanent; and to predicate the definition, or any part\nof it (genus or difference), is to enounce an essential proposition. But\na proprium, being no part of a definition, though it always goes along\nwith it, does not show what a thing is; nor of course does an accident;\nso that to predicate either of these is to enounce an accidental\nproposition.\n\nAnother school of Metaphysicians denies the existence of Universal Ideas\nor Forms; the real things, according to them, are individuals; which,\nso far as any of them resemble one another, are regarded as forming\nclasses; and the only Universal is the class-name, which is applied\nuniversally in the same sense. Hence, they are called Nominalists. The\nsense in which any name is applied, they say, is derived from a\ncomparison of the individuals, and by abstraction of the properties they\nhave in common; and thus the definition is formed. _Universalia post\nrem_ is their motto. Some Nominalists, however, hold that, though\nUniversals do not exist in nature, they do in our minds, as Abstract\nIdeas or Concepts; and that to define a term is to analyse the concept\nit stands for; whence, these philosophers are called Conceptualists.\n\nSuch questions belong to Metaphysics rather than to Logic; and the\nforegoing is a commonplace account of a subject upon every point of\nwhich there is much difference of opinion.\n\n\u00a7 10. The doctrine of the Predicaments, or Categories, is so interwoven\nwith the history of speculation and especially of Logic that, though its\nvitality is exhausted, it can hardly be passed over unmentioned. The\npredicaments of Aristotle are the heads of a classification of terms as\npossible predicates of a particular thing or individual. Hamilton\n(_Logic_: Lect. xi.) has given a classification of them; which, if it\ncannot be found in Aristotle, is an aid to the memory, and may be thrown\ninto a table thus:\n\n Substance [Greek: ousia] (1)\n {Quantity [Greek: poson] (2)\n Attribute {Quality [Greek: poion] (3)\n {Relation [Greek: pros ti] (4)\n\n { Where [Greek: pou] (5)\n { When [Greek: pote] (6)\n\n { Action [Greek: poiein] (7)\n Modes of Relation { Passion [Greek: paschein] (8)\n\n { Posture [Greek: keisthai] (9)\n { Habit [Greek: echein] (10)\n\nTaking a particular thing or individual, as 'Socrates,' this is\nSubstance in the proper sense of the word, and can never be a predicate,\nbut is the subject of all predicates. We may assert of him (1) Substance\nin the secondary sense (species or genus) that he is a man or an animal;\n(2) Quantity, of such a height or weight; (3) Quality, fair or dark; (4)\nRelation, shorter or taller than Xanthippe; (5) Where, at Athens; (6)\nWhen, two thousand and odd years ago; (7) Action, that he questions or\npleads; (8) Passion, that he is answered or condemned; (9) Posture, that\nhe sits or stands; (10) Habit, that he is clothed or armed.\n\nThus illustrated (_Categori\u00e6_: c. 4), the predicaments seem to be a list\nof topics, generally useful for the analysis and description of an\nindividual, but wanting in the scientific qualities of rational\narrangement, derivation and limitation. Why are there just these heads,\nand just so many? It has been suggested that they were determined by\ngrammatical forms: for Substance is expressed by a substantive;\nQuantity, Quality and Relation are adjectival; Where and When,\nadverbial; and the remaining four are verbal. It is true that the parts\nof speech were not systematically discriminated until some years after\nAristotle's time; but, as they existed, they may have unconsciously\ninfluenced his selection and arrangement of the predicaments. Where a\nprinciple is so obscure one feels glad of any clue to it (_cf._ Grote's\n_Aristotle_, c. 3, and Zeller's _Aristotle_, c. 6). But whatever the\norigin and original meaning of the predicaments, they were for a long\ntime regarded as a classification of things; and it is in this sense\nthat Mill criticises them (_Logic_: Bk. I. c. 3).\n\nIf, however, the predicaments are heads of a classification of terms\npredicable, we may expect to find some connection with the predicables;\nand, in fact, secondary Substances are species and genus; whilst the\nremaining nine forms are generally accidents. But, again, we may expect\nsome agreement between them and the fundamental forms of predication\n(_ante_, chap. i. \u00a7 5, and chap. ii \u00a7 4): Substance, whether as the\nfoundation of attributes, or as genus and species, implies the\npredication of co-inherence, which is one mode of _Co-existence_.\nQuantity is predicated as equality (or inequality) a mode of _Likeness_;\nand the other mode of _Likeness_ is involved in the predication of\nQuality. Relation, indeed, is the abstract of all predication, and ought\nnot to appear in a list along with special forms of itself. 'Where' is\nposition, or _Co-existence_ in space; and 'When' is position in time, or\n_Succession_. Action and Passion are the most interesting aspect of\n_Causation_. Posture and Habit are complex modes of _Co-existence_, but\ntoo specialised to have any philosophic value. Now, I do not pretend\nthat this is what Aristotle meant and was trying to say: but if\nLikeness, Co-existence, Succession and Causation are fundamental forms\nof predication, a good mind analysing the fact of predication is likely\nto happen upon them in one set of words or another.\n\nBy Kant the word 'Category' has been appropriated to the highest forms\nof judgment, such as Unity, Reality, Substance, and Cause, under which\nthe understanding reduces phenomena to order and thereby constitutes\nNature. This change of meaning has not been made without a certain\ncontinuity of thought; for forms of judgment are modes of predication.\nBut besides altering the lists of categories and greatly improving it,\nKant has brought forward under an old title a doctrine so original and\nsuggestive that it has extensively influenced the subsequent history of\nPhilosophy. At the same time, and probably as a result of the vogue of\nthe Kantian philosophy, the word 'category' has been vulgarised as a\nsynonym for 'class,' just as 'predicament' long ago passed from\nScholastic Logic into common use as a synonym for 'plight.' A minister\nis said to be 'in a predicament,' or to fall under the 'category of\nimpostors.'\n\n\n\n\nCHAPTER XXIII\n\nDEFINITION OF COMMON TERMS\n\n\n\u00a7 1. Ordinary words may need definition, if in the course of exposition\nor argument their meaning is liable to be mistaken. But as definition\ncannot give one the sense of a popular word for all occasions of its\nuse, it is an operation of great delicacy. Fixity of meaning in the use\nof single words is contrary to the genius of the common vocabulary;\nsince each word, whilst having a certain predominant character, must be\nused with many shades of significance, in order to express the different\nthoughts and feelings of multitudes of men in endlessly diversified\nsituations; and its force, whenever it is used, is qualified by the\nother words with which it is connected in a sentence, by its place in\nthe construction of the sentence, by the emphasis, or by the pitch of\nits pronunciation compared with the other words.\n\nClearly, the requisite of a scientific language, 'that every word shall\nhave one meaning well defined,' is too exacting for popular language;\nbecause the other chief requisite of scientific language cannot be\ncomplied with, 'that there be no important meaning without a name.'\n'Important meanings,' or what seem such, are too numerous to be thus\nprovided for; and new ones are constantly arising, as each of us pursues\nhis business or his pleasure, his meditations or the excursions of his\nfancy. It is impossible to have a separate term for each meaning; and,\ntherefore, the terms we have must admit of variable application.\n\nAn attempt to introduce new words is generally disgusting. Few men have\nmastered the uses of half the words already to be found in our classics.\nMuch more would be lost than gained by doubling the dictionary. It is\ntrue that, at certain stages in the growth of a people, a need may be\nwidely felt for the adoption of new words: such, in our own case, was\nthe period of the Tudors and early Stuarts. Many fresh words, chiefly\nfrom the Latin, then appeared in books, were often received with\nreprobation and derision, sometimes disappeared again, sometimes\nestablished their footing in the language: see _The Art of English\nPoetry_ (ascribed to Puttenham), Book III. chap. 4, and Ben Jonson's\n_Poetaster_, Act. V. sc. I. Good judges did not know whether a word was\nreally called for: even Shakespeare thought 'remuneration' and\n'accommodate' ridiculous. But such national exigencies rarely arise; and\nin our own time great authors distinguish themselves by the plastic\npower with which they make common words convey uncommon meanings.\n\nFluid, however, as popular language is and ought to be, it may be\nnecessary for the sake of clear exposition, or to steady the course of\nan argument, to avoid either sophistry or unintentional confusion, that\nwords should be defined and discriminated; and we must discuss the means\nof doing so.\n\n\u00a7 2. Scientific method is applicable, with some qualifications, to the\ndefinition of ordinary words. Classification is involved in any problem\nof definition: at least, if our object is to find a meaning that shall\nbe generally acceptable and intelligible. No doubt two disputants may,\nfor their own satisfaction, adopt any arbitrary definition of a word\nimportant in their controversy; or, any one may define a word as he\npleases, at the risk of being misunderstood, provided he has no\nfraudulent intention. But in exposition or argument addressed to the\npublic, where words are used in some of their ordinary senses, it should\nbe recognised that the meaning of each one involves that of many\nothers. For language has grown with the human mind, as representing its\nknowledge of the world: this knowledge consists of the resemblances and\ndifferences of things and of the activities of things, that is, of\nclasses and causes; and as there is such order in the world, so there\nmust be in language: language, therefore, embodies an irregular\nclassification of things with their attributes and relations according\nto our knowledge and beliefs. The best attempt (known to me) to carry\nout this view is contained in Roget's _Thesaurus_, which is a\nclassification of English words according to their meanings: founded, as\nthe author tells us, on the models of Zoology and Botany, it has some of\nthe requisites of a Logical Dictionary.\n\nPopular language, indeed, having grown up with a predominantly practical\npurpose, represents a very imperfect classification philosophically\nconsidered. Things, or aspects, or processes of things, that have\nexcited little interest, have often gone unnamed: so that scientific\ndiscoverers are obliged, for scientific purposes, to invent thousands of\nnew names. Strong interests, on the other hand, give such a colour to\nlanguage, that, where they enter, it is difficult to find any\nindifferent expressions. _Consistency_ being much prized, though often\nthe part of a blockhead, _inconsistency_ implies not merely the absence\nof the supposed virtue, but a positive vice: _Beauty_ being attractive\nand _ugliness_ the reverse, if we invent a word for that which is\nneither, 'plainness,' it at once becomes tinged with the ugly. We seem\nto love beauty and morality so much as to be almost incapable of\nsignifying their absence without expressing aversion.\n\nAgain, the erroneous theories of mankind have often found their way into\npopular speech, and their terms have remained there long after the\nrejection of the beliefs they embodied: as--lunatic, augury, divination,\nspell, exorcism: though, to be sure, such words may often be turned to\ngood account, besides the interest of preserving their original sense.\nLanguage is a record as well as an index of ideas.\n\nLanguage, then, being essentially classificatory, any attempt to\nascertain the meaning of a word, far from neglecting its relations to\nothers, should be directed toward elucidating them.\n\nEvery word belongs to a group, and this group to some other larger\ngroup. A group is sometimes formed by derivation, at least so far as\ndifferent meanings are marked merely by inflections, as _short_,\n_shorter_, _shorten_, _shortly_; but, for the most part, is a conflux of\nwords from many different sources. _Repose_, _depose_, _suppose_,\n_impose_, _propose_, are not nearly connected in meaning; but are\nseverally allied in sense much more closely with words philologically\nremote. Thus _repose_ is allied with _rest_, _sleep_, _tranquillity_;\n_disturbance_, _unrest_, _tumult_; whilst _depose_ is, in one sense,\nallied with _overthrow_, _dismiss_, _dethrone_; _restore_, _confirm_,\n_establish_; and, in another sense, with _declare_, _attest_, _swear_,\n_prove_, etc. Groups of words, in fact, depend on their meanings, just\nas the connection of scientific names follows the resemblance in\ncharacter of the things denoted.\n\nWords, accordingly, stand related to one another, for the most part,\nthough very irregularly, as genus, species, and co-ordinate species.\nTaking _repose_ as a genus, we have as species of it, though not exactly\nco-ordinate with one another, _tranquillity_ with a mental differentia\n(repose of mind), _rest_, whether of mind or body, _sleep_, with the\ndifferentia of unconsciousness (privative). Synonyms are species, or\nvarieties, wherever any difference can be detected in them; and to\ndiscriminate them we must first find the generic meaning; for which\nthere may, or may not, be a single word. Thus, _equality_, _sameness_,\n_likeness_, _similarity_, _resemblance_, _identity_, are synonyms; but,\nif we attend to the ways in which they are actually used, perhaps none\nof them can claim to be a genus in relation to the rest. If so, we must\nresort to a compound term for the genus, such as 'absence of some sort\nof difference.' Then _equality_ is absence of difference in quantity;\n_sameness_ is often absence of difference in quality, though the usage\nis not strict: _likeness_, _similarity_, and _resemblance_, in their\nactual use, perhaps, cannot be discriminated; unless _likeness_ be the\nmore concrete, _similarity_ the more abstract; but they may all be used\ncompatibly with the recognition of more or less difference in the things\ncompared, and even imply this. _Identity_ is the absence of difference\nof origin, a continuity of existence, with so much sameness from moment\nto moment as is compatible with changes in the course of nature; so that\negg, caterpillar, chrysalis, butterfly may be identical for the run of\nan individual life, in spite of differences quantitative and\nqualitative, as truly as a shilling that all the time lies in a drawer.\n\nCo-ordinate Species, when positive, have the least contrariety; but\nthere are also opposites, namely, negatives, contradictories and fuller\ncontraries. These may be regarded as either co-ordinate genera or the\nspecies of co-ordinate genera. Thus, _repose_ being a genus,\n_not-repose_ is by dichotomy a co-ordinate genus and is a negative and\ncontradictory; then _activity_ (implying an end in view), _motion_\n(limited to matter), _disturbance_ (implying changes from a state of\ncalm), _tumult_, etc., are co-ordinate species of _not-repose_, and\nare therefore co-ordinate opposites, or contraries, of the species of\n_repose_.\n\nAs for correlative words, like _master and slave_, _husband and wife_,\netc., it may seem far-fetched to compare them with the sexes of the\nsame species of plants or animals; but there is this resemblance between\nthe two cases, that sexual names are correlative, as 'lioness,' and that\none sex of a species, like a correlative name, cannot be defined without\nimplying the other; for if a distinctive attribute of one sex be\nmentioned (as the lion's mane), it is implied that the other wants it,\nand apart from this implication the species is not defined: just as the\ndefinition of 'master' implies a 'slave' to obey.\n\nCommon words, less precise than the terms of a scientific nomenclature,\ndiffer from them also in this, that the same word may occur in different\ngenera. Thus, _sleep_ is a species of _repose_ as above; but it is also\na species of _unconsciousness_, with co-ordinate species _swoon_,\n_hypnotic state_, etc. In fact, every word stands under as many\ndistinct genera, at least, as there are simple or indefinable qualities\nto be enumerated in its definition.\n\n\u00a7 3. Partially similar to a scientific nomenclature, ordinary language\nhas likewise a terminology for describing things according to their\nqualities and structure. Such is the function of all the names of\ncolours, sounds, tastes, contrasts of temperature, of hardness, of\npleasantness; in short, of all descriptive adjectives, and all names for\nthe parts and processes of things. Any word connoting a quality may be\nused to describe many very different things, as long as they agree in\nthat quality.\n\nBut the quality connoted by a word, and treated as always the same\nquality, is often only analogically the same. We speak of a _great_\nstorm, a _great_ man, a _great_ book; but _great_ is in each case not\nonly relative, implying small, and leaving open the possibility that\nwhat we call great is still smaller than something else of its kind, but\nit is also predicated with reference to some quality or qualities, which\nmay be very different in the several cases of its application. If the\nbook is prized for wisdom, or for imagination, its greatness lies in\nthat quality; if the man is distinguished for influence, or for courage,\nhis greatness is of that nature; if the storm is remarkable for\nviolence, or for duration, its greatness depends on that fact. The word\n_great_, therefore, is not used for these things in the same sense, but\nonly analogically and elliptically. Similarly with good, pure, free,\nstrong, rich, and so on. 'Rest' has not the same meaning in respect of\na stone and of an animal, nor 'strong' in respect of thought and muscle,\nnor 'sweet' in respect of sugar and music. But here we come to the\nborder between literal and figurative use; every one sees that\nfigurative epithets are analogical; but by custom any figurative use may\nbecome literal.\n\nAgain, many general names of widely different meaning, are brought\ntogether in describing any concrete object, as an animal, or a\nlandscape, or in defining any specific term. This is the sense of the\ndoctrine, that any concrete thing is a conflux of generalities or\nuniversals: it may at least be considered in this way; though it seems\nmore natural to say, that an object presents these different aspects to\na spectator, who, fully to comprehend it, must classify it in every\naspect.\n\n\u00a7 4. The process of seeking a definition may be guided by the following\nmaxims:\n\n(1) Find the usage of good modern authors; that is (as they rarely\ndefine a word explicitly), consider what in various relations they use\nit to denote; from which uses its connotation may be collected.\n\n(2) But if this process yield no satisfactory result, make a list of the\nthings denoted, and of those denoted by the co-ordinate and opposite\nwords; and observe the qualities in which the things denoted agree, and\nin which they differ from those denoted by the contraries and opposites.\nIf 'civilisation' is to be defined, make lists of civilised peoples, of\nsemi-civilised, of barbarous, and of savage: now, what things are common\nto civilised peoples and wanting in the others respectively? This is an\nexercise worth attempting. If poetry is to be defined, survey some\ntypical examples of what good critics recognise as poetry, and compare\nthem with examples of bad 'poetry,' literary prose, oratory, and\nscience. Having determined the characteristics of each kind, arrange\nthem opposite one another in parallel columns. Whoever tries to define\nby this method a few important, frequently occurring words, will find\nhis thoughts the clearer for it, and will collect by the way much\ninformation which may be more valuable than the definition itself,\nshould he ever find one.\n\n(3) If the genus of a word to be defined is already known, the process\nmay be shortened. Suppose the genus of poetry to be _belles lettres_\n(that is, 'appealing to good taste'), this suffices to mark it off from\nscience; but since literary prose and oratory are also _belles lettres_,\nwe must still seek the differentia of poetry by a comparison of it with\nthese co-ordinate species. A compound word often exhibits genus and\ndifference upon its face: as 're-turn,' 'inter-penetrate,'\n'tuning-fork,' 'cricket-bat'; but the two last would hardly be\nunderstood without inspection or further description. And however a\ndefinition be discovered, it is well to state it _per genus et\ndifferentiam_.\n\n(4) In defining any term we should avoid encroaching upon the meaning of\nany of the co-ordinate terms; for else their usefulness is lessened: as\nby making 'law' include 'custom,' or 'wealth' include 'labour' or\n'culture.'\n\n(5) If two or more terms happen to be exactly synonymous, it may be\npossible (and, if so, it is a service to the language) to divert one of\nthem to any neighbouring meaning that has no determinate expression.\nThus, Wordsworth and Coleridge took great pains to distinguish between\nImagination and Fancy, which had become in common usage practically\nequivalent; and they sought to limit 'imagination' to an order of poetic\neffect, which (they said) had prevailed during the Elizabethan age, but\nhad been almost lost during the Gallo-classic, and which it was their\nmission to restore. Co-ordinate terms often tend to coalesce and become\nsynonymous, or one almost supersedes the other, to the consequent\nimpoverishment of our speech. At present _proposition_ (that something\nis the fact) has almost driven out _proposal_ (that it is desirable to\nco-operate in some action). Even good writers and speakers, by their own\npractice, encourage this confusion: they submit to Parliament certain\n'propositions' (proposals for legislation), or even make 'a proposition\nof marriage.' Definition should counteract such a tendency.\n\n(6) We must avoid the temptation to extend the denotation of a word so\nfar as to diminish or destroy its connotation; or to increase its\nconnotation so much as to render it no longer applicable to things which\nit formerly denoted: we should neither unduly generalise, nor unduly\nspecialise, a term. Is it desirable to define _education_ so as to\ninclude the 'lessons of experience'; or is it better to restrict it as\nimplying a personal educator? If any word implies blame or praise, we\nare apt to extend it to everything we hate or approve. But _coward_\ncannot be so defined as to include all bullies, nor _noble_ so as to\ninclude every honest man, without some loss in distinctness of thought.\n\nThe same impulses make us specialise words; for, if two words express\napproval, we wish to apply both to whatever we admire and to refuse both\nto whatever displeases us. Thus, a man may resolve to call no one great\nwho is not good: greatness, according to him, connotes goodness: whence\nit follows that (say) Napoleon I. was not great. Another man is\ndisgusted with greatness: according to him, good and great are mutually\nexclusive classes, sheep and goats, as in Gray's wretched clench:\n\"Beneath the good how far, yet far above the great.\" In feet, however\n'good' and 'great' are descriptive terms, sometimes applicable to the\nsame object, sometimes to different: but 'great' is the wider term and\napplicable to goodness itself and also to badness; whereas by making\n'great' connote goodness it becomes the narrower term. And as we have\nseen (\u00a7 3), such epithets may be applicable to objects on account of\ndifferent qualities: _good_ is not predicated on the same ground of a\nman and of a horse.\n\n(7) In defining any word, it is desirable to bear in mind its\nderivation, and to preserve the connection of meaning with its origin;\nunless there are preponderant reasons for diverting it, grounded on our\nneed of the word to express a certain sense, and the greater difficulty\nof finding any other word for the same purpose. It is better to lean to\nthe classical than to the vulgar sense of 'indifferent,' 'impertinent,'\n'aggravating,' 'phenomenal.'\n\n(8) Rigorous definition should not be attempted where the subject does\nnot admit of it. Some kinds of things are so complex in their qualities,\nand each quality may manifest itself in so many degrees without ever\nadmitting of exact measurement, that we have no means of marking them\noff precisely from other things nearly allied, similarly complex and\nsimilarly variable. If so we cannot precisely define their names.\nImagination and fancy are of this nature, civilisation and barbarism,\npoetry and other kinds of literary expression. As to poetry, some think\nit only exists in metre, but hardly maintain that the metre must be\nstrictly regular: if not, how much irregularity of rhythm is admissible?\nOthers regard a certain mood of impassioned imagination as the essence\nof poetry; but they have never told us how great intensity of this mood\nis requisite. We also hear that poetry is of such a nature that the\nenjoyment of it is an end in itself; but as it is not maintained that\npoetry must be wholly impersuasive or uninstructive, there seems to be\nno means of deciding what amount or prominence of persuasion or\ninstruction would transfer the work to the region of oratory or science.\nSuch cases make the method of defining by the aid of a type really\nuseful: the difficulty can hardly be got over without pointing to\ntypical examples of each meaning, and admitting that there may be many\ndivergences and unclassifiable instances on the border between allied\nmeanings.\n\n\u00a7 5. As science began from common knowledge, the terms of the common\nvocabulary have often been adopted into the sciences, and many are still\nfound there: such as weight, mass, work, attraction, repulsion,\ndiffusion, reflection, absorption, base, salt, and so forth. In the more\nexact sciences, the vague popular associations with such words are\nhardly an inconvenience: since those addicted to such studies do not\nexpect to master them without undergoing special discipline; and, having\nprecisely defined the terms, they acquire the habit of thinking with\nthem according to their assigned signification in those investigations\nto which they are appropriate. It is in the Social Sciences, especially\nEconomics and Ethics, that the use of popular terminology is at once\nunavoidable and prejudicial. For the subject-matters, industry and the\nconduct of life, are every man's business; and, accordingly, have always\nbeen discussed with a consciousness of their direct practical bearing\nupon public and private interests, and therefore in the common language,\nin order that everybody may as far as possible benefit by whatever light\ncan be thrown upon them. The general practice of Economists and\nMoralists, however, shows that, in their judgment, the good derived from\nwriting in the common vocabulary outweighs the evil: though it is\nsometimes manifest that they themselves have been misled by\nextra-scientific meanings. To reduce the evil as much as possible, the\nfollowing precautions seem reasonable:\n\n(1) To try to find and adopt the central meaning of the word (say rent\nor money) in its current or traditionary applications: so as to lessen\nin the greater number of cases the jar of conflicting associations. But\nif the central popular meaning does not correspond with the scientific\nconception to be expressed, it may be better to invent a new term.\n\n(2) To define the term with sufficient accuracy to secure its clear and\nconsistent use for scientific purposes.\n\n(3) When a popular term has to be used in a sense that departs from the\nordinary one in such a way as to incur the danger of misunderstanding,\nto qualify it by some adjunct or \"interpretation-clause.\"\n\nThe first of these rules is not always adhered to; and, in the progress\nof a science, as subtler and more abstract relations are discovered\namongst the facts, the meaning of a term may have to be modified and\nshifted further and further from its popular use. The term 'rent,' for\nexample, is used by economists, in such a sense that they have to begin\nthe discussion of the facts it denotes, by explaining that it does not\nimply any actual payment by one man to another. Here, for most readers,\nthe meaning they are accustomed to, seems already to have entirely\ndisappeared. Difficulties may, however, be largely overcome by\nqualifying the term in its various relations, as produce-rents,\nground-rents, customary rents, and so forth, (Cf. Dr. Keynes' _Scope\nand Method of Political Economy_, chap. 5.)\n\n\u00a7 6. Definitions affect the cogency of arguments in many ways, whether\nwe use popular or scientific language. If the definitions of our terms\nare vague, or are badly abstracted from the facts denoted, all arguments\ninvolving these terms are inconclusive. There can be no confidence in\nreasoning with such terms; since, if vague, there is nothing to protect\nus from ambiguity; or, if their meaning has been badly abstracted, we\nmay be led into absurdity--as if 'impudence' should be defined in such a\nway as to confound it with honesty.\n\nAgain, it is by definitions that we can best distinguish between Verbal\nand Real Propositions. Whether a term predicated is implied in the\ndefinition of the subject, or adds something to its meaning, deserves\nour constant attention. We often persuade ourselves that statements are\nprofound and important, when, in fact, they are mere verbal\npropositions. \"It is just to give every man his due\"; \"the greater good\nought to be preferred to the less\"; such dicta sound well--indeed, too\nwell! For 'a man's due' means nothing else than what it is just to give\nhim; and 'the greater good' may mean the one that ought to be preferred:\nthese, therefore, are Truisms. The investigation of a definition may be\na very valuable service to thought; but, once found, there is no merit\nin repeating it. To put forward verbal or analytic propositions, or\ntruisms, as information (except, of course, in explaining terms to the\nuninstructed), shows that we are not thinking what we say; for else we\nmust become aware of our own emptiness. Every step forward in knowledge\nis expressed in a real or synthetic proposition; and it is only by means\nof such propositions that information can be given (except as to the\nmeaning of words) or that an argument or train of reasoning can make any\nprogress.\n\nOpposed to a truism is a Contradiction in Terms; that is, the denying of\na subject something which it connotes (or which belongs to its\ndefinition), or the affirming of it something whose absence it connotes\n(or which is excluded by its definition). A verbal proposition is\nnecessarily true, because it is tautologous; a contradiction in terms is\nnecessarily false, because it is inconsistent. Yet, as a rhetorical\nartifice, or figure, it may be effective: that 'the slave is not bound\nto obey his master' may be a way of saying that there ought to be no\nslaves; that 'property is theft,' is an uncompromising assertion of the\ncommunistic ideal. Similarly a truism may have rhetorical value: that 'a\nNegro is a man' has often been a timely reminder, or even that \"a man's\na man.\" It is only when we fall into such contradiction or tautology by\nlapse of thought, by not fully understanding our own words, that it\nbecomes absurd.\n\nReal Propositions comprise the predication of Propria and Accidentia.\nAccidentia, implying a sort of empirical law, can only be established by\ndirect induction. But propria are deduced from (or rather by means of)\nthe definition with the help of real propositions, and this is what is\ncalled 'arguing from a Definition.' Thus, if increasing capacity for\nco-operation be a specific character of civilisation, 'great wealth' may\nbe considered as a proprium of civilised as compared with barbarous\nnations. For co-operation is made most effectual by the division of\nlabour, and that this is the chief condition of producing wealth is a\nreal proposition. Such arguments from definitions concerning concrete\nfacts and causation require verification by comparing the conclusion\nwith the facts. The verification of this example is easy, if we do not\nlet ourselves be misled in estimating the wealth of barbarians by the\nostentatious \"pearl and gold\" of kings and nobles, where 99 per cent. of\nthe people live in penury and servitude. The wealth of civilisation is\nnot only great but diffused, and in its diffusion its greatness must be\nestimated.\n\nTo argue from a definition may be a process of several degrees of\ncomplexity. The simplest case is the establishing of a proprium as the\ndirect consequence of some connoted attribute, as in the above example.\nIf the definition has been correctly abstracted from the particulars,\nthe particulars have the attributes summarised in the definition; and,\ntherefore, they have whatever can be shown to follow from those\nattributes. But it frequently happens that the argument rests partly on\nthe qualities connoted by the class name and partly on many other facts.\n\nIn Geometry, the proof of a theorem depends not only upon the definition\nof the figure or figures directly concerned, but also upon one or more\naxioms, and upon propria or constructions already established. Thus, in\nEuclid's fifth Proposition, the proof that the angles at the base of an\nisosceles triangle are equal, depends not only on the equality of the\nopposite sides, but upon this together with the construction that shows\nhow from the greater of two lines a part may be cut off equal to the\nless, the proof that triangles that can be conceived to coincide are\nequal, and the axiom that if equals be taken from equals the remainders\nare equal. Similarly, in Biology, if colouring favourable to concealment\nis a proprium of carnivorous animals, it is not deducible merely from\ntheir predatory character or any other attribute entering into the\ndefinition of any species of them, but from their predatory character\ntogether with the causes summarised in the phrase 'Natural Selection';\nthat is, competition for a livelihood, and the destruction of those that\nlabour under any disadvantages, of which conspicuous colouring would be\none. The particular coloration of any given species, again, can only be\ndeduced by further considering its habitat (desert, jungle or\nsnowfield): a circumstance lying wholly outside the definition of the\nspecies.\n\nThe validity of an argument based partly or wholly on a definition\ndepends, in the first place, on the existence of things corresponding\nwith the definition--that is, having the properties connoted by the name\ndefined. If there are no such things as isosceles triangles, Euclid's\nfifth Proposition is only formally true, like a theorem concerning the\nfourth dimension of space: merely consistent with his other assumptions.\nBut if there be any triangles only approximately isosceles, the proof\napplies to them, making allowance for their concrete imperfection: the\nnearer their sides approach straightness and equality the more nearly\nequal will the opposite angles be.\n\nAgain, as to the things corresponding with terms defined, according to\nDr. Venn, their 'existence' may be understood in several senses: (1)\nmerely for the reason, like the pure genera and species of Porphyry's\ntree; the sole condition of whose being is logical consistency: or (2)\nfor the imagination, like the giants and magicians of romance, the\nheroes of tragedy and the fairies of popular superstition; whose\nproperties may be discussed, and verified by appeal to the right\ndocuments and authorities (poems and ballads): or (3) for perception,\nlike plants, animals, stones and stars. Only the third class exist in\nthe proper sense of the word. But under a convention or hypothesis of\nexistence, we may argue from the definition of a fairy, or a demigod, or\na dragon, and deduce various consequences without absurdity, if we are\ncontent with poetic consistency and the authority of myths and romances\nas the test of truth.\n\nIn the region of concrete objects, whose properties are causes, and\nneither merely fictions nor determinations of space (as in Geometry), we\nmeet with another condition of the validity of any argument depending on\na definition: there must not only be objects corresponding to the\ndefinition, but there must be no other causes counteracting those\nqualities on whose agency our argument relies. Thus, though we may infer\nfrom the quality of co-operation connoted by civilisation, that a\ncivilised country will be a wealthy one, this may not be found true of\nsuch a country recently devastated by war or other calamity. Nor can\nco-operation always triumph over disadvantageous circumstances.\nScandinavia is so poor in the gifts of nature favourable to industry,\nthat it is not wealthy in spite of civilisation: still, it is far\nwealthier than it would be in the hands of a barbarous people. In short,\nwhen arguing from a definition, we can only infer the _tendency_ of any\ncausal characteristics included in it; the unqualified realisation of\nsuch a tendency must depend upon the absence of counteracting causes. As\nsoon as we leave the region of pure conceptions and make any attempt to\nbring our speculations home to the actual phenomena of nature or of\nhuman life, the verification of every inference becomes an unremitting\nobligation.\n\n\n\n\nCHAPTER XXIV\n\nFALLACIES\n\n\n\u00a7 1. A Fallacy is any failure to fulfil the conditions of proof. If we\nneglect or mistake the conditions of proof unintentionally, whether in\nour private meditations or in addressing others, it is a Paralogism: but\nif we endeavour to pass off upon others evidence or argument which we\nknow or suspect to be unsound, it is a Sophism.\n\nFallacies, whether paralogisms or sophisms, may be divided into two\nclasses: (a) the Formal, or those that can be shown to conflict with one\nor more of the truths of Logic, whether Deductive or Inductive; as if we\nattempt to prove an universal affirmative in the Third Figure; or to\nargue that, as the average expectation of life for males at the age of\n20 is 19-1/2 years, therefore Alcibiades, being 20 years of age, will\ndie when he is 39-1/2; (b) the Material, or those that cannot be clearly\nexhibited as transgressions of any logical principle, but are due to\nsuperficial inquiry or confused reasoning; as in adopting premises on\ninsufficient authority, or without examining the facts; or in mistaking\nthe point to be proved.\n\n\u00a7 2. Formal Fallacies of Deduction and Induction are, all of them,\nbreaches of the rule 'not to go beyond the evidence.' As a detailed\naccount of them would be little else than a repetition of the foregoing\nchapters, it may suffice to recall some of the places at which it is\neasiest to go astray.\n\n(1) It is not uncommon to mistake the Contrary for the Contradictory,\nas--A is not taller than B, .'. he is shorter.\n\n(2) To convert _A._ or _O._ simply, as--\n\n All Money is Wealth .'. All Wealth is Money;\n\nor--Some Wealth is not Money .'. Some Money is not Wealth.\n\nIn both these cases, Wealth, though undistributed in the convertend, is\ndistributed in the converse.\n\n(3) To attempt to syllogise with two premises containing four terms, as\n\n The Papuans are savages;\n The Javanese are neighbours of the Papuans:\n .'. The Javanese are savages.\n\nSuch an argument is excluded by the definition of a Syllogism, and\npresents no formal evidence whatever. We should naturally assume that\nany man who advanced it merely meant to raise some probability that\n'neighbourhood is a sign of community of ideas and customs.' But, if so,\nhe should have been more explicit. There would, of course, be the same\nfailure of connection, if a fourth term were introduced into the\nconclusion, instead of into the premises.\n\n(4) To distribute in the conclusion a term that was undistributed in the\npremises (an error essentially the same as (2) above), i.e., Illicit\nprocess of the major or minor term, as--\n\n Every rational agent is accountable;\n Brutes are not rational agents:\n .'. Brutes are not accountable.\n\nIn this example (from Whately), an illegitimate mood of Fig. I., the\nmajor term, 'accountable,' has suffered the illicit process; since, in\nthe premise, it is predicate of an affirmative proposition and,\ntherefore, undistributed; but, in the conclusion, it is predicate of a\nnegative proposition and, therefore, distributed. The fact that nearly\neverybody would accept the conclusion as true, might lead one to\noverlook the formal inconclusiveness of the proof.\n\nAgain,\n\n All men are two-handed;\n All two-handed animals are cooking animals:\n .'. All cooking animals are men.\n\nHere we have Bramantip concluding in A.; and there is, formally, an\nillicit process of the minor; though the conclusion is true; and the\nevidence, such as it is, is materially adequate. ('Two-handed,' being a\npeculiar differentia, is nugatory as a middle term, and may be cut out\nof both premises; whilst 'cooking' is a proprium peculiar to the species\nMan; so that these terms might be related in U., _All men are all\ncookers_; whence, by conversion, _All cookers are men_.)\n\n(5) To omit to distribute the middle term in one or the other premise,\nas--\n\n All verbal propositions are self-evident;\n All axioms are self-evident:\n .'. All axioms are verbal propositions.\n\nThis is an illegitimate mood in Fig. II.; in which, to give any\nconclusion, one premise must be negative. It may serve as a formal\nillustration of Undistributed Middle; though, as both premises are\nverbal propositions, it is (materially) not syllogistic at all, but an\nerror of classification; a confounding of co-ordinate species by assuming\ntheir identity because they have the generic attribute in common.\n\n(6) To simply convert an hypothetical proposition, as--\n\n If trade is free, it prospers;\n .'. If trade prospers, it is free.\n\nThis is similar to the simple conversion of the categorical A.; since it\ntakes for granted that the antecedent is co-extensive with the\nconsequent, or (in other words) that the freedom of trade is the sole\ncondition of, or (at least) inseparable from, its prosperity.\n\nThe same assumption is made if, in an hypothetical syllogism, we try to\nground an inference on the affirmation of the consequent or denial of\nthe antecedent, as--\n\n If trade is free it prospers:\n It does prosper;\n .'. It is free.\n It is not free;\n .'. It does not prosper.\n\nNeither of these arguments is formally good; nor, of course, is either\nof them materially valid, if it be possible for trade to prosper in\nspite of protective tariffs.\n\nAn important example of this fallacy is the prevalent notion, that if\nthe conclusion of an argument is true the premises must be trustworthy;\nor, that if the premises are false the conclusion must be erroneous.\nFor, plainly, that--\n\nIf the premises are true, the conclusion is true, is a hypothetical\nproposition; and we argue justly--\n\n The premises are true;\n .'. The conclusion is true;\n or, The conclusion is false;\n .'. The premises are false (or one of them is).\n\nThis is valid for every argument that is formally correct; but that we\ncannot trust the premises on the strength of the conclusion, nor reject\nthe conclusion because the premises are absurd, the following example\nwill show:\n\n All who square the circle are great mathematicians;\n Newton squared the circle:\n .'. Newton was a great mathematician.\n\nThe conclusion is true; but the premises are intolerable.\n\nHow the taking of Contraries for Contradictories may vitiate Disjunctive\nSyllogisms and Dilemmas has been sufficiently explained in the twelfth\nchapter.\n\n\u00a7 3. Formal Fallacies of Induction consist in supposing or inferring\nCausation without attempting to prove it, or in pretending to prove it\nwithout satisfying the Canons of observation and experiment: as--\n\n(1) To assign the Cause of anything that is not a concrete event: as,\ne.g., why two circles can touch only in one point. We should give the\n'reason'; for this expression includes, besides evidence of causation,\nthe principles of formal deduction, logical and mathematical.\n\n(2) To argue, as if on inductive grounds, concerning the cause of the\nUniverse as a whole. This may be called the fallacy of transcendent\ninference: since the Canons are only applicable to instances of events\nthat can be compared; they cannot deal with that which is in its nature\nunique.\n\n(3) To mistake co-existent phenomena for cause and effect: as when a\nman, wearing an amulet and escaping shipwreck, regards the amulet as the\ncause of his escape. To prove his point, he must either get again into\nexactly the same circumstances without his amulet, and be\ndrowned--according to the method of Difference; or, shirking the only\nsatisfactory test, and putting up with mere Agreement, he must show, (a)\nthat all who are shipwrecked and escape wear amulets, and (b) that their\ncases agree in nothing else; and (c), by the Joint Method, that all who\nare shipwrecked without amulets are drowned. And even if his evidence,\naccording to Agreement, seemed satisfactory at all these points, it\nwould still be fallacious to trust to it as proof of direct causation;\nsince we have seen that unaided observation is never sufficient for\nthis: it is only by experiment in prepared circumstances that we can\nconfidently trace sequence and the transfer of energy.\n\nThere is the reverse error of mistaking causal connection for\nindependent co-existence: as if any one regards it as merely a curious\ncoincidence that great rivers generally flow past great towns. In this\ncase, however, the evidence of connection does not depend merely upon\ndirect Induction.\n\n(4) _Post hoc, ergo propter hoc_: to accept the mere sequence of\nphenomena, even though often repeated, as proving that the phenomena are\ncause and effect, or connected by causation. This is a very natural\nerror: for although, the antecedents of a phenomenon being numerous,\nmost of them cannot be its cause, yet it is among them that the cause\nmust be sought. Indeed, if there is neither time nor opportunity for\nanalysis, it may seem better to accept any antecedent as a cause (or, at\nleast, as a sign) of an important event than to go without any guide.\nAnd, accordingly, the vast and complicated learning of omens, augury,\nhoroscopy and prophetic dreams, relies upon this maxim; for whatever the\norigin of such superstitions, a single coincidence in their favour\ntriumphantly confirms them. It is the besetting delusion of everybody\nwho has wishes or prejudices; that is, of all of us at some time or\nother; for then we are ready to believe without evidence. The fallacy\nconsists in judging off-hand, without any attempt, either by logic or by\ncommon sense, to eliminate the irrelevant antecedents; which may include\nall the most striking and specious.\n\n(5) To regard the Co-Effects (whether simultaneous or successive) of a\ncommon cause as standing in the direct relation of cause and effect.\nProbably no one supposes that the falling of the mercury in his\nthermometer causes the neighbouring lake to freeze. True, it is the\nantecedent, and (within a narrow range of experience) may be the\ninvariable antecedent of the formation of ice; but, besides that the two\nevents are so unequal, every one is aware that there is another\nantecedent, the fall of temperature, which causes both. To justify\ninductively our belief in causation, the instances compared must agree,\nor differ, in one circumstance only (besides the effect). The flowing\ntide is an antecedent of the ebbing tide; it is invariably so, and is\nequal to it; but it is not the cause of it: other circumstances are\npresent; and the moon is the chief condition of both flow and ebb. In\nseveral instances, States that have grown outrageously luxurious have\ndeclined in power: that luxury caused their downfall may seem obvious,\nand capable of furnishing a moral lesson to the young. Hence other\nimportant circumstances are overlooked, such as the institution of\nslavery, the corruption and rapacity of officials and tax-gatherers, an\narmy too powerful for discipline; any or all of which may be present,\nand sufficient to explain both the luxury and the ruin.\n\n(6) To mistake one condition of a phenomenon for the whole cause. To\nspeak of an indispensable condition of any phenomenon as the cause of\nit, may be a mere conventional abbreviation; and in this way such a mode\nof expression is common not only in popular but also in scientific\ndiscussion. Thus we say that a temperature of 33\u00b0 F. is a cause of the\nmelting of ice; although that ice melts at 33\u00b0 F., must further depend\nupon something in the nature of water; for every solid has its own\nmelting-point. As long, then, as we remember that 'cause,' used in this\nsense, is only a convenient abbreviation, no harm is done; but, if we\nforget it, fallacy may result: as when a man says that the cause of a\nfinancial crisis was the raising of the rate of discount, neglecting the\nother conditions of the market; whereas, in some circumstances, a rise\nof the Bank-rate may increase public confidence and prevent a crisis.\n\nWe have seen that the direct use of the Canons of Agreement and\nDifference may only enable us to say that a certain antecedent is a\ncause or an indispensable condition of the phenomenon under\ninvestigation. If, therefore, it is important to find the whole cause,\nwe must either experiment directly upon the other conditions, or resort\nto the Method of Residues and deductive reasoning; nor must we be\ncontent, without showing (where such precision is possible) that the\nalleged cause and the given phenomenon are equal.\n\n(7) To mistake a single consequence of a given cause for the whole\neffect, is a corresponding error; and none so common. Nearly all the\nmistakes of private conduct and of legislation are due to it: To cure\ntemporary lassitude by a stimulant, and so derange the liver; to\nestablish a new industry by protective duties, and thereby impoverish\nthe rest of the country; to gag the press, and so drive the discontented\ninto conspiracy; to build an alms-house, and thereby attract paupers\ninto the parish, raise the rates, and discourage industry.\n\n(8) To demand greater exactness in the estimate of causes or effects\nthan a given subject admits of. In the more complex sciences, Biology,\nPsychology, Sociology, it is often impossible to be confident that all\nthe conditions of a given phenomenon have been assigned, or that all its\nconsequences have been traced. The causes of the origin of species and\nof the great French Revolution have been carefully investigated, and\nstill we may doubt whether they have all been discovered, or whether\ntheir comparative importance has been rightly determined; but it would\nbe very unreasonable to treat those things as miraculous and\nunintelligible. We read in the _Ethics_, that a properly cultivated mind\nknows what degree of precision is to be expected in each science. The\ngreatest possible precision is always to be sought; but what is possible\ndepends partly on the nature of the study and partly upon the state of\nscientific preparation.\n\n(9) To treat an agent or condition remote in time as an unconditional\ncause: for every moment of time gives an opportunity for new\ncombinations of forces and, therefore, for modifications of the effect.\nThus, although we often say that Napoleon's Russian expedition was the\ncause of his downfall, yet the effect was subject to numerous further\nconditions. Had the natives not burnt Moscow, had the winter been\nexceptionally mild, had the Prussians and Austrians not risen against\nhim, the event might have been very different. It is rash to trace the\nliberties of modern Europe to the battle of Marathon. Indeed, our powers\nof perception are so unequal to the subtlety of nature, that even in\nexperimental science there is time for molecular changes to occur\nbetween what we treat as a cause and the effect as we perceive it; and,\nin such cases, the strictly unconditional cause has not been discovered.\n\n(10) To neglect the negative conditions to which a cause is subject.\nWhen we say that water boils at 212\u00b0 F., we mean \"provided the pressure\nbe the same as that of the atmosphere at about the sea-level\"; for under\na greater pressure water will not boil at that temperature, whilst under\nless pressure it boils at a lower temperature. In the usual statement of\na law of causation, 'disturbing,' 'frustrating,' 'counteracting'\ncircumstances (that is, negative conditions) are supposed to be absent;\nso that the strict statement of such a law, whether for a remote cause,\nor for an immediate cause (when only positive conditions are included),\nis that the agent or assemblage of conditions, _tends_ to produce such\nan effect, other conditions being favourable, or in the absence of\ncontrary forces.\n\n(11) It is needless to repeat what has already been said of other\nfallacies that beset inductive proof; such as the neglect of a possible\nplurality of causes where the effect has been vaguely conceived; the\nextension of empirical laws beyond adjacent cases; the chief errors to\nwhich the estimate of analogies and probabilities, or the application of\nthe principles of classification are liable; and the reliance upon\ndirect Induction where the aid of Deduction may be obtained, or upon\nobservation where experiment may be employed. As to formal fallacies\nthat may be avoided by adhering to the rules of logical method, this may\nsuffice.\n\n\u00a7 4. There remain many ways in which arguments fall short of a tolerable\nstandard of proof, though they cannot be exhibited as definite breaches\nof logical principles. Logicians, therefore, might be excused from\ndiscussing them; but out of the abundance of their pity for human\ninfirmity they usually describe and label the chief classes of these\n'extra-logical fallacies,' and exhibit a few examples.\n\nWe may adopt Whately's remark, that a fallacy lies either (1) in the\npremises, or (2) in the conclusion, or (3) in the attempt to connect a\nconclusion with the premises.\n\n(1) Now the premises of a sound argument must either be valid\ndeductions, or valid inductions, or particular observations, or axioms.\nIn an unsound argument, then, whose premises are supported by either\ndeduction or induction, the evidence may be reduced to logical rules;\nand its failure is therefore a 'logical fallacy' such as we have already\ndiscussed. It follows that an extra-logical fallacy of the premises must\nlie in what cannot be reduced to rules of evidence, that is, in bad\nobservations (\u00a7 5), or sham axioms (\u00a7 6).\n\n(2) As to the conclusion, this can only be fallacious if some other\nconclusion has been substituted for that which was to have been proved\n(\u00a7 7).\n\n(3) Fallacies in the connection between premises and conclusion, if all\nthe propositions are distinctly and explicitly stated, become manifest\nupon applying the rules of Logic. Fallacies, therefore, which are not\nthus manifest, and so are extra-logical, must depend upon some sort of\nslurring, confusion, or ambiguity of thought or speech (\u00a7 8).\n\n\u00a7 5. Amongst Fallacies of Observation, Mill distinguishes (1) those of\nNon-observation, where either instances of the presence or absence of\nthe phenomenon under investigation, or else some of the circumstances\nconstituting it or attending upon it, though important to the induction,\nare overlooked. These errors are implied in the Formal Fallacies of\nInduction already treated of in \u00a7 3 (paragraphs (3) to (7)).\n\nMill's class (2) comprises fallacies of Malobservation. Malobservation\nmay be due to obtuseness or slowness of perception; and it is one\nadvantage of the physical sciences as means of education, that the\ntraining involved in studying them tends to cure these defects--at\nleast, within their own range.\n\nBut the occasion of error upon which Mill most insists, is our proneness\nto substitute a hasty inference for a just representation of the fact\nbefore us; as when a yachtsman, eager for marvels, sees a line of\nporpoises and takes them for the sea-serpent. Every one knows what it is\nto mistake a stranger for a friend, a leaf for a sparrow, one word for\nanother. The wonder is that we are not oftener wrong; considering how\nsmall a part present sensation has in perception, and how much of every\nobject observed is supplied by a sort of automatic judgment. You see\nsomething brown, which your perceptive mechanism classes with the\nappearance of a cow at such a distance; and instantly all the other\nproperties of a cow are supplied from the resources of former\nexperience: but on getting nearer, it turns out to be a log of wood. It\nis some protection against such errors to know that we are subject to\nthem; and the Logician fulfils his duty in warning us accordingly. But\nthe matter belongs essentially to Psychology; and whoever wishes to\npursue it will find a thorough explanation in Prof. Sully's volume on\n_Illusions_.\n\nAnother error is the accumulation of useless, irrelevant observations,\nfrom which no proof of the point at issue can be derived. It has been\nsaid that an important part of an inductive inquirer's equipment\nconsists in knowing what to observe. The study of any science educates\nthis faculty by showing us what observations have been effective in\nsimilar cases; but something depends upon genius. Observation is\ngenerally guided by hypotheses: he makes the right observations who can\nframe the right hypotheses; whilst another overlooks things, or sees\nthem all awry, because he is confused and perverted by wishes,\nprejudices or other false preconceptions; and still another gropes about\nblindly, noting this and docketing that to no purpose, because he has no\nhypothesis, or one so vague and ill-conceived that it sheds no light\nupon his path.\n\n\u00a7 6. The second kind of extra-logical Fallacy lying in the premises,\nconsists in offering as evidence some assertion entirely baseless or\nnugatory, but expressed in such a way as to seem like a general truth\ncapable of subsuming the proposition in dispute: it is generally known\nas _petitio principii_, or begging the question. The question may be\nbegged in three ways:\n\n(1) There are what Mill calls Fallacies _a priori_, mere assertions,\npretending to be self-evident, and often sincerely accepted as such by\nthe author and some infatuated disciples, but in which the cool\nspectator sees either no sense at all, or palpable falsity. These sham\naxioms are numerous; and probably every one is familiar with the\nfollowing examples: That circular motion is the most perfect; That every\nbody strives toward its natural place; That like cures like; That every\nbane has its antidote; That what is true of our conceptions is true of\nNature; That pleasure is nothing but relief from pain; That the good,\nthe beautiful and the true are the same thing; That, in trade, whatever\nis somewhere gained is somewhere lost; That only in agriculture does\nnature assist man; That a man may do what he will with his own; That\nsome men are naturally born to rule and others to obey. Some of these\ndoctrines are specious enough; whilst, as to others, how they could ever\nhave been entertained arouses a wonder that can only be allayed by a\nlengthy historical and psychological disquisition.\n\n(2) Verbal propositions offered as proof of some matter of fact. These\nhave, indeed, one attribute of axioms; they are self-evident to any one\nwho knows the language; but as they only dissect the meaning of words,\nnothing but the meaning of words can be inferred from them. If anything\nfurther is arrived at, it must be by the help of real propositions. How\ncommon is such an argument as this: 'Lying is wrong, because it is\nvicious'--the implied major premise being that 'what is vicious is\nwrong.' All three propositions are verbal, and we merely learn from them\nthat lying is _called_ vicious and wrong; and to make that knowledge\ndeterrent, it must be supplemented by a further premise, that 'whatever\nis called wrong ought to be avoided.' This is a real proposition; but it\nis much more difficult to prove it than 'that lying ought to be\navoided.' Still, such arguments, though bad Logic, often have a\nrhetorical force: to call lying not only wrong but vicious, may be\ndissuasive by accumulating associations of shame and ignominy.\n\nDefinitions, being the most important of verbal propositions (since they\nimply the possibility of as many other verbal propositions as there are\ndefining attributes and combinations of them), need to be watched with\nespecial care. If two disputants define the same word in different ways,\nwith each of the different attributes included in their several\ndefinitions they may bring in a fresh set of real propositions as to the\nagency or normal connection of that attribute. Hence their conclusions\nabout the things denoted by the word defined, diverge in all directions\nand to any extent. And it is generally felt that a man who is allowed to\ndefine his terms as he pleases, may prove anything to those who, through\nignorance or inadvertence, grant that the things that those terms stand\nfor have the attributes that figure in his definitions.\n\n(3) _Circulus in demonstrando_, the pretence of giving a reason for an\nassertion, whilst in fact only repeating the assertion itself--generally\nin other words. In such cases the original proposition is, perhaps,\nreally regarded as self-evident, but by force of habit a man says\n'because'; and then, after vainly fumbling in his empty pocket for the\ncoin of reason, the habit of symbolic thinking in words only, without\nreference to the facts, comes to his rescue, and he ends with a\nparaphrase of the same assertion. Thus a man may try to prove the\nnecessity of Causation: 'Every event must have a cause; because an event\nis a change of phenomena, and this implies a transformation of something\npre-existing; which can only have been possible, if there were forces in\noperation capable of transforming it.' Or, again: 'We ought not to go to\nwar, because it is wrong to shed blood.' But, plainly, if war did not\nimply bloodshed, the unlawfulness of this could be nothing against war.\nThe more serious any matter is, the more important it becomes either to\nreason thoroughly about it, or to content ourselves with wholesome\nassertions. How many 'arguments' are superfluous!\n\n\u00a7 7. The Fallacy of surreptitious conclusion (_ignoratio elenchi_), the\nmistaking or obscuring of the proposition really at issue, whilst\nproving something else instead. This may be done by substituting a\nparticular proposition for an universal, or an universal for a\nparticular. Thus, he who attacks the practice of giving in charity must\nnot be content to show that it has, in this or that case, degraded the\nrecipient; who may have been exceptionally weak. Or, again, to dissuade\nanother from giving alms in a particular case, it is not enough to show\nthat the general tendency of almsgiving is injurious; for, by taking\npains in a particular case, the general tendency may often be\ncounteracted.\n\nSometimes an argument establishing a wholly irrelevant conclusion is\nsubstituted for an _argumentum ad rem_. Macaulay complains of those\napologists for Charles I. who try to defend him as a king, by urging\nthat he was a good judge of paintings and indulgent to his wife.\n\nTo this class of Fallacies belongs the _argumentum ad hominem_, which\nconsists in showing not that a certain proposition is true, but that\nCritias ought to accept it in consistency with his other opinions. Thus:\n'In every parish the cost of education ought to be paid out of the\nrates: you, at least, have said that there can be no sound economy,\nunless local expenses are defrayed from local funds.' But whether this\nis a fallacy depends, as Whately observes, upon whether it is urged as\nactually proving the point at issue, or merely as convicting the\nopponent of inconsistency. In the latter case, the argument is quite\nfair: whatever such a conclusion may be worth.\n\nSimilarly with the _argumentum ad populum_: 'this measure is favourable\nto such or such a class; let them vote for it.' An appeal to private\ngreed, however base, is not fallacious, as long as the interest of the\nclass is not _fraudulently_ substituted for the good of the nation. And\nmuch the same may be said for the _argumentum ad verecundiam_. When a\nquestion of morals is debated as a question of honour among thieves,\nthere is no fallacy, if the moral issue is frankly repudiated. The\nargument from authority is often brought under this head: 'such is the\nopinion of Aristotle.' Although this does not establish the truth of any\nproposition, it may be fairly urged as a reason for not hastily adopting\na contrary conclusion: that is, if the subject under discussion be one\nas to which Aristotle (or whoever the authority may be) had materials\nfor forming a judgment.\n\nA negative use of this fallacy is very common. Some general doctrine,\nsuch as Positivism, Transcendentalism, Utilitarianism, or Darwinism, is\nheld in common by a group of men; who, however, all judge independently,\nand therefore are likely to differ in details. An opponent exhibits\ntheir differences of opinion, and thereupon pretends to have refuted the\ntheory they agree in supporting. This is an _argumentum ad scholam_, and\npushes too far the demand for consistency. In fact it recoils upon the\nsophist; for there is no sense in quoting men against one another,\nunless both (or all) are acknowledged to speak with the authority of\nlearning and judgment, and therefore the general doctrine which they\nhold in common is the more confirmed.\n\nThis is an example of the paralogism of 'proving too much'; when a\ndisputant is so eager to refute an opponent as to lay down, or imply,\nprinciples from which an easy inference destroys his own position. To\nappeal to a principle of greater sweep than the occasion requires may\neasily open the way to this pitfall: as if a man should urge that 'all\nmen are liars,' as the premise of an argument designed to show that\nanother's assertion is less credible than his own.\n\nA common form of _ignoratio elenchi_ is that which Whately called the\n'fallacy of objections': namely, to lay stress upon all the\nconsiderations against any doctrine or proposal, without any attempt to\nweigh them against the considerations in its favour; amongst which\nshould be reckoned all the considerations that tell against the\nalternative doctrines or proposals. Incontestable demonstration can\nrarely be expected even in science, outside of the Mathematics; and in\npractical affairs, as Butler says, 'probability is the very guide of\nlife'; so that every conclusion depends upon the balance of evidence,\nand to allow weight to only a part of it is an evasion of the right\nissue.\n\n\u00a7 8. Fallacies in the connection of premises and conclusion, that cannot\nbe detected by reducing the arguments to syllogistic form, must depend\nupon some juggling with language to disguise their incoherence. They may\nbe generally described as Fallacies of Ambiguity, whether they turn upon\nthe use of the same word in different senses, or upon ellipsis. Thus it\nmay be argued that all works written in a classical language are\nclassical, and that, therefore, the history of Philosophy by Diogenes\nL\u00e6rtius, being written in Greek, is a classic. Such ambiguities are\nsometimes serious enough; sometimes are little better than jokes. For\njokes, as Whately observes, are often fallacies; and considered as a\nprop\u00e6deutic to the art of sophistry, punning deserves the ignominy that\nhas overtaken it.\n\nFallacies of ellipsis usually go by learned names, as; (1) _a dicto\nsecundum quid ad dictum simpliciter_. It has been argued that since,\naccording to Ricardo, the value of goods depends solely upon the\nquantity of labour necessary to produce them, the labourers who are\nemployed upon (say) cotton cloth ought to receive as wages the whole\nprice derived from its sale, leaving nothing for interest upon capital.\nRicardo, however, explained that by 'the quantity of labour necessary to\nproduce goods' he meant not only what is immediately applied to them,\nbut also the labour bestowed upon the implements and buildings with\nwhich the immediate labour is assisted. Now these buildings and\nimplements are capital, the labour which produced them was paid for, and\nit was far enough from Ricardo's mind to suppose that the capital which\nassists present labour upon (say) cotton cloth has no claim to\nremuneration out of the price of it. In this argument, then, the word\nlabour in the premise is used _secundum quid_, that is, with the\nsuppressed qualification of including past as well as present labour;\nbut in the conclusion labour is used _simpliciter_ to mean present\nlabour only.\n\n(2) _A dicto secundum quid ad dictum secundum alterum quid_. It may be\nurged that, since the tax on tea is uniform, therefore all consumers\ncontribute equally to the revenue for their enjoyment of it. But written\nout fairly this argument runs thus: Since tea is taxed uniformly _4d.\nper lb._, all consumers pay equally for their enjoyment of it _whatever\nquantity they use_. These qualifications introduced, nobody can be\ndeceived.\n\n(3) _A dicto simpliciter ad dictum secundum quid_, also called _fallacia\naccidentis_. Thus: To take interest upon a loan is perfectly just,\ntherefore, I do right to exact it from my own father in distress. The\npopular answer to this sort of blunder is that 'circumstances alter\ncases.' We commit this error in supposing that what is true of the\naverage is likely to be true of each case; as if one should say: 'The\noffices are ready to insure my house [with thousands of others] against\nfire at a rate per annum which will leave them heavy losers unless it\nlasts a hundred years; so, as we are told not to take long views of\nlife, I shall not insure.'\n\nThe Fallacy of Division and Composition consists in suggesting, or\nassuming, that what is true of things severally denoted by a term is\ntrue of them taken together. That every man is mortal is generally\nadmitted, but we cannot infer that, therefore, the human race will\nbecome extinct. That the remote prospects of the race are tragic may be\nplausibly argued, but not from that premise.\n\nChanging the Premises is a fallacy usually placed in this division;\nalthough, instead of disguising different meanings under similar words,\nit generally consists in using words or phrases ostensibly differing, as\nif they were equivalent: those addressed being expected to renounce\ntheir right to reduce the argument to strict forms of proof, as needless\npedantry in dealing with an author so palpably straightforward. If an\norator says--'Napoleon conquered Europe; in other words, he murdered\nfive millions of his fellow creatures'--and is allowed to go on, he may\ninfer from the latter of these propositions many things which the former\nof them would hardly have covered. This is a sort of hyperbole, and\nthere is a corresponding meiosis, as: 'Mill _admits_ that the Syllogism\nis useful'; when, in fact, that is Mill's _contention_. It may be\nsupposed that, if a man be fool enough to be imposed upon by such\ntransparent colours, it serves him right; but this harsh judgment will\nnot be urged by any one who knows and considers the weaker brethren.\n\n\u00a7 9. The above classification of Fallacies is a rearrangement of the\nplans adopted by Whately and Mill. But Fallacies resemble other\nspontaneous natural growths in not submitting to precise and definite\nclassification. The same blunders, looked at from different points of\nview, may seem to belong to different groups. Thus, the example given\nabove to illustrate _fallacia accidentis_, 'that, since it is just to\ntake interest, it is right to exact it from one's own father,' may also\nbe regarded as _petitio principii_, if we consider the unconditional\nstatement of the premise--'to take interest upon a loan is perfectly\njust'; for, surely, this is only conditionally true. Or, again, the\nfirst example given of simple ambiguity--'that whatever is written in a\nclassical language is classical, etc.,' may, if we attend merely to\nthe major premise, be treated as a bad generalisation, an undue\nextension of an inference, founded upon a simple enumeration of the\nfirst few Greek and Latin works that one happened to remember.\n\nIt must also be acknowledged that genuine wild fallacies, roaming the\njungle of controversy, are not so easily detected or evaded as specimens\nseem to be when exhibited in a Logician's collection; where one surveys\nthem without fear, like a child at a menagerie. To assume the succinct\nmode of statement that is most convenient for refutation, is not the\nnatural habit of these things. But to give reality to his account of\nfallacies an author needs a large space, that he may quote no\ninconsiderable part of literature ancient and modern.\n\nAs to the means of avoiding fallacies, a general increase of sincerity\nand candour amongst mankind may be freely recommended. With more honesty\nthere would be fewer bad arguments; but there is such a thing as\nwell-meaning incapacity that gets unaffectedly fogged in converting A.,\nand regards the refractoriness of O., as more than flesh and blood can\nendure. Mere indulgence in figurative language, again, is a besetting\nsnare. \"One of the fathers, in great severity called poesy _vinum\nd\u00e6monum_,\" says Bacon: himself too fanciful for a philosopher. Surely,\nto use a simile for the discovery of truth is like studying beauty in\nthe bowl of a spoon.\n\nThe study of the natural sciences trains and confirms the mind in a\nhabit of good reasoning, which is the surest preservative against\nparalogism, as long as the terms in use are, like those of science, well\ndefined; and where they are ill defined, so that it is necessary to\nguard against ambiguity, a thorough training in politics or metaphysics\nmay be useful. Logic seems to me to serve, in some measure, both these\npurposes. The conduct of business, or experience, a sufficient time\nbeing granted, is indeed the best teacher, but also the most austere and\nexpensive. In the seventeenth century some of the greatest philosophers\nwrote _de intellectus emendatione_; and if their successors have given\nover this very practical inquiry, the cause of its abandonment is not\nsuccess and satiety but despair. Perhaps the right mind is not to be\nmade by instruction, but can only be bred: a slow, haphazard process;\nand meanwhile the rogue of a sophist may count on a steady supply of\ndupes to amuse the tedium of many an age.\n\n\nFINIS.\n\n\n\n\nQUESTIONS\n\n_The following questions are chiefly taken from public examination\npapers: Civil Service_ [S], _Oxford_ [O], _Cambridge_ [C], _London_ [L].\n\n\nI. TERMS, ETC.\n\n1. What is a Term? Explain and illustrate the chief divisions of Terms.\nWhat is meant by the Connotation of a Term? Illustrate. [S]\n\n2. \"The connotation and denotation of terms vary inversely.\" Examine\nthis assertion, explaining carefully the limits within which it is true,\nif at all. [S]\n\n3. Exemplify the false reasoning arising from the confusion of Contrary\nand Contradictory Terms. [S]\n\n4. Discuss the claims of the doctrine of Terms to be included in a\nLogical System. Distinguish between a General and an Abstract Term. [S]\n\n5. Explain and illustrate what is meant by the Denotation and\nConnotation of a Term. What terms have both, and what have one only? [S]\n\n6. Distinguish between Abstract and Concrete Names. To which of these\nclasses belong (a) adjectives, (b) names of states of consciousness? Are\nany abstract names connotative? [S]\n\n7. Distinguish between (a) Proper and Singular Terms, (b) Negative and\nPrivative, (c) Absolute and Relative. Illustrate.\n\n8. What connection is there between the Connotation and the Relativity\nof Names?\n\n9. Examine the logical relations between the following pairs of terms:\n(a) happy and happiness; (b) happy and unhappy; (c) 'the juryman' and\n'the jury'; (d) parent and offspring.\n\nExplain the technical words used in your answer. [C]\n\n10. Distinguish between _name_; _part of speech_; _term_: and illustrate\nby reference to the following--use, useful, usefully. [C]\n\n11. Describe the nature of _Collective_ terms; examine in particular any\ndifficulties in distinguishing between these and general or abstract\nterms. [C]\n\n12. Distinguish between _positive_, _negative_, and _privative_ names.\nOf what kind are the following, and why--parallel, alien, idle, unhappy?\nWhat ambiguity is there in the use of such a term as \"not-white\"? [C]\n\n\nII. PROPOSITIONS AND IMMEDIATE INFERENCE.\n\n13. What is meant by (1) the Conversion, and (2) the Contra-position of\na proposition? Apply these processes, as far as admissible, to the\nfollowing:--\n\n (a) All invertebrates have cold blood.\n\n (b) Some cold-blooded animals are not invertebrates.\n\n (c) No wingless birds are songsters.\n\n (d) Some winged birds are not songsters.\n\nWhat can you infer from (a) and (b) jointly, and what from (c) and (d)\njointly? [S]\n\n14. \"The author actually supposes that, because Professor Fawcett denies\nthat all wealth is money, he denies that all money is wealth.\" Analyse\nthe differences of opinion implied in the above passage. [S]\n\n15. Take any universal affirmative proposition; convert it by obversion\n(contraposition); attach the negative particle to the predicate, and\nagain convert. Interpret the result exactly, and say whether it is or is\nnot equivalent to the original proposition. [S]\n\n16. What information about the term \"solid body\" can we derive from the\nproposition, \"No bodies which are not solids are crystals\"? [S]\n\n17. Discuss the proposal to treat all propositions as affirmative.\n\n18. Convert the proposition \"A is probably B.\" What information does the\nproposition give us concerning B? [S]\n\n19. Show in how many ways you can deny the following assertions: All\ncathedral towns are all cities; Canterbury is the Metropolitan see. [S]\n\n20. Explain the nature of a _hypothetical_ (or conditional) proposition.\nWhat do you consider the radical difference between it and a\ncategorical? [S]\n\n21. What is the function of the _copula_? In what different manners has\nit been treated? [S]\n\n22. Convert \"A killed C unjustly\"; \"All Knowledge is probably useful\";\n\"The exception proves the rule\"; \"Birds of a feather flock together.\"\n[S]\n\n23. What is modality? How are modals treated by (a) formal logic and (b)\nby the theory of induction? [S]\n\n24. What is the subject of an impersonal proposition? Give reasons for\nyour answer. [S]\n\n25. Is the categorical proposition sufficiently described as referring a\nthing or things to a class? [S]\n\n26. Enumerate the cases in which the truth or falsity of one proposition\nmay be formally inferred from the truth or falsity of another.\nIllustrate these cases, and give to each its technical name. [S]\n\n27. Illustrate the relation of Immediate Inferences to the Laws of\nThought.\n\n28. Explain what is meant by (a) Symbolic Logic; (b) the Logic of\nRelatives. Describe some method of representing propositions by means\nof diagrams; and indicate how far any particular theory of the import of\npropositions is involved in such representation. [S]\n\n29. Explain the exact nature of the relation between two _Contradictory_\npropositions; and define Conversion by Contraposition, determining what\nkind of propositions admit of such conversion.\n\nGive the contradictory and the contrapositive of each of the following\npropositions:--\n\n (a) All equilateral triangles are equiangular;\n\n (b) No vertebrate animal has jaws opening sideways;\n\n (c) Wherever A and B are both present, either C or D is also\n present. [S]\n\n30. Define Obversion and Inversion, and apply these processes also to\nthe above three propositions.\n\n31. Propositions can be understood either in extension or in intension.\nExplain this, and discuss the relative value of the two interpretations.\n[S]\n\n32. Distinguish between real and verbal propositions; and explain the\nimportance of the distinction.\n\n33. Illustrate the process called 'change of Relation.'\n\n\nIII. SYLLOGISM AND MEDIATE INFERENCE.\n\n34. What is a Syllogism? Find, without reference to the mnemonic verses,\nin what different ways it is possible to prove syllogistically the\nconclusion _No S is P_; and show the equivalence between these different\nways. [S]\n\n35. From what points of view can the syllogism be regarded\n\n (1) as being, (2) as not being, a _petitio principii_? [S]\n\n36. What are the figures of syllogism? For what kind of arguments are\nthey severally adapted? [S]\n\n37. What is meant by Mood and Figure? How can the validity of a Mood be\ntested? Should there be four Figures or three? [S]\n\n38. Construct syllogisms in Camenes, Datisi and Baroco, and reduce them\nto the corresponding moods of the first figure.\n\n39. Explain the meaning of \"ostensive\" and \"indirect\" Reduction. Show\nthat any Mood of the second Figure may be reduced in either way.\n\n40. Show that A cannot be proved except in the First Figure. Express the\nfollowing reasoning in as many syllogistic figures as you can: Some\ntheorists cannot be trusted, for they are unwise. [S]\n\n41. Discuss the possibility of reducing the argument _a fortiori_ to the\nsyllogistic form. [S]\n\n42. Can a false conclusion be reached through true premises, or a true\nconclusion through false premises? Give reasons for your answer. [S]\n\n43. Can we under any circumstances infer a relation between X and Z from\nthe premises--\n\n Some Y's are X's\n Some Y's are Z's? [S]\n\n44. Take an apparent syllogism subject to the fallacy of negative\npremises, and inquire whether you can correct the reasoning by\nconverting one or both of the premises into the affirmative form. [S]\n\n45. Enumerate the faults to which a syllogism is liable, giving\ninstances of each. [S]\n\n46. State any Enthymeme, and expand it into (1) a Syllogism, (2) an\nEpicheirema, (3) a Sorites; and give in each case the technical name of\nthe Mood or Order that results.\n\n47. State any Disjunctive Syllogism, and change it (1) into a\nHypothetical, (2) into a Categorical; and discuss the loss or gain, in\ncogency or significance involved in this process.\n\n48. Can the Syllogism be treated as merely a consequence of the \"Laws of\nThought\"? If not, why not; and what else does it imply?\n\n49. Prove that with three given propositions (of the forms A., E., I.,\nO.) it is never possible to construct more than one valid syllogism. [C]\n\n50. Distinguish between a Constructive and a Destructive Hypothetical\nSyllogism; and show how one may be reduced to the other. [C]\n\n\nIV. INDUCTION, ETC.\n\n51. What constitutes a Valid Induction? Distinguish it from a legitimate\nhypothesis. [S]\n\n52. Is it possible to form true universal propositions about facts if we\nhave not actually observed all the individuals designated by the subject\nof the proposition? If so, how? [S]\n\n53. \"Perfect induction is demonstrative and syllogistic; imperfect\ninduction is neither.\" Explain the difference between perfect and\nimperfect induction, and examine the truth of this assertion. [S]\n\n54. Why is it that one should not regard night as the cause, nor even as\na universal condition of day? Explain \"cause\" and \"condition.\" [S]\n\n55. What do you understand by an experiment? Can you say how many\nexperiments are required to establish (1) a fact, (2) a law of nature?\n\n56. How would you define _antecedent_, _cause_, _effect_, _consequent_?\n[S]\n\n57. England is the richest country in the world, and has a gold\ncurrency. Russia and India, in proportion to population, are poor\ncountries and have little or no gold currency. How far are such kind of\nfacts logically sufficient to prove that a gold currency is the cause of\na nation's wealth? [S]\n\n58. A man having been shot through the heart immediately falls dead.\nInvestigate the logical value of such a fact as proving that all men\nshot through the heart will fall dead. [S]\n\n59. Explain the process of induction called the Method of Difference,\nand give some new instances of its application. How is it related to the\nMethod of Concomitant Variations? What is the Major Premise implied in\nall these methods? [S]\n\n59A. Examine the position, that the Canons of Experiment are useless,\nbecause the work of preparing the experiments must have been done before\nthe canons can be applied.\n\n60. Explain the logical cogency of experiments in the search for\nphysical causes. [S]\n\n61. If the effects of A B C D are fully expressed by a b c d, and those\nof B C D by b c d, what inductive inference can be drawn and on what\nprinciple? State the canon according to which it is drawn. [S]\n\n62. Compare the advantage of observation and experiment as means of\ngaining data for Reasoning. [S]\n\n63. Compare the cogency of different Inductive Methods, showing the kind\nof evidence each requires, and the principle on which it is based. [S]\n\n64. Compare the Canons of Agreement and Difference (1) as to the\ndifficulty of finding or preparing actual Instances for them, and (2) as\nto their conclusiveness.\n\n65. Describe what is meant by residual phenomena, and estimate their\nvalue in inductive science. [S]\n\n66. What is the argument from Analogy? How does it differ from (a)\nInduction, (b) metaphorical argument? [S]\n\n67. What are the various senses in which the word Analogy has been used?\nDistinguish, giving instances, between good and bad analogies. [S]\n\n68. How do you distinguish between what Mill calls the Geometrical,\nPhysical, and Historical Methods?\n\n68A. The Comparative Method is appealed to where direct evidence is\nwanting. Explain this.\n\n69. What is meant by a doctrine being unverifiable? If a conclusion\nreached by deduction does not agree with the facts, where must we look\nfor error?\n\n70. There are certain cases in which failure of verification is fatal to\na theory, and other cases in which it is of comparatively little\ncogency. How would you distinguish between these classes of cases? [S]\n\n71. Taking the \"evolution,\" or any other proposed hypothesis, how should\none proceed (a) to show whether it satisfies the conditions of a\nlegitimate hypothesis sufficiently to entitle it to investigation, and\n(b) to test it with a view to its acceptance or rejection as a truth of\nscience? [S]\n\n72. What do you mean by saying that \"a phenomenon has been\nsatisfactorily explained\"?\n\n73. Explain and illustrate the Historical Method of Sociological\ninquiry. [S]\n\n74. What is the relation of the theory of Probability to Logic? [S]\n\n75. Explain and discuss the doctrine that Induction is based upon the\nTheory of Probability. [S]\n\n75A. What are the logical grounds of the Law of Error?\n\n76. Explain the nature and use of Classification, the means to, and\ntests of, its successful performance. [S]\n\n77. What is Definition and what is its use? Mention various difficulties\nthat occur in the process, and show how they are to be met. [S]\n\n78. Propose rules for a good Division and a good Definition, and\nexemplify the breach of them. [S]\n\n79. Examine the validity of the idea of Real Kinds. [O]\n\n80. What kind of words are indefinable, and why? When do we define by\nnegation and by example? [S]\n\n81. Distinguish between the province and aims of classification and\n(logical) division. Illustrate. [S]\n\n82. What is an _infima species_ or _species specialissima_? Compare the\nuse of the terms _genus_ and _species_ in Logic with that which is\ncommon in speaking of animals or plants. [S]\n\n83. How far does the formation of Definitions and Classifications\nconstitute the end of Science? [S]\n\n84. Examine the methodological relations between Definition,\nClassification and Nomenclature. [S]\n\n85. Give instances of \"Differentia,\" \"Property,\" \"Inseparable Accident\";\nand examine, with reference to your instances, how far it is possible to\ndistinguish them. [S]\n\n\nV. MISCELLANEOUS.\n\n86. \"People can reason without the help of Logic.\" Why is this not a\nsufficient objection to the study? In your answer show distinctly why\nLogic should be studied. [S]\n\n87. What is the meaning of the assertion that Logic is concerned with\nthe form, and not with the matter, of thought? [S]\n\n88. \"Neither by deductive nor inductive reasoning can we add a tittle to\nour implicit knowledge.\" (Jevons.) Explain and criticise. [S]\n\n89. What is the logical foundation of the indirect method or _reductio\nad absurdum_? Is it applicable to non-mathematical subjects? [S]\n\n90. On what grounds do we believe in the reality of an historical event?\n[S]\n\n91. \"Facts are familiar theories.\" Explain and discuss this. [O]\n\n92. Wherein lies the difficulty of proving a negative? [O]\n\n93. Can any limits be assigned to the possible unification of the\nsciences? [O]\n\n94. Are the results of inductive inference necessarily certain? [O]\n\n95. The method of deductive science is hypothetical. Explain and\ndiscuss. [O]\n\n96. \"The uniformity of Nature can never be more than a working\nhypothesis.\" Explain and criticise.\n\n97. \"Without speculation there is no good and original observation.\"\nWhy? [O]\n\n98. Can the provinces of induction and deduction be kept separate? [O]\n\n99. How far is the relation of logical dependence identical with that of\ncausation? [O]\n\n99A. Discuss the position that the forms of Logic are meaningless apart\nfrom their application.\n\n100. State in syllogistic form (mood and figure) the following\narguments:--\n\n (a) As polygamy is in many countries legal, we may infer the\n variability of the moral standard.\n\n (b) If gold is wealth, to export it diminishes the national\n resources.\n\n (c) If all good people are happy, unhappiness is an\n indication of vice.\n\n (d) One may be sure of the benefits of inuring young\n children to cold, from the strength exhibited by all men and\n women thus treated in infancy.\n\n (e) Where there is no law, there is no injustice.\n\n (f) \"Dissimulation is but a faint kind of policy or wisdom;\n for it asketh a strong wit and a strong heart to know when to\n tell the truth, and to do it; therefore it is the weaker sort\n of politicians that are the greatest dissemblers.\" (Bacon.)\n\n (g) Money being a barren product, it is contrary to nature\n to make it reproduce itself. Usury, therefore, is unnatural,\n and, being unnatural, is unjustifiable.\n\n (h) The study of mathematics is essential to a complete\n course of education, because it induces a habit of close and\n regular reasoning. [S]\n\n101. Explain and illustrate the following terms:--Subalternans, _Vera\nCausa_, Plurality of Causes, Law of Nature, Empirical Law, _Summum\nGenus_, Predicament, _Arbor Porphyriana_, Axiom, Universe of discourse\n(_suppositio_), Antinomy, Dilemma, Realism, Dichotomy, etc.\n\n102. Is there any distinction and, if so, what, between a complete\nDescription and an Explanation? [C]\n\n103. On what principles have fallacies been classified? To what extent\ndo you think a satisfactory classification of Fallacies possible? [C]\n\n104. Examine how far conceptions of Persistence and of Invariable\nConcomitance of Properties are involved in the methodological\napplication of the conception of Cause.\n\n104A. Inquire whether the two following propositions can be reconciled\nwith one another: (a) The same conjunction of antecedents is invariably\nfollowed by the same consequent; (b) We never find the same concurrence\nof phenomena a second time. [C]\n\n105. Using the term Logic in a wide sense, so as to include Methodology,\ninquire how far a Logic of Observation is possible, and show in what it\nwill consist. [C]\n\n106. What is Proof?\n\nExplain and discuss the following dicta:--(a) _Qui nimium probat, nihil\nprobat_: (b) A bad proof is worse than no proof; (c) The exception\nproves the rule; (d) Negatives cannot be proved. [C]\n\n107. Examine how far the rules of immediate and syllogistic inference\nare modified by differences of interpretation of the categorical\nproposition in respect of the existence of the subject. [S]\n\n108. \"An effect is but the sum of all the partial causes, the\nconcurrence of which constitutes its existence.\" \"The cause of an event\nis its invariable and unconditional antecedent.\" Explain and compare\nthese two theories of causation. Does either alone exhaust the\nscientific conception of cause? [S]\n\n109. Under what logical conditions are statistical inferences\nauthorised, and what is the nature of their conclusions? [S]\n\n110. Distinguish between Psychology, Metaphysics, and Logic; and discuss\nbriefly their mutual relations. [S]\n\n111. All processes of inference in which the ultimate premises are\nparticular cases are equally induction.\n\nInduction is an inverse deduction.\n\nExplain and contrast these two theories of the relation of induction to\ndeduction. [S]\n\n112. What are the Fallacies specially incident to Induction?--or to the\napplication of the theory of Probabilities? [S]\n\n113. What is meant by the _personal error_ (or _personal equation_) in\nobservation? Discuss its importance in different branches of knowledge.\n[S]\n\n114. Define and illustrate:--Paralogism, _ignoratio elenchi_, _fallacia\naccidentis_, _argumentum ad verecundiam_, illicit process, undistributed\nmiddle, etc.\n\n115. State the three fundamental laws of thought, explain their meaning,\nand consider how far they are independent of each other? [L]\n\n116. Enumerate the \"Heads of Predicables\" and define their meaning.\nDiscuss their logical importance. [L]\n\n117. Upon what grounds has it been asserted that the conclusion of a\nsyllogism is drawn, not from, but according to, the major premise? Are\nthey valid? [L]\n\n118. \"Experiment is always preferable to observation.\" Why is this?\nExplain from the example of any science how observation and experiment\nsupplement each other. [L]\n\n119. What is a hypothesis? Distinguish between a working hypothesis and\nan established hypothesis, so as to bring out the conditions on which\nthe latter depends. [L]\n\n120. Explain how good scientific nomenclature and terminology are\nconnected with the purposes of good classification. [L]\n\n\n\n\n\n_Printed in Great Britain by Hazell, Watson & Viney, Ld., London and\nAylesbury for Simpkin, Marshall, Hamilton, Kent & Co. Ltd._\n\n[Transcriber's Note:\n\nThe following corrections were made to the original text:\n\nPage 40: \"inedequate\" changed to \"inadequate\"\nPage 42: \"classily\" changed to \"classify\"\nPage 90: \"alledging\" changed to \"alleging\"\nPage 128: missing comma added: \"Camenes, Dimaris\"\nPage 141: \"evalued\" changed to \"evaluated\"\nPage 147: \"tellens\" changed to \"tollens\": \"and the Modus tollens\"\nPage 170: \"impredictable\" changed to \"unpredictable\"\nPage 210: missing word 'a' added: \"Sesostris conquered a great\"\nPage 307: \"either\" changed to \"neither\"\nPage 315: \"inductions\" changed to \"induction\"\nPage 401: \"quality\" changed to \"quantity\"\nPage 401: \"propoedeutic\" changed to \"prop\u00e6deutic\"]","title":"Logic: Deductive and Inductive","tradition":"philosophy-ethics","translated_text":null,"word_count":131227}