THE GIFT OF _X:£jt....rM^ A.4IALQ. ^rpJi^J,... Cornell University Library 3 1924 031 234 390 olin.anx ^^ Cornell University Library The original of tliis bool< is in tine Cornell University Library. There are no known copyright restrictions in the United States on the use of the text. http://www.archive.org/details/cu31924031234390 By the same Author. Fifth Edition, crown 8vo, limp cloth, 38. 6d. A STUDENrS HANDBOOK OF PSYCHOLOGY AND ETHICS. Crown Svo, limp cloth, 3s. &d. ETHICS. An Introductory Manual for the use of University Students. Edited with Memoir and Notes. JOHNSON'S LIFE OF ADDISON. Crown 8vo, cloth, 2s. 6d. JOHNSON'S LIFE OF SWIFT. Crown 8vo, cloth, 2s. JOHNSON'S LIFE OF POPE. Crown 8vo, cloth, 2s. 6d. %* The Lives of Swift and Pope, together, sewed, 2s. ad. JOHNSON'S LIFE OF MILTON. Crown 8vo, cloth, 2s. 6d. JOHNSON'S LIFE OF DEYDEN. Crown 8vo, cloth, 2s. 6i. \* The Lives of Milton and Detden, together, sewed, 2s. 6«. " The notes are full, much patient and discriminating care having been displayed in tracing Johnson's annotations and references to their original sources. Not only young students, but older readers will derive much profit from the perusal of these volumes which maybe regarded as notable additions to Johnsonian literature." — Jo\tmal of Education. LONDON: GEOKGE BELL AND SONS. GEORGE BELL & SONS LONDON : YORK ST., COVENT GARDEN NEW YORK : 66, FIFTH AVENUE AND BOMBAY : 53, ESPLANADE ROAD CAMBRIDGE : DEIGHTON, BELL & CO. LOGIC AN INTRODUCTORY MANUAL FOR THE USE OF UNIVERSITY STUDENTS BY F. RYLAND, M.A. AUTHOR OF "A HANDBOOK OF PSYCHOLOGY," "ETHICS," ETC. LONDON GEORGE BELL AND SONS 1896 s CHISWICK PRESS ;— CHARLES WHITTINGHAM AND CO. TOOKS COURT, CHANCERY LANE, LONDON. PREFACE. The present work is intended to serve as an introduc- tory manual for the use of students. Like the author's " Psychology " and his " Ethics " it follows, in the main, the customary and traditional lines adopted by most English teachers, and authori- tatively laid down by the English universities. In particular the author believes the book will prove of service to those reading Logic for the London B.A. Pass Examination. At the same time attention has been called to certain aspects of the subject which seem of great importance, but which have apparently escaped the notice of examiners. Thus in Chapter VII. there is a brief exposition of the relation between the purely formal Laws of Thought and the regulative principles that underlie actual thinking about concrete things, in which the conditions of abstract thought are never entirely fulfilled. Obligations to previously published works are fully acknowledged in the text ; but the author desires here to express his thanks to Mr. W. E. Tanner, M.A., of the University of London, who has very kindly assisted him with many useful corrections and suggestions. PniNEY, Jarmwry, 1896. CONTENTS. CHAPTER I. THE SCOPE OF LOGIC. PAGE 1. Inference 1 2. The Validity of Inference 3 3. Material and Formal Inferences .... 7 4. Deduction and Induction 10 5. Logic as a Science and an Art H 6. Logic and other Sciences 13 CHAPTER II. TEBUS. § 1. Propositions 16 2. Terms 17 3. Amhignity in Terms 18 4. Connotation and Denotation 19 5. Concrete and Abstract Terms 23 6. Singular and General Terms 25 7. Collective and Distributive Terms .... 27 8. Relative and Absolute Terms 28 9. Positive, Negative, and Privative Terms ... 29 10. Contrary and Contradictory Terms .... 31 vm CONTENTS. CHAPTEE III. CATEGOBICAL PKOPOSITIONS. § 1. JudgraentB and Propositions 2. Categorical and Conditional Propositions 3. Quality and Quantity of Categorical Propositions 4. Infinite, Exceptive, and Exclusive Propositions 5. Opposition of Categorical Propositions 6. Analytic and Synthetic Propositions 7. Predication 8. Predication and Existence .... PAGE 32 32 33 36 37 40 41 45 CHAPTEE IV. CONDITIONAL PROPOSITIONS. 1. Hypothetical Propositions 47 2. Disjunctive Propositions 50 3. The Opposition of Conditional Propositions . . 51 CHAPTEE V. THE PEEDICABLES AND CATEGORIES. 1. The Predicahles 53 2. Infimse Species 5& 3. The Categories or Predicaments . ... 59 CHAPTEE VI. DEFINITION AND DIVISION. 1. Kinds of Definition 62. 2. Eules of Definition 63 3. Limits of Definition 66 4. Division 67 5. Eules of Division 68 6. Porphyry's Tree 71 CONTENTS. IX OHAPTEE VII. THE LAWS OP THOUGHT. PAGE § 1. The Laws of Thought 73 2. Laws of Identity and Contradiction .... 74 3. Law of Excluded Middle 77 4. Laws of Homogeneity, Heterogeneity, and Con- tinuity 79 5. Principle of Sufficient Eeason 81 CHAPTEE VIII. IMMEDIATE INFEKENOE. § 1. Inference 83 2. Obversion 84 8. Conversion 86 4. Contraposition 88 5. Inversion 89 OHAPTEE IX. THE SYLLOGISM, 1. The Syllogism ...;.... 91 2. Axioms of the Syllogism 92 3. Eules of the Syllogism 93 4. The Valid Moods 98 5. Figures of the Syllogism 99 6. The Special Eules and Canons 102 7. Eeduotion 105 8. • Diagrammatic Eepresentation of Syllogisms . . 109 X CONTENTS. CHAPTEB X. CRITICISM OF THE SYLLOGISM. COMPOUND AND lEEEGULAB SYLLOGISMS. PAGE § 1. The Dtility of the Syllogism Ill 2. Mill's Attack on the Syllogism 112 3. Quasi- Syllogistic Arguments 116 4. Numerical Syllogisms. Ultra-total Distribution . 118 5. Enthymemes 119 6. Pro-Syllogisms 121 7. Sorites 123 CHAPTBE XL CONDITIONAL REASONINGS. § 1. Hypothetical Syllogisms 126 2. Disjunctive Syllogisms 129 3. Dilemmas 131 CHAPTER XII. QUANTIFICATION OF THE PREDICATE AND EQUATIONAL LOGIC. § 1. Quantification of the Predicate 135 2. The New Propositions 136 3. Symbolic Logic 140 4. The Logical Alphabet 141 5. Other Methods of Working Problems . . . 144 CHAPTER XIII. INDUCTION. § 1. Induction . . . . ' 148 2. Perfect or Formal Induction 150 3. Laws and Uniformities 153 4. Laws of Nature and Empirical Laws ... . 156 CONTENTS. XI CHAPTEE XIV. UNIFOEMITY OF NATURE AND CAUSATION. PAGE ( 1. The Grroiind of Induction 158 2. The Law of Causation 160 3. Plurality of Causes 164 4. Conjunction of Causes and Intermixture of Effects . 166 CHAPTER XV. OBSEKVATION AND EXPERIMENT. 1. Observation 169 2. Experiment 171 3. Non-observation and Mal-observation . . . 174 4. Perception and Inference 177 5. Fact 178 CHAPTEB XVI. THE INDUCTIVE METHOD. 1. Method 180 2. Analysis and Synthesis 181 3. Classification in Induction 185 4. Generalization 187 5. Inductions only Probable 189 CHAPTEB XVII. HYPOTHESIS. 1. The Use of Hypothesis . . . . . .192 a. . Kinds of Hypotheses 194 3. Permissible Hypotheses 196 4. Verification 198 5. Subordinate Uses of Hypotheses .... 200 Xll CONTENTS. CHAPTEB XVIII. mill's methods of experimental inquiey. 1. The Method of Agreement . . . 2. Method of Agreement and Plurality of Causes 3. Method of Difference 4. The Joint Method . 5. Method of Eesidues . 6. Method of Concomitant Variations 7. Mill's Treatment of the Methods 8. How the Methods are actually Employed PAGE 202 205 ''^•207 211 213 215 216 218 CHAPTER XIX. EXPLANATION. § 1. Explanation 221 2. Exceptional Phenomena 223 3. Extension of Empirical Laws 226 4. Analogy 228 CHAPTER XX. CLASSIFICATION. 1. Classification and Formal Division . 2. Artificial and Natural Classification 3. Special and General Classification. ;. 4. Classification not the Work .of Nature. 5. Classification by Type 6. Classification by Series . . , . . 232 234 237 238 241 242 CONTENTS. XIU ■ CHAPTER XXI. SCIENTIFIC LANGDAGE. PAGE § 1. Language and Thought 245 2. Scientific Language 247 3. Termindlogy and Nomenclature .... 249 CHAPTEE XXIL FALLACIES. § 1. Old Classification of Fallacies 251 2. Mill's Classification of Fallacies . . . .253 3. Purely Logical Fallacies 255 4. Semi-Logical Fallacies 256 5. Material Fallacies 258 6. Petitio Principii and other Material Fallacies . . 262 7. FaUaoies of Observation 265 APPENDICES. A. Books Eecommended 267 B. Examples for Solution 268 C. London B.A. Questions 275 Index 288 LOGIC. CHAPTER I. THE SCOPE OF LOGIC. § 1. Inference. When from any piece of knowledge a fresh piece of knowledge is arrived at without our having any new ex- perience, we have inference. From experiments made with the finger and the top bar of the grate, a child comes to the knowledge that if at any future time he puts his finger on the bar when the fire is alight he will get burnt — this is inference. The inference may be wider : he may arrive at the knowledge that if he puts his finger on any bar of any grate, when the fire is alight, he will get burnt. But in either case he gets at fresh knowledge without any further appeal to experience. This process takes many different shapes. In its simplest form it is practically unconscious ; it is, at any rate, performed with the minimum of conscious- ness. Much of what passes as direct perception turns out to be really inferential. Psychology shows us that B 2 LOGIC. when we perceive an object, the mind almost uncon- sciously goes through a complicated process which is, in many respects, analogous to fully conscious inference. On a small basis of sensation we instantly build up a big superstructure of perception. We see a minute patch of greyish-blue colour in the horizon, and instantly say, "I see a church." This practically involves a large number of inferences. We unconsciously jump to the conclusion that if we came up to the greyish- blue patch, we should find a large stone building of a particular kind. There has been unconscious, or as it is better called, sub-conscious, inference in localizing the cause of the impression, and in re- cognizing the object as one of a class. Not even the simplest act of perception is free from the element of inference ; and the mistakes which occasionally occur are evidence of this. When I recognize, or think I recognize, my friend Jones across the street, I proceed from a piece of actual experience — certain visual sen- sations — but I erect on this a mass of inferences which may be erroneous. The knowledge I get is out of all proportion to the foundation of actual experience on which it rests. There is a great deal of inference of a somewhat more conscious kind, which, however, is still so simple as to be scarcely recognized as inference. Such ele- mentary acts of thought are seldom translated into words, but are registered, as it were, automatically by our mental machinery. In this way the child and the dog lay up for themselves a great ieal of knowledge THE SCOPE OF LOGIC. 6 from a small basis of experience. Even the applica- tion of old knowledge to a new case involves inference of this sort. A great deal of what is called " intui- tion " is inference of this kind. The rapidly-formed judgments of the clever business man, or the artist, or the great military commander, are frequently of this nature. They seem almost to be direct percep- tions ; the grounds on which they rest, and the steps by which they are reached, cannot be distinguished by those who form them. Only the skilled psychologist can hope to detect them. Finally, there are the fully conscious inferences which are ordinarily expressed in words. They vary enormously in complexity. Some are quite simple and concrete, and scarcely need the use of formal language at all : others are extremely complex or extremely abstract, and involve the employment of symbols more exact than those of everyday language — e.g., the symbols of mathematics. It is with these fully con- scious inferences that Logic has to do. § 2. The Validity of Inference. As we have seen, we are constantly making in- ferences. Many of these inferences are so rapid and so little conscious that it seems impossible to criticise them. Others are made slowly and with difficulty in the full light of consciousness ; they can be easily reproduced and examined. Logic is the science which lays down the general 4 LOGIC. conditions of valid, conscious inference. It undertakes to explain on what condition conscious inferences may be riglitly drawn. By valid inference we mean inference which gives us results in accordance with experience as a whole ; not my experience only, but that of all men. If from the proposition, " All fires burn," I draw the conclu- sion that this fire will not burn, I obviously draw a ■conclusion which my own experience and that of others will easily show to be false. If from a con- sideration of a triangle I come to the conclusion that all the angles are together equal to one right angle, I shall have a result which I myself shall probably abandon on further reflection, and of whose truth I shall at any rate never succeed in convincing any qualified person. The final appeal of the validity of an inference must be to the thought of all competent persons. What the experts, after careful examination, declare to be valid, that must be accepted as vahd ; and beyond the judg- ment of experts — which includes every person capable -of thinking and reflecting on his thought — we cannot go. If the question is raised, " Who is to decide whether a given person who disagrees with the rest of mankind on a given influence, is * capable ' or not ? " we can only reply once more, the consensus of experts. The inference is right because the qualified judges accept it ; and the judges can only be admitted as qualified by their agreement with the normal standard of judgment. THE SCOPE OF LOGIC. 5 This, after all, is our last resort, not only in matters of truth, but in matters of taste and conduct. Art and Morality, as well as Science must appeal to the old test of Catholic orthodoxy, quod semper, quod ubique, quod ab omnibus. Fortunately the number of abnormal persons in the world is less in the case of knowledge than in the case of art and morality. Where inclination and interest do not distort the judgment, most persons (not obviously insane or idiotic) will arrive at the same conclusion, provided the question be sufficiently simple to admit of a full knowledge of its conditions. From these results we can generalize and lay down canons by which we shall be able to test all inferences in which the conditions are similarly simple. The minority which really disputes the multiplication table, or the rules of deductive inference, is microscopic. The conditions of quantitative inference laid down by the mathematician, and the still more general condi- tions of qualitative inference laid down by the logician, have practically never been challenged ; though some would-be reformers have proposed to express them in a somewhat different way, and others have been unable to see the advantage of laying them down at all. Most of the inferences we make, even on compara- tively difficult subjects, are made very rapidly, and though we can often bring into full consciousness the steps which led to our conclusion, we do not neces- sarily do this. If, however, the conclusion at which we arrive dissatisfies us, if we feel inclined to challenge b LOGIC. it, we re-state the grounds to ourselves and examine them. As thus re-stated, the grounds are necessarily not quite the same as before. Considerations which did not come into full consciousness are now brought clearly forward in a definite shape. They must be put in such a way as to make themselves obvious to anybody and everybody who cares to inquire into the matter. Logic, then, does not profess to represent the actual process by which conclusions are arrived at, but the process by which they must be arrived at, if they are to be accepted by everybody. I may know, in an indefinite and confused fashion, certain things about a person accused of a crime, and this knowledge may make me feel certain that he is guilty of that crime. It is not, however, until the facts are marshalled in a certain way, and their dependence on other facts clearly shown that I can consider the case proved; because it is not till this has been done that all other persons will necessarily draw the same inference from them that I immediately did. When the grounds on which a conclusion rests have been displayed in such a way that the vast majority of sane persons will inevitably draw that conclusion, we say that the conclusion is proved. An inference may be valid and yet not be proved ; but if it is valid it must be susceptible of proof. Unless we can believe it possible to give grounds for accepting it which shall be objectively valid — i.e., valid for everybody, at any rate all experts — we cannot regard it as a valid inference. THE SCOPE OF LOGIC. 7 We may now amend our former definition, and say that Logic is the science which deals with the con- ditions of proof, instead of the conditions of valid inference. § 3. Material and Formal Inferences. If some one tells me that he has a collie, I can at once infer that the animal wiU have certain attributes — say a head and tail, four legs, long silky hair, and so forth. This inference depends on my knowledge of collies. I have seen a good many, I have seen pictures of a good many, and heard about a good many, and I have read descriptions of them in books. These grounds for my new, inferred knowledge 1 can put before myself in words ; but they finally rest on ex- perience. By the use of my senses I have acquired them, either directly or indirectly; by my own ob- servation of collies, or through the observation of friends, artists, and authors. This kind of inference arising from an acquaintance with the subject matter, or content, of our objects of thought is called material inference. From knowledge of other collies I get to have knowledge of this new collie which I have never seen ; a new case is reached. If, however, I have come to know that " No collies are crustaceans," I can at once infer that my friend's collie is not a crustacean, even if I do not clearly understand what a collie is, or what a crustacean is. Here my inference depends, not on my knowledge 8 LOGIC of collies, but on the form of the proposition as presented to me. The certainty of the inference is not diminished by my ignorance. It is independent of the matter, or content, of the thought. Ifc can be expressed symbolically. If " No X is Y," then " this X is not Y." The conditions of these formal inference^ can be laid down quite clearly and definitely, and witl much more detail than those of material inferences, an)l therefore the greater part of most manuals of Logic is taken up by them. ' But the material inferences are at least equally in^- portant. The amount of fresh knowledge to be got by manipulating the form is after all very limited ; anji fresh material of knowledge has constantly to be got by experience. Yet that of which we have direct expe- rience, that is, immediate perception by our own senses, is necessarily very small. To settle under what con- ditions we may extend our limited experience to fresh cases, though a difficult task and impossible of entire fulfilment, is so important that it cannot be set aside. Some logicians, e.g., Mill, have refused the name inference to formal inferences, on the ground that no really new knowledge is obtained in them. But by new knowledge they mean knowledge of new cases, not previously included. If from the truth that "All collies are silky-haired " I arrive at the truth that my friend's collie is silky-haired, I do not get at a fresh case, because my friend's collie is included in the all. And if I infer from it that " Some silky-haired animals are collies," I again do not get beyond the original set of THE SCOPE OF LOGIC. 9 cases included in the original statement. Such in- ferences Mill regards as unworthy of the name ; they are "mere verbal transformations." If, however, we are going to refuse the name " in- ference " to these cases, we shall have to go a great deal further. When a mathematician solves an equation he gets at no fresh fact. However complex the original equation, he gets at the meaning of x (which was there all the time) by eliminating what he does not want, until he gets x on one side of the equation and its value on the other. It would be an absurd abuse of language to declare that the process of solving a diflScult quad- ratic equation involves no inference, because the value of X was all along implied, and we have simply disen- tangled this from its accompaniment. When from a given judgment or judgments we arrive at another judgment, differing from the given judgments in form or in matter, we have inference. In formal in- ference, as well as in material inference, there is a real progress of thought from what is known to what is unknown. Omniscience might correctly discern all the formal implications of a proposition, as it might do the value of X in an equation, in one and the same act of thought ; but men have to pass with some difficulty from a statement to the statements which are implied by its form. That the process is not always easy will be seen when we come to Chapters VIII. and IX. 10 LOGIC. § 4. Deduction and Induction. Deduction is formal inference from a proposi- tion to one as general or less general. If I pass from the statement that " No dogs are crustaceans " to the statement that " No crustaceans are dogs," I pass to one of the same degree of generality as the original. I refer in each case to the whole of the dogs and the whole of the crustaceans, and exclude them from each other. If I pass from " All men are mortal ' to " Socrates is a mortal," I pass from a general truth to a particular case. Both inferences are formal in character ; and no fresh cases are involved. When from observing many dogs I come to the conclusion that " all dogs are mammals," I exceed the limits of my knowledge by going to fresh cases of which I know nothing. My new proposition extends much farther than I or anyone else can ever profess to have direct knowledge. The conclusion is wider than the knowledge on which it is based. The process by which we arrive at it is called Induction. Under the head of Deduction we include all formal inference. We may deductively infer a new conclusion : (1) From a single given proposition ; (2) From two or more given propositions. The first is called immediate inference; the second mediate inference. Some writers prefer to place imrne- diate inference in a separate class, apart from deduction as well as induction. Mr. Welton calls them (or some of them) eductions. THE SCOPE OF LOGIC. 11 Most inductions are material ; but one particular type of induction belongs to the class of formal in- ferences. (See Chapter XII. § 2.) § 5. Logic as a Science and an Art. Logic teaches us the conditions of proof. It analyses our thoughts from this point of view. It does not profess to exhibit what consciously or unconsciously takes place in our mind when we think. That task belongs to Psychology. Logic shows under what con- ditions one may draw valid inferences. Logic, as it gives an account of the conditions of valid inference, is a science. A Science is a systematic account of facts of any kind, with an explanation of those facts whenever explanation is possible. The arrangement of facts which it adopts is dictated only by speculative interest. It employs definition, and classification, and reasoning only in order that the facts may be understood. An Art keeps practice always in view. It classifies, and defines, and reasons, with a view to arriving at rules and not at general truths. Many studies partake of the nature both of science and art. An ordinary text-book on Arithmetic or on Music gives rules as well as principles. In such a book we find discussion of general principles of number or of harmony ; but it devotes more attention to rules for working exercises, and to attaining facility in certain operations. In an ordinary treatise on Logic more 12 LOGIC. space is devoted to the scientific treatment of the con- ditions of proof, and less to the practical rules for avoiding error in reasoning. But both aspects of the matter are considered. All arts are based on science, and in the case of Logic the scientific basis is very prominent and very important. If error in reasoning were impossible, a science of Logic might still exist, though it would cease to have any practical value ; but there would be no art of Logic to teach us to do properly what we could not avoid doing properly. As an art Logic is useful, for it shows us the likely sources of error, and tells us how to avoid them. It gives us methods of testing reasonings of whose validity we feel any doubt. It exercises our intellects in the way best calculated to strengthen them, and thus furnishes a course of mental gymnastics devised on scientific principles. One man may of course be stronger without bodily gymnastics than another man with their assistance. But gymnastics are of service in strengthening the weak, and even adding to the strength of the strong. If good, they develop all the muscles of the body, and do not permit some of them to degenerate because they are not required in every- day use. Just so it is with Logic. Some who have studied Logic are bad reasoners ; and some men who have never opened a Logic book are good reasoners. But Logic as an art improves all in some degree ; and it insures that the reasoning powers shall be exercised in aU. sorts of ways. The tendency of particular THE SCOPE OF LOGIC. 13 studies is often to develop ability along certain special lines at the expense of ability along other lines. Most scientific men are accurate thinkers within their own sphere ; but their training does not always enable them to reason fairly and clearly about other subjects. The metaphysician sometimes makes a bad biologist ; and the biologist is not always a conspicuous success as a metaphysician. The lawyer, when he applies his mind to politics, is often inclined to demand a kind of proof of which the subject is incapable. In fact, one of the services which Logic performs is to show us the limitations of knowledge, and especially to make clear to us the sort of proof of which any given subject is capable. The mathematician, the biologist, and the politician deal with subjects which are susceptible of proofs of very different kinds. § 6. Logic and other Sciences. As a pure science Logic deals only with the general conditions of proof. It has nothing to do with the par- ticular conditions of special inquiries. It is even more abstract than mathematics, which deal with the relations of quantity and number. Logic deals only with the relations of co-existence and likeness. Mr. Spencer says that Logic " concerns itself with the most general laws of correlation among existences considered as objective." This, however, is not quite true, since it is concerned only with these in so far as they afford ground for the criticism of inferences. 14 LOGIC. Logic is marked off from Metaphysics by the fact that while Metaphysics is a criticism of knowledge as a whole, Logic deals only with the process of inference, and those processes which are subsidiary to inference, such as definition and classification. Metaphysics takes into account the ultimate basis of our knowledge. It examines and tries to explain the meaning of those ideas which underlie all our knowledge, the practical knowledge of the business man as well as the specula- tive knowledge of the savant. It analyses such concepts as Identity, Time, Space, Substance, Cause, Subject, and Object, many of which play no part in Logic. The general conditions of inference are independent of Time and Space ; and although Identity, Substance, and Cause need to be examined by the logician more than by the man of science or the practical man, his analysis of them does not go very deep. He is only concerned to find a working account of them, such as may subserve his purpose ; their full analysis does not trouble him. The relation of Logic to Psychology has been several times touched on. The logician has nothing to do with large portions of the territory of mental science. WiU and Emotion, and even Perception and Memory, con- cern him very little. Even with regard to Reasoning he does not try, as the psychologist does, to represent what actually goes on in the mind. He does not classify and explain mental phenomena as such ; but he lays down the form which certain mental activities must be made to take if they are to be THE SCOPE OF LOGIC. 15 regarded as valid. Psychology is descriptive and explanatory ; Logic is regulative. Logic deals with thoughts expressed in language or some symbolical equivalent of language. The mere concept, or judgment, or reasoning as it exists in the mind is not the subject matter of the logician; but the concept, judgment, or reasoning expressed in words, or some substitute for words. CHAPTEK II. TERMS. § 1. Propositions. A JUDGMENT expressed in words is called a proposi- tion. The logician analyses a simple or categorical proposition into three parts : Subject, predicate and copula. Snow . . . is . . . white (subject) (copula) (predicate) Snow ... is not . . . hot (subject) (copula) (predicate) The subject is the name of that about which the asser- tion is made; the predicate is the expression of that which is asserted about the subject ; the copula (a part of the verb to be) is the mere symbol of assertion. Confining ourselves to simple propositions, we may say that only propositions of the type S is P (or S is not P) are in strictly logical form. Here the predi- cate is quite detached from the copula ; whereas in ordinary language the two are blended and confused by the use of verbs which not only show that an assertion is made, but assert something specific. Thus TERMS. 1 7 the logician and the grammarian differ in their analysis of a proposition. The latter is concerned with the actual usages of language and is not concerned with the possibility of drawing correct inferences, so ho does not trouble to separate the copula is or is not from the predicate. The former does not mind his analysis appearing uncolloquial and uncouth ; but he is extremely anxious to see exactly what is predicated. Let the proposition to be analysed be : " The curfew tolls the knell of parting day.'' The grammarian calls everything after the word curfew the predicate, and subdivides this up into verb and object. The logician arranges it thus : " The curfew — is — tolling the knell of parting day," and calls all after the word is the predicate. § 2. Terms. The subject and the predicate are called the terms of the proposition, because they form the ends or termini of it. In practice, however, term is used for any word, or group of words, used as a subject or pre- dicate of a proposition, or capable of being so used. Every term then is a name, which can be made the subject of an assertion or the predicate of an assertion It may consist of one word or many. Victoria, and the present Queen of England and Empress of India arc both single terms, though one consists of only one word c 18 LOGIC. and the other of nine ; both refer to and denote only one and the eame object. A word which when standing alone can be used as a term (subject or predicate) is called a categorematic word (Greek xatnyopecii, I assert). A word which requires the addition of a categorematic word to enable it to form a term is called a syncategorematic word (Greek ) some place in an exposition of prepositional forms, we see that "the addition of U and Y does not tend towards simplification, but the reverse ; and that their full force can be expressed in other ways " (Keynes). 140 LOGIC. § 3. Symbolic Logic. We have seen that for purposes of inference we may fix our attention entirely on the denotation of terms. A proposition may be looked on as a statement that a given class S is included in or is excluded from another class P. Though this is not the primary and natural meaning of the proposition, it is often con- venient to adhere to it. Thus the rules of immediate inference and of the syllogism are usually justified by reference to the denotation exclusively. This point of view being developed, it tends to (1) an equational treatment of propositions, such as the quantification of the predicate aims at ; and (2) a quasi-mathematical treatment based on the doctrine of combination. If there be taken two terms, A and B, we can obviously form four classes : A B, A not-B, B not- A, not-A not-B, or (writing A for not- A) A B, A B, A B, A B, or (writing a for not A) A B, A b, a B, a b. We can express any proposition by declaring that one or more of these classes is occupied or is empty. Prac- tically it is found most convenient to express a universal proposition by denying that certain classes are empty, and a particular by affirming that certain classes have some occupants. Thus : " All A is B " is written A B = (or A b = 0), which denies that the compartment assigned to the class made up of A's which are not B's, contains anything ; and " No A is B " is written A B = 0. QUANTIFICATION OF THE PREDICATE. 141 The symbol now most frequently used to indicate that a compartment has some occupants is the letter v, so that " Some A is B " is written A B = i> ; and " Some A is not B " is written A B = w (or A b = ij). § 4. The Logical Alphabet. Where there are three terms (with their negatives) there will be eight possible combinations, none contain- ing a term and its negative, but each containing each of the terms or its negative.' For each of the four groups previously mentioned A B, A b, a B and a b, may be qualified by either C or c. Similarly, if there are four terms (with their negatives), there will be sixteen combinations. What these are will be most easily seen by writing A eight times, and A (or, as a more convenient negative, a) eight times ; then write alongside of the first four A's four B's, followed by four b's side by side with the next four A's, then four B's again and four b's again. Then write C twice, and c twice alternately ; then D and d alternately. ABC ABC ABc ABc Ab ' This is not an ordinary case of combinations. If the condi- tions mentioned were not made, there would be twenty possible combinations according to the well-known formula. 142 LOGIC. Ab Ab A b, etc. When completed, the sixteen combinations will run as follows : ABCD aBCD ABCd aBCd ABcD aBcD ABcd aB cd A.bCD abCD AbCd abCd AbcD abcD Abed abed They form what is called by Jevons the Logical Alphabet. Each of the general propositions negatives one or more of them ; and these negatived combinations may be obliterated. The combinations which remain are to be collected and some general expressions found for them. The method is throughout one of elimination or exclusion. Any combination at variance with any statement in the premises must be omitted. To take an easy example worked out by Jevons {« Principles of Science," p. 100). " All metals except gold and silver are opaque ; therefore, what is not opaque is either gold or silver or is not metal." Let A stand for metal ; B for gold ; C for silver ; and D for opaque. QUANTIFICATION OF THE PREDICATE. 143 The premises may be expressed thus : Abc = AbcD (1) B = B d (2) C = C d (3) B = B c (4) And as gold and silver are both metals : B =AB (5) C = A C (6) Now, first, it is obvious that we may do what in algebra would be called multiplying both sides of an equation by the same thing. Thus, if all M's are N's, aU L M's are L N's ; and if A = b, all A C = A b C Jevons calls this inference by added determinants. Secondly, it is obvious that any term which contains a contradiction must disappear. Thus A a = 0, and A B C c = 0. And, thirdly, it is obvious that to repeat the same letter makes no difference to a term. A "red, red house " is a " red house ; " an " immortal, immortal, immortal poem " is " an immortal poem." In other words, A A = A. ' This requires some qualification. It is only true on condi- tion that the new qualifying term introduced on both sides has exactly the same meaning on both sides, and comparative words (such as " little " and " large ") are liable to change of meaning according to the substantive with which they are placed. They have not always the same denotation. To use the old example, a flea is an animal ; but we cannot infer that a large flea is a large animal. 144 LOGIC. Determining both sides of equation (1) by d (or, as we may call it, multiplying both sides by d), we get : A b c d = (7) In the same way (using D for factor) from (2) and (3) we get BD =0 CD =0 (8) (9) From (4), (5), (6) we get BC =0 aB =0 aC =0 (10) (11) (12) We must now strike out every combination which contains any of the expressions we have found = 0. All these compartments of the universe are declared empty. Thus the only combinations left are A B c d, AbCd, Abe D, abcD, abed. We only want to know about d (not opaque things). We find that the only combinations which are d, are A B c d, Ab C d, abed; that is, gold metal, silver metal, and things which are not gold, and not silver, and not metal. Q. E. D. § 5. Other methods of working problems. When there are five terms we shall have thirty-two combinations, and when there are six terms, sixty-four. To write out all these afresh each time we have to work a problem, involves a great deal of labour. QUANTIFICATION OF THE PHEDICATB. 145 Jevons suggests the use of a logical slate, that is a slate on which the combinations of letters up to five or six terms are engraved. This will serve for all problems alike. " The conditions of the problem can then be written down on the unoccupied part of the slate, and the proper series of combinations being chosen, the contradictory combinations can be struck out with the pencil." He found such a slate of con- siderable utility (" Principles of Science," p. 96), Another plan is to have the combinations printed ; two or three hundred copies may be obtained for a shilling or two. A method which I have found serviceable may be described here. Confining our attention, for simplicity's sake, to four terms, let us copy down in one column the sixteen combinations given above, on p. 142, on a ruled paper. Take a slip of stiff paper and cut out a rectangular space, which will just show the first eight combinations, all which contain A. If this is applied, all the combinations containing a disapjiear. Now take another slip, and cut out two rectangular spaces, half the size of the former, in it, so as to show only those combinations containing B. Make similar slips for C and D. The last will show every other combination only. On the four slips write A, B, C, and D, re- spectively. By superposing any one, or more than one, of these, we can show or we can obliterate all the com- binations containing a given term or terms. This will very much lessen the labour of deleting those combi- nations which are destroyed by the premises. 1. 146 LOGIC. Diagrams may often be used with advantage. For three terms we want a diagram like this : This gives us every possible combination of A, B, C, and their contradictions. The parts which are found non-existent, according to the information given in the premises, may be shaded out. What is left will represent the possible combinations. The diagram for four terms is as follows : For more than four terms the diagrams are too complicated to be of any practical service.^ Besides the Logical Alphabet and the diagrammatic method, we may employ various directly symbolic methods. These are too difficult to be even indicated in such a work as this ; and the student is referred to Dr. Venn's " Symbolic Logic." All, however, pro- ceed on the same principle as the logical alphabet. All possible classes which can be constituted by a given set of terms have to be taken into account, and the ' See Dr. Venn's " Symbolic Logic," chap. v. QUANTIFICATION OF THE PREDICATE. 147 classes which are impossible, according to the con- ditions laid down by the premises, are rejected. The student should exercise himself in trying to solve easy problems by means of the methods ex- plained in the last two or three sections. Some questions will be found in the Appendix to this volume. CHAPTER XIII. INDUCTION. § 1. Induction. Induction is the process of inference by which we get at general truths from particular facts or cases. After examining the cases A, B, C, D, etc., in which the phenomenon x is accompanied by the phenomenon y, we infer that all instances in which x occurs will also exhibit y. It proceeds from singulars or particu- lars to universal propositions, and it is almost entirely material in character ; that is, it depends on the rela- tions between things, rather than on the general form in which we think or express our thoughts. Like the word " deduction," the word " induction" is used to express both the process of inference and the result of the process. When we speak of an induction, we generally mean the latter, that is, the general statement arrived at by inference. Universal propositions may of course be got at by ■deduction from some previously known propositions of 9> universal character. But the series must have a beginning ; and we must come at last either to intui- tion or to induction to furnish us with ultimate premises. INDUCTION. 149 By intuition is meant a process of immediate know- ledge, where the mind, on being confronted with a statement, or with facts, recognizes without conscious inference the truth underlying. The 9,xioms of mathe- matics are probably first apprehended in this way. Whether such a power exists at all in the mind has been doubted, and at any rate the greatest part of our ultimate truths clearly come from experience of facts, and are due to a process of unconscious induction. Almost every science consists partly of universal propositions arrived at by induction, and partly of de- ductions from these. In some sciences the inductive part is comparatively small, and the deductive part very large ; such sciences are Physics and Political Economy. In other cases, the deductive part is reduced to a very small amount, and the science mainly consists of general truths, which have been discovered by means of induction, as with Botany and Zoology. A great deal of inference from known cases to new cases takes the form which Mill calls " reasoning from particulars to particulars," and for which Jevons sug- gested the name traduction. A child finds that several little frogs which he touches are cold, and he there- after expects that other frogs will prove cold if he gets them into his hands. He does not consciously formulate any conclusion of this kind ; there is simply the unconscious expectation of which he is not aware, but of which he would become aware if he met with a contradictory instance. If he begins to think about 150 LOGIC. the matter at all, he will probably be driven to put it into the form of a universal proposition, " All frogs are cold." The process of generalization, which is the essential feature of induction, can only take place safely under certain conditions, and it is the business of Logic to indicate those conditions. As, however, the process does not depend on the general forms of our thinking, but on the varying circumstances of things, Logic can- not prescribe the conditions of valid inductive inference as minutely and exactly as it does the conditions of valid deductive inference. Inductive Logic tends to become more an applied science than does deductive Logic. § 2. Perfect or Formal Induction. There is, however, an exception to the statement that Induction is not a formal process, but depends mainly on the nature of things. If we enumerate every case in which a phenomenon x occurs, and find that in every case x is accompanied by the pheno- menon y, we may conclude with formal certainty that " All cases of x are y." Every single Cabinet Minister being found to be a Home Ruler, we may safely infer (whether we quite know what " Cabinet Minister " or " Home Ruler " means, or not), that " All the Cabinet Ministers are Home Rulers." The new statement adds nothing to our knowledge of facts, but it puts our knowledge in a slightly difierent form, by con- INDUCTION. 151 necting the predicate with one general term, " Cabinet Minister," instead of with a number of separate singular terms. It is a convenience to be able to sum up a group of fifteen or sixteen separate propositions in one. There is inference, but the inference is of the slightest character, next door to a " mere verbal transformation." Such inferences are called perfect inductions. They may be represented syllogistically, but not in a mood which is recognized in Aristotelian logic. Thus: Cases A, B, C, D are Y, Cases A, B, C, D are all the X's, .'. AU the X's are Y. Here the mood is A A A in the third figure, in which it is usually invalid. But in this case the middle term is distributed in both premises — being a collection of singular terms — and the minor term is properly dis- tributed in its premise, which is a U proposition. The great bulk of inductions belong to the class of material or real inductions, in which the subject of the universal proposition refers to fresh cases never actually examined. These are of much greater value than the former, but are never of the same distinct certainty. Hence they have been called imperfect inductions. It may be observed that imperfect induction cannot be represented syllogistically. Various attempts have been made to force it into a syllogistic shape, but all 152 LOGIC. are unsatisfactory. If we take a syllogism of the form just given we get a false minor. Cases A, B, C, D do not now form all the X's, but only a very small portion of it. If, on the other hand, we put the reason- ing in the following form, we transfer to the major premise the whole of the inference. That is, the induction has really taken place before we profess to begin it. All A's which I have observed, and all which I have not observed, are B, The two together are all A's ; .-. All A's are B. The formal process simply adds together the two classes. The real inference is that by which we reach the major premise. Mill, however, held with Whately, that aU inductive arguments may be thrown into the form of a syllogism. The suppressed major in the case of ordinary induc- tions is, " What is true of the instances A, B, C, etc., is true of aU the instances." This in turn leads, by a series of syllogisms, to a syllogism which has for its major premise the principle or axiom of the Uniformity of Nature. This is the " ultimate major premise of all induction." It is curious that Mill, who held that the syllogistic process was not really an inference at all (Chap. X., § 2), should also maintain that the inductive process is essentially syllogistic. Both de- duction and induction must therefore be only a process of verbal transformation, and there can be no such INDUCTION. 153 thing as real inference, except from particulars to particulars. § 3. Laws and Uniformities. The result of generalization is called a Law. "Whenever over a given range one fact is accom- panied or followed at any interval by another fact, we call this a uniformity" says MiU. A Law is the ex- pression of a uniformity by means of words or symbols. The word Law is used in two or three distinct senses. When we are talking of politics or jurispru- dence, a law means a general command given by a government to its subjects. It is distinguished from particular orders, or acts of the executive, by being addressed to every person belonging to a certain cate* gory. In this sense a general rule of a school is a " law," or a rule binding all the boys of a particular form ; while an order addressed to Brown or Jones is not a law. This idea of general command was trans- ferred to theology, and from theology to science. The creative fiat was regarded as a law, which of course in any exact sense it could not be. Only in a rough analogical sense could the tendencies found in the natural world be regarded as due to laws promul- gated by God. A law implies intelligence, and the possibility of obedience or disobedience. It was never open to a stone to obey or disobey the " law of gravi- tation." Nature may be the expression of God's will : 154 LOGIC. but law and obedience are alike impossible without rationality. Modern science has got rid of the theological impli- cation in the idea of " law of Nature." It suggests no opinion as to their origin. Whether theist, or atheist, or agnostic in his theological opinions, the man of science, as such, means nothing by Law except the expression of a uniformity which has been detected among natural phenomena. The element of command in the original idea has gone ; only the element of generality remains. Strictly speaking there are no laws of Nature or in Nature. What we call a law of Nature is our ex- pression of what we believe we have observed. It is a mental product, due to abstraction and generaliza- tion. Man does not discover laws already immanent in Nature ; he invents abstract expressions to describe what he observes. These laws are always, in one sense of the term, hypothetical. They imply that if the objects of a class conform to a recognized type they will have certain qualities. Nature makes indi- viduals diifering in all kinds of ways. Man " sorts " these individuals, and although he ascribe objective validity to his classes, they are, as Locke long ago showed, the creation not of Nature, but of man.' And thus the so-called laws of Nature, which depend on these classifications, are never entirely objective. Uniformity is read into Nature by man. It is just as true to say that Nature is infinitely various as to ' See Chap. XX. below. INDUCTION. 165 say that she is entirely uniform. She is at once both and neither. DiiFerence and likeness are both mental realities. They are relations which exist only for conscious minds. Uniformities among phenomena are of two main kinds, those of Sequence and those of Co-existence ; " Every X is followed by Y," or " Every X is accom- panied by Y." The first class embraces two subdivisions — those of mere sequence, and those of causation. It is the latter which are of chief importance. Laws of succes- sion are the most valuable of all truths, says Mill ; and of these the laws of causation are the only ones which are perfectly " indefeasible " and " co-extensive with human experience." Uniformities of co-existence include the truths of number and space — unless indeed these are to be re- garded, not as observed uniformities, but as intuitively perceived relations — and the properties of natural sub- stances whether organic or inorganic. These uniformi- ties of co-existence are less general and less certain than those of sequence. " Uniformities which obtain in the co-existence of phenomena," says Dr. Bain, meaning those in which causation is not known to play a part, " are entitled to reception only as empirical laws ; and are not to be presumed true except within the limits of time, place, and circumstance in which the observa- tions were made, or except in cases strictly adjacent " (" Logic," ii. 122). The student should notice that we often put into 156 LOGIC. the language of co-existence what is really a matter of sequence. " We term the snake ' deadly ' just as we term it ' supple ' or ' many-ribbed,' thus transferring the occasional sequence [viz., death following on its bite] to a place among permanent co-existences " (Venn, "Empirical Logic," p. 92). § 4. Laws of Nature and Empirical Laws. The term Law of Nature, in its original quasi- theological sense, was generally confined to those great general uniformities which are found everywhere and always. Thus the presence of gravity was regarded as due to a law of Nature ; but the presence of thirty- two teeth in an adult human being, or the acidity of lemons, was not so regarded. God was perhaps sup- posed to have separately willed the great facts and tendencies which men discovered to be universal, or almost universal ; while the smaller facts of Nature were thought to have come into being as a conse- quence of the former, without any further creative act. Modern writers keep up something of this distinc- tion, without the theological suggestion underlying it. While the expression, " Law of Nature " is sometimes loosely used for any observed uniformity, it is more commonly kept for the most ultimate, simple, and fundamental laws, of which the more complex and concrete laws are special cases. Thus, the movement of a planet in an ellipse is derivable from, and can be INDUCTION. 157 resolved into, the law which expresses the action of gravitation, and Newton's first two laws of motion. Such a particular or special law, when shown to be dependent on more ultimate laws, is called a derivative law. Bacon called these derivative laws axiomata. media, that is, truths of moderate generality intermediate between mere facts and the highest generalizations. The expression of an observed uniformity which has not yet been resolved into simpler and more ultimate laws, but is presumed to be capable of such resolution, is an empirical law. It rests only on the evidence of experience (kfjmuplat). The most ultimate laws which we know are, of course, not derivative, and they are arrived at from experience ; but they are not empirical laws in this specific sense, since they are not presumed to be resolvable into laws still simpler. CHAPTER XIV. UNIFORMITY OF NATURE AND CAUSATION. § 1. The Ground of Induction. Generalization is possible only because Nature is uniform. It is this external condition which makes it possible for us to make material inferences. All in- ductive laws are particular cases of uniformity, are expressions that the uniformity holds good within a certain sphere. Or, as Hume puts it in his " Inquiry concerning Human Understanding," " All inferences from experience suppose as their foundation that the future will resemble the past, and that similar powers will be conjoined with similar qualities." It covers regularity of sequence (including cases of causation) and regularity of co-existence. In every real induction (as opposed to "perfect," or formal induction,) there is a leap to the future. We assume that the cases we have not yet examined will resemble those which we have examined. This assumption can never be entirely warranted by ex- perience, since experience can only refer to the cases we have met with. Its justification, as Professor Bain says, is entirely practical, and lies in the fact UNIFORMITY OF NATURE AND CAUSATION. 159 that without it. we cannot take the slightest step, while " with it we can do a,nything " (" Deduction," pp. 273, 274). We must always assume Nature is such that what- ever is true in one case of a given kind is true in all similar cases. Whether this truth is ultimately a law of things or a law of mind, or whether the two state- ments ultimately mean the same, has been discussed by philosophers. Nature is uniform, it would seem, because otherwise experience is impossible. What we mean by Nature is the ordered Cosmos ; a mere chaos of unrelated sensations turning up without any order would not be Nature, and would be, in point of fact, inconceivable. Human life and human consciousness could not exist without some degree of uniformity. The Law of Homogeneity, as we have seen (Chap. VII. § 4), lays down that however different two objects of thought may be, they can always be brought under some higher concept. Likeness always lies hid beneath apparent differences. In any group of phenomena there is likeness, expressible as a law, if we only know where to look for it. The principle of the Uniformity of Nature includes what is called the Law of Causation, but it includes something more. It implies that the same bundles of qualities go together, but it does not necessarily imply that these bundlesgotogetherbecause they are produced in common. The regularity may not be due to causation at all. There is indeed a growing tendency to assume that all cases of uniformity are due to common origin 160 LOGIC. and to similar conditions of production. The theory of evolution has done much to justify this belief. The similarities which are observed throughout the organic kingdoms have been traced, with every probability, by Darwin and his disciples, to common ancestry. Even the similarities observed among inorganic things, such as minerals and stars, have been ascribed, with high probability, to the fact of a common origin. It is possible then that all cases of uniformity may be due to uniformity of causation. But we are not at present in a position to prove this, and we may hold that Induction would be possible even if the Law of Causation were unknown. § 2. The Law of Causation. This Law of Causation has been variously stated, but it contains practically three propositions, two of which are necessary to its expression, whUe the third is necessary if it is to be of any practical value. They are as follows : (1) That every phenomenon that takes place in time, (or in other words, every event) has a cause. (2) That the same effects follow the same ante- cedents. (3) That the same antecedents do as a matter of fact recur. The first of these is a part of Leibnitz's Law of Sufficient B,eason (Chap. VII., § 5). It is of course not provable. It is an assumption which we are obliged to make, and which we constantly do make in practice. UNIFOEMITY OF NATURE AND CAUSATION. 161 In so far as we do not make it, or forget it, we suflFer in our contact with Nature and Society. The same thing may be said of the second pro- position. This is a part of what we have called the Law of the Uniformity of Nature, but it is an important part of what is implied in the Law of Causation, as generally understood. There has been an infinite deal of discussion about this extremely important idea of causality, and philo- sophers are as a rule in marked disagreement with ordinary practical men, and even with men of science, as to what it really means. The logician is not bound to go deeply into this dispute ; it will be sufficient for him to find a working definition which will serve practical and scientific purposes, even if this does not profess to be a completely accurate definition. The notion of cause as held by average unsophis- ticated people, e.g., by the business man and the ordi- nary medical practitioner, seems to be well expressed in the words of Keid : " The name of a cause ... is properly given to that being only which by its active power produces some change in itself or in some other being. Active power, therefore, is a quality in the cause which enables it to produce the effect " (Reid's " Works," Hamilton, p. 603). This view is really a survival of Aristotehan and scholastic teaching, like most of the floating and uncritical philosophy which masquerades as Common Sense. Hume attacked the common-sense doctrine. He pointed out that no such thing as Force, Power, or M 162 LOGIC. Energy is ever an object of experience. " One event follows another, but we never can observe any tie between them. They seem conjoined, but not con- nected" ("Inquiry concerning Human Understanding," Section VII.). He gets rid of the metaphysical nexus, or bond, of power, and retains mere sequence. Mill developed Hume's doctrine. With him the cause of a phenomenon is the " antecedent, or the concurrence of antecedents, on which it is invariably and uncon- ditionally consequent " (" Logic," Book III., Chap. V., §6). As a matter of fact the cause is always a concur- rence of antecedents, a group of circumstances, all of which must be present to bring about the effect. The cause of the flame seen when a match is struck is not simply the act of striking, but also the composition on the match and on the box, the heat produced by the friction, the presence of oxygen in the air, and many other less obvious conditions besides. We must even include what are called negative conditions, such as the absence of wiad in the air and the absence of damp on the box. The word cause is applied sometimes to one and sometimes to another of this large group of invari- able antecedents, according to the special interest and point of view which we are taking. If a man is killed by a gun, what is the cause of his death ? For the ordinary man it is sufficient to say that the bullet was the cause. But for any special purpose much more is needed. The doctor at the inquest says the man died from a gunshot wound in his neck. A UNIFORMITY OF NATURE AND CAUSATION. 16S scientific physiologist would be able to go much further, and point out exactly how the wound brought about the death, whether by shock to the nerves which control the heart and lungs, or by the influx of blood into the air-chambers of the lungs, and so on. The expert in guns would point out how the gun came to explode, and how the missile came to hit the man. The physicist would explain how the explosion was brought about by the ex- pansion of gases contained in the powder. The lawyer would be interested in the exact psychological conditions which determined the pulling of the trigger ; the act of the man who held the gun is for him the cause of the victim's death. The moralist would lay most stress on the recklessness or malice which led to the pulling of the trigger ; for him the cause of the death lies in th& character of the man who held the gun. These events form a chain, or rather a continuous series, all the parts of which are marked off and distinguished by different classes of people in somewhat different ways. What the lawyer calls part of the " effect," the doctor calls the "cause." Instead of a chain of distinct links we have a rope on which portions have been marked off. And different portions of this rope, at different distances, are fixed upon as cause of the man's death. Keeping in mind the absolute continuity of this series,^ and the large number of concomitant conditions which at every point are presupposed, we see that if we want to be exact we shall have to say that the whole state of the universe at any moment is the cause of its whole state at the next ; otherwise we may accidentally 164 LOGIC. omit something of importance. It is, for instance, just possible that some electric or chemical condition of the atmosphere, of which we at present know nothing, may be necessary to the explosion of the powder. But such a conception of cause as this is of no practical value. We must omit the vast majority of concomitant phenomena and confine ourselves to what we call relevant or material circumstances, even at the risk of overlooking something important. The logician, then, takes an intermediate view. He substitutes for the single antecedent of the " plain man " a group of antecedents, and he includes nega- tive antecedents. For his purposes he leaves out of sight the conception of energy passing over from cause to offect, while he does not necessarily deny that such a conception is implied by the idea of cause, if it be thoroughly analyzed. § 3. Plurality of Causes. The second proposition included under the Law of ■Causation was this, that the same antecedents are fol- lowed by the same effects. The same antecedents never do recur, if we take a sufficiently large group. Certainly the same state of the whole universe is never repeated; but we need not go so far as that to see that absolute repetition does not occur. While by increasing the size of our group we secure greater accuracy, we secure it at the expense of practical utility, for the larger the gi'oup of antecedents the less frequently will it recur. UNIFORMITY OF NATURE AND CAUSATION. 165 Can we turn the second proposition round and say that the same effects are always preceded by the same antecedents ? At first sight it would seem that we cannot. A gunshot wound in the heart always kills a man ; but a man may die of ten thousand other things than a gunshot wound in the heart. This is what Mill calls the Plurality of Causes, and what Professor Fowler calls the " Vicariousness of causes." It seems obvious enough that the same effect may be produced now by one cause, now by another. But reflection shows that this is only so long as we keep to the loose, popular treatment of cause and effect, which defines the cause with more accuracy than it does the effect. We take the effect, death, in a generic and abstract sense, not discriminating between the different kinds of death; while we take the cause in a specific and determined sense. If we say precisely what sort of death the man died, how he fell, the appearances presented by the internal and external organs, then we shall find that only one cause is possible. "Had we been equally exhaustive in our enunciation of the constituent elements in the aggregate effect as we were in those of the cause, no such plurality would have been pos- sible," says Dr. Venn.^ And he adds : " So clearly is this recognized whenever it becomes important to take ' Dr. Venn's treatment of the logical aspect of causation is by lar the clearest and best that I know. Much of this chapter is due to his lectures, his " Logic of Chance," and his " Empirical Logic." 166 LOGIC. it into consideration, that the whole procedure in a trial for murder, or in any coroner's court, rests upon the assumption that if we are particular enough in our assignment of the effect there is no possibility left for any plurality of causes " (" Empirical Logic," p. 62). § 4. Conjunction of Causes and Intermix- ture of Effects. In very simple and abstract cases of causation, where certain factors are out of all proportion more important than others in the production of the effect, we may often think of an effect as due to a single prominent antecedent. In considering the movement of a billiard ball on the table, we think only of the progress in a straight line in the direction of propul- sion. The total effect is really much more complex ; since, if we want to be precise, we ought to take into account the movements of the earth on its axis and round the sun, and even the movement of the whole solar system towards a certain point in the constella- tion Hercules. Disregarding these, we must not forget that even the movement on which we fix our exclusive attention is really due not merely to the stroke of the cue, but also to the nature of the ball, the cloth, the table, and the floor; to mention no other co-factors. In abstract inquiries we may confine our attention to only one cause; and thus in mechanics we may speak of a body as moving under the impulse of only UNIFORMITY OF NATURE AND CAUSATION. 167 one force. This must not, however, be regarded as a normal type. We cannot in any actual and concrete cases assign a single cause for a single event. All instances of causation are cases of what MiU calls the interference of causes and intermixture of effects. Mill probably leaves most of his readers under the impression that normally each cause produces its own efiPect, and that the intermixture of effects is a peculiar and somewhat unusual occurrence. Whether he actually held this view is difficult to settle ; but at any rate it is erroneous. Two kinds of concurrence of causes are distinguished by Mill. " In the one, which is exemplified by the joint operation of different forces in mechanics, the separate effects of all the causes continue to be pro- duced, but are compounded with one another, and disappear in one total." Such a total effect is called a compound effect. " In the other, illustrated by the case of chemical action, the separate effects cease entirely, and are succeeded by phenomena altogether different, and governed by different laws." Such an effect, differing in kind from the results of the separate causes acting independently, is called a heteropathic effect^ Mill has overstated his case a little. Even in chemical combinations the separate effects do not "cease entirely." Hydrogen and oxygen exploded together produce water ; and although this is very different in some respects from its component gases, it resembles • Mm, "Logic," III. X. §4. 168 LOGIC. them in others. The weight, for instance, is the sum of the weights of the components. But the whole discussion is somewhat unreal ; because, if we take at all a scientific view of causa- tion, we can never hope to assign particular effects (or rather particular portions of the total effect) to par- ticular factors. In actual Nature, as opposed to the abstractions of the class-room, a vast number of co- operant conditions are always present, and we can only say with diffidence how far any of them can be omitted. We can never hope to analyze a case of causation into a group of phenomena. A, B, C, D, fol- lowed by another group, a b c d, so that A produces a, B produces b, and so on. CHAPTER XV. OBSEKVATION ANU EXPERIMENT. § 1. Observation. All our knowledge — with some small and disputable exceptions — comes from experience, either directly by perception, or indirectly by way of inference from perception. Nearly all deductions have for premises propositions which assert matters of fact. Thus the first step in knowledge is due to perception either of facts of external nature, or of facts of consciousness. Observation means systematic and careful percep- tion. It involves voluntary attention, directed on the object. When we thus purposely attend to an object, the object is ordinarily perceived with greater quick- ness, vividness, definiteness, and completeness than when we merely just notice it. Features which would be overlooked become clear, and are distinguished from other features with which they are at first con- founded. A certain abstraction of attention from other objects is involved in this concentration of con- sciousness on the given object. In order to secure the fullest operation of our per- ceptive powers, some analysis of a complex object 170 LOGIC. is necessary. Some small object, some special group of phenomena, or some single aspect of an object has to be isolated. This is done to some extent by the act of attention itself, as we have seen ; but that it may be carried out more thoroughly, artificial changes are made in the conditions of observation; a flower is removed from the plant, the flower is broken up into its constituent parts, and sections of these parts are made and considered separately. Special instruments are brought to bear in order to effect this analysis and isolation, e.g., the dissecting-knife, the live-box, and the test-tube. Other instruments are employed for rendering minute phenomena perceptible. Such are the microscope and the telescope ; the spectroscope, as used by chemists for purposes of chemical analysis ; and the photo- graphic camera, as used by the astronomer to detect stars whose light is too feeble to affect the retina. When quantitative results are required, special instru- ments are necessary for measuring the extent or inten- sity of phenomena. The measuring rod, the balance, the chronometer, the barometer, and thermometer are well-known instances of such artificial aids to ob- servation. Other instruments are used to economize time and attention, by effecting automatic registration of results. The occurrence of direct sunlight is recorded by a burning-glass arrangement, and the photographic camera is employed very largely for purposes of registration. OBSERVATION AND EXPERIMENT. 171 § 2. Experiment. Professor Fowler says that to experiment is "not only to observe, but also to place the phenomena under peculiarly favourable circumstances as a preliminary to observation" (" Induction," p. 38). If we take this definition, we shall not be able to refuse the term experiment, even to the proceedings of the field observer, who plucks a leaf in order to examine it with more exactness than he could do on the bush where it grows. The amateur who takes home a butterfly to identify it becomes an experimentalist, as well as the physiologist who employs vivisection. In fact, we may say that in nearly all real observation — that is, careful, prolonged, and attentive perception — the conditions are to some extent altered to suit the special needs of the observer. Meteorological obser- vatories are placed on lofty mountains and on out- of-the-way islands to secure favourable opportunities not presented elsewhere. When a total eclipse of the sun, or a transit of Venus, is expected, astronomical expeditions are sent to many dififerent parts of the world in order to take advantage of the variety of conditions under which the phenomenon may be seen. Mill regards tlie essential difference between obser- vation and experiment as lying in the fact that in the former " we find an instance in nature suited to our purposes," and that in the latter " by an artificial arrangement of circumstances we make one " (" Logic," Bk. iii. chap. vi. § 2). Of course in the strict sense of 172 LOGIC. the word we never make an instance. Nature always does the work, we can only bring about the conditions under which the event takes place. When we say that we produce a phenomenon artificially, we can never mean more than this. The difference then between observation and experi- ment becomes one of degree. Where the conditions under which the facts occur are considerably altered, by bringing fresh forces to bear on the thing observed, so that for all observers the phenomena themselves are considerably altered, we call it experiment. Where the conditions are not markedly changed, or where they produce change in the phenomena only for the individual observer, we usually call it observation. If an astronomer goes to the Cape to observe an eclipse, the changes in the phenomena are not considerable, and exist only for him. To an astronomer who re- mains in Europe there is no change. If a physiologist produces a series of changes in the body of an animal by some operation on the brain, the changes are con- siderable, and they exist for any competent observer who sees the animal. All artificial interference with living things pro- duces changes which must be taken into account ; so that the phenomena must no longer be regarded as strictly normal. The phenomena observed during dissection and experiment are not the same phe- nomena as those of normal life ; though by the exercise of scientific imagination we may construct the normal phenomena from the hints given us. OBSERVATION AND EXPERIMENT. 173 The vital relations which give a meaning to the phenomena are only too apt to disappear during the process of analysis. The chief advantages of experiment over observa- tion are these : (1) We can multiply our instances to almost any extent. Instead of waiting for an infrequent concurrence of conditions, we can at once produce that concurrence ; and then the eifect follows. (2) We can isolate the phenomena to be studied, so that they are presented apart from disturbing circumstances which distract the attention, and in other ways render the given phenomena difficult to observe. (3) We can vary the circumstances, so that we can clearly separate the necessary conditions from the conditions which are not necessary. (4) We can prove by experiment that a given group of conditions is actually the cause, or at any rate one of the causes, of a given effect ; since by artificially producing the given group of antecedents we shall in that case obtain the effect. We suspect that the multiplication of a certain microbe in the blood causes a specific disease ; we can prove that this is so, at any rate sometimes and under some conditions, if when we artificially produce this multi- plication of the microbes in the body, the disease is actually produced. Where experiment is impossible Induction is at a great disadvantage. As we shall see, experiment is the chief means by which generalizations are verified, and Verification is the chief characteristic which marks off scientific induction from futile guessing. 1 74 LOGIC, On the special difficulties in the application of this method of verification, see Chap. XVIII. § 3 below. § 3. Non-observation and Mal-observa- tion. In both observation proper and experiment two im- portant conditions are clearly necessary if the results are to be the basis of correct inferences. We must be careful not to overlook anything that ought to be observed ; and we must be careful not to believe we observe phenomena which are not there to be observed. We must guard against Non-observation and Mal- observation. The plain man seldom realizes how difficult the work of observation really is. To him nothing seems easier than to perceive facts which are before us; except, perhaps, to refrain from perceiving what is not before us. In practice, both conditions are difficult to comply with; and only trained observers can as a rule be trusted to accurately perceive and to accurately record their perceptions. A few hours in a court of law listening to the evidence of witnesses .in (say) a commercial case will shake the faith of the plain man. He must come to the conclusion either that at least half the eminently respectable witnesses are lying, or that human facul- ties of perception are no more infallible than those of inference. Here is another instance. A few years ago, during the "dull season," a controversy was raised in OBSERVATION AND EXPERIMENT. 175 one of the daily newspapers as to whether eucalyptol would rid a room of house-flies. Some of the cor- respondents asserted that it did, and some that it did not ; and both parties gave their conclusions as the result of personal observation, which as a rule they detailed. The uniformity of Nature seemed to be temporarily suspended in regard to house-flies. There are, of course, some phenomena which can- not be easily overlooked, e.g., a rash on a patient's face. But there are others which require trained skill to recognize, and sometimes the use of instruments which can only be properly employed by experts ;. e.g., the sounds caused by certain diseases of the heart. In the latter case, besides delicate senses, which have been thoroughly educated, we want prolonged attention and considerable previous experience. We want what psychologists call preadjustment of attention. We must know exactly what we expect to find. Everybody who has used a microscope knows that,^ in order to find a minute object in the field, it is impor- tant to have a mental picture of what we wish to see. The same thing is true when we try to recognize a distant object, e.g., a ship at sea, or the face of a friend in a great crowd. But this very preadjustment of attention involves a special danger. What we expect to see we want to see, or fear to see ; and what we want to see, or fear to see, we are liable to see, whether it exists or not. The expectant attention distorts the perception, and illusion follows. The facts become accommodated to- 176 LOGIC the image which we have formed beforehand. The medical man who expects to find a certain symptom, sometimes thinks he perceives it although it does not exist. Valetudinarians, it is well known, are constantly a prey to imaginary symptoms ; their fears produce the phenomena which they dread; and, for just the same reason, the terrified child sees a ghost in a haunted room. The most practised observers have been known to find traces of organic structure in non-organic things. The so-called Eozoon Canadense was taken for a fossil organism by Sir W. Dawson, Dr. Carpenter, and other scientific men, though all, or nearly all, recent geologists regard it as inorganic. Professor Haeckel thought he found the characteristics of organic matter in an inorganic slime, which he named in honour of Professor Huxley. Multiplication of instances under different circum- stances, the use of different lenses with the same instru- ment, altering the light, shifting the stage of the micro- scope, the employment of other instruments besides our own, can guard us to some extent against such errors. Not less important will be the comparison of our own observations with those of others. The sugges- tion sometimes advanced by anti-vivisectionists — that when an experiment has once been made, there is no need to repeat it — betrays the most profound ignorance of the conditions under which scientific study must necessarily be conducted. Merely negative results go for very little. The fact that up to the present I have not noticed a phenomenon. OBSERVATION AND EXPERIMENT. 177 or even the fact that no one has yet noticed a pheno- menon, does not prove that there is nothing to be perceived. § 4. Perception and Inference. All our actual perceptions involve a certain amount of inference, as we have already seen (Chap. I. § 1, above). But we cannot draw a clear line, and say where the data of sense end, and the stage of sub- -conscious inference begins. The data of sense are an abstraction, an ideal which our analysis never reaches. Pure sensation, as Dr. James Ward says, is a psycho- logical myth. What we call sensation is already a complex mental product. There is a tendency amongst unskilled observers and persons without philosophical training to regard as perception a great deal that is not only inference, but highly precarious inference, which a little psycho- logical analysis would have served to detect. Thus the redoubtable Mr. Sherlock Holmes misleads his amiable companion. Dr. Watson, by telling him on a certain occasion that " Observation shows me that you have been to Wigmore Street Post-office this morning ; " when it is clear, from the explanation which he gives, that this is merely a probable inference, based on the fact that he had noted some red mud on Dr. Watson's boot, and that there was some red mud of a similar kind in front of the post-office, and, so far as he had observed, nowhere else in the neighbour- N 178 LOGIC. hood.' All that observation could really tell the de- tective was, at most, that there was some reddish sub- stance adhering to the boot. Everything else was inference. What a man sees depends on many circumstances. The delicacy of his organs, the attention he pays, the amount of his previous knowledge, the external con- ditions of observation, all influence the result. A savage brought into a library literally does not see the same things as the librarian. He sees strips of red and blue, he does not see books. He does not distinguish the volumes of a series from each other, or from the shelf on which they are placed. § 5. Pact. The word " fact " is used in two or three senses. It means, etymologically speaking, something done (factum). What has actually occurred is a fact. From this meaning it is easy to pass to others; and fact comes to mean any phenomenon or group of phenomena actually observed in time or space — an event or a thing — ^thought of more or less as individual and dis- tinct. In this sense it is opposed to a general truth or law, which is the formulation of a uniformity observed in many separate instances. Such a law is based on the facts, that is, the separate observed instances. What is observed is real ; at least it is real if the ' " The Sign of Pour," chap, i., pp. 11, 12. OBSERVATION AND EXPERIMENT. 179' conditions of observation are normal, and the observer is normal. Our nearest approach to objective truth lies in the perception of external facts. Even the most intelligent persons differ in their inferences from, concrete facts ; but it is assumed that they cannot iu their perceptions, their senses being supposed to be equally delicate, their knowledge and attention being supposed the same, and the conditions of observation equally favourable. This is not exactly true, but it is- on the whole correct. Hence, when we say anything is "a fact," we mean that it is objectively true, true for everybody. Is it a law or a fact that the tide is caused by the- moon and sun ? It is a law, in the sense in which law is- opposed to fact ; since this is not a phenomenon given us in perception, but a uniformity inferred from a large number of observations. It is &fact, in the sense in which law is not opposed to fact ; since the law or uniformity is true. CHAPTER XVI. THE INDUCTIVE METHOD. § 1. Method. ^T method we mean, as Hamilton says, " the arrange- ment and elaboration of cognitions according to definite rules, with the object of conferring on these (the cognitions) a logical perfection " (" Logic," § Ixxx). Men of science first get at their facts, from their facts make their generalizations, and from these make their •deductions. It is the business of Logic to point out the general conditions to which these processes must conform if the results are to be correct. Our reasoning powers act to a large extent automatically, and apart from direct volitional control. Logic does not so much undertake to show how we must reason, as to show the conditions which will preserve us from serious error. Thus in Deduction, Logic does not prescribe the syl- logism as a necessary form if we want to reason pro- perly ; but as a convenient form for stating our reasonings if we wish to test them. The purpose which we have in hand will determine the special kind of arrangement which ought to be adopted. The method of exposition is not necessarily THE INDUCTIVE METHOD. 181 the same as the method of discovery and proof. The order in which our facts and ideas shall be exhibited is a matter of the greatest importance. The dependence of one thought on another can only be adequately seen when care has been bestowed on making clear the implied relations between the different propositions to which we have been brought to assent. In the con- fused thinking of the plain man about politics or theology there is frequently a startling inability to differentiate premises from conclusions, hypotheses from axioms, and definitions from enunciations. Any arrangement of the material of thought, so as to exhibit its logical relations, and thus render the processes of thought easy, systematic, and safe, may be called a method. Consequently the word is used in many different connections. We may speak of the method of Induction, the method of Deduction, the method of Discovery, Mill's methods. Bacon's method, the analytic method, the synthetic method, the experi- mental method. By a natural transition we may apply the term to any rule for dealing with our material in such a way as to give us valid and useful inferences. Thus we speak of the method of Least Squares, and so forth. § 2. Analysis and Synthesis. Analysis means the division of a whole ; the break- ing of it into parts in order that it may be more com- 182 LOGIC. pletely examined and understood. This may be a physical process, as in chemistry, or a mental process, as in psychology. In the one case we obtain separately the simpler constituents of a compound ; in the other we obtain in ideal (not actual) isolation the simpler constituents of a mental state. Synthesis means the placing together of simpler wholes with the purpose of producing a new whole of a more complex character. When two physical wholes, such as a portion of sulphuric acid and another of copper, are combined to form sulphate of copper or blue vitriol, we have synthesis. The construction of a box out of six pieces of wood is a case of synthesis. So is the formation of a compound notion, such as "black board " or "ecclesiastical monarchy," by putting together the simple ideas of which it is the sum. A little reflection will show us that synthesis and analysis are usually found together. For the purpose of synthesis a preliminary analysis is usually requisite ; and so too analysis is often possible only by means of simultaneous synthesis. In a prolonged effort of con- struction or of reasoning, both processes may have to be performed many times. Thus the neat and pro- perly shaped boards of which the box is made, and the pure metallic copper, have to be separated from what is found with them. A process of analysis has to be gone through before the synthesis is begun. The idea " ecclesiastical " and the idea " monarchy" are the results of many successive acts of analysis and syn- thesis. THE INDUCTIVE METHOD. 183 If we are to completely understand the nature and the conditions which produce a given whole, it is obvious that we need both processes. We must be able to pull it to pieces and to build it up again. By means of synthesis we verify the results of our previous analysis. And we must remember that the material elements which we can perceive by means of the senses are not the only elements which a complete analysis will yield. The human body is something more than a pile of anatomical scraps. A muscle is something more than the carbon, oxygen, nitrogen, and so forth, into which the chemist's analysis resolvesit. The original vital union in which the elements are bound cannot be always imitated or reproduced by the artificial syn- thesis of the scientific man. Something escapes him. As Wordsworth puts it — " We murder to dissect." The complete natural synthesis is very different from the clumsy and incomplete synthesis which science is able to produce. All abstraction is primarily a process of analysis. All comparison is primarily a process of synthesis. "We resolve analytically the presentation-complexes [objects of perception] of our concrete experience only in order to establish certain relations among them. The most appropriate term for all such conscious ' relating ' or discernment of relation is comparison." " Comparison thus involves abstraction ; abstraction, 184 LOGIC. even in the case of a single object, may be said to involve the rudiment of comparison." ' An attempt is sometimes made to identify induction with analysis and deduction with synthesis. This is to be avoided. Synthesis and analysis are, of course, much wider terms than induction and deduction. Definition, Division, Judgment, Immediate Inference, etc., all involve both analysis and synthesis. So do Deduction and Induction. A deductive syllogism may be regarded as a process of synthesis because it unites the contents (or matter) of two propositions in a third. But it is also a process of analysis, because it splits up the meaning of the middle term. Thus the syllogism, All birds are two-legged. All linnets are birds, .*. All linnets are two-legged, analyses the meaning of bird, or that group of attri- butes which we associate with the name bird, and asserts of linnets part of that meaning. Viewed, how- ever, from the point of view of denotation, there is synthesis. The class linnets is now added to the other classes which compose the superior class — two- legged things. Induction in the same way may be regarded as a process of analysis, because it breaks up the whole group of attributes implied by the name (connotation), ' See Sully, " Outlines of Psychology," pp. 244 seq., 251 seq., 290 seq. THE INDUCTIVE METHOD. 185 or ordinarily found in connection with those that are so implied. We assert of all birds part of what we per- ceive in the case of all those we examine. But in doing so we have synthesis as well, because we group all the individual objects into a whole, " All birds." Since the formation of every concept is at once a process of analysis and of synthesis, and since the for- mation of a judgment also involves both processes, it is idle to regard any given process pf reasoning as essentially analytic, or essentially synthetic. § 3. Classification in Induction. We start with a number of separate propositions, each of which we will suppose proved. " The thing A has the quality Q," " the thing B has the quality Q," " the thing C has the quality Q," etc. Our first need is to group A, B, C, etc., into a class, so that we may know exactly what group of attributes ordinarily go together, and that we may be able to identify this group wherever we see it. We recognize A, B, C, etc., as belonging to a class S already acknowledged, or we construct a new class, which includes them and all other things exactly resembling them. Induction, then, presupposes a classification. Some- times the class is ready to hand as the result of pre- vious observation and inference ; sometimes a new class has to be formed. Mill did not quite adequately recognize the importance of this step, but it has been emphasized by Whewell (whose knowledge of the 186 LOGIC. history of science made him Mill's superior in ques- tions of this kind), by Dr. Venn, and other logicians. Induction, says Dr. Bowen, involves the " correct- ness of the preceding classifications that have been made of the objects of sense." The more accurate are our Definition and our Division, the more safely can in- ductions be made. The classifications of the abstract sciences, such as geometry, are so precise, that universal propositions may be safely made from the examination of one instance. What is found true of a single circle is true of all ; because the mathematician's circle is not the rough figure he draws, but the ideal circle which absolutely conforms to the definition. Even the chemist has something of the same certainty. As long as he means by " water," HjO, whatever he finds true of one drop will probably be true of all under pre- cisely similar conditions ; only that he cannot be certain whether a given property which he discovers in a special sample of water belongs to perfectly pure water (H^O) as such, or only to the present sample, which consists of HjO, plus some unknown impurities. "When the class is not a recognized one, the case presents many difficulties. Let us suppose a medical man, at the beginning of the influenza epidemic, con- fronted with a number of cases in which he notices a very yellow tongue. In many respects the cases difier. He sees some resemblance, however, and on the supposition that he has never heard of influenza, or, at any rate, knows nothing about it, be will have to try to form the conception of a disease, which shall THE INDUCTIVE METHOD. 187 always present certain symptoms, or, at least, several out of a group of symptoms. Let us suppose that lie now consults other medical men, or reads the " Lancet," and learns to call this disease, so marked out, " influenza." He has introduced what Whewell calls an " appropriate general conception," and has fixed it with a name. § 4. Generalization. The next step will be to see whether the symptom, yellow tongue, is always present or not. This will enable us to affirm, or to deny, the statement that " all influenza patients have a yellow tongue." The possible truth of the judgment is suggested by the few cases examined which first aroused interest in the matter. As a matter of fact probably the medical man would begin with an indefinite class, not waiting to get an exact conception, but saying, " All the patients suffering from this undetermined but striking disease have yellow tongues." The mind, in other words, starts with a hypothetical class, and makes a hypothetical generalization about the members of it. Then as he sought for evidence of the generalization, he would gradually define his class more accurately. But sometimes at any rate the class is found ready made ; and sometimes it is marked off clearly as the first step before generalizing. In a few cases of influenza he finds that the patients 188 LOGIC. have yellow tongues : will this always be found to occur ? Is Q a quality of every S ? The test of this lies in the examination of instances. Suppose only those instances are examined which come spontaneously to hand, and that no contradictory cases are discovered. If we therefore conclude that the generalization is true, that every S is Q, we are employing that type of induction called by Bacon inductio per enumerationem simpKcem. It is extremely likely to mislead, as Bacon pointed out. Even if we examine a very large number of instances, we do not prove our generalization unless we have taken care that any negative instances that do exist shall be brought to our notice. There may be S's which are not Q, and before we can say that " All S's are Q," we must feel sure that such contradictory instances, if they exist, could not have escaped our notice. We must take our S's from different parts of the world, under different circumstances, and so on. The adult influenza patients may have yellow tongues, but not the young ones. The patients in London may have that symptom but not those in the country. There are, of course, degrees of probability in asser- tions made on a small foundation. The case of abstract objects, like the circles and triangles of the geometer has been already mentioned. In the case of natural objects belonging to a well-defined class, we know that great similarity exists. What is true of several samples of carefully distilled water, or of THE INDUCTIVE METHOD. 189 several specimens of the common frog, is likely to be true of all. This is what we mean by the uniformity of Nature ; which is the ground on which our right to generalize is based. (See above. Chap. XIV. § 1). Caeteris paribus, the more exactly and distinctly the class S has been defined, the safer will our gene- ralization be. A statement which we should not be able to make with regard to all water we can make more safely of distilled water ; and stiU more safely about water distilled by some given process and kept in a certain kind of vessel, at a certain tempera- ture. A statement which cannot be made of all trout may perhaps be made with safety about trout of a certain age, living in a certain river, during a given season. § 5. Inductions only probable. Since we can never be sure with regard to natural objects, first, that our definition of a class is sufficiently exact, and, secondly, that even within that class abso- lute uniformity reigns, no real inductions are quite certain. Putting aside the unimportant class of purely formal inductions (Chap. XIII., § 2), we may say that no inductions can give us more than a high degree of probability. The propositions of physical science, however care- fully tested, are at best only plurative propositions. We may be sure that most A's are B's, but we can never be certain that all A's are B's. Exceptional 190 LOGIC. cases may turn up at any time, and only the most reckless of scientific men will claim absolute certainty for the vast majority of the laws they at present accept. Thus no universal proposition regarding the co- existence or sequence of phenomena, which rests on experience, can be regarded as absolutely certain. No statement that " every X is Y " where the rela- tion between X and Y is not guaranteed by the mean- ing of the terms — is not, in other words, purely formal — is more than probably true ; unless every case of X has been examined. The probability may be very small or very great, but it never becomes certainty. In formal inferences, given the truth of the premises, the result is absolutely certain — always supposing that the process of inference is correctly performed. At the same time it is most important to remember that for all practical purposes a well-tested induction may be regarded as practically certain. Where we can act freely and without misgiving on the assump- tion that " X is Y," without any hint as to the possi- bility of an exception occurring to us, however wide our experience, we have what is as good as certainty. The element of doubt is infinitesimal ; and it is only for purely theoretic purposes that we describe the pro- position " X is Y " as merely a probable one. For theoretic purposes the uncertainty, however, still exists. We cannot say that even the Law of Gravitation, or the Laws of Motion are so completely established that an exception is impossible. Prima facie an explanation contradicting one of these wide THE INDUCTIVE METHOD. 191 uniformities, which have survived the tests of centuries of careful observation and experiment, is a bad explana- tion, and involves an absurdity. But " cocksureness," although a favourite attitude with those scientific men whose minds have not been disciplined by philosophy, is out of place even here. The probability in favour of — say, the Law of Gravitation — may be so great as not to make it worth while for some individual scien- tific man, who has plenty of other work to do, to investigate the alleged exceptions. But the pro- bability is never so great that we can say that time spent on the inquiry is absolutely wasted. CHAPTEK XVII. HYPOTHESIS. § 1. The Use of Hypothesis. Keflection on the actual process by whicli we arrive at general truths of a scientific or practical character shows us that we usually start from a small basis of observed fact, and that a hypothesis is then formed — that is, a supposition which we know to be at present unproved, but which we think capable of being proved or disproved. This hypothesis takes the form of a general statement, from which we proceed to reason. If " X is Y," then such or such a result will follow. We next proceed to test the truth of the con- clusion thus deduced ; and if we are satisfied, we con- sider the hypothesis as proved. When the proof is so thorough that any reversal seems impossible, a hypothesis is often called a theory. " The discovery of a universal law, is always a guess on the part of the imagination made possible by a knowledge of facts. This knowledge is recalled to our memory by the resemblance of the given case to analogous earlier cases" (Lotze, "Logic," § 269). HYPOTHESIS. 193 This is one of the chief services which the imagination renders in science. The actual method of discovery pursued in science, and to a large extent pursued in practical life, com- monly consists of four steps : (1) Preliminary observation. — Only a few instances are usually taken, and these are not as a rule very systematically treated. The use of tables of instances, of statistics, of curves, and so on, is serviceable how- ever, in suggesting hypotheses. (2) The formation of a hypothesis. — The chief problem is the selection of what Whewell calls "an appropriate conception," the grouping of the facts together under some common term. Mill seems to have overlooked the importance and diflSculty of this step, and to have thought that the extension of our JTxdgment to fresh cases, the universalizing of the proposition, was the most difficult part of the business. (3) Deductive reasoning from the hypothesis to facts which will be found to exist if the hypothesis be correct. This may take the form of ordinary deduc- tion ; or the form of mathematical reasoning, in which quantitative terms are employed. (4) Verification. — Some of the results of this deduc- tive procedure are compared with fact by means of fresh observations and experiments. This leads to the confirmation of the hypothesis, its rejection, or its modification. An experiment which in itself is adequate to decide the truth of a hypothesis, is called by Bacon an o 194 LOGIC. experimentum cruets; crux being the Latin word for a direction post put at the crossing of roads. A famous experimentum crucis was that of Pascal, who caused a barometer to be taken up the Puy de Dome, and thus definitely negatived the " abhorrence of a vacuum " theory. The process of Induction, as actually pursued, thus turns out to be a process of inverse deduction. Given the conclusion, that " S is P," we have to discover the premises, one or both, which will yield us this conclusion. § 2. Kinds of Hypotheses. Hypotheses vary as to their subject-matter, and as to the use they are intended to serve. As to their subject-matter, Mill divides them into two classes : (1) Those in which the law of action for a cause is assumed, the cause being known to exist. When the movement of the vanes of a radiometer was known to be due to the action of the rays of light falling on it, the manner in which these produced their effect was stiU open to question, and different hypotheses were put forward to explain it. (2) Those in which the cause, or agent, is assumed, the law according to which it was supposed to act being some known law. When a photographic plate is sub- mitted to the action of rays of light coming through a large telescope, properly moved so as to counteract the movement of the earth, many specks are found on it HYPOTHESIS. 195 which cannot be referred to any stars visible even in the strongest telescope. A hypothesis of the highest probability refers these specks to the action of rays proceeding from stars so faint that they can never became visible to the naked eye. Here a cause (rays of invisible light) is supposed to exist, and to act in accordance with the ascertained laws of photo- graphic action. (3) We may add another to Mill's two kinds. A hypothesis may be one which assumes the co-existence, or collocation, of two or more facts which are not known to co-exist in this particular case. Mill, it may be here remarked, apparently regards the employment of hypothesis as to some extent abnormal. His language is not very consistent. In one part of his chapter on Hypothesis ("Logic," III. xiv. § 5), he allows that hypotheses " are necessary steps in the progress to something more certain ; and nearly everything which is now theory was once hypothesis." But, on the whole, he seems to think that the normal method of discovery begins with a direct " induction to ascertain the law," presumably on the lines of one of his Four Methods explained below — and he speaks with contempt of Dr. Whewells account of induction, in which the importance of hypothesis was recognized. He puts the terms "in- duction " and " hypothesis " in marked antithesis. He unduly narrows the field of hypothesis, and restricts the use of the term, so as to exclude from it such an obvious instance as the nebular hypo- 196 LOGIC. thesis of Laplace ; and he lays down unnecessarily stringent conditions, not only of proof, but of general permissibility. § 3. Permissible Hypotheses. What hypotheses are permissible, and what are not ? The usual answer is as follows : (1) A permissible hypothesis (or, as some writers would say, a valid hypothesis) must not conflict with facts already ascertained, or with laws already proved true. However, since certainty with regard to laws of nature is only relative, we cannot say that a hypo- thesis which apparently conflicts with any observed uniformity is necessarily unworthy of investigation. Other things equal, a hypothesis which is in apparent contradiction with well-ascertained laws, is less worthy of attention than one which is not. But there is always the possibility, (i) that the well-ascertained law, though true in the main, is liable to counteraction in particular cases not yet noted; and (ii) that the apparent conflict between the new hypothesis and the old law can be shown, after further observation and discussion, not to exist. (2) A permissible hypothesis must be capable of leading to deductive reasoning, and the results of such reasoning must be capable of verification. (3) When the hypothesis belongs to the second kind mentioned in § 2, and supposes the existence of a HYPOTHESIS. 197 given cause acting in accordance with known laws, the cause or agent assumed to exist must be a vera causa. To the expression vera causa, used by Newton, no very definite meaning can be assigned. The condition is taken to mean that the cause must be (a) one already known to exist ; or (Jti) one capable of being known ; or (c) one whose existence involves no self-contradic- tion, that is, which is formally possible, because con- tradicting no law of thought, (a) Newton seems to have attached the first of these meanings to his ex- pression. But this is certainly too stringent a quali- fication ; if we insist on it, any hypothesis which involves the existence "of a fresh planet or a fresh element hitherto unknown, would be ruled out of court. (li) The second meaning is supported by Mill ; but it is not entirely satisfactory. Any cause which can be imagined, is capable of being known, if it does exist, under some conditions, though not perhaps those we have at our command. If we require that it should be capable of being known under our present conditions of knowledge, we come back to the same stringent conditions as the first, (c) The thu'd meaning may be accepted, though it in- volves a further change in the connotation of the term. It is equivalent to Lotze's requirement that a hypo- thesis may not legitimately involve anything which cannot be represented to the mind. We may not suppose a circular square to exist, but we may suppose atoms, ether, etc., because so far as our present know- 198 LOGIC. ledge goes there is nothing self-contradictory in these suppositions (" Logic," § 277). (4) Other things equal, a hypothesis which does not require auxiliary hypotheses, is to be preferred to one that does. A good hypothesis should be indepen- dent, as well as consistent and complete. One which requires bolstering up with a number of other un- proved suppositions, is never satisfactory. § 4. Verification. The demand for the most thorough verification of hypotheses which are to be received as laws, is the chief feature which distinguishes modern scientific method from ancient. The seventeenth century thinkers wrongly ascribed the failure of mediaeval science to the use of hypotheses. Newton boasted, " Hypotheses non fingo," and yet his discovery of the Law of Gravitation was a clear case of the use of a hypothesis properly verified. By verification we mean showing that the hypo- thesis gives deductive results which are in agreement with fact. " Agreement with fact," says Jevons, " is the sole and sufficient test of a true hypothesis " (" Principles of Science," p. 510). The more facts with which it can be shown to be in agreement, that is the more facts for which the assumed law or cause will account, and the fewer with which it is in apparent disagreement, the more credence will be placed in it. If we are certain of the fact, " a single absolute HYPOTHESIS. 199 conflict between fact and hypothesis is fatal to the hypothesis," as Jevons says. But what we call a fact of observation is, it must always be remembered, to a large extent a partly unconscious inference, depend- ing tacitly on certain premises. It is usually a generalization which is itself not absolutely certain. And the real conflict may be between the new hypo- thesis and an old one which has never been properly tested. Thus Newton laid aside his hypothesis of universal gravitation for many years, because he found that it came in conflict with some observations founded on a false estimate then in use as to the radius of the earth. A hypothesis which is regarded as proved is some- times called a theory.^ But as proof is, strictly speak- ing, only relative, we never get more than a very high degree of probability. Thus we cannot draw an abso- lute distinction between hypothesis and theory. As veriflcation proceeds, and more and more facts are found explicable by the hypothesis, while more and more of the apparent discrepancies with other facts and with received theories are explained away, the hypothesis gradually becomes known as a theory. Thus Darwin's hypothesis of Natural Selection is commonly spoken of as the Darwinian theory ; and no ' The word "theory" is ambiguons. It is used for (a) an un- proved hypothesis — a use to be avoided; (b) a proved hypothesis of any kind; (c) a proved hypothesis of a complex kind — a whole system of ascertained knowledge, such as the theory of the tides. 200 LOGIC. one would think now of speaking of the Newtonian hypothesis of universal gravitation. § 5. Subordinate Uses of Hypotheses. Hypotheses serve : ' (1) To give us general propositions, which must be afterwards verified, as already explained. These hypotheses are intended to be proved and converted into theories, and are put forward in that hope. (2) As a guide to observation and experiment. Such are put forward as mere working hypotheses, without any great hope of their proving correct, but that we may have some kind of guidance in dealing with our accumulated results of observation. A man confronted with a huge mass of facts, for instance with whole volumes of statistics, must make a beginning some- where. Anything is better than mere haphazard plunging, so he assumes temporarily that a certain relation obtains, that any case of A is a case of B ; and holding this likely, he begins to try to verify it. If any other course strikes him as more likely, he abandons his working hypothesis. When we try to find an object, we follow such a course. We must begin somewhere, and so we assume that the table before us is the best place to begin with ; but if we do not see the object, we form another guess and try the cupboard or the floor. These working hypotheses, then, differ from the others in being put forward without any great ex- HYPOTHESIS. 201 pectation of their being true, as a guide to observation and experiment. And we may connect their use with the same psychological truth to which allusion was made in the last chapter but one. If observation is to be effective there must be preadjustment of atten- tion, or anticipatory imagination. (3) There are other hypotheses which do not seem to be put forward with any distinct idea of proving them. Classification involves inference, conscious or unconscious ; and is itself necessary for fresh in- ferences. When we classify or describe phenomena which are tolerably well understood, the element of inference is not very prominent. If I identify a given building as a church, or a number of birds as pigeons, there seems little that can be called guess-work. Sub-conscious inference is present, however, and there is always a leap forwards from the actual sense-data, guaranteed more or less by our previous knowledge. In cases where it is impossible to prove that our inference is correct, the classification or description remains hypothetical. Unexplained facts are grouped together, and a common name is given for the sake of reference. The expression " electrical fluid " is such a descriptive hypothesis. " When a phenomenon is of an unusual kind we cannot even speak of it without using some analogy. Every word imphes some resemblance between the thing to which it is applied and some other thing " (Jevons). CHAPTER XVIII. mill's methods of experimental inquiey. § 1. The Method of Agreement. Mill devotes an important part of his treatment of Induction, to a consideration of what he calls the " methods of experimental inquiry." ^ These he seems to regard as the methods by which are ordi- narily discovered the uniformities of phenomena which we call natural laws. Whether they are used as Mill thought they were used is open to question, and something will be said at the end of the chapter on the subject. But there is no doubt that the methods laid down by Mill, and before him by Bacon and other writers, are useful for the purposes of suggesting hypotheses, and of testing hypotheses already formed. The first method is that of Agreement. We examine a number of cases in which a given phenomenon, A, occurs, and find it in every case accompanied by another phenomenon, X, while all the other accom- ' In this phrase there is apparently no reference to the more precise use of the term " experiment" in antithesis to " observa- tion." By experimental inquiry Mill means here inquiry based on experience. mill's methods of experimental inquiry. 203 panying circumstances differ, more or less. We are entitled to assume tliat A and X are causally con- nected. Mill states what he calls the " canon " of the Method of Agreement in these words ; " If two or more instances of the phenomenon under investigation have only one circumstance in common, the circumstance in which alone all the instances agree, is the cause (or effect) of the given phenomenon." The basis of this may be expressed in some words of Hume which Mill perhaps had in his mind: "Where several different objects produce the same effect, it must be by means of the quality which we discover to be common amongst them." ' The Method of Agreement when employed loosely is practically the same thing as what Bacon calls "inductio vulgaris," or "inductio per simplicem enumerationem." We notice the circumstance X, which always precedes or accompanies the circum- stance A, and infer that X is the cause (or part of the cause) of A. It differs from " inductio per enumera- tionem simplicem" only in the thoroughness with which the process is performed, and the care that is taken to select instances ; so that if contrary instances occur, in which A occurs without X, they may be noticed and taken into account. As a means of suggestion such a method is of the greatest value. Running our eye over a table of ' " Treatise of Human Nature," bk. i., pt. iii., sec. xv. Hume also gives in a loose form the foundation principles of the methods of Difference and of Concomitant Tariations. 204 LOGIC. instances, we notice that A is frequently preceded by X, and we form the hypothesis that X is the cause of A. We continue to employ the same process, but now as a test of our newly-formed hypothesis. It is no longer a method of suggestion, but one of verifica- tion. If we come across a contrary instance we shall have to explain it away (show that it is not really an exception) or give up our hypothesis, or modify our hypothesis in some way. Or having used the Method of Agreement to suggest a hypothesis, we may lay it aside, and turn to some other method to test the guess which we have made. The Method of Agreement has been symbolized thus. Let us use capital letters for antecedent or accompanying circumstances, and small letters for phenomena which we regard as consequent on them. Then if we have a number of instances presenting the antecedents A B C, A D E, A F G, A H K, etc., and the consequents, a b c, a d e, a f g, a h k, etc., we know that A is the cause of a. But this way of symbolizing the process is open to very grave objection. It suggests that one antecedent can be ordinarily assigned to one consequent ; that A is the cause of a, and B of b, etc. As a matter of fact no such simple relation exists.^ The whole group of antecedents, A B C, is the cause of the whole group a b c ; and we cannot couple A with a, B with b, C with c. It would be better to symbolize thus : ■ See Chap. XIV. § 3, mill's methobs of experimental inquiry. 205 X B C D E, A B' C D' R, X F G H J, A F G' S T, X K L M N, A K L M U, XOPQZ, AO'FWY, etc. etc. Here the same letters sometimes appear in both columns to indicate that some of the circumstances remain to all intents and purposes unchanged; others appear in the second column with (') affixed to indi- cate that they have undergone a change but are still recognizable. Finally some fresh circumstances have appeared, and have taken the place of others. In all this flux of phenomena, however, when we have A as a consequent we have X as an antecedent. We there- fore assume that for the phenomenon A to occur in a group of phenomena, X must also be present as an antecedent. § 2. Method of Agreement and Plurality of Causes. Regarded as a method of proof, it is subject to what Mill calls a " characteristic imperfection." The phe- nomenon A may be due to X in the cases we have examined, not in others. In the second instance it may have been due to H ; that is, it would have occurred even if X had been absent as long as H was present ; in the third it may have been due to M, and so on. This is the familiar fact which we have already met 206 LOGIC. with, as, "the plurality of causes," or " vicariousness of causes." ^ The more cases we examine the less likely are we to overlook this. If we take a sufficiently large number, we are likely to come across some in which X will be absent while A is present. This will at once suggest that X is not absolutely necessary to the production of A. But if the connection between X and A occur more frequently than the laws of probability will account for, we must assume that X is not a mere casual antecedent. It is, probably, at any rate sometimes necessary. We cannot however assume this without further proof ; and our use of the Method of Agree- ment is almost necessarily tentative and preparatory. The result, therefore, of the existence of plurality of causes is that the method can practically only be used as a method of suggestion. " The conclusions which it yields when the number of instances compared is small, are of no real value, except as in the character of sug- gestions they may lead either to experiments bringing them to the test of the Method of Difference, or to reasoning which may explain and verify them deduc- tively " (Mill). Even if the number of instances be very large, however, the method will give us no very certain results.^ As a method of proof or verification, it can only be used provisionally. It will serve as a kind of coarse sieve, and will somewhat narrow down possible 1 See Chap. XIV., § 3. " See Dr. Venn's discussion, "Empirical Logic," chap. xvii. pp. 421-6. mill's methods of experimental inquiry. 207 hypotheses. It will select for us a certain number of antecedents as probably concerned in the production of A, but not enable us to pin our faith on one. There is another objection to the method, arising from the fact that we can never be sure that we know all the antecedents in our instances. The groujjs of phenomena XBCDE, XFGHJ, etc., may be all accompanied by some unnoticed phenomenon, which may be an essential circumstance if A is to be produced, while X and the other phenomena may be none of them absolutely necessary. The presence of a specific microbe has doubtless been the real cause of many diseases which have been put down to changes of temperature, indigestible food, wounds, etc. But either the means of detection at hand were not equal to the discovery of this necessary antecedent, or the atten- tion of observers had not been directed to it. § 3. Method of Difference. If we can obtain two instances, in one of which a given phenomenon A occurs, while in the other A does not occur, no other difference being noticeable ; and if we can detect some other phenomenon X which is pre- sent when A is present, and absent when A is absent, while its presence is always accompanied by the presence of A, this phenomenon X is causally connected with A. Mill's " canon " of the Method of Difference is expressed thus : — " If an instance in which the phe- nomenon under investigation [designated by A, above] occurs, and an instance in which it does not occur, have 208 LOGIC, every circumstance in common save one, that one occurring only in the former ; the circumstance in which alone the two instances differ, is the effect, or the cause, or an indispensable part of the cause of the phenomenon."^ Like the Method of Agreement, this supposes a simplicity which is not found in Nature. But it avoids some of the difficulties which interfere with the use of the first method. It does not try to determine all the conditions ; two instances are taken which are practically alike, except in one particular, though we may not be able to assign all the phenomena. Suppose that A B C D E be one of them, and B C D E the other; there may be a large number of other phe- nomena, F G H, etc., common to both, but these do not concern us, because we take the utmost pains to insure that, whatever they are, they are present in both instances. In order that the two instances may be as nearly alike as possible, it is necessary that we should " take one and the same thing, or event, as nearly as possible at two consecutive instants. There is really no other way open to us ; for by supposition, we do not know all the antecedents, and therefore we cannot certainly secure them by the most painstaking selection.'"' Thus let B C D E represent a galvanometer on a ' We cannot, properly speaking, distinguish between "the cause " and " an indispensable part of the cause." No single circumstance can in any strict sense be "the cause." * Venn, " Empirical Logic," p. 414. mill's methods of experimental inquiry. 209 certain table in a certain room, at a certain time ; and let ABODE represent everything exactly the same, except that the needle is deflected. What we have to find out is what fresh antecedent or concomitant phe- nomenon has appeared. Say it is a large key which I have placed on the table. This is again removed, and the needle swings back to its old position. A few repetitions of the experiment assure us that the presence of the key on the table is the only circum- stance of importance which has varied. We therefore have the right to assume that the presence of the key is causally connected with the deflection of the needle ; either as an essential part of the cause or as part of the effect. We know that it is not the latter ; therefore it is the former. But a little reflection shows that it is, in strictness, impossible to be assured that two instances differ only in the presence and absence of a single attribute, A. When the key was put down on the table many small changes occurred; movements of the body caused vibrations in the floor and in the air ; minute optical, electrical, thermal, and physiological changes took place, which we have not reckoned with. We may assume that these unestimated phenomena did not cause the deflection of the needle ; but this is only an assumption, an inference resting on grounds more or less satisfactory. Nature is so complex, and our knowledge so limited, that it is always possible that some phenomenon of importance has been overlooked. A large number of repetitions of an experiment, under P 210 LOGIC. varying conditions, help to diminish the uncertainty ; but it is never entirely removed. This method is obviously mainly serviceable for the purpose of verification. It will only be by accident that it suggests a possible cause (as at first in the instance of the galvanometer) ; but when we suspect a cause we can add just this one new fact to our instances, and see whether the effect which it is sup- posed to produce will actually be produced. This is how we employed the method in the second and further repetitions of the experiment with the key. All the circumstances remaining otherwise the same in our group of antecedents, we introduced the sus- pected cause (presence of the key on the table), and saw that the anticipated result followed. The Method of Difference is, therefore, only applic- able under artificial conditions. It is essentially a method of experimental verification. It is employed to determine whether the hypothetical cause really produces the effect which we presume to be due to it. Where experiment is impossible, other methods, e.g., that of Agreement, have to be resorted to. Mill says it is " perfectly rigorous in its proof" of causation. The method, however, only proves that, in this given instance before us, X is a necessary condi- tion for the production of A ; it does not prove that A is always produced when X is present, nor that X is always necessary to the production of A. In other instances, perhaps, Y may be substituted for X with the same results. mill's methods of expeeimental inquiet. 211 § 4. The Joint Method. What Mill calls the Joint Method of Agreement and Difference is, in reality, a double employment of the Method of Agreement, positive and negative. Mill's canon runs thus : " If two or more instances in which the phenomenon occurs have only one circum- stance in common, while two or more instances in which it does not occur have nothing in common save the absence of that circumstance ; the circumstance in which alone the two sets of instances [ j differ, is the effect, or the cause, or an indispensable part of the cause, of the phenomena." Jevons wished to insert " always or invariably " in the place where we have printed a pair of square brackets; since Mill's canon, without this addition, would be satisfied with the following instances : ABC a b c BC bo ADE a d e DE de AFG af g FG fg When obviously the two pairs, A B C, B C with their consequents, would enable us to at once apply the Method of Difference. The following instances would satisfy the canon, as amended by Jevons : ABC a b c PQ pq ADE a d e RS r s AFG af g TW t w We collect instances of the presence of the phe- 212 LOGIC. nomenon under investigation, and instances of its absence. If we are seeking the cause of a, then we take instances in which a is present, and find that among their immediate antecedents or concomitants A is always present, and that where a is absent, A is absent from among the antecedents and concomitants. Or if we already suspect A is the cause of a, we can use the method as one of verification ; for taking instances in which A occurs as an antecedent or con- comitant, we find a always present among the con- sequents, and when A is absent, a is also absent. It should be noticed, however, that the negative instances add very little to the efficiency of the method, unless they are cognate to the positive instances. They must be cases " as much resembling them [the positive] as possible," as Mill himself^ remarks (" Logic," Bk. III. ch. ix. § 1). If we are seeking a cause for the phenomenon of animal heat, it is of little use to select instances of the absence of heat from the mineral, or even the vegetable king- dom. These help us very slightly. But negative instances taken from the animal kingdom throw con- siderable light on the problem. The more analogous our negative instances are to our positive, the more nearly does the method approach in validity to the direct Method of Difference. Our formulae must be something of this kind : ABC a b c B'C b'c' ADE a d e D'E' d'e' AFG af g FG' f'g' mill's methods op experimental inquiry. 213 Chemistry gives us opportunities for getting analo- gous instances. Various specimens of a substance, if pure, differ so little that B C and B' C are almost exactly the same ; and the presence and absence of the A may be regarded as the only difference. So that the method passes over into that of Difference. In Sociology, on the other hand, we never get two cases so much alike that we cannot discern many other disparities, as well as the presence and absence of A. § 5. Method of Residues. The three methods hitherto noticed have been all methods of elimination. " The Method of Agreement stands on the ground that whatever can be eliminated, is not connected with the phenomenon by any law. The Method of Difference has for its foundation, that whatever cannot be eliminated, is connected with the phenomenon by a law." ^ And the Joint Method obviously stands on the same basis. The fourth method formulated by Mill, that of Residues, is a modification of the Method of Dif- ference. From the known effects of A and B sepa- rately, we infer their conjoint effect, and subtract this (a b) from the tolal effect to be investigated, a b c. The remaining part of the effect, c, is due to any fui:ther antecedent, C, which we may discover. ' MiU, "Logic,»III. viii. §3. 214 LOGIC. Mill's cation runs thus : " Subduct from any phe- nomenon such part as is known by previous induc- tions to be the effect of certain antecedents, and the residue of the phenomenon is the effect of the remaining antecedents." Jevons cites as simple instances the ascertaining of the exact weight of any commodity in a cart, by weighing the cart and load, and then subtracting the known weight of the cart. The method usually requires quantitative data, as in this case ; but it can be applied qualitatively. Certain unpleasant symptoms (c) noticed after dinner, must be due to a special dish (C), because the feelings (a b) produced by other dishes (A B) are well known, and can be mentally subtracted, or as Mill calls it, subducted, from the total effect. A little consideration will show that the Method of Hesidues is not very conclusive as a method of proof. We can never be certain that C is the only residual antecedent ; some difference in temperature, in our manner of spending the day, or in our general health, may really have caused the unpleasant feelings which we have placed to the credit of the suspected dish. But the method is valuable as a means of suggestion. The study of residual phenomena is a most fertile source of great discoveries. The discovery of the planet Neptune, by Adams and Leverrier in 1846, was due to it. In the year 1894 it led to the discovery of a new constituent of our atmosphere, argon. Supple- mented by deductive verification, which shows, a mill's methods of experimental inquiry. 215 priori, that C may be a cause of c, or by experimental verification by the Method of Difference, the method is of the greatest value. § 6. Method of Concomitant Variations. This method is another special application of the Method of Difference. If we have a set of antecedents, A B C D, even if A cannot be entirely removed, it may be modified in amount or in some other way. If a corresponding change occurs in the group of conse- quents a b c d, so that one of them, a, becomes modi- fied in amount, or in some other way, we assume that there is some causal connection between A and a. In cases where a complete vacuum cannot be produced, we may often argue with great security that the pre- sence of air (or some other fluid) is a necessary condi- tion of certain phenomena — because, as the vacuum becomes more and more perfect, the phenomena diminish in amount. Mill's canon is stated in these words : — " Whatever phenomenon varies in any manner whenever another phenomenon varies in some particular manner, is either a cause or an effect of that phenomenon, or is connected with it through some fact of causation." The Method of Concomitant Variations can be applied when the Method of Difference cannot. It is thus specially valuable to determine the effects of causes which are always present to some extent, though in very various degrees — such as gravity and 216 LOGIC. heat. It can be easily applied when the cause varies in quantity ; it is thus specially serviceable when we have exact quantitative data. As Professor Bain points out, it is not liable to be frustrated by intermixture of effects as most of the other methods are. " If a cause happens to vary alone, the effect will also vary alone, and cause and effect may be thus singled out under the greatest complications. Thus, when the appetite for food increases with the cold, we have a strong evidence of connection between these two facts, although other circumstances may operate in the same direction " (Bain, "Induction," III. viii. § 6). It must be remembered, (1) that the law of variation which the quantities seem to follow within the range of our observation may not hold outside it. Change of quantity may, after a time, produce change of kind ; what Mill calls a heteropathic effect may be produced. Friction carried beyond a certain point may produce an explosion. Pleasant stimulation if steadily increased, passes, after a while, into pain. And (2) different laws of variation may produce results which, within narrow limits, shall be practically identical. § 7. Mill's Treatment of the Methods. The exact position which Mill intends to assign to his "methods of experimental inquiry," or "methods of induction," is not quite clear. The ordinary means by which we arrive at the laws which are exhibited by " complex effects " (and we mill's methods of expeeimental inquiry. 217 have seen that all phenomena are complex effects ^) he calls the Complete Deductive Method. It consists of three steps : (1) Induction, by means of the " methods of experimental inquiry " ; (2) Ratiocination, a calcula- tion from these known laws what will be the effect in any given combination of these causes ; (3) Verifica- tion, by direct observation, or by new inductions, or by deduction. This statement of the Complete Deduc- tive Method bears some resemblance to the account given in Chap. XVII. § 1 above. But it will be noticed that Mill regards his first step as in itself a complete induction, and as giving us a result which is thereby known to be true. The third step, which he calls verification, is not a proof of the truth of the general law, but of the results of the deductive process. He regards the "methods of experimental inquiry " as giving results which are in themselves certain, and which do not require verification. Indeed, he expressly draws a distinction between this Direct Complete Deductive Method, and the In- verse Complete Deductive Method, where the forma- tion of a Hypothesis is substituted for the direct use of the experimental methods. It is true that he occasion- ally speaks of Hypothesis as a possible part of the ordinary method of discovery, and in some places he speaks of his Four Methods of experimental inquiry as though they were "tests for induction similar to the syllogistic test of ratiocination." But on the • See Chap. XIV. § 4, above. 218 LOGIC. whole he seems to think that they are the normal and ordinary method of arriving at general propositions after observation of phenomena. The most important statement on the other side, which if it stood alone would be quite conclusive, and which gives a much truer view of the real value of the method, is that at the end of Bk. III., chap. x. § 3. He points out here that, owing to the interference of causes with one another, and the intermixture of effects — a case which he recog- nizes, though not with adequate emphasis — the four methods of inductive investigation are of secondary importance. " The instrument of Deduction," he says, " alone is adequate to unravel the complexities proceeding from this source ; and the four methods have little more in their power than to supply premises for, and a verification of, our deductions." If this be Mill's final view, which is open to doubt, it comes to much the same as that advocated here that the famous Methods are of value : (1) To suggest hypotheses ; (2) As a means of verification of hypotheses. § 8. How the Methods are actually em- ployed. Let us take a case which actually occurred. In August, 1883, an epidemic of typhoid fever occurred in Camden Town. The medical officer, Mr. Shirley Murphy, prepared a plan of the district, on which he marked all the houses which had been attacked. His mill's methods of experimental inquiry. 219 scientific knowledge at once suggested to him a number of hypotheses as to the origin of the attack. Putting them briefly, they were (1) the Regent's Canal ; (2) the water supply ; (3) the sanitary arrangements in the houses ; (4) the milk supply. The use of his plan, and inquiry at the houses, showed that the first three hypotheses were invalid. The houses attacked were not usually near the canal. Two water companies supplied the district, and houses supplied by both com- panies were attacked with impartiality. Sanitary de- fects existed both in attacked houses, and in those which escaped the disease ; while the sanitary arrangements in some of the attacked houses were perfect. So far the positive and negative Methods of Agreement (Joint Method) had been applied as a means of testing the hypotheses arrived at, — ^not, be it noticed, to suggest the hypotheses, which were largely due to deductive reasoning from general laws of hygiene. The fourth hypothesis remained. By the applica- tion of the Method of Residues, the case in favour of this fourth hypothesis was not proved (as Mill suggests) but perceptibly strengthened. Now, by a direct use of the Method of Agreement, " it was discovered that out of 431 persons attacked, 368 were definitely known to obtain their milk from one particular milkman, Mr. X., while the remaining 63 might well have indirectly obtained it from him also Out of all the houses attacked, 78 per cent, received their milk from Mr. X." This use of the Method of Agreement was, however, probably twofold. After the first score 220 LOGIC. or so of cases a strong suspicion was probably aroused in Mr. Murphy's mind that Mr. X.'s milk was the true causa sine qua non ; while the subsequent cases were, it would appear, rather used by way of test, or verifica- tion, of the hypothesis so formed. Whether this was so, the report ^ give* no information. Mr. Murphy now definitely verified his hypothesis by examining the shop and premises of Mr. X., and the farms from which Mr. X. obtained the milk. He succeeded in proving that one of these farms, near St. Albans, was infected with typhoid, and thus finally showed the adequacy and truth of his hypothesis. As the older logicians would have said, he proved that the typhoid fever infection in Mr. X.'s milk was a vera ' All the details of Mr. Murphy's admirable investigation I have taken from the " Pall Mall Gazette," of October 15th, 1883. CHAPTEE XIX. EXPLANATION. § 1. Explanation. The object of explanation is to show that some given fact, or given law, is not exceptional, but that it can be brought under some law or laws already known to be true. It is our answer to the question, " Why does this occur in this way ? " It relates a fact hitherto isolated in experience, to other facts. Scientific explanation does not differ materially from popular explanation. It is, however, more precise and better verified. And it differs from popular expla- nation in offering laws which are simpler in themselves and of wider application, though they may be less familiar, while popular explanation hesitates to do this. The scientific man explains by reference to things which are in the phrase of the mediaeval philosophers " notiora naturcB," and not " notiora nobis," The law of universal gravitation is simpler and more abstract, and thus wider in scope, than the law that tea-cups left unsupported fall to the ground ; but it is less familiar. A fact is explained by being brought under some law. It is shown to be a particular case of some 222 ' LOGIC. uniformity. Why does this phenomenon occur here now ? Because it is a case of a certain kind, which ■comes under a particular law. Why do I observe certain movements in the cilia of a rotifer under the microscope ? The answer may be, that all rotifera pre- sent these appearances ; or it may go deeper, and sug- gest some causal relation between these movements and the structure of the animals. But in either case the fact is brought under a general law. A general law, however, is only one degree less isolated than a single fact. We are driven to bring such a law under laws still more general. Mill enumerates three kinds of explanations which may be applied to laws. (1) The law that " A is B " may be resolved into the laws that " A is X," and " A is Y," and the law that where " X and Y are conjoined, B is produced," Thus, to use Mill's example, the orbit of a planet is shown to be due to the fact that the planet is acted upon by two forces, the tangential impulse and the force of gravity, and that the joint effect of these two is movement in a closed curve. Each of these laws is simpler and less specialized than the law that the planet moves in such an orbit. Here, as Dr. Venn insists,' there is something more than mere generalization. There is analysis as well. (2) Detecting an intermediate link in the sequence of causation. The sequence, A is followed by B, is ' " Empirical Logic," pp. 498, sq. EXPLANATION. 223 shown to be a complex case due to the two laws that A produces X, and that X produces B. We never succeed in getting the causal relation so precise, that no intermediate event can possibly be interposed between A and B. The simplest sequence with which we are familiar can usually be analyzed by scientific men into a series of events. Thus the production of a flame when a match is struck resolves itself into several consecutive events : (a) friction produces heat of a sufficient intensity, and (b) this heat breaks up some of the unstable chemical composition on the head of the match ; (c) some ingredients of this being liberated unite with explosive energy with the free oxygen of the air; (d) this sets fire to all the rest of the composition. (3) A specific law is shown to be a particular case of a wider law. The explanation that tea-cups fall to the ground because every particle of matter attracts every other, is, in point of fact, a re-statement of the same fact as part of a large group of facts. It does not attempt to break them up and analyze them; but merely generalizes, and shows that the case of tea-cups is included in a uniformity of incalculably wider reach. § 2. Exceptional Phenomena. A scientific law is only the expression of one ob- served uniformity. If the uniformity has been inade- quately expressed, we have an exception. The excep- 224 LOGIC. tion arises from want of precision in our expression of what we have observed. The preliminary classifica- tion has, perhaps, been badly performed, and the sub- ject of our proposition is at fault. We have said " All A is X," when we should have said " All A B is X." If we come across an A C which is not X, we call it an exception to the rule that " every A is X." Or we have imperfectly described the phenomena observed in the instances examined, and said " All A is X," in- stead of " All A is X'." Here, as long as X' closely re- sembles X, we do not find or notice any irregularity. But if the quality X' happens to differ considerably from X in some special case, we call this case an ex- ception. In such cases we can see that the exception is an exception to our expression of a uniformity, which we believe we have observed. As a matter of fact, the uniformity does not exist, and our law is only an ap- proximation to the truth. The fault lies with us. There are no laws in Nature herself. Man makes the laws, as he makes the classes ; both are purely subjective ; and the laws depend on the classifi- cation. Hence all laws are in their essence abstract and hypothetical. If the individual things of which we are speaking completely conform to our definition, if they are true members of the class we have marked off, they will possess the qualities which our " law " declares to be possessed by all members of the class. Exceptional phenomena are of the greatest value in science. They arouse wonder, and draw attention not EXPLANATION. 225 only to themselves but to the laws to 'which they are exceptions. Psychologists tell us that one of the chief factors in producing efficient attention is novelty ; and although what is familiar may be as worthy of notice as wha.t is new and strange, it does not affect us in the same way. Bacon drew attention to the importance of excep- tional phenomena for the purpose of scientific discovery. His instanticB monodietB, or instantia irregulares, and his instantioB deviantes are examples. He recognizes not only their stimulating effect on the mind, but also the danger which arises from the disproportionate im- pression they make, to the exclusion of others equally instructive. By instantim monodicce he mean^ irregular kinds, "miracula specierum," while the instantiee de- viantes are as it were " errores naturae," and are " mira- cula individuorimi," or what modern naturalists call " sports." Jevons, in his " Principles of Science " (chap, xxix.), gives a classification of exceptional phenomena, but it has small value. § 3. Extension of Empirical Laws. Derivative laws, as we have. seen, are those unifor-,. mities which have been shown to be special cases of more general and certain laws, or are supposed to be capable of such affiliation on more general and certain laws. The latter, it will be remembered, are called empirical laws. All such derivative laws, being ex vi termini com- Q 226 LOGIC. paratively specific and narrow, are more liable to ex- ception than the wider laws. The law, "A follows B," and the law " B follows C," are less liable to ex- ception than the law " A follows C," which is a deriva- tive law depending on both. If an effect requires for its production the presence of several conditions, it is more liable to counteraction than an effect which requires fewer conditions. The flaming of a match when struck is more liable to be hindered than the production of heat by friction, or than the deflagration of the head of the match when sufficient heat is produced. There are two possibilities of frustration instead of only one. The collocation, or co-presence, of all the necessary conditions is more difficult to secure than the presence of only those circumstances which produce heat, or the presence of only those circumstances which, when heat exists, produce deflagration. We can never be quite certain that the conditions necessary for the production of a highly specific effect (and to such effects derivative laws commonly refer) are present. But experience will give us a very high degree of probability that collocations which have been observed to occur will continue to occur within narrow limits of time and space. How do we know the sun will rise to-morrow ? The phenomenon of sunrise depends on certain optical laws, and on the continued existence of certain material objects. The continued existence of a luminous sun and of a revolving earth is implied. The laws of the pro- pagation of light might remain the same; but if sun or EXPI-ANATION. 227 earth disappeared, or changed their nature suddenly, the sun might not rise. That they will remain un- changed is an inference justified by very long ex- perience, and by our ignorance of any cause which might produce the change within twenty-four hours. " The chance, therefore, that the sun may not rise to- morrow amounts to the chance that some cause, which has not manifested itself in the smallest degree during five thousand years, will exist to-morrow in such in- tensity as to destroy the sun or the earth, the sun's light or the earth's rotation, or to produce an immense disturbance in the effect resulting from these causes." "^ The extension of an empirical law rests then on the probabilities of the continued uniformity of very com- plex phenomena. " In proportion, therefore, to our ignorance of the causes on which the empirical law depends, we can be less assured that it will continue to hold good ; and the further we look into futurity, the less improbable is it that some one of the causes, whose co-existence gives rise to the derivative uni- formity, may be destroyed or counteracted." ^ A cause which is at present too small in amount to arrest attention, may, after a sufficient lapse of time, bring- about an exception ; and the uniformity may disappear. Derivative laws, whether resolved or as yet unre- solved (empirical laws), can, then, only be extended to cases adjacent in time. They cannot be extended to cases adjacent in place, unless the new cases to which ' Mm, ''■ Logic," III. six. § 2. » 11. § 3. 228 LOGIC. they are extended are "presumably within the in- fluence of the same individual agents." If we know that the same causes are at work, we may extend the generalization to fresh cases. A special modifi- cation of some biological form found in some part of a country is likely to be found in other adjacent parts, where the same causes are at work. And even though we do not know that the same causes are acting, we may be able to assume it with considerable probability. Even if we do not know that the same conditions are present in other adjacent places, we may commonly assume that they are. But the narrower the limit of space the more probability there will be in our inference., Uniformities of mere co-existence are, as already renaarked (Chap. XIII. § 3) less certain than those which rest on causation. They are purely empirical, laws. § 4. Analogy. It is usual in works on Logic to draw a distinction; between what is called the proper use of the term Analogy, and the loose, or popular use. In the, former and stricter sense we mean by it a resemblance, between the relations of things ; in the latter sense we mean by it any resemblance between the things, them- . selves, which yet amounts to a great deal less than,, absolute likeness. " Analogy," says Kant, " does not signify, as is commonly thought, an imperfect likeness between two EXPLANATION. 229 things, but a perfect likeness of relations between two quite dissimilar things." And most other logicians express themselves in a similar way. When in the early years of this century Pitt was called the " pilot that weathered the storm," we have an analogy even in the stricter sense. The analogy may be expressed in the same way as a mathematical proportion, which is the declaration of the equality between two ratios or relations of number. Pilot : ship : : Pitt : state. Pilot : storm : : Pitt : French Revolution. Ship : storm : : state : French Revolution. Such an analogy gives rise to metaphor and similes of the most effective kind. As a foundation for argu- ment it has considerable value ; as a foundation for proof very little. It suggests lines of thought ; but he who uses it is always open to the objection that the analogy is superficial and fanciful. To prove that the analogy is real and substantial will usually take more trouble than to prove the original point without the assistance of analogy. Thus it is more satisfactory to attack directly the question : " Ought the colonies to assist England by arms against foreign foes ? " or " Ought they to contribute to the expenses of imperial defence ? " directly, than to try and establish the analogy — Mother : children : : England : colonies. The. looser type includes any kind of resemblance. The " argument frojn analogy " very often means 230 ] LOGIC. merely tlie argument from likeness. Kesemblance of relation usually involves some degree of resemblance in the things. Two objects, A and B, resemble each other in several points. They possess in common the qualities V, w, X, etc., and we infer that because A possesses further the quality y, B will also possess it. Logicians commonly contrast this process with In- duction. Generalization, or Induction, involves many objects, A, B, C, D, etc., all possessed of at least two properties, x and y; and we infer that another object, M, which possesses x, will also possess y, on the ground that we have found that in all the other cases x and y went together. Here the number of cases examined is large, while the qualities we are concerned with may be only two in number. The denotation is wide ; the connotation may be narrow. On the other hand, in the argument from analogy or resemblance we may have only two objects to compare, and therefore we need more than the one point of agreement, x, in order to infer the presence of another, y, when we do not know that the two are causally connected. Every additional quality will strengthen the argument. The connotation should be large, because the denotation is small. Mill says that in cases where the resemblance is very great, the dissimilarity very small, and our know- ledge of the subject matter extensive, the argument from 'analogy (resemblance) comes very near a valid induction. This however seems to be an error. " In all cases," says Lotze, " when we believe we can EXPLANATION. 231 prove by analogy, the analogy in fact is distinctly not the ground of the conclusiveness of the proof; it is only the inventive play of thought by which we arrive at the discovery of a sufficient ground of proof " (" Logic," § 214). Analogy is of the greatest value as a means for suggestion. It suggests hypotheses, both induc- tive and descriptive ; and the mind that readily sees analogies is usually fertile in new ideas. But in no case is analogy a substitute for proof. It can at best only lead to a very low degree of prob- ability ; whereas, inductions proper, that is, generali- zations arrived at after examination of many instances, even when not regarded as absolutely proved, often have the very highest degree of probabihty. The argument for the existence of consciousness in the lower animals is an argument from analogy ; and every psychologist feels the inadequate nature of it. CHAPTER XX. CLASSIFICATION. § 1. Classification and Formal Division. The process of classification is involved not only in aU processes of judgment and reasoning, but in those of conception and perception. Directly we name an object we implicitly refer it to a class. If we think of an attribute we implicitly divide all things into two classes — those which possess, and those which do not possess, the attribute. Some automatic and half-con- scious or unconscious classification is therefore involved in the use of general names. When by the process of Definition we render clear and distinct the exact connotation of a name, that is, the attributes implied by it, we at the same time render more definite the classes to which it applies. It is important to understand the relation between the process of Division already described (Chap. VI. §§ 4, 5), and the process of Classification. Logical Division is a purely formal process. Given a class of objects. A, we can point out a priori, without reference to any particular subject matter, to what general con- ditions the classification must conform if it is to be of CLASSIFICATION. 233 any value, theoretical or practical. Whatever A may be, the rules given in Chap. VI. § 5, must be com" phed with. In material or applied Logic, we can go farther than this. Taking some notice of the subject matter with which we deal, we can lay down a few general truths as to the kinds of classification best adapted to certain departments of knowledge. No longer assuming that we are dealing with mere symbols, and taking into account the fact that our names and concepts are not absolutely objective — that the world of percep- tion and practice can never be adequately represented by A's and B's — we point out the differences of proce- dure which will properly be followed in grouping various kinds of things. We have already remarked that even in what is called Formal Division the pro- cess is not absolutely formal and a priori; since the fundamentum divisionis must be an attribute not in- cluded in the connotation of the name. But whereas in formal division oux fundamenta divisionis are assumed to be already given, here we explicitly point out the kinds of attributes best adapted for fundamenta di- visionis. Material Logic, then, proposes to lay down general principles for our guidance in the matter of classifi- cation. Passing beyond the automatic classification already spoken of as involved in all thought and speech, it aims at showing us how we may best, for the pur- poses of clear thought and valid inference, arrange the objects with which we have to deal. In the words of 234 LOGIC. Mill:—" The general problem of Classification in refer- ence to these purposes [viz., those of Inductive Logic] may be stated as follows : To provide that things sh^U be thought of in such groups, and those groups in such order, as will best conduce to the remembrance and to the ascertainment of their laws." The importance of classification to induction has already been dwelt on (Chap. XVI. § 3). All valid generalization involves the correctness of the preceding classification. § 2. Artificial and Natural Classification. It is clear that classification is of two difierent kinds. We may classify objects on lines which are obviously arbitrary and, so to speak, artificial ; or we may endeavour to conform to the classes which seem to come from the hand of Nature. If we divide animals into those which are five feet long and upwards, and those which are less than five feet ; or into those which have been exhibited in the Zoological Gardens, London, and those which have not, we are dividing in a purely arbitrary way. Our fundamentum divisionis is made by ourselves for some special and very limited purpose. Our classification is in no sense a natural one. When a collector is dealing with artifi- cial objects, such as books, book-plates, or postage stamps, several kinds of classification may be equally rational and convenient, because serviceable for equally important ends, and all are equally artificial. CLASSIFICATION. ,235 When, however, we come to natural objects, above all to plants and animals, this is not the case. Nature seems to give us our classes ready made. All that we have to do is to try to recognize them. If we do not recognize them, the penalty we pay is incapacity to draw useful and valid inductions. How many general propositions can be affirmed of just those animals in the Zoological Gardens, as opposed to animals not confined there ? But of some well-marked " natural class," such as lions or reindeer, a number of general truths can be ascertained — important attri- butes can be found which wiU. be true of all members of that class. These "natural classes" are distinguished by an immense number of common attributes which are, at any rate at first sight, more or less independent and unconnected. While we can indicate in a moment the essential points of resemblance between the members of the class " white things " or "heavy things," there is no likelihood of our ever discovering all the attributes common to different specimens of the kinds " sulphur " or "man." Real Kinds, or Natural Kinds, is the name given by Mill to the classes thus marked off" by an indefinite number of common attributes. He apparently conceived of the co-existence of the perma- nent attributes as uncaused, and inexplicable. Al- though he lived till a period when the doctrines of Darwin and Wallace and Spencer had been generally accepted by scientific men, he made no alteration in his view. 236 LOGIC. Real Kinds are for Mill classes marked off by an inexhaustible number of differences, not referrible to any common cause. They are " classes between which there is an impassable barrier." The distinction thus drawn between a Natural and an Artificial classification, between one which best fits natural objects, and one which can only be applied satisfactorily to artificial objects, is less absolute than Mill imagined. To begin with, artificial objects, like books or pictures, which certainly cannot be said to belong to classes " made by Nature " present many, indeed an indefinitely large number of common attri- butes. Massive scientific treatises have been written on the common characters which are found in particular classes of books, or in paintings attributed to a parti- cular school. Such artificial groups present many of the features which Mill attributes only to natural groups. Then again, the line cannot be drawn sharply be- tween a classification due to the recognition of one or two attributes only, and a classification due to the recognition of an inexhaustible number of attributes. The attributes of dog or man are not, as Mill thought, independent ; but are probably in a very large de- gree "referrible to a common cause," and "de- rivable from each other." On the other hand, the presence of one or two attributes in even an artificial object commonly involves the presence of many others. That a coin is issued in France, or that a picture is a seventeenth-century Dutch one, involves CLASSIFICATION. 237 a loUg tifain of consequences, more or less independent, in appearance, but more or less connected in reality. § 3. Special and General Classification. It is better to substitute for the distinction between Artificial and Natural classifications, the distinction between classification for special purposes and for general purposes.^ A classification of the former kind aims at fulfilling some quite definite and limited pur- poses. The aim of classification of names and addresses in a directory is, clearly, that they may be easily found. The classification adopted is therefore alphabetical. No general propositions can be drawn as to the people whose names begin with the same letter. The obvious merit of the arrangemeqt " con- sists in the extreme celerity with which it isolates the element we are in search of, the alternatives being twenty-four [or rather twenty-six] at every step, and all but one being instantly laid aside." Our aim being to identify, an individual and ascertain his address, this is by far the best arrangement. But it yields us no further information ; except in so far as the " Mac's and O's " can be grouped together as Celtic names, and the Browns' and Smiths as purely English ones. A classification of individuals under their trade would give us materials for interesting speculation as to the popularity or the reverse of certain trades, the localir ties in which they are carried on, and so forth. This , , '■ VjBHni " Empiric^'Logic," eb?;p. ,xii,i. . | 238 LOGIC, would approach a " Natural" or general classification, which has for its two chief purposes the easy remem- brance of knowledge already obtained, and " aid and stimulus to fresh study." If a general system of classification is followed, we gain the power of making a "maximum amount of aggregate assertions with a minimum number of pro- positions." In other words, we can make many true universal propositions about the class. We can make many assertions about the class of brewers, or of painters, or of SQlicitors, each of which assertions wiU apply to a large number of individuals. § 4. Classification not the Work of Nature. In the third book of his " Essay concerning Human Understanding," Locke lays down the doctrine that, even in the case of natural objects, classification is the work not of Nature, but of man. The classes " depend on such collections of ideas as men have made ; and not on the real nature of things." In a certain sense they are " arbitrary," since they depend on the acci- dents of special needs and temporary conditions. Objects are, indeed, made by Nature to resemble each other, but the classes are made by the mind of man, which selects such points of resemblance between things as interest it most, and classifies the things in accordance with those interests. This doctrine is accepted by modem writers. Mill, for instance, speaking of " natural " and " artificial " CLASSIFICATION. 239 classification, says : " The differences [between objects] are made by nature in both cases ; while the recog- nition of those differences as grounds of classification and of naming, is equally, in both cases, the act of man ; only in the one case, the ends of language and of classi- fication would be subverted if no notice were taken of the difference, while, in the other case, the necessity of taking notice of it depends on the importance or un- importance of the particular qualities in which the difference happens to consist " (" Logic," Bk. I, Chap. VII. §4). Mill, however, did not fully recognize the implica- tions of the statement, or he would hardly have com- mitted himself to the doctrine of Natural Kinds. All classification is relative to some definite purpose. The anthropologist, the theologian, the psychologist, the artist, the lawyer, classify men in different ways. But no classification is in itself better than any other. There is a growing disposition to assume that the particular classification which suits the purposes of what is called Natural Science, and especially of the sciences connected with Biology, is somehow or other absolutely superior in kind to all others. This, how- ever, is a mistake. The purely speculative interests of the man of science are best served by the special classification he adopts ; but those speculative interests have no claim to over-ride all others. For his limited and definite purpose the biologist places man with the higher apes. Man differs from them only in degree ; between them and him there is " an all-pervading 240 LOGIC. ^militude of structure," to use the words of Sir Richard Owen. The zoologist classifies by reference to morphological characteristics. And on that ground he is hardly justified in making Man an " Order," side by side with the great and highly varied orders, such as the Insectivora, and the Quadrumana. All this may be granted ; while at the same time the psychologist, the theologian, and the moralist, may claim that {or their purposes — purposes more essential to actual conduct, that is to the real and necessary business of life — we must draw a much broader and deeper distinction between Man and Ape. The biolo- gist can lay no sort of claim to having seen deeper into the purposes of Nature than other men. When we speak of a scientific classification, we mean one specially adapted for the purposes of some one science, or perhaps of several sciences. A satis- factory scientific classification will thus be the " general " kind, already spoken of. It will "classify objects according to the whole of their resemblances and differences, so far as they are recognized by the science in whose service the classification is made " (Fowler, " Inductive Logic," p. 55). At the same time, while it takes care that the properties it selects for fundamenta divisionis are (1) marks of other pro- perties, both numerous and important, it will also see that they are themselves (2) notable and important properties, easily observed. It is impossible to classify natural objects in such a way that all of them shall easily fall into a well- CLASSIFICATION. 241 defined class. The boundaries of species, as Locke said, are not immovable : Nature from time to time presents us with objects that fall into no recognized class. The Law of Continuity is found to be true in all departments of experience ; and the isolated cases of a Natural History Museum, as we have already remarked, imply a discreteness which does not exist in the actual world. § 5. Classification by Type. The classes recognized by the scientific man, that is the careful and systematic student of Nature, are suggested by the general and bolder resemblances between objects ; but they are revised and rendered definite by drawing up precise lists of the attributes which entitle an object to be placed in a class. In other words, they are suggested by Type, and deter- mined by Definition, Dr. Whewell, the famous Master of Trinity College, Cambridge, who was the most powerful critic of Mill's doctrine of Induction, maintained that the classes recognized by science, the Natural Kinds of Mill, are " given by Type and not by Definition." " The class," says Whewell, " is determined, not by a boundary line without, but by a central point within ; not by what it strictly excludes, but by what it emi- nently includes ; by an example, not by a precept ; in short, instead of a Definition, we have a Type for our direction." By a Type, he means "an example of B 242 LOGIC. any class, for instance, a species of a genus which is considered as eminently possessing the character of the class. " " The type must be connected by many affinities with most of the others of its group ; it must be near the centre of the crowd, and not one of the stragglers." ' Mill admits that there is some truth in this doc- trine. " Our conception of the class, the image in our minds which is representative of it, is that of a specimen complete in all the characters [which are found in most of the objects in the class, and most of which characters are found in all the objects] ; most naturally a specimen which, by possessing them all in the greatest degree in which they are ever found, is the best fitted to exhibit clearly, and in a marked manner, what they are. It is by a mental reference to this standard, not instead of, but in illustration of, the definition of the class, that we usually and advan- tageously determine whether any individual or species belongs to the class or not" ("Logic," Bk. IV. Chap. VII. § 4). And for the higher development of classification which is termed serial, Mill recognizes that the assumption of a Type is absolutely necessary. § 6. Classification by Series. The work of classification is only half done if it results merely in the recognition of a number of unconnected ' Whewell, " History of Scientific Ideas," ii., 120-122 ; quoted by MilL CLASSIFICATION. 243 groups. The groups must be arranged under each other in such a way, that those which are most nearly alike are brought nearest each other. Any division which arranges widely different classes together, and separates those which closely resemble one another, is •pro tanto a bad and useless one. The obvious resource is to take some salient phenomenon exhibited by all the groups, and to arrange them according to the degree in which they exhibit it. Such an arrangement is called a serial classification. It obviously puts the instances into a convenient order for the application of the Method of Concomitant Variations. Thus the general aim of zoological classification may be regarded as the exhibi- tion of the phenomenon of Life, in a series extending from its slightest and simplest form in the Protozoa, to its fullest and most complex form in Man. As already remarked, the assumption of Type Species is indispensable for purposes of serial arrangement. Where natural objects are dealt with, however, no arrangement of classes can be strictly serial. What we constantly find is an arrangement which requires not one, but two or three dimensions of space to exhibit it ; it wiU require not a linear series, but rather a set of lines radiating in as many directions as space possesses. Where only one phenomenon varies regu- larly, the groups can be placed in a line one below another ; where several phenomena vary, this simple arrangement is no longer possible. This Dr. Whewell seems to have seen, for he thought the doctrine of " a 244 LOGIC. series of organized beings " to be " bad and narrow philosophy." Mill's reply' shows that he did not intend us to understand by a series one line only, *' It would surely be possible to arrange all places (for example) in the order of their distance from the North Pole, though there would be not merely a plurality, but a whole circle of places at every single gradation in the scale." > Footnote to "Logic," Bk. IV., Ohap. VIII., § 1. CHAPTER XXI. SCIENTIFIC LANGUAGE. § 1. Language and Thought. Language serves three chief purposes : (1) it serves as a means of communicating our thoughts ; (2) it serves as a means of recording our thoughts ; (3) it serves as a means of directly assisting thought. Any system of signs, auditory, or visual, or tactual, which answers these purposes, is a language. It is not necessary to dwell on the first two parts r the third deserves a moment's consideration. Psy- chology shows us that language is practically essential to thought. Without language general notions, or concepts, could scarcely exist. It is the name which binds together the group of simpler ideas that we call its connotation; and which enables us to recall this group, and to wield it as a whole. In thinking, we substitute the verbal sign for the mass of dimly recalled presentations, and of unpresentable relations of these presentations, which is what we call a con- cept. If one had always to call up even a faint image of a dog when one's thoughts involved a reference to dogs, thinking would be difficult. But what repre- 246 LOGIC. sentation is there to call up when we think about fidelity, or homogeneity, or susceptibility ? Some repre- sentation is necessary, and the name serves the pur- pose as nothing else could. An auditory, or visual, or muscular representation of the name becomes nascent, that is, begins to rise in consciousness ; and before we are fully conscious of it, our thought has passed on to something else. But this symbol of a thought has done its work. In algebra, when we have to deal with long and complex expressions, we often substitute for them some simple symbol, such as the Greek letter 2. We can now treat 2 as if it were an ordinary term, and use it almost mechanically, knowing all the time that we could, if necessary, substitute for it the whole of the expression for which it stands. This serves as an illustration of the use of the name. We can use it almost mechanically, so long as we know that at any moment we can recall the list of attributes which form its connotation. Language is thus a direct help to thought. It secures the thought the moment that it arises, if we wish it, in the form of a proposition, or in the still more convenient and compact form of a term. When we have to think over a matter of difficulty, we find ourselves repeating the premises and the conclusion to ourselves in unuttered language. With some men this mental language passes into the muscular move- ments of articulation, and with others it becomes actual audible language. SCIENTIFIC LANGUAGE. 247 § 2. Scientific Language. Clearly, then, accurate thinking requires the exist- ence of accurate language. For all three purposes mentioned — for communication, for record, and for assistance in the act of thought itself, it will be best: (1) That each word should stand for only one group of attributes. (2) That each important group of attributes, whether regarded as an independent " thing," or as an abstrac- tion, should have a name to itself. Language, then, should not be ambiguous ; and it should be very copious. These conditions are not completely fulfilled in any language actually spoken by men.^ Language has grown up in a casual way ; it has not been made to serve the purposes of theorists, it is a practical instrument used by plain and ignorant people in their daily con- cerns. Thus it is always ambiguous. Even when a new word is borrowed from science, with an exact connota- tion, the journalist and the man in the street set to work to blur it, for exactness in thought is their last interest. Again, the burden of a large vocabulary is one against which the plain man rebels. Stock adjec- tives, like " nice " and " awful," are the result of this revolt. They are always usable, because they have next to no meaning. Most of us want to get on with as few words as possible ; and if a new slang expres- ^ See above. Chap. II. § 3. 248 LOGIC. sion or current catchword comes into use, it is at the expense of another which goes out of use. A vocabu- lary of a few hundred words will express all that most men, and nearly all women, want to say, and a great deal more than they want to think. To obviate these defects in ordinary language, pre- cise thinkers have had to invent a language of their own. The "jargon of the philosophers," which dis- gusted the Humanists of the sixteenth and seventeenth centuries, was a necessary condition of exact thought. " The learned gibberish " of the Scholastics, which Locke thought a resource of priestcraft, was a neces- sity of the case. No science has ever made any pro- gress without a special language of its own. Indeed Condillac, the French philosopher (d. 1780), who popularized and extended the sceptical results of Locke's " Essay," caHed science " une langue bien faite," a well-made language.^ Algebra shows the utility of a well-constructed language, chiefly as a mechanical aid to thought ; Zoology shows its utility chiefly as a means of record. All the sciences exem- plify it, however, in some degree. And until a science has been able to develop a proper "jargon " of its own it seldom makes much progress. We have already seen how Psychology and Political Economy suffer from this defect (Chap. II. § 3). The same difficulty meets the student of Politics. The terms law, sovereign, rights, freedom, he has to take from popular language, and he finds them full of ambigui- ' " Langue des Calculs," p. 7. SCIENTIFIC LANGUAGE. 249 ties. In the newer sciences there is less danger. In Organic Chemistry fresh names are constantly being introduced, and their connotation is rendered precise from the beginning. Words like Triphenylguanidine, Acetaldehyde, Glycocoll, may not be pretty, but they at least have the merit of definiteness, and of suggest- ing their meaning to experts. § 3. Terminology and Nomenclature. A Terminology is a system of terms. It will include names of things and names of attributes. All the elements of which the compound wholes recognized by a science as its subject matter are composed must have a name ; all the instruments and methods employed, all the qualitative phenomena observed, and all the quantitative facts also. The terminology, then, will include all words used in the description of the pheno- mena dealt with in the science. It must contain " a name for every important result of abstraction — ^that is, a name for every important common property or aggregate of common properties, which we detect by comparison of the facts." The Nomenclature is a particular part of what is usually called the Terminology of a science. Calling what we have spoken of above the descriptive ter- minology of the science, the nomenclature will include the rest of the Terminology, that is, all the other specific technical words used, viz., the names of all the classes into which the science divides its subject 250 LOGIC. matter. In Zoology the nomenclature will include all subdivisions of Animal ; all the names of sub- kingdoms, divisions, classes, orders, genera, species, and varieties. It is impossible, however, to draw a clear line between the two things. The descriptive terminology and the nomenclature pass into each other. In the group of sciences we call Biology morphological terms (for instance, muscle, bone, limb) belong to the nomen- clature of Anatomy, but to the descriptive terminology of Zoology. We cannot always draw a clear distinc- tion between " things " and groups of attributes which we do not recognize as things. CHAPTER XXII. FALLACIES. § 1. Old Classification of Fallacies. Fallacies are errors of inference. Any error in inference is a fallacy, whether due to a mere blunder or to some moral source, such as bias and indifference. But while the mistake in inference is a fallacy, the origin of the mistake is not taken into account. The logician leaves to the psychologist the task of pointing out the causes which are likely to lead to the adoption of false beliefs, by predisposing to accept insufficient evidence, or to neglect certain classes of evidence. According to Kant, a sophism is a fallacy designedly perpetrated in order to arrive at a conclusion known not to be true, or known to be absurd. A paralogism, is an involuntary fallacy which deceives ourselves. But sophism, paralogism, and fallacy are often used, without any distinction, to mean the same thing. The classification of the errors of reasoning is in a very unsatisfactory state, and little has been done of value since Aristotle wrote. In his logical treatises fallacies are divided into two groups : 252 LOGIC. (1.) Fallacies in dictione, or as we should say, formal fallacies, which can be detected even by some one who has no knowledge of the subject matter of the reasoning. (2.) Fallacies extra dictionem, or material fallacies, which can only be detected by some one having a know- ledge of the special subject matter. Formal fallacies have been divided by Whately into two sub-classes : (a) Purely logical fallacies, such as arise from a breach of the rules of the syllogism, (b) Semi-logical fallacies which arise from want of precision in the use of language. This classification is unsatisfactory, since it overlooks to a great extent the errors likely to arise in the processes of Induction, and those belonging to the subsidiary processes of Definition and Division. And, besides this, the classes overlap ; since some of the Material fallacies might be equally well considered as fallacies of the Semi-logical type ; while what may be regarded as one of the purely logical fallacies (breach of the rule of the Syllogism which forbids an ambiguous middle term) may be regarded equally well as a Semi-logical fallacy (Equivocation). In fact, it is generally open to us to represent a given error as due either to the preliminary processes which give us our proposition, or to the formal process of inference. FALLACIES. 253 § 2. Mill's Olassification of Fallacies. Mill has given us a more complete scheme of classification. He first recognizes a class of fallacies of Simple Inspection; which includes "not only all cases in which a proposition is helieved and held for true, literally without any extrinsic evidence, either of specific experience or general reasoning; but those more frequent cases in which simple inspection creates & presumption in favour of a proposition; not suflScient for belief, but sufficient to cause the strict principle of a regular induction to be dispensed with, and creating a predisposition to believe it on evidence which would be seen to be insufficient if no such presumption existed" ("Logic," V. ii. § 2). In this class he places many philosophic opinions which he himself rejects, as well as certain " natural prejudices," as he calls them. Obviously such a metaphysical dust-bin is a convenience for a philosopher who wants to get rid of doctrines which he thinks it waste of time to examine in detail. Amongst the venerable proposi- tions which Mill relegates to his rubbish-heap is " that whatever is inconceivable must be false," which many great thinkers, from Descartes and Leibnitz to Pro- fessor Sidgwick and Mr. Herbert Spencer, have con- sidered the touchstone of all knowledge and the foundation of all philosophy. Apparently any sufficiently general and abstract proposition which Mill considered absurd might be 254 LOGIC. regarded as a fallacy of simple inspection, even although it had approveditself to minds of the greatest subtlety and power. Passing over this point, it is obviously the case that " simple inspection creates a presumption in favour " of many propositions which are perfectly true, and which may be rigidly inferrible from other true propositions. When we hear that Lord Rayleigh and Professor Ramsay have discovered a new element, we feel a '' predisposition to believe it " on evidence much slighter than we should require to make us accept the peculiar doctrines of Mr. Sinnett and Madam BlS,vat- sky. How far this presumption is a reasonable one is a matter for ai'gument; but that' it does exist, and that it causes us to demand a less rigid demonstration than we should require of the reality of one of Madam B18,vatsky's miracles, is not sufficient to make us consider the belief in the existence of argon, as due to a fallacy of Simple Inspection. All other fallacies Mill calls fallacies of Inference, and he divides them in a way which will be easily understood from the following table, without much further explanation. FALLACIES. 255 Fallacies of Inference. ■ From evidence distinctly conceived . Inductive fallacies . /' Fallacies of Observation. I 2. Fallacies of Generalization. Deductive fallacies . 3. Fallacies of Batiocinatiou. From evidence indis- tinctly conceived .... 4. Fallacies of Confusion. In the last class he places those cases of error which arise when the premises " have never been conceived in so distinct a manner as to produce any clear con- sciousness by what means they were carried out ; as in the case of what is called reasoning in a circle." He brings under it all the "semi-logical fallacies," and the material fallacies of petitio principii and ignoratio elenchi. As we have already said, no classification of fallacies that has yet been proposed can be considered satis- factory. The plan we shall adopt is to give the traditional list of fallacies, the names of which have become classical, and have become part and parcel of ordinary and non-technical vocabulary. § 3. Purely Logical Fallacies. (1) The chief of these are infractions of the rules of the Syllogism, e.g. (a) Fallacy of four terms (quaternio terminorum) which is a breach of Kule 1 ; but usually 256 LOGIC. arises from the use of an ambiguous middle term, which is forbidden by Rule 3. (6) Fallacy of undistributed middle, (c) Fallacyof illicit process, {d) Fallacy of negative premises, and those due to a breach of Rule 6. (2) But to these syllogistic fallacies, we must add the fallacies of Immediate Inference, such as simple conversion of universal affirmatives, arising from illicit distribution of an undistributed term. (3) Fallacies of Conditional reasonings, such as denying the antecedent, and affirming the consequent. (4) Fallacies of Definition, such as the fallacy known as circulus in definiendo, (5) Fallacies of Division, such as cross-division. § 4. Semi-Logical Fallacies. These are all " fallacies of confusion," to use Mill's term ; due to the use of language wanting in precision. The old Logics mention six, but they are of very various importance. (1.) Fallacy of Equivocation, in which the same word is used, but is used in two or more different senses. As we have seen, all, or nearly all, words are equivocal in some degree, and our first care must be to see that the words that we use have exactly the same meaning in all the propositions of a reasoning. The most fre- quent case is that of ambiguous middle term ; ^ but we may have a term used in a different sense in the con- clusion and in the premise in which it occurs. ^ See p. 252, above. FALLACIES. 257 (2.) Fallacy of Amphibology, in which a sentence is so constructed as to be ambiguous from its form. The Latin construction of accusative and infinitive is specially liable to this disadvantage. In English the careless use of pronouns, and specially of relative pro- nouns, is a frequent cause of ambiguity. The follow- ing verbal tangle is from a daily newspaper : " Her own story was that she had a quarrel with the deceased, first about her wages, and secondly about the soup, and that she seized the deceased by the throat, and she fell, and when she got up she was looking for something to strike her with, and upon this she struck the deceased a blow in the throat, and she fell and died almost instantaneously." As English is scarcely an inflected language, the collocation of words is of great importance. A school- girl once wrote in an examination paper, "The ' Iliad ' is the story of the siege of Troy by Homer ; " but it was a popular novelist who told us that a gentleman "drove away from the church where he had been married in a coach and six." (3.) The Fallacy of Composition is that in which am- biguity arises &om taking a middle term distributively in one proposition and collectively in another, without due notice. Thus, we may have a middle term used dis- tributively in the major, and collectively in the minor premise ; * or a term may be used distributively in a premise, and collectively in the conclusion. * See p. 252, above. 258 LOGIC. When we argue that because a trades-union can artificially raise wages in one trade, all the trades unions can artificially raise wages in all trades by acting together, we commit this fallacy ; for a trades- union can often only raise wages in its own trade at the expense of the welfare of other groups of workmen. (4.) Fallacy of Division. If, on the contrary, we proceed from a collective use of a term to a distribu- tive use of it, without due notice, we have the fallacy of division. If we argue that because CathoUcs hold that all the bishops of the Church collectively cannot err, therefore they must hold that any individual bishop is infallible, we attribute to them this fallacy. (5.) Fallacy of Accent. Ambiguity may arise from false accent. Jevons cites the time-honoured case from 1 Kings, xiii. 27 : " And he spake to his sons saying, Saddle me the ass. And they saddled Aztw." Some unfortunate reader mistook the italics, which indicate that the word " him " is not in the original Hebrew, as a mark of accent. (6.) Fallacy, of Figure of Speech, in which some colloquial or some rhetorical expression is taken liter- ally, or vice versa. § 5. Material Fallacies. Aristotle mentions seven kinds of fallacies extra dictionem, that is, fallacies not lying in the method of expression, but due to the subject matter. They are as follows : FALLACIES. 25& (1.) Fallacy of Accident, also called the fallacy a dicto simpliciter ad dictum secundum quid. Here the error consists in inferring, that what is true generally of a class of things, is true in any given special case,^ which may be marked by some individual or specific peculiarity, rendering the predicate inapplicable. It is the fallacy most likely to occur when we apply a general law to a particular case. It is the besetting sin of the political idealist and doctrinaire. The man often commits it who solves all problems by the appli- cation of some wide formula, such as "Peace is the greatest of all blessings," or, "Liberty is the most valuable possession a man can have," or, "Order is the one thing politically needful." So do those who argue (as John Bright and the laisser-faire Liberals did) that because interference with free contract ia undesirable, some particular factory legislation is un- desirable, without looking at the special circumstances of the case. (2.) Converse fallacy of Accident, or the fallacy which proceeds a dicto secundum quid ad dictum sim- pliciter. When a statement has been made with an explicit, or implicit, condition, we must not, of course, repeat it without the condition. In so doing, we generalize from a special case, which may afford no ground whatever for the inference. Just as in the fallacy of accident we apply a general law without caution to a case which does not really come under it, we here infer a general law from a case which is not really an example of the law. 260 LOGIC. When the Puritan settlers in New England passed their three famous resolutions — " B,esolved, ^rst, that the Earth is the Lord's and the fulness thereof; secondly, that He hath given it to His Saints ; thirdly, that we are His Saints " — they committed the fallacy at least twice. Whenever a text is torn from its con- text and is stated as a general truth without reference to the particular circumstance under which it appears in Scripture the fallacy is committed. Both these fallacies of Accident then are due to the confusion between the general and the special. We forget that almost all statements are implicitly conditional, that they presuppose a number of con- ditions which they do not assert. If a physician tells us that a particular drug will cure a certain complaint, he tacitly implies a large ^roup of favourable circumstances. It will not cure the complaint under all circumstances whatever. It is only the ignorant and foolish man, who, finding the medicine serviceable in his own case, will attempt to persuade everybody else who suffers from the same disease to take it. Hence the need of constantly reminding us that " S is P " only mutatis mutandis, or only cceteris paribus. On the other hand, absolute precision of language, even if attainable, would be dearly purchased at the cost of intolerable verbosity. We must make rough general propositions, and we must apply them. But all the same we must remember, in the words of the homely proverb, that " circumstances alter cases." FALLACIES. 261 Lotze rightly points out that both fallacies of acci- dent can be brought under the fallacy of ambiguous middle. The reader will have no difficulty in testing this statement. (3.) Ignoratio Elenchi. The -elenchus was the tech- nical term for a syllogism put forward with a view to confute an adversary. If the adversary declined to notice the elenchus, and continued to argue at large without any reference to our refutation of his thesis, he was said to commit the fallacy of ignoring the elenchus. The meaning of ignoratio elenchi has been widened to cover all cases of answering to the wrong point, of refusing to notice the argument of an opponent, and continuing to prove some other point than that which he has attacked. Whately called this wider form, the fallacy of Irrelevant Conclusion. All such rhetorical shifts as the argumentum ad hominem — in which, instead of disproving that " S is P," we show that our opponent is not the right man to bring forward the statement " S is P," or that he is dishonest, or that he is incapable — come under it. So does the argumentum ad verecundiam, the appeal to the veneration in which some person who holds the doctrine we support is rightly held, and the insigni- ficance of the objector. The argumentum ad populum may be regarded as another type of the ignoratio elenchi, in which the real point in dispute is kept out of sight by an appeal to the special prejudices of the ignorant and the foolish, who form the majority of every large body of men. 262 LOGIC. § 6. Petitio Piiacipii and other Material Fallacies. There axe four other fallacies extra dictionem to be mentioned. (4.) Petitio Principii, or Begging the Question, taQaxis, the employment, for the purpose of proof, of a premise which itself is only true on the assumption that the conclusion is true. It is sometimes called circulus in probando. This fallacy often takes the form of using what Bentham called a " question-begging epithet ;" some word — which implies or suggests the attribute we wish to prove of the subject — ^is employed to describe the sub- ject. Heretical, universal, unconstitutional, are favourite question-begging appellatives. A moralist who seeks to show that we may never tell an untruth in the interests of euphemism because all telling of untruths is lying, really assumes the whole point at issue ; for a lie does not merely mean untruth, but immoral and indefensible untruth. As Whately remarks : — " The English language is perhaps the more suitable for the fallacy of petitio principii, from its ' being formed from two distinct languages, and thus abounding in synonymous ex- pressions, which have no resemblance in sound, and no connection in etymology ; " so that a sophist may bring forward a proposition expressed in words of Saxon origin, and give as a reason for it, the very same pro- position stated in words of Latin origin; e.g., "to FALLACIES. 263 allow every man an unbounded freedom of speech must always be, on the whole, advantageous to the State ; for it is' highly conducive to the interests of the community, that each individual should enjoy a liberty, perfectly unlimited, of expressing his sentiments." In the same way, scientific " men are exposed to the danger of fancying that a statement in highly tech- nical terms, derived from Greek, of the simple fact to be explained, constitutes an explanation of it. We cannot legitimately explain why children are some- times subject to the same diseases as their parents by the use of such terms as heredity. The difficulty lies in the fact that some diseases appear to be transmitted, while others apparently are not. We do not give a reason for the former by saying in technical language that they are transmitted. (5.) Non Causa pro Causa. This is the fallacy of false generalization. In some cases, a sign or symptom, C, from which the presence of B may legitimately be inferred, is taken as the cause of B, when it is really a concomitant part of the efiect of a cause A. Thus some of the symptoms of a disease are often regarded as the cause of the rest. As Oesterlen says: — "We are in danger of confounding cause and effect to- gether if we assert that grief may give rise to disease of the stomach, and even to cancer of that organ ; or that the habit of sleeping after dinner causes obesity, congestion of the brain, and apoplexy."' Even if a fact. A, is known to precede another fact, ' "Medical Logic," Sect. VII. 264 LOGIC. B, sometimes, or even always, we cannot necessarily infer that A is the cause of B. Against this fallacy of false generalization, known as that of post hue ergo propter hoc, aU the apparatus of inductive methods, the cautions as to the use of hypotheses, and the rigid rules as to the need of verification, are directed. (6.) Fallacy of non sequitur. Under this might be brought all fallacies of inference, that is, all fallacies whatever, and no advantage is gained by regarding it as a separate class. (7.) Fallacy of Many Questions. Aristotle points out that questions are often asked to which a single " Yes " or " No " cannot be answered. Before such questions can be answered they must be analyzed into their constituent parts. Barristers practising before weak or lazy judges sometimes ask unfair questions of this sort, with the object of getting some unpleasant admission from a witness. " Have you left off beating your mother ? " is a crude specimen of this form of forensic wit. But whenever we try to pin a man down to the use of some ambiguous epithet, with the object of turning the admission against him, we commit the same fallacy, or rather sophism. Thus, if we ask a High Church clergyman if he is a Protestant, or demand from a Broad Churchman if he believes in the inspiration of the Bible, we ask questions which can only be properly answered after some preliminary explanation, and not with a simple affirmative or negative. The old scholastic writers used to say in such cases, "Dis- FALLACIES. 265 tinguOj" " I make a distinction;" and this is the best way of dealing with the matter. § 7. Fallacies of Observation. In his first class, fallacies of Observation, Mill recognizes two subdivisions — fallacies of non-observation and fallacies of mal-observation. In the former we overlook what is before us to be observed ; our error is of a negative character. In the latter we perceive wrongly, and make a positive mistake by apparently perceiving what is not there to be perceived. We have seen that in all perception there is implicit and sub-conscious inference (Chap. I. § 1). But it is doubtful whether we can lay down any principles underlying valid observation. Not only is the process sub-conscious, but it eludes retrospective analysis ; we cannot reinstate in clear consciousness the steps by which the result was obtained. The process of reasoning is also sometimes practically unconscious, but in reasoning we can usually bring clearly before the mind the phases or elements of the complex process in such a way that we can test their validity. In observation there is no means of doing this. We cannot even draw the line between what is directly given us in perception, as it were, from outside, and what we add to it. To a few hints in the shape of visual sensation we join an enormous mass of sub- conscious inference. But we cannot draw the line where the one begins and the other leaves off. 266 LOGIC, Although we can give general rules for avoiding €rror in observation, we cannot formulate any prin- ciples which must be complied with if observation is to be correct. There is no logic of observation. Indeed, Logic begins where observation leaves off. It deals with such knowledge as has been expressed in propositions. APPENDIX A. BOOKS RECOMMENDED. I. GENEEAL. Welton : Manual of Logic. 2 vols. Bain : Logic. 2 vols. Fowler: Logic. Mill: System of Logic. n. SPECIAL. Jevons : Prindj^les of Science. Keynes : Formal Logic. Venn : Symbolic Logic. „ Logib of Chance. „ Empirical Logic. De Morgan : Formal Logic. Boole : Investigation of the Laws of Thought. Mansel : Prolegomena Logica. Whewell : Novum OrgoMwm, Renovatum, in. FOR FURTHER READING (PRINCIPALLY CRITICAL). Bradley, H. : Principles of Logic. Bosanquet : Logic or the Morphology of Knowledge. 268 LOGIC. Lotze : Logic. 2 vols, (transl.). Sigwart : Logic. 2 vols, (transl.). Hamilton : Lectures on Logic. 2 vols. Mansel: Introduction and Appendix to his edition of Aldrich's Artis Logicce Rudimenta. IV. MAINLY OP HISTORICAL INTEREST. Aristotle : Organon (various logical treatises, of which there is a translation in Bohn's Library). Bacon : Novum Orgwnvm, (ed. by Fowler). Amauld : L'Art de Penser (translated by T. S. Baynes as the Port-Royal Logic). Whewell : On the Philosophy of Discovery. „ History of the Inductive Sciences. APPENDIX B. EXAMPLES FOE SOLUTION. I. IMMEDIATE mFERENCE. Put each of the following into exact logical form, and give its obverse, converse (where possible), and contra- positive (where possible). 1. All wise men are modest. 2. The Jews are monotheists. 3. No mortals are perfectly happy. 4. Some lawyers are not honest. 5. All lawyers are not knaves. APPENDIX B. 269 6. All 's well that ends well. 7. Whatever is, is right. 8. No smoking allowed. 9. All living tissue is organic. 10. Some murmur when their sky is clear. 11 . A fool at forty is a fool indeed. 12. All cannot receive this saying. 13. All the perfumes of Arabia will not sweeten this little hand. 14. Some acids do not contain oxygen. 15. They laugh that win. 16. The square of four is sixteen. 17. To be good is to be happy. 18. Brutus killed Caesar. 19. No end of people were there. 20. All hope abandon, ye who enter here. 21. The better the day the better the deed. 22. No small dissension arose. 23. All the witnesses were not trustworthy. 24. None knows where the shoe pinches but the wearer. 25. No man is a hero to his valet. 26. Milton wrote " Paradise Lost." 27. Only the actions of the just SmeU sweet and blossom in the dust. 28. KJnowledge is power. 29. Some are bom great. 30. Who drives fat oxen should himself be fat. 31. A bank-note is an order to pay gold on demand. 32. No men are braver than some blacks. 33. All exercises are not so easy as they look. 34. He who is capable of making a piui is capable of pick- ing a pocket. 270 LOGIC. 35. Mtya j3t/3\tov fiiya kokov. 36. Beading maketh a full man. 37. Life is not all beer and skittles. 38. Some of the guests were not all they should be. 39. Beati possidentes. 40. He is gentle that doth gentle deeds. 41. What's yours is mine, what 's mine is my own. 42. There is no mind without motion. 43. All I want is justice. 44. Most women have no character at all. 45. There are criminals who deserve reward. ir. MEDIATE INPEEENCE AND FALLACIES. Put the following reasonings into exact logical form, identify the form, and where any fallacy (or apparent fallacy) occurs, explain it : 1. My letter has not been answered, therefore it must have miscarried. 2. He cannot be a gentleman, for no gentleman would do such a thing. 3. The whale is warm-blooded, and is therefore not a fish. 4. It is going to be hot, for there is a haze on the hills. 5. These books are all by X, therefore most of them are sure to be rubbish. 6. The members of the club are not aU good players, for Jones belongs to it. 7. He must be musical, for he is always going to concerts. APPENDIX B. 271 8. Things-in-themselves are of no importance, seeing that they are not knowable. 9. A salaried clerk may be at the same time a man of letters : for Charles Lamb was both. 10. Every criminal is more or less insane : but the insane ought not to be punished : therefore no criminal should be punished. 11. The cruel are not always cowardly : for Richard III., Peter the Great, etc., were brave. 12. The company must certainly be a sound one, because the Chairman is a peer. 13. She is a woman, therefore may be woo'd ; She is a woman, therefore may be won. 14. Many educated men do not write good English, for not even all University men do so. 15. Members of Parliament are not chosen for inde- pendence of judgment, though such men are best qualified for the ofSce : therefore few of those best qualified become members. 16. The books in the library are all novels, which are not what I care for : consequently no books that I care for are in it. 17. Among those who distinguished themselves were some recruits, since all the troops (many of whom were recruits) did so. 18. All these men have passed, which shows that some very stupid persons manage to do so. 19. Some eminent men have not obtained university dis- tinction, which is therefore no conclusive proof of real ability. 20. No really musical person would applaud that, though some of the audience are doing so. 272 LOGIC. 21. Some of the books had evidently not been read, for they had not even been cut; 22. As some of the witnesses contradicted each other, there must have been perjury somewhere. 23. The whole family has been vaccinated, yet some have had small-pox; therefore vaccination is no safe- guard. 24. None of the family have been vaccinated and none have had smaU-pox; therefore vaccination is unnecessary. 25. Many Englishmen have foreign surnames, and must therefore have been originally of foreign extraction. 26. Some of these books are not well bound, for they are going to pieces as no well-bound books would do. 27. Some of these books will not be much read — they are too abstruse. 28. This is something I don't know, and is therefore not knowledge. 29. Teetotallers do not use alcoholic drinks, and this man does not do so : therefore he is a teetotaller. 30. He that is of God heareth God's words ; ye therefore hear them not, because ye are not of God. 31. Practice makes perfect: therefore a neighbour who practises all the time is a perfect neighbour. 32. To play all day is a proof of great idleness : so this violinist must be a very idle person. 33. That no reasonable man holds this view is not dis- proved by the fact that Mr. X. holds it. 34. None of the party suffered, though some drank the water of the place : therefore this does not always cause mischief. 35. No English peer can sit in the House of Commons : for he is vpto facto a member of the House of APPENDIX B. 273 Lords, and no man can be a member of both Houses. 36. If I write long letters lie is bored: if short, he is offended : therefore I won't write at all. 37. He cannot have been there — otherwise I should have seen him. 38. A London graduate is sure of the post: I am a London graduate, and am therefore sure of it. 39. Only contented people are wise : therefore the tramp contented in his rags is a wise man. 40. You are not what I am : I am a man : therefore, you are not a man. 41. One patent stove saves half the ordinary amount of fuel : therefore two would save all. 42. If virtue is voluntary, vice is voluntary ; virtue is voluntary, therefore so is vice. 43. A. B and C D are each of them equal to E F : therefore they are equal to each other. 44. He is the greatest lover of any one who seeis that person's greatest good; a virtuous man seeks the greatest good for himself; therefore a virtuous man is the greatest lover of himself. 45. Warmth is agreeable, therefore cold is disagreeable. 46. Warm countries alone produce wines: Spain is a warm country ; therefore Spain produces wines. 47. All that glitters is not gold : tinsel glitters, therefore it is not gold. 48. Every hen comes from an egg ; every egg comes from a hen ; therefore every egg comes from an egg. 49. What we eat grew in the fields ; loaves of bread are what we eat ; therefore loaves of bread grew in the the fields. T 274 LOGIC. 50. He who is most hungry eats most ; he who eats least is most hungry ; therefore he who eats least eats most. 51. Wine is a stimulant; therefore, in a case where stimulants are hurtful, wine is hurtful. 52. Theft is a crime ; theft was encouraged by the laws of Sparta ; therefore the laws of Sparta encouraged crime. 53. Either you or I must be mistaken : (1) I am not : therefore you must be. (2) Tou are : therefore I am not. 54. If he is drunk, he is incapable. (1) He is drunk, and therefore is incapable : (2) He is not drunk, and therefore is not incapable : (3) He is incapable, and therefore is drunk : (4) He is not incapable, and therefore is not drunk. 56. No one is a better cricketer than W. Gr. : W. G-. is a better cricketer than you: therefore no one is a better cricketer than you. 56. All Laplanders are poets ; Homer was a Laplander ; therefore Homer was a poet. 57. All these men are quite sufficient for the job ; you are one of them, and are therefore quite sufficient for it. 58. No man can serve two masters ; for either he will hate the one and love the other ; or else he will hold to the one, and despise the other. 59. What is done can never be undone ; therefore this knot can never be undone. 60. There is a pressure of one pound on any square inch of the interior surface of this vessel; therefore there is a pressure of one pound on every square inch of the surface. APPENDIX C. 2V5 61. Since the end of poetry is pleasure, that cannot be unpoetical with which all are pleased. 62. The Divine Law commands us to honour kings ; Louis XrV. is a king ; therefore the Divine Law commands us to honour Louis XIV. 63. None but Whigs vote for Mr. B. All who vote for Mr. B. are ten-pound householders. Therefore none but Whigs are ten-pound householders. 64. The members of the board were all either bondholders or shareholders, but not both; and the bond- holders, as it happened, were all on the board. 65. Given that everything is either Q or E, and that all E is Q, unless it is not P, prove that all P is Q. 66. Griven that P is Q E, and that p is q r ; show that Q is P E, (and) E is P Q. 67. It is known of certain things that (1) where the quality A is, B is not ; (2) where B is, and only where B is, C and D are. Derive from these conditions a description of the class of things in which A is not present, but C is. APPENDIX C. LONDON B.A. QUESTIONS. 1. Distinguish hypothesis from theory. Explain the use of hypothesis in scientific procedure. Show, by a concrete example, how far the imagination, and how far the reason, has entered into the construction of a 276 LOGIC. workable hypothesis. By what criticism would you test all hypotheses ? (B.A. 1890.) 2. Grive a detailed definition of the following terms from your owu point of view : thought, feeling, sensation, perception, judgment, reasoning, proof, verification, evidence. (B.A. 1890.) 3. Examine the following : " Every bird comes from an egg ; every egg comes from a bird ; therefore every egg comes from an egg." (B. A. 1890.) " No reason without language." " No language without reason." Comment critically on tliese aphorisms. (B.A. 1890.) 4. Distinguish analysis from synthesis in full detail. Explain the function and value of each in the scientific study of phenomena, and the way in which they co-operate in the formation of a scientific theory of any group of phenomena. (B.A. 1890.) 5. Distinguish the various kinds of logical inference, and show their relations to one another. (B.A. 1890.) 6. Examine: (a) " All responsible beings are rational ; responsi- bility increases with the increase of rationahty ; some dogs are more rational than some men; therefore some dogs are more responsible than some men." (/3) " If I am to pass this examination, I shall pass it, whether I answer correctly, or not : if I am not to pass it, I shall fail, whether I answer correctly or not : therefore, it is of no consequence how I answer the questions." (B.A. 1890.) 7. Distinguish between the psychological and the logical treatment of thought, with special reference to the APPENDIX C. 277 qiiestion whether all our thinking is carried out by concepts, as the logician understands them. (B.A., 1891.) €. Give the contradictory, also the converse, the obverse and the contrapositive of each of the following propositions : (a) It cannot be doubted that every man pursues his own interest. (6) The writer of the document was A. B. (c) About one in three of the candidates were University men. (B.A., 1891.) 5. G-ive a brief account of the predicates, and point out any difficulties in adjusting them to modern scientifie thought. (B.A., 1891.) 10; Is Logic bound by the ordinary usages of language ? Discuss the question in connection with the follow- ing topics : (a) The quantification of the predicate. (6) The proper logical interpretation of the form, " Some S is P." (B.A., 1891.) 11. What do you consider to be the real distinction between a categorical and a hypothetical proposition? Are the processes of immediate inference applicable to hypothetical propositions ? (B.A., 1891.) 12. Discuss, both logically and historically, the relation of induction to deduction. (B.A., 1891.) 13. Bring out the logical peculiarities of mathematical rea- soning, and inquire whether it is radically distinct from other forms of scientific reasoning. (B.A., 1891.) 14. Unfold the nature of hypothesis, assigning (if you can) a definite meaning to the expressions " legitimate ^TS LOGIC. V hypothesis " and " vera causa." Is hypothesis an essential factor in inductive investigation? (B.A., 1891.) 15. What do you understand by Laws of Thought ? What different views have been held as to their origin and significance ? How would you distinguish them from Laws of Nature? (B.A., 1892.) 16. Distinguish verbal from real Predication, and show how the five predicables bring out the distinction. (B.A., 1892.) 17. State and compare some of the most important methods of classifying Fallacies known to you. (B.A., 1892'.) 18. In what relation does the causal judgment stand to the Uniformity of Nature ? (B.A., 1892.) 19. How many distinct methods of experimental research does Logic recognize ? Give examples of each and show how they co-operate. (B.A., 1892.) 20. Illustrate the logical principles of classification from any one of the sciences of Chemistry, Botany, or Physics. (B.A., 1892.) 21. Amplify, and apply a logical test to, the following arguments : (a) The theory of evolution is true, because it is accepted by every scientific biologist. (&) A good temper is a sign either of a good con- science or of a good digestion; therefore the conscientious and the healthy will always possess a good temper. ~ (c) To call a person an animal is to speak the truth ; therefore to call him an ass (which is to call him an animal) is to speak the truth. (d) The laws of Nature can never be broken. Social APPENDIX C. 279 law is a part of the general system of Nature; therefore it cannot be broken. (B.A., 1892.) 22. Give the contradictory, the obverse, the converse, and the contrapositive of the following : (a) Private vices are public benefits. (6) Not to know me argues thyself unknown. (c) Beauty and use are identical. (d) No man is always consistent. (B.A., 1892.) 23. Bring out the exact scope of Logic, defining its relation (1) to the special sciences ; (2) to psychology ; (3) to philosophy or theory of knowledge. (B.A., 1893.) 24. What is meant by saying that Logic deals only with the form of thought ? Show how the use of symbols enables us to examine the form of our thought. (B.A., 1893.) 25. Bring out fully the peculiarities of the class-symbol not- A. What is meant by calling it infinite ? Is it found in the propositions of every-day life ? (B.A., 1893.) 26. State and illustrate what you understand by Ob- version. On what laws or axioms does the validity of this process depend ? (B.A., 1893.) 27. Explain fully the limitations of the conclusions obtain- able in the Third Figure of the Syllogism. Are these limitations got rid of by applying Obversion (Per- mutation) to the premises ? (B.A., 1893.) 28. Discuss the proposition that the cause invariably pre- cedes the effect. Have recent discussions served to confirm MiU's view on this subject? (B.A., 1893.) 29. What is a Coincidence, and how can it be distinguished 280 LOGIC. from a real connection of events ? What would you understand by the " explanation of a coinci- dence"? (B.A., 1893.) 30. Discuss the requirements of Definition as applied to scientific terms. How far do the rules of formal de- finition carry us in this case ? (B.A., 1893.) 31. Bring out the meaning, and estimate the logical value, of the three Laws of Thought. (B.A., 1894.) 32. State the different ways in which Terms may be classi- fied, giving an illustration of each. Have all the distinctions equal logical importance ? (B.A., 1894.) 33. On what grounds has the Quantification of the Predi- cate been maintained? Estimate these grounds critically. (B.A., 1894.) 34. State, and critically examine, the various ways in which Induction has been said to differ from Deduction. (B.A., 1894.) 35. Explain the following fallacies, giving an example of each: ignoratio elenchi, non causa pro causa, a dicto secundum quid, a/i0i/3oX(a, false analogy, mal- observation. (B.A., 1894.) 36. Briefly explain, and give an account of, sorites, epi- cheirema, inductio per simpHcem enumerationem, nota notae, a crucial instance, elimination of chance. (B.A., 1894.) 37. What do you understand by classification in Science ? Show how the Sciences have been advanced, as the principles of classification have improved. (B.A., 1894.) 38. Examine the logical form and validity of the following arguments : (a) A fish is cold-blooded and breathes by gills.; APPENDIX C. 281 neither of these things is true of a whale ; there- fore it is not a fish. (6) A is never found without B, and B is never found without C ; therefore C is never found without A. (c) To assault another is wrong ; consequently a soldier who assaults an enemy does wrong. (B.A., 1894.) 39. In what different ways has the relation of Logic to Psychology been conceived ? Give your own view of the distinction and of the connection between them. (B.A., 1895.) 40. Discuss the meaning and the logical importance of the distinction between Concrete and Abstract Terms. Explain fully how it happens that it is sometimes difficult to say to which of these classes a particular Term should be referred. (B.A., 1895.) 41. Bring out the meaning of each of the following ac- counts of the proposition, " All men are mortal," and say which is logically to be preferred : (a) All men have the attribute mortality. (6) Men = mortal men. (c) Men form part of the class mortals. (d) If a subject has the attributes of a man, it has also the attribute mortality. (B.A, 1895.) 42. Give a brief account of the several kinds of Immediate Inference, pointing out which are reversible, and showing on what principles or assumptions their legitimacy depends. (B.A., 1895.) 43. Explain the syllogistic rules respecting two negative and two particular premises, pointing out the grounds on which they rest. Do the following break either of these rules ? 282 LOGIC. (a) This person is very learned, and also very- sociable; consequently some very sociable per- sons are very learned. (6) No man is a proper object of contempt ; at the same time no man is perfectly admirable ; conse- quently some beings who are not perfectly ad- mirable are not proper objects of contempt, (c) The majority of English people have but litt"[e literary taste ; and the majority of English people read ; from which it follows that some who read have but little literary taste. (B.A., 1895.) 44. State what you consider the best definition of Cause, as required for logical purposes. Has the recent development of scientific conceptions affected the logical doctrine of Causation ? (B.A., 1895.) 46. What does the Logician understand by Explanation? What different kinds are there ? Can we be certain that any scientific explanation is complete and final ? (B.A., 1895.) 46. Discuss the connection between Hypothesis and In- ductive Investigation; and show, by means of an example, what constitutes the complete verification of a Hypothesis. (B.A., 1895.) INDEX. Absolute terms, 28. Abstract terms, 23. Accent, fallacy of, 259. Accident, fallacy of, 259. Accidents, 56. Added determinants, 143. Affirming the consequent, 127. Aforticfri, 117. Alphabet, Logical, 141 sq. Amphibology, fallacy of, 257. Analogy, 228 sq. Analysis and Synthesis, 181 sq. Analytic propositions, 40. Argumentum ad hominem, 261. Artificial classification, 234. Begging the Question, 262. Categories, 59 sq. Causation, Law of, 160 sq. Causes, Plurality of, 164 sq. ; conjunction of, 166 sq. Classification and Induction, 185. Classification, 232 sq. ; artificial and natural, 234 sq. ; Classifi- cation and Division, 232 sq. ; special and general, 237 sq. ; not the work of Nature, 238 sq. ; Classification by type, 241 sq. ; by series, 242. Collective terms, 27. Composition, fallacy of, 257. Comprehension of terms, 23. Concrete terms, 23. Conditionals, 48 sq. Connotation, 19 sq. Continuity, Law of, 80 sq., 241 sq. Contradictory and contrary terms, 31 ; propositions, 38 sq. Contraposition, 88. Conversion, 86. Definition, 62; real and nomina,!, 62 ; imperfect, 63. Denotation, 19 sq. Denying the antecedent, 127. Dichotomy, 69. Dictum de diverso, 104. Dictum de exe/mplo, 104. Dictum de omni et nulla, 92 sq. Dictum de reciproeo, 104. Differentia, 55. DUemma, 131 sq. Disjunctive propositions, 50 ; syl- logisms, 129 sq. 284 LOGIC. Distribution of subject and predi- cate, 35. Distributive tenus, 27. Division, 67. Division, fallacy of, 258. Effect, 165 ; intermixture of effects, 167. Empirical Law, 157 ; extension of, 225 sq. Enthymemes, 119 sq. Epicheirema, 122 sq. Episyllbgisin, 122. Equivocation, fallacy of, 256 sq. Eulerian diagi'ams, 109 sq. Exceptional phenomena, 223 sq. Exceptive propositions, 36. Exclusive propositions, 36. Existential propositions, 46. Experimental Inquiry, Methods of, 202 sq. Experiment, 171 sq. ; difficulties in way of proof by, 209 sq. Explanation, 63, 221 sq. Explanation of a word, 63 ; of a law or fact, 221. Exponible propositions, 36. Extension of Terms, 23. Fact, 178. Fallacies, classification of, 251 sq. ; simple inspection, 253 sq. ; purely logical fallacies, 255; semi-logical, 256. GaJenian figure, 102. Generalization, 187. General terms, 26. Genus, 55. Heterogeneity, Law of, 79 sq. Ileteropathic effects, 216. Homogeneity, Law of, 79. Hypothesis, 192 sq. ; kinds of hypotheses, 194 sg'. ; permissible hypotheses, 196 ; subordinate use of, 200 sq. Hypothetical propositions, 47 sq. ; syllogisms, 126 sg. Ignoratio elenchi, 261. Ignotumper ignotius, 64. Illicit process, 95. Imperfect figures of the syllogism, 106, Induction and classification, 185; results of induction not abso- lutely certain, 189. Induction, 148 sq. ; perfect and imperfect, 151 ; ground of, 158 sq. Inference, 1 sq., 83 sq., m sq. ; material and formal, 7 sq. ; immediate and mediate, 10. Infinite or indefinite terms, 30. Infinite propositions, 36. Intermixture of effects, 167. Intuition, 149. Inversion, 89 sq. Joint Method, 211 sq. Language and thought, 245 sq. ; scientific language, 247 sq. Laws of Thought, 73 sq. Law, 153, 179; Law of Nature, 154. Linea predicamentalis, 7^ Logic, scope of, l\sq. ; u^S^ of, 12. Logical alphabet, 142. INDEX. 285 Logical diagrams, 109 sq., 146 sq. Logical slate, 145. Mal-observation, fallacy of, 175, 265. Metaphysics and logic, 14. Method, 180 sq. Method, Joint, 211 sq. Method of Agreement, 202 sq. Method of Concomitant Varia- tions, 215 sq. Method of Difference, 207 sq. Method of Kesidues, 213 sq. Methods of Experimental Inquiry, 202 ; how actually employed, 218 sq. ; Mill's treatment of, 216 sq. Modal propositions, 33. Modus ponens, 126 ; tollens, 127 ; tollendo ponens, 129 ; ponendo tollens, 129. Moods of syllogism, 99. Natural kinds, 235. Nature, Laws of, 154 sq. Negative terms, 29. Nomenclature, 249 sq. Non causa pro causa, 263. Non-observation, fallacy of, 175, 265. Non sequitur, 264. Nota notcE, 93. Hotiora naturce, 65, 221. Observation, 169 sq. Obversion, 84. Opposition of categorical pro- positions, ZSsq. .; of conditional propositions, 5\ sq. , • ■• Paralogism, 251. Particular propositions, 34. Perception, 177 sq. Petitio principii, 262. Plurality of causes, 164 sq., 205 sq. Plurative propositions, 37. Polysyllogisms, 122. Porphyry's tree, 71. Positive terms, 29 sq. Predicables, 53. Predicaments, 59. Predication, 41*2'. ; and existence, 45 sq. Privative terms, 30. Proper names, 25. Propositions, 16. Propositions, 32 sq. Proprium or property, 53. Prosyllogisms, 121 sq. Psychology and Logic, 14. Pure and modal propositions, 33. Quality of propositions, 33. Quantification of the predicate^ 135 sq. ; new propositions, 136 sq. Quantity of propositions, 33. Quasi-syllogisms, 117. Quaternio terminorum, 95. Real kinds, 58, 235 sq. Beductio ad ahsurdum, 107. Reduction of syllogisms, 105 sq. Relative terms, 28. Singular terms, 25 sq. Sophism, 251. Sorites, 123 sq. 286 LOGIC Species, 55 sq. ; infimee species, 56 sq. ; species prsedicabilis, 56. Subaltern propositions, 38 ; spe- cies, 56. Svibcontrary propositions, 39. Sufficient Reason, Law of, 81 sq. Summum genus, 59, 60. Syllogism, 91 sq. ; utility of, 111 sq. ; MiU's attack on, 112 sq. ; numerical syllogisms, 118; hypothetical, 126 sq. Symbolic logic, 140 sq. Synthetic propositions, 40. Terminology, 249 sq. Terms, 17 ; ambiguity in, 18. Theory, 199. Traduction, 149. Ultra-total distribution, 118. Uniformity, 153, 155 sq. Uniformity of Nature, 154 .■iq., 224. Universal propositions, 34. Universe of discourse, 78. Validity of inference, 4. Vera causa, 197. Verification, 198 sq., 217. Vicariousness of causes, 165. CHISWICK FKESS :— CHARLES WHITTINGHAM AND CO. TOOKS COURT, CHANCERY LANE, LONDON. By the same Author. Fifth Edition, Crown &vo, limp cloth, 3«. 6rf. A STUDENT'S HANDBOOK OF PSYCHOLOGY AND ETHICS EXTRACTS PROM NOTICES OP THE FIRST EDITION. "A very useful directory — references are given to, and extracts are made from all the best Authors." — Examiner. 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Waterloo Days. By C. A. Eaton, IS. and IJ. 6c?. Wellington, Life of. By 'An Old Soldier.' 5J. ' Werner's Templars in Cyprus. Trans, by E. A. M. Lewis. 3s. 6d. Westropp's Handbook of Archaeology. Si- Wheatley. On the Book of Common Prayer. 3s. 6d. Wheeler's Dictionary of Noted Names of Fiction. 55. White's Natural History of Selbome. Ss. Wleseler's Synopsis of the Gospels. S-J. wmiam of UalmesbuTy's Chronicle. S-f- Wright's Dictionary of Obsolete and Provincial English. 2 vols. ^. each. Xenophon. Trans, by Rev. J. S. Wat- son and Rev. H. Dale. 3 vols. 51. ea. Young's Travels in France, 1787-89, (M. Betham-Edwards.) 3J. 6d. Tour in Ireland, 1776-9. (A. W. Hutton.) 2 vols. 3s. 6d. each, Tule-Tide Stories (B, Thorpe.) 5s, New Editions, fcap. 8vo. 2s. 6d. each net. THE ALDINE EDITION OF THB BRITISH POETS. 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